O’LEVEL NOTES FORM 1 – 4

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Basic Mathematics For Form Four Full Notes, LINEAR PROGRAMMING. Linear programming – is a branch of mathematics which deals with either minimizing the cost or maximizing the profit. It gives the best way of utilizing the scarce resources available. It is so called because it only involves equations and inequalities which are linear. Simultaneous Equation. One of the methods used in solving linear simultaneous equations is a graphical method. Two linear simultaneous equations in two unknowns can be graphically solved by passing through the following procedures. Draw the two lines which represent the two equations on the xy – plane this is done by deter mining at least two points through which each line passes, the intercept are commonly used Determine the point of intersection of the two lines. This point of intersection is the solution to the system of equations. FACT: If two straight lines are not parallel then they meet at only one point: In case the lines do not meet, there is no solution to the corresponding system of simultaneous equations. Example 1 Graphically solve the following system of simultaneous equations. Example 2 Find the solution to the following system of simultaneous equations by graphical method. Solving Simultaneous Equations Graphically Solve simultaneous equations graphically Example 3 Solve the following simultaneous equations graphically and check your solution by a non-graphical method: Example 4 Find the solution to the following system of simultaneous equations by graphical method. Exercise 1 Find the solution to the following systems of simultaneous equations graphically. Try: Ali paid 34 shillings for 10 oranges and 35 mangoes. Moshi went to the same market and paid 24 shillings for 16 oranges and 18 mangoes. What was the price for a mango and for an orange? Inequalities Forming Linear Inequalities in Two Unknowns from Word Problems Form linear inequalities in two unknowns from word problems Linear inequalities Normally any straight line drawn on xy – plane separates it into two disjoint sets. These sets are called half – planes Consider the equation y = 5 drawn on the xy plane as shown below. From the figure above, all points above the line, that is all points in the half plane A which is above the line satisfy the relation y>5 and those lying in the half plane B which is below the given line, satisfy the relation y< 5. Shading of Regions In linear programming usually the region of interest is left clear that is we shade unwanted region(s). NB: When shading the half planes we consider the inequalities as the equations but dotted lines are used for the relations with > or < signs and normal lines are used for those with ≥ or ≤ signs. Consider the inequalities x>0, y>0 and 2x + 3y >12 represented on the xy-plane In this case we draw the line x=0, y= 0 and 2x+3y=12 but the point about the inequality signs for each equation must be considered. From the figure above, the clear region satisfy all the inequalitiesx>0, y>0 and 2x + 3y >12, these three lines are the boundaries of the region. The Solution Set of Simultaneous Linear Inequalities Graphically Find the solution set of simultaneous linear inequalities graphically Example 5 Draw and show the half plane represented by 8x + 2y ≥16 Feasible Region Definition: In the xy plane the region that satisfies all the given inequalities is called the feasible region (F.R) Example 6 Indicate the feasible region for the inequalities 2x+3y ≥ 12 and y-x ≤ 2. Determine the solution set of the simultaneous inequalities y + x ≥3 and x-2y ≤ 9. Example 7 Fatuma was given 30 shillings to buy oranges and mangoes. An orange costs 2 shillings while a mango costs 3 shillings. If the number of oranges bought is at least twice the number of mangoes, show graphically the feasible region representing the number of ranges and mangoes she bought, assuming that no fraction of oranges and mangoes are sold at the market. Solution:- Let x be the number of oranges she bought and y the number of mangoes she bought. Now the cost of x and y together is 2x + 3y shillings which must not exceed 30 shillings. Inequalities: 2x + 3y ≤30 ……… (i) and x≥2y …………….. (ii), Also because there is no negative oranges or mangoes that can be bought, then x≥ and y≥0 ……….. (iii) Now the line 2x + 3y ≤30 is the line passing through (0, 10) and (15,0) and the line x≥2y or x – 2y ≥ 0 is the line which passes through (0,0) and (2,1). Exercise 2 For practice. Draw the graph of the equation 2x – y = 7 and show which half plane is represented by 2x – y >7 and the one represented by 2x – y 3 – x on the same axes and indicate the feasible region. A post office has to transport 870 parcels using a lorry, The Objective Function An Objective Function from Word Problems Form an objective function from word problems Linear programming components Any linear programming problem has the following: Objective Alternative course (s) of action which will achieve the objective. The available resources which are in limited supply. The objective and its limitations should be able to be expressed as either linear mathematical equations or linear inequalities. Therefore linear programming aims at finding the best use of the available resources. Programmingis the use of mathematical techniques in order to get the best possible solution to the problem Steps to be followed in solving linear programming problems; Read carefully the problem, if possible do it several times. Use the variables like x and y to represent the resources of interest. Summarize the problem by putting it in mathematical form using the variables let in step (b) above. In this step you need to formulate the objective function and inequalities or constraints. Plot the constraints on a graph From your graph, identify the corner points. Use the objective function to test each corner point to find out which one gives the optimum solution. Make conclusion after finding or identifying the optimum point among the corner points. Maximum and Minimum Values Corner Points on the Feasible Region Locate corner points on the feasible region Example 8 A student has 1200 shillings to spend on exercise books. At the school shop an exercise book costs 80shillings, and at a stationery store it costs 120 shillings. The school shop has only 6 exercise books left and the student wants to obtain the greatest number of exercise books possible using the money he has. How many exercise books will the student buy from each site? Therefore the student will buy 6 exercise books from each site. Example 9 A nutritionist prescribes a special diet for patients containing the following number of Units of vitamins A and B per kg, of two types of food f1 and f2 If the daily minimum in take required is 120 Units of A and 70 units of B, what is the least total mass of food a patient must have so as to have enough of these vitamins? Solution: Let x be the number of kg(s) of F1 that patient gets daily and y be the number of kg(s) of F2 to be taken by the patient daily. Objective function: F (x, y) = (x + y) minimum f (C) = 10 + 0 = 10 So f (B) = 6.8 is the minimum Therefore the least total mass of food the patient must have is 6.8 kilograms The Minimum and Maximum Values using the Objective Functio Find the minimum and maximum values using the objective function Example 10 A farmer wants to plant coffee and potatoes. Coffee needs 3 men per hectare while potatoes need also 3 men per hectare. He has 48 hired laborers available. To maintain a hectare of coffee he needs 250 shillings while a hectare of potatoes costs him 100 shillings. . Find the greatest possible land he can sow if he is prepared to use 25,000 shillings. Solution: Let x be the number of hectares of coffee to be planted and y be the number of hectares of potatoes to be planted. Objective function: f (x, y) = (x, + y) maximum 3x + 3y ≤ 48 or x + y ≤16 ………….(i) 250x + 100y≤ 25,000 Or 5x + 2y ≤ 500………(ii) x ≥ 0 ……………………(iii) y≥ 0 ……………………(iv) Using the objective function f (x, y) = (x + y) maximum, f (A) = (0 + 250) = 250 f (B) = (0+16) = 16 f (C) = (16+0) = 16 f(D) = (100+0)= 100 (maximum) Therefore the greatest possible area to be planted is 250 hectors of potatoes. NB: In most cases L.P problems must involve non-negativity constraints (inequalities) that are x ≥ 0 and y ≥ 0. This is due to the fact that in daily practice there is no use of negative quantities. Example 11 A technical school is planning to buy two types of machines. A lather machine needs 3m2 of floor space and a drill machine needs 2m2 of floor space. The total space available is 30m2. The cost of one lather machine is 25,000 shillings and that of drill machine is 30,000 shillings. The school can spend not more than 300,000 shillings, what is the greatest number of machines the school can buy? Solution: Let x be the number of Lather machines and y be the number of drill machines to be bought Objective function: f(x, y) = (x + y) max Inequalities: 3x + 2y ≤ 30.. ………………….(i) 25,000x + 30,000y ≤300,000 Or 5x + 6y ≤ 60……………………..(ii) x ≥ 0 ……………………………….(iii) y ≥ 0…………………… ………….(iv) Since the incomplete machine can’t work, then B = (8, 3) or (7, 4).That is approximating values of x and y to the possible integers without affecting the given inequalities or conditions. Now by using the objective function, f (A) = 0 + 10 = 10 f(B) = 7 + 4 0r f (B) = 8 + 3 = 11 f (C) = 10 + 0 = 10 f (D) = 0 + ) = 0 So f (B) gives the maximum number of machines which is 11. Therefore the greatest number of machines that can be bought by the school is 11 machines. Exercise 3 1. Show on a graph the feasible region for which the restrictions are: y ≤ 2x, x≥ 6, y≥2 and 2x + 3y ≤30 From the graph at which point does: y – x take a maximum value? x + y take a maximum value? y – x take a maximum value? 2. With only 20,000 shillings to spend on fish, John had the choice of buying two types of fish. The price of a single fish type 1 was 2,500shillings and each fish of type 2 was sold at 2,000 shillings. He wanted to buy at least four of type 1. What is the greatest number of fish did John buy? How many of each type could he buy? 3. How many corner points does the feasible region restricted by the inequalities? x≥0, y ≥ 0, 3x + 2y ≤ 18 and 2x + 4y ≤16 have? Which corner point maximizes the objective function f (x, y) = 2x + 5y?, Matrices and Transformation, Topic 6: Vectors - Basic Mathematics Form Four, Trigonometry, Probability, Three Dimensional Figures, Area and Perimeter, Coordinate Geometry, Statistics, Similarity

Topic 5: Trigonometry – Basic Mathematics Form Four

Topic 5: Trigonometry – Basic Mathematics Form Four Trigonometric Ratios The Sine, Cosine and ...

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Basic Mathematics For Form Four Full Notes, LINEAR PROGRAMMING. Linear programming – is a branch of mathematics which deals with either minimizing the cost or maximizing the profit. It gives the best way of utilizing the scarce resources available. It is so called because it only involves equations and inequalities which are linear. Simultaneous Equation. One of the methods used in solving linear simultaneous equations is a graphical method. Two linear simultaneous equations in two unknowns can be graphically solved by passing through the following procedures. Draw the two lines which represent the two equations on the xy – plane this is done by deter mining at least two points through which each line passes, the intercept are commonly used Determine the point of intersection of the two lines. This point of intersection is the solution to the system of equations. FACT: If two straight lines are not parallel then they meet at only one point: In case the lines do not meet, there is no solution to the corresponding system of simultaneous equations. Example 1 Graphically solve the following system of simultaneous equations. Example 2 Find the solution to the following system of simultaneous equations by graphical method. Solving Simultaneous Equations Graphically Solve simultaneous equations graphically Example 3 Solve the following simultaneous equations graphically and check your solution by a non-graphical method: Example 4 Find the solution to the following system of simultaneous equations by graphical method. Exercise 1 Find the solution to the following systems of simultaneous equations graphically. Try: Ali paid 34 shillings for 10 oranges and 35 mangoes. Moshi went to the same market and paid 24 shillings for 16 oranges and 18 mangoes. What was the price for a mango and for an orange? Inequalities Forming Linear Inequalities in Two Unknowns from Word Problems Form linear inequalities in two unknowns from word problems Linear inequalities Normally any straight line drawn on xy – plane separates it into two disjoint sets. These sets are called half – planes Consider the equation y = 5 drawn on the xy plane as shown below. From the figure above, all points above the line, that is all points in the half plane A which is above the line satisfy the relation y>5 and those lying in the half plane B which is below the given line, satisfy the relation y< 5. Shading of Regions In linear programming usually the region of interest is left clear that is we shade unwanted region(s). NB: When shading the half planes we consider the inequalities as the equations but dotted lines are used for the relations with > or < signs and normal lines are used for those with ≥ or ≤ signs. Consider the inequalities x>0, y>0 and 2x + 3y >12 represented on the xy-plane In this case we draw the line x=0, y= 0 and 2x+3y=12 but the point about the inequality signs for each equation must be considered. From the figure above, the clear region satisfy all the inequalitiesx>0, y>0 and 2x + 3y >12, these three lines are the boundaries of the region. The Solution Set of Simultaneous Linear Inequalities Graphically Find the solution set of simultaneous linear inequalities graphically Example 5 Draw and show the half plane represented by 8x + 2y ≥16 Feasible Region Definition: In the xy plane the region that satisfies all the given inequalities is called the feasible region (F.R) Example 6 Indicate the feasible region for the inequalities 2x+3y ≥ 12 and y-x ≤ 2. Determine the solution set of the simultaneous inequalities y + x ≥3 and x-2y ≤ 9. Example 7 Fatuma was given 30 shillings to buy oranges and mangoes. An orange costs 2 shillings while a mango costs 3 shillings. If the number of oranges bought is at least twice the number of mangoes, show graphically the feasible region representing the number of ranges and mangoes she bought, assuming that no fraction of oranges and mangoes are sold at the market. Solution:- Let x be the number of oranges she bought and y the number of mangoes she bought. Now the cost of x and y together is 2x + 3y shillings which must not exceed 30 shillings. Inequalities: 2x + 3y ≤30 ……… (i) and x≥2y …………….. (ii), Also because there is no negative oranges or mangoes that can be bought, then x≥ and y≥0 ……….. (iii) Now the line 2x + 3y ≤30 is the line passing through (0, 10) and (15,0) and the line x≥2y or x – 2y ≥ 0 is the line which passes through (0,0) and (2,1). Exercise 2 For practice. Draw the graph of the equation 2x – y = 7 and show which half plane is represented by 2x – y >7 and the one represented by 2x – y 3 – x on the same axes and indicate the feasible region. A post office has to transport 870 parcels using a lorry, The Objective Function An Objective Function from Word Problems Form an objective function from word problems Linear programming components Any linear programming problem has the following: Objective Alternative course (s) of action which will achieve the objective. The available resources which are in limited supply. The objective and its limitations should be able to be expressed as either linear mathematical equations or linear inequalities. Therefore linear programming aims at finding the best use of the available resources. Programmingis the use of mathematical techniques in order to get the best possible solution to the problem Steps to be followed in solving linear programming problems; Read carefully the problem, if possible do it several times. Use the variables like x and y to represent the resources of interest. Summarize the problem by putting it in mathematical form using the variables let in step (b) above. In this step you need to formulate the objective function and inequalities or constraints. Plot the constraints on a graph From your graph, identify the corner points. Use the objective function to test each corner point to find out which one gives the optimum solution. Make conclusion after finding or identifying the optimum point among the corner points. Maximum and Minimum Values Corner Points on the Feasible Region Locate corner points on the feasible region Example 8 A student has 1200 shillings to spend on exercise books. At the school shop an exercise book costs 80shillings, and at a stationery store it costs 120 shillings. The school shop has only 6 exercise books left and the student wants to obtain the greatest number of exercise books possible using the money he has. How many exercise books will the student buy from each site? Therefore the student will buy 6 exercise books from each site. Example 9 A nutritionist prescribes a special diet for patients containing the following number of Units of vitamins A and B per kg, of two types of food f1 and f2 If the daily minimum in take required is 120 Units of A and 70 units of B, what is the least total mass of food a patient must have so as to have enough of these vitamins? Solution: Let x be the number of kg(s) of F1 that patient gets daily and y be the number of kg(s) of F2 to be taken by the patient daily. Objective function: F (x, y) = (x + y) minimum f (C) = 10 + 0 = 10 So f (B) = 6.8 is the minimum Therefore the least total mass of food the patient must have is 6.8 kilograms The Minimum and Maximum Values using the Objective Functio Find the minimum and maximum values using the objective function Example 10 A farmer wants to plant coffee and potatoes. Coffee needs 3 men per hectare while potatoes need also 3 men per hectare. He has 48 hired laborers available. To maintain a hectare of coffee he needs 250 shillings while a hectare of potatoes costs him 100 shillings. . Find the greatest possible land he can sow if he is prepared to use 25,000 shillings. Solution: Let x be the number of hectares of coffee to be planted and y be the number of hectares of potatoes to be planted. Objective function: f (x, y) = (x, + y) maximum 3x + 3y ≤ 48 or x + y ≤16 ………….(i) 250x + 100y≤ 25,000 Or 5x + 2y ≤ 500………(ii) x ≥ 0 ……………………(iii) y≥ 0 ……………………(iv) Using the objective function f (x, y) = (x + y) maximum, f (A) = (0 + 250) = 250 f (B) = (0+16) = 16 f (C) = (16+0) = 16 f(D) = (100+0)= 100 (maximum) Therefore the greatest possible area to be planted is 250 hectors of potatoes. NB: In most cases L.P problems must involve non-negativity constraints (inequalities) that are x ≥ 0 and y ≥ 0. This is due to the fact that in daily practice there is no use of negative quantities. Example 11 A technical school is planning to buy two types of machines. A lather machine needs 3m2 of floor space and a drill machine needs 2m2 of floor space. The total space available is 30m2. The cost of one lather machine is 25,000 shillings and that of drill machine is 30,000 shillings. The school can spend not more than 300,000 shillings, what is the greatest number of machines the school can buy? Solution: Let x be the number of Lather machines and y be the number of drill machines to be bought Objective function: f(x, y) = (x + y) max Inequalities: 3x + 2y ≤ 30.. ………………….(i) 25,000x + 30,000y ≤300,000 Or 5x + 6y ≤ 60……………………..(ii) x ≥ 0 ……………………………….(iii) y ≥ 0…………………… ………….(iv) Since the incomplete machine can’t work, then B = (8, 3) or (7, 4).That is approximating values of x and y to the possible integers without affecting the given inequalities or conditions. Now by using the objective function, f (A) = 0 + 10 = 10 f(B) = 7 + 4 0r f (B) = 8 + 3 = 11 f (C) = 10 + 0 = 10 f (D) = 0 + ) = 0 So f (B) gives the maximum number of machines which is 11. Therefore the greatest number of machines that can be bought by the school is 11 machines. Exercise 3 1. Show on a graph the feasible region for which the restrictions are: y ≤ 2x, x≥ 6, y≥2 and 2x + 3y ≤30 From the graph at which point does: y – x take a maximum value? x + y take a maximum value? y – x take a maximum value? 2. With only 20,000 shillings to spend on fish, John had the choice of buying two types of fish. The price of a single fish type 1 was 2,500shillings and each fish of type 2 was sold at 2,000 shillings. He wanted to buy at least four of type 1. What is the greatest number of fish did John buy? How many of each type could he buy? 3. How many corner points does the feasible region restricted by the inequalities? x≥0, y ≥ 0, 3x + 2y ≤ 18 and 2x + 4y ≤16 have? Which corner point maximizes the objective function f (x, y) = 2x + 5y?, Matrices and Transformation, Topic 6: Vectors - Basic Mathematics Form Four, Trigonometry, Probability, Three Dimensional Figures, Area and Perimeter, Coordinate Geometry, Statistics, Similarity

Topic 4: Probability – Basic Mathematics Form Four

Topic 4: Probability – Basic Mathematics Form Four Normally we are living in the ...

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Basic Mathematics For Form Four Full Notes, LINEAR PROGRAMMING. Linear programming – is a branch of mathematics which deals with either minimizing the cost or maximizing the profit. It gives the best way of utilizing the scarce resources available. It is so called because it only involves equations and inequalities which are linear. Simultaneous Equation. One of the methods used in solving linear simultaneous equations is a graphical method. Two linear simultaneous equations in two unknowns can be graphically solved by passing through the following procedures. Draw the two lines which represent the two equations on the xy – plane this is done by deter mining at least two points through which each line passes, the intercept are commonly used Determine the point of intersection of the two lines. This point of intersection is the solution to the system of equations. FACT: If two straight lines are not parallel then they meet at only one point: In case the lines do not meet, there is no solution to the corresponding system of simultaneous equations. Example 1 Graphically solve the following system of simultaneous equations. Example 2 Find the solution to the following system of simultaneous equations by graphical method. Solving Simultaneous Equations Graphically Solve simultaneous equations graphically Example 3 Solve the following simultaneous equations graphically and check your solution by a non-graphical method: Example 4 Find the solution to the following system of simultaneous equations by graphical method. Exercise 1 Find the solution to the following systems of simultaneous equations graphically. Try: Ali paid 34 shillings for 10 oranges and 35 mangoes. Moshi went to the same market and paid 24 shillings for 16 oranges and 18 mangoes. What was the price for a mango and for an orange? Inequalities Forming Linear Inequalities in Two Unknowns from Word Problems Form linear inequalities in two unknowns from word problems Linear inequalities Normally any straight line drawn on xy – plane separates it into two disjoint sets. These sets are called half – planes Consider the equation y = 5 drawn on the xy plane as shown below. From the figure above, all points above the line, that is all points in the half plane A which is above the line satisfy the relation y>5 and those lying in the half plane B which is below the given line, satisfy the relation y< 5. Shading of Regions In linear programming usually the region of interest is left clear that is we shade unwanted region(s). NB: When shading the half planes we consider the inequalities as the equations but dotted lines are used for the relations with > or < signs and normal lines are used for those with ≥ or ≤ signs. Consider the inequalities x>0, y>0 and 2x + 3y >12 represented on the xy-plane In this case we draw the line x=0, y= 0 and 2x+3y=12 but the point about the inequality signs for each equation must be considered. From the figure above, the clear region satisfy all the inequalitiesx>0, y>0 and 2x + 3y >12, these three lines are the boundaries of the region. The Solution Set of Simultaneous Linear Inequalities Graphically Find the solution set of simultaneous linear inequalities graphically Example 5 Draw and show the half plane represented by 8x + 2y ≥16 Feasible Region Definition: In the xy plane the region that satisfies all the given inequalities is called the feasible region (F.R) Example 6 Indicate the feasible region for the inequalities 2x+3y ≥ 12 and y-x ≤ 2. Determine the solution set of the simultaneous inequalities y + x ≥3 and x-2y ≤ 9. Example 7 Fatuma was given 30 shillings to buy oranges and mangoes. An orange costs 2 shillings while a mango costs 3 shillings. If the number of oranges bought is at least twice the number of mangoes, show graphically the feasible region representing the number of ranges and mangoes she bought, assuming that no fraction of oranges and mangoes are sold at the market. Solution:- Let x be the number of oranges she bought and y the number of mangoes she bought. Now the cost of x and y together is 2x + 3y shillings which must not exceed 30 shillings. Inequalities: 2x + 3y ≤30 ……… (i) and x≥2y …………….. (ii), Also because there is no negative oranges or mangoes that can be bought, then x≥ and y≥0 ……….. (iii) Now the line 2x + 3y ≤30 is the line passing through (0, 10) and (15,0) and the line x≥2y or x – 2y ≥ 0 is the line which passes through (0,0) and (2,1). Exercise 2 For practice. Draw the graph of the equation 2x – y = 7 and show which half plane is represented by 2x – y >7 and the one represented by 2x – y 3 – x on the same axes and indicate the feasible region. A post office has to transport 870 parcels using a lorry, The Objective Function An Objective Function from Word Problems Form an objective function from word problems Linear programming components Any linear programming problem has the following: Objective Alternative course (s) of action which will achieve the objective. The available resources which are in limited supply. The objective and its limitations should be able to be expressed as either linear mathematical equations or linear inequalities. Therefore linear programming aims at finding the best use of the available resources. Programmingis the use of mathematical techniques in order to get the best possible solution to the problem Steps to be followed in solving linear programming problems; Read carefully the problem, if possible do it several times. Use the variables like x and y to represent the resources of interest. Summarize the problem by putting it in mathematical form using the variables let in step (b) above. In this step you need to formulate the objective function and inequalities or constraints. Plot the constraints on a graph From your graph, identify the corner points. Use the objective function to test each corner point to find out which one gives the optimum solution. Make conclusion after finding or identifying the optimum point among the corner points. Maximum and Minimum Values Corner Points on the Feasible Region Locate corner points on the feasible region Example 8 A student has 1200 shillings to spend on exercise books. At the school shop an exercise book costs 80shillings, and at a stationery store it costs 120 shillings. The school shop has only 6 exercise books left and the student wants to obtain the greatest number of exercise books possible using the money he has. How many exercise books will the student buy from each site? Therefore the student will buy 6 exercise books from each site. Example 9 A nutritionist prescribes a special diet for patients containing the following number of Units of vitamins A and B per kg, of two types of food f1 and f2 If the daily minimum in take required is 120 Units of A and 70 units of B, what is the least total mass of food a patient must have so as to have enough of these vitamins? Solution: Let x be the number of kg(s) of F1 that patient gets daily and y be the number of kg(s) of F2 to be taken by the patient daily. Objective function: F (x, y) = (x + y) minimum f (C) = 10 + 0 = 10 So f (B) = 6.8 is the minimum Therefore the least total mass of food the patient must have is 6.8 kilograms The Minimum and Maximum Values using the Objective Functio Find the minimum and maximum values using the objective function Example 10 A farmer wants to plant coffee and potatoes. Coffee needs 3 men per hectare while potatoes need also 3 men per hectare. He has 48 hired laborers available. To maintain a hectare of coffee he needs 250 shillings while a hectare of potatoes costs him 100 shillings. . Find the greatest possible land he can sow if he is prepared to use 25,000 shillings. Solution: Let x be the number of hectares of coffee to be planted and y be the number of hectares of potatoes to be planted. Objective function: f (x, y) = (x, + y) maximum 3x + 3y ≤ 48 or x + y ≤16 ………….(i) 250x + 100y≤ 25,000 Or 5x + 2y ≤ 500………(ii) x ≥ 0 ……………………(iii) y≥ 0 ……………………(iv) Using the objective function f (x, y) = (x + y) maximum, f (A) = (0 + 250) = 250 f (B) = (0+16) = 16 f (C) = (16+0) = 16 f(D) = (100+0)= 100 (maximum) Therefore the greatest possible area to be planted is 250 hectors of potatoes. NB: In most cases L.P problems must involve non-negativity constraints (inequalities) that are x ≥ 0 and y ≥ 0. This is due to the fact that in daily practice there is no use of negative quantities. Example 11 A technical school is planning to buy two types of machines. A lather machine needs 3m2 of floor space and a drill machine needs 2m2 of floor space. The total space available is 30m2. The cost of one lather machine is 25,000 shillings and that of drill machine is 30,000 shillings. The school can spend not more than 300,000 shillings, what is the greatest number of machines the school can buy? Solution: Let x be the number of Lather machines and y be the number of drill machines to be bought Objective function: f(x, y) = (x + y) max Inequalities: 3x + 2y ≤ 30.. ………………….(i) 25,000x + 30,000y ≤300,000 Or 5x + 6y ≤ 60……………………..(ii) x ≥ 0 ……………………………….(iii) y ≥ 0…………………… ………….(iv) Since the incomplete machine can’t work, then B = (8, 3) or (7, 4).That is approximating values of x and y to the possible integers without affecting the given inequalities or conditions. Now by using the objective function, f (A) = 0 + 10 = 10 f(B) = 7 + 4 0r f (B) = 8 + 3 = 11 f (C) = 10 + 0 = 10 f (D) = 0 + ) = 0 So f (B) gives the maximum number of machines which is 11. Therefore the greatest number of machines that can be bought by the school is 11 machines. Exercise 3 1. Show on a graph the feasible region for which the restrictions are: y ≤ 2x, x≥ 6, y≥2 and 2x + 3y ≤30 From the graph at which point does: y – x take a maximum value? x + y take a maximum value? y – x take a maximum value? 2. With only 20,000 shillings to spend on fish, John had the choice of buying two types of fish. The price of a single fish type 1 was 2,500shillings and each fish of type 2 was sold at 2,000 shillings. He wanted to buy at least four of type 1. What is the greatest number of fish did John buy? How many of each type could he buy? 3. How many corner points does the feasible region restricted by the inequalities? x≥0, y ≥ 0, 3x + 2y ≤ 18 and 2x + 4y ≤16 have? Which corner point maximizes the objective function f (x, y) = 2x + 5y?, Matrices and Transformation, Topic 6: Vectors - Basic Mathematics Form Four, Trigonometry, Probability, Three Dimensional Figures, Area and Perimeter, Coordinate Geometry, Statistics, Similarity

Topic 3: Three Dimensional Figures – Basic Mathematics Form Four

Topic 3: Three Dimensional Figures – Basic Mathematics Form Four Three Dimensional Figures Sometimes ...

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Basic Mathematics For Form Four Full Notes, LINEAR PROGRAMMING. Linear programming – is a branch of mathematics which deals with either minimizing the cost or maximizing the profit. It gives the best way of utilizing the scarce resources available. It is so called because it only involves equations and inequalities which are linear. Simultaneous Equation. One of the methods used in solving linear simultaneous equations is a graphical method. Two linear simultaneous equations in two unknowns can be graphically solved by passing through the following procedures. Draw the two lines which represent the two equations on the xy – plane this is done by deter mining at least two points through which each line passes, the intercept are commonly used Determine the point of intersection of the two lines. This point of intersection is the solution to the system of equations. FACT: If two straight lines are not parallel then they meet at only one point: In case the lines do not meet, there is no solution to the corresponding system of simultaneous equations. Example 1 Graphically solve the following system of simultaneous equations. Example 2 Find the solution to the following system of simultaneous equations by graphical method. Solving Simultaneous Equations Graphically Solve simultaneous equations graphically Example 3 Solve the following simultaneous equations graphically and check your solution by a non-graphical method: Example 4 Find the solution to the following system of simultaneous equations by graphical method. Exercise 1 Find the solution to the following systems of simultaneous equations graphically. Try: Ali paid 34 shillings for 10 oranges and 35 mangoes. Moshi went to the same market and paid 24 shillings for 16 oranges and 18 mangoes. What was the price for a mango and for an orange? Inequalities Forming Linear Inequalities in Two Unknowns from Word Problems Form linear inequalities in two unknowns from word problems Linear inequalities Normally any straight line drawn on xy – plane separates it into two disjoint sets. These sets are called half – planes Consider the equation y = 5 drawn on the xy plane as shown below. From the figure above, all points above the line, that is all points in the half plane A which is above the line satisfy the relation y>5 and those lying in the half plane B which is below the given line, satisfy the relation y< 5. Shading of Regions In linear programming usually the region of interest is left clear that is we shade unwanted region(s). NB: When shading the half planes we consider the inequalities as the equations but dotted lines are used for the relations with > or < signs and normal lines are used for those with ≥ or ≤ signs. Consider the inequalities x>0, y>0 and 2x + 3y >12 represented on the xy-plane In this case we draw the line x=0, y= 0 and 2x+3y=12 but the point about the inequality signs for each equation must be considered. From the figure above, the clear region satisfy all the inequalitiesx>0, y>0 and 2x + 3y >12, these three lines are the boundaries of the region. The Solution Set of Simultaneous Linear Inequalities Graphically Find the solution set of simultaneous linear inequalities graphically Example 5 Draw and show the half plane represented by 8x + 2y ≥16 Feasible Region Definition: In the xy plane the region that satisfies all the given inequalities is called the feasible region (F.R) Example 6 Indicate the feasible region for the inequalities 2x+3y ≥ 12 and y-x ≤ 2. Determine the solution set of the simultaneous inequalities y + x ≥3 and x-2y ≤ 9. Example 7 Fatuma was given 30 shillings to buy oranges and mangoes. An orange costs 2 shillings while a mango costs 3 shillings. If the number of oranges bought is at least twice the number of mangoes, show graphically the feasible region representing the number of ranges and mangoes she bought, assuming that no fraction of oranges and mangoes are sold at the market. Solution:- Let x be the number of oranges she bought and y the number of mangoes she bought. Now the cost of x and y together is 2x + 3y shillings which must not exceed 30 shillings. Inequalities: 2x + 3y ≤30 ……… (i) and x≥2y …………….. (ii), Also because there is no negative oranges or mangoes that can be bought, then x≥ and y≥0 ……….. (iii) Now the line 2x + 3y ≤30 is the line passing through (0, 10) and (15,0) and the line x≥2y or x – 2y ≥ 0 is the line which passes through (0,0) and (2,1). Exercise 2 For practice. Draw the graph of the equation 2x – y = 7 and show which half plane is represented by 2x – y >7 and the one represented by 2x – y 3 – x on the same axes and indicate the feasible region. A post office has to transport 870 parcels using a lorry, The Objective Function An Objective Function from Word Problems Form an objective function from word problems Linear programming components Any linear programming problem has the following: Objective Alternative course (s) of action which will achieve the objective. The available resources which are in limited supply. The objective and its limitations should be able to be expressed as either linear mathematical equations or linear inequalities. Therefore linear programming aims at finding the best use of the available resources. Programmingis the use of mathematical techniques in order to get the best possible solution to the problem Steps to be followed in solving linear programming problems; Read carefully the problem, if possible do it several times. Use the variables like x and y to represent the resources of interest. Summarize the problem by putting it in mathematical form using the variables let in step (b) above. In this step you need to formulate the objective function and inequalities or constraints. Plot the constraints on a graph From your graph, identify the corner points. Use the objective function to test each corner point to find out which one gives the optimum solution. Make conclusion after finding or identifying the optimum point among the corner points. Maximum and Minimum Values Corner Points on the Feasible Region Locate corner points on the feasible region Example 8 A student has 1200 shillings to spend on exercise books. At the school shop an exercise book costs 80shillings, and at a stationery store it costs 120 shillings. The school shop has only 6 exercise books left and the student wants to obtain the greatest number of exercise books possible using the money he has. How many exercise books will the student buy from each site? Therefore the student will buy 6 exercise books from each site. Example 9 A nutritionist prescribes a special diet for patients containing the following number of Units of vitamins A and B per kg, of two types of food f1 and f2 If the daily minimum in take required is 120 Units of A and 70 units of B, what is the least total mass of food a patient must have so as to have enough of these vitamins? Solution: Let x be the number of kg(s) of F1 that patient gets daily and y be the number of kg(s) of F2 to be taken by the patient daily. Objective function: F (x, y) = (x + y) minimum f (C) = 10 + 0 = 10 So f (B) = 6.8 is the minimum Therefore the least total mass of food the patient must have is 6.8 kilograms The Minimum and Maximum Values using the Objective Functio Find the minimum and maximum values using the objective function Example 10 A farmer wants to plant coffee and potatoes. Coffee needs 3 men per hectare while potatoes need also 3 men per hectare. He has 48 hired laborers available. To maintain a hectare of coffee he needs 250 shillings while a hectare of potatoes costs him 100 shillings. . Find the greatest possible land he can sow if he is prepared to use 25,000 shillings. Solution: Let x be the number of hectares of coffee to be planted and y be the number of hectares of potatoes to be planted. Objective function: f (x, y) = (x, + y) maximum 3x + 3y ≤ 48 or x + y ≤16 ………….(i) 250x + 100y≤ 25,000 Or 5x + 2y ≤ 500………(ii) x ≥ 0 ……………………(iii) y≥ 0 ……………………(iv) Using the objective function f (x, y) = (x + y) maximum, f (A) = (0 + 250) = 250 f (B) = (0+16) = 16 f (C) = (16+0) = 16 f(D) = (100+0)= 100 (maximum) Therefore the greatest possible area to be planted is 250 hectors of potatoes. NB: In most cases L.P problems must involve non-negativity constraints (inequalities) that are x ≥ 0 and y ≥ 0. This is due to the fact that in daily practice there is no use of negative quantities. Example 11 A technical school is planning to buy two types of machines. A lather machine needs 3m2 of floor space and a drill machine needs 2m2 of floor space. The total space available is 30m2. The cost of one lather machine is 25,000 shillings and that of drill machine is 30,000 shillings. The school can spend not more than 300,000 shillings, what is the greatest number of machines the school can buy? Solution: Let x be the number of Lather machines and y be the number of drill machines to be bought Objective function: f(x, y) = (x + y) max Inequalities: 3x + 2y ≤ 30.. ………………….(i) 25,000x + 30,000y ≤300,000 Or 5x + 6y ≤ 60……………………..(ii) x ≥ 0 ……………………………….(iii) y ≥ 0…………………… ………….(iv) Since the incomplete machine can’t work, then B = (8, 3) or (7, 4).That is approximating values of x and y to the possible integers without affecting the given inequalities or conditions. Now by using the objective function, f (A) = 0 + 10 = 10 f(B) = 7 + 4 0r f (B) = 8 + 3 = 11 f (C) = 10 + 0 = 10 f (D) = 0 + ) = 0 So f (B) gives the maximum number of machines which is 11. Therefore the greatest number of machines that can be bought by the school is 11 machines. Exercise 3 1. Show on a graph the feasible region for which the restrictions are: y ≤ 2x, x≥ 6, y≥2 and 2x + 3y ≤30 From the graph at which point does: y – x take a maximum value? x + y take a maximum value? y – x take a maximum value? 2. With only 20,000 shillings to spend on fish, John had the choice of buying two types of fish. The price of a single fish type 1 was 2,500shillings and each fish of type 2 was sold at 2,000 shillings. He wanted to buy at least four of type 1. What is the greatest number of fish did John buy? How many of each type could he buy? 3. How many corner points does the feasible region restricted by the inequalities? x≥0, y ≥ 0, 3x + 2y ≤ 18 and 2x + 4y ≤16 have? Which corner point maximizes the objective function f (x, y) = 2x + 5y?, Matrices and Transformation, Topic 6: Vectors - Basic Mathematics Form Four, Trigonometry, Probability, Three Dimensional Figures, Area and Perimeter, Coordinate Geometry, Statistics, Similarity

Topic 2: Area and Perimeter – Basic Mathematics Form Four

Topic 2: Area and Perimeter – Basic Mathematics Form Four Area of any Triangle ...

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Basic Mathematics For Form Four Full Notes, LINEAR PROGRAMMING. Linear programming – is a branch of mathematics which deals with either minimizing the cost or maximizing the profit. It gives the best way of utilizing the scarce resources available. It is so called because it only involves equations and inequalities which are linear. Simultaneous Equation. One of the methods used in solving linear simultaneous equations is a graphical method. Two linear simultaneous equations in two unknowns can be graphically solved by passing through the following procedures. Draw the two lines which represent the two equations on the xy – plane this is done by deter mining at least two points through which each line passes, the intercept are commonly used Determine the point of intersection of the two lines. This point of intersection is the solution to the system of equations. FACT: If two straight lines are not parallel then they meet at only one point: In case the lines do not meet, there is no solution to the corresponding system of simultaneous equations. Example 1 Graphically solve the following system of simultaneous equations. Example 2 Find the solution to the following system of simultaneous equations by graphical method. Solving Simultaneous Equations Graphically Solve simultaneous equations graphically Example 3 Solve the following simultaneous equations graphically and check your solution by a non-graphical method: Example 4 Find the solution to the following system of simultaneous equations by graphical method. Exercise 1 Find the solution to the following systems of simultaneous equations graphically. Try: Ali paid 34 shillings for 10 oranges and 35 mangoes. Moshi went to the same market and paid 24 shillings for 16 oranges and 18 mangoes. What was the price for a mango and for an orange? Inequalities Forming Linear Inequalities in Two Unknowns from Word Problems Form linear inequalities in two unknowns from word problems Linear inequalities Normally any straight line drawn on xy – plane separates it into two disjoint sets. These sets are called half – planes Consider the equation y = 5 drawn on the xy plane as shown below. From the figure above, all points above the line, that is all points in the half plane A which is above the line satisfy the relation y>5 and those lying in the half plane B which is below the given line, satisfy the relation y< 5. Shading of Regions In linear programming usually the region of interest is left clear that is we shade unwanted region(s). NB: When shading the half planes we consider the inequalities as the equations but dotted lines are used for the relations with > or < signs and normal lines are used for those with ≥ or ≤ signs. Consider the inequalities x>0, y>0 and 2x + 3y >12 represented on the xy-plane In this case we draw the line x=0, y= 0 and 2x+3y=12 but the point about the inequality signs for each equation must be considered. From the figure above, the clear region satisfy all the inequalitiesx>0, y>0 and 2x + 3y >12, these three lines are the boundaries of the region. The Solution Set of Simultaneous Linear Inequalities Graphically Find the solution set of simultaneous linear inequalities graphically Example 5 Draw and show the half plane represented by 8x + 2y ≥16 Feasible Region Definition: In the xy plane the region that satisfies all the given inequalities is called the feasible region (F.R) Example 6 Indicate the feasible region for the inequalities 2x+3y ≥ 12 and y-x ≤ 2. Determine the solution set of the simultaneous inequalities y + x ≥3 and x-2y ≤ 9. Example 7 Fatuma was given 30 shillings to buy oranges and mangoes. An orange costs 2 shillings while a mango costs 3 shillings. If the number of oranges bought is at least twice the number of mangoes, show graphically the feasible region representing the number of ranges and mangoes she bought, assuming that no fraction of oranges and mangoes are sold at the market. Solution:- Let x be the number of oranges she bought and y the number of mangoes she bought. Now the cost of x and y together is 2x + 3y shillings which must not exceed 30 shillings. Inequalities: 2x + 3y ≤30 ……… (i) and x≥2y …………….. (ii), Also because there is no negative oranges or mangoes that can be bought, then x≥ and y≥0 ……….. (iii) Now the line 2x + 3y ≤30 is the line passing through (0, 10) and (15,0) and the line x≥2y or x – 2y ≥ 0 is the line which passes through (0,0) and (2,1). Exercise 2 For practice. Draw the graph of the equation 2x – y = 7 and show which half plane is represented by 2x – y >7 and the one represented by 2x – y 3 – x on the same axes and indicate the feasible region. A post office has to transport 870 parcels using a lorry, The Objective Function An Objective Function from Word Problems Form an objective function from word problems Linear programming components Any linear programming problem has the following: Objective Alternative course (s) of action which will achieve the objective. The available resources which are in limited supply. The objective and its limitations should be able to be expressed as either linear mathematical equations or linear inequalities. Therefore linear programming aims at finding the best use of the available resources. Programmingis the use of mathematical techniques in order to get the best possible solution to the problem Steps to be followed in solving linear programming problems; Read carefully the problem, if possible do it several times. Use the variables like x and y to represent the resources of interest. Summarize the problem by putting it in mathematical form using the variables let in step (b) above. In this step you need to formulate the objective function and inequalities or constraints. Plot the constraints on a graph From your graph, identify the corner points. Use the objective function to test each corner point to find out which one gives the optimum solution. Make conclusion after finding or identifying the optimum point among the corner points. Maximum and Minimum Values Corner Points on the Feasible Region Locate corner points on the feasible region Example 8 A student has 1200 shillings to spend on exercise books. At the school shop an exercise book costs 80shillings, and at a stationery store it costs 120 shillings. The school shop has only 6 exercise books left and the student wants to obtain the greatest number of exercise books possible using the money he has. How many exercise books will the student buy from each site? Therefore the student will buy 6 exercise books from each site. Example 9 A nutritionist prescribes a special diet for patients containing the following number of Units of vitamins A and B per kg, of two types of food f1 and f2 If the daily minimum in take required is 120 Units of A and 70 units of B, what is the least total mass of food a patient must have so as to have enough of these vitamins? Solution: Let x be the number of kg(s) of F1 that patient gets daily and y be the number of kg(s) of F2 to be taken by the patient daily. Objective function: F (x, y) = (x + y) minimum f (C) = 10 + 0 = 10 So f (B) = 6.8 is the minimum Therefore the least total mass of food the patient must have is 6.8 kilograms The Minimum and Maximum Values using the Objective Functio Find the minimum and maximum values using the objective function Example 10 A farmer wants to plant coffee and potatoes. Coffee needs 3 men per hectare while potatoes need also 3 men per hectare. He has 48 hired laborers available. To maintain a hectare of coffee he needs 250 shillings while a hectare of potatoes costs him 100 shillings. . Find the greatest possible land he can sow if he is prepared to use 25,000 shillings. Solution: Let x be the number of hectares of coffee to be planted and y be the number of hectares of potatoes to be planted. Objective function: f (x, y) = (x, + y) maximum 3x + 3y ≤ 48 or x + y ≤16 ………….(i) 250x + 100y≤ 25,000 Or 5x + 2y ≤ 500………(ii) x ≥ 0 ……………………(iii) y≥ 0 ……………………(iv) Using the objective function f (x, y) = (x + y) maximum, f (A) = (0 + 250) = 250 f (B) = (0+16) = 16 f (C) = (16+0) = 16 f(D) = (100+0)= 100 (maximum) Therefore the greatest possible area to be planted is 250 hectors of potatoes. NB: In most cases L.P problems must involve non-negativity constraints (inequalities) that are x ≥ 0 and y ≥ 0. This is due to the fact that in daily practice there is no use of negative quantities. Example 11 A technical school is planning to buy two types of machines. A lather machine needs 3m2 of floor space and a drill machine needs 2m2 of floor space. The total space available is 30m2. The cost of one lather machine is 25,000 shillings and that of drill machine is 30,000 shillings. The school can spend not more than 300,000 shillings, what is the greatest number of machines the school can buy? Solution: Let x be the number of Lather machines and y be the number of drill machines to be bought Objective function: f(x, y) = (x + y) max Inequalities: 3x + 2y ≤ 30.. ………………….(i) 25,000x + 30,000y ≤300,000 Or 5x + 6y ≤ 60……………………..(ii) x ≥ 0 ……………………………….(iii) y ≥ 0…………………… ………….(iv) Since the incomplete machine can’t work, then B = (8, 3) or (7, 4).That is approximating values of x and y to the possible integers without affecting the given inequalities or conditions. Now by using the objective function, f (A) = 0 + 10 = 10 f(B) = 7 + 4 0r f (B) = 8 + 3 = 11 f (C) = 10 + 0 = 10 f (D) = 0 + ) = 0 So f (B) gives the maximum number of machines which is 11. Therefore the greatest number of machines that can be bought by the school is 11 machines. Exercise 3 1. Show on a graph the feasible region for which the restrictions are: y ≤ 2x, x≥ 6, y≥2 and 2x + 3y ≤30 From the graph at which point does: y – x take a maximum value? x + y take a maximum value? y – x take a maximum value? 2. With only 20,000 shillings to spend on fish, John had the choice of buying two types of fish. The price of a single fish type 1 was 2,500shillings and each fish of type 2 was sold at 2,000 shillings. He wanted to buy at least four of type 1. What is the greatest number of fish did John buy? How many of each type could he buy? 3. How many corner points does the feasible region restricted by the inequalities? x≥0, y ≥ 0, 3x + 2y ≤ 18 and 2x + 4y ≤16 have? Which corner point maximizes the objective function f (x, y) = 2x + 5y?, Matrices and Transformation, Topic 6: Vectors - Basic Mathematics Form Four, Trigonometry, Probability, Three Dimensional Figures, Area and Perimeter, Coordinate Geometry, Statistics, Similarity

Topic 1: Coordinate Geometry – Basic Mathematics Form Four

Topic 1: Coordinate Geometry – Basic Mathematics Form Four Equation of a Line The ...

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Rates and Variations, Basic Mathematics For Form Three Full Notes All Topics, Sequence And Series, Rates And Variations, Functions, Relations, Geometric And Transformations, Mathematics Form II

Basic Mathematics For Form Three Full Notes All Topics

Basic Mathematics For Form Three Full Notes All Topics Download Form 3 Mathematics Notes ...

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Partnerships, Topic 9: Manufacturing Account - Book Keeping Form Three, Book-Keeping Form One Notes New Syllabus, Topic 7: Basic Financial Statements - Book Keeping Notes Form One New Syllabus, Trial Balance, Meaning of Books of Prime Entry: Books of prime entry: Are the books in which transactions are recorded before being posted to their respective ledgers. Books of prime entry: Are the books of account that are used to record any transaction for the first time. When a particular transaction has occurred for the first time in a business should be entered into the primary books known as books of prime entry/books of original entry/ subsidiary books/daily books/ journals before being posted to their respective ledger accounts. The word Journal is adopted from a French word which means “daily recording” THE TYPES OF BOOKS OF PRIME ENTRY: There six (06) types of books prime entry which are; Purchases day book (purchases journal) Sales day book (sales journal) Purchases returns day book (Returns outwards journal) Sales returns day book (Returns inwards journal) Cash book Journal proper (General journal) USE OF BOOKS OF PRIME ENTRY: The following are brief descriptions and purpose of each of the book of prime entry: Purchases day book (purchases journal) this journal is used to record details of goods bought by the business with the promise that payment will be made in the future. Purchase returns daybook (purchase returns journal): the purchase returns daybook is used to record transactions related to purchase returns, or returns of goods to suppliers who supplied goods on credit (creditors). Sales day book (sales journal): is the journal used to record details of goods sold on credit with the promise that payment will be received in the future. Sales returns daybook (sales returns journal): this book is used to record details of transactions related to sales returns, or returns of goods from customers to whom goods were sold on credit (debtors). Cash book: is the book used to record transactions related to receipt and payment of cash as well money placed into the bank (bank deposits) and those taken from the bank (bank withdrawals). Cash book is divided into different categories which are Single columns cash book. Two columns’ cash book. Three columns’ cash book. Petty cash book General journal (journal proper) this book of prime entry is used to record transactions related to other items, which according to their nature are not recorded in any other books of prime entry. SOURCE DOCUMENTS/ACCOUNTING INFORMATION: These are documents from which transactions to be recorded in the books of prime entry are extracted. They are documents used in the books of prime entry. These documents are used in the books of prime entry. Source documents can be summarized as follows INVOICE This is a document issued when goods are sold or bought on credit. Sales invoice is issued when goods are sold on credit whereas purchases invoice is issued when credit purchases are made. Invoices are used in preparation of sales day book and purchases day book. DEBIT NOTE is the document prepared and sent by the seller to the buyer to adjust undercharges on the invoice. This document is used by the buyer in preparation of Purchases returns day book/ Returns outwards journal CREDIT NOTE is the document sent by the seller to the buyer to correct an overcharge on an invoice. This document is used in preparation of sales returns day book/ returns inwards journal. CHEQUE: This is a written order by a customer to his/her bank to pay a specified sum of money to the named person at a specific period of time. Is the document used by the drawer to withdraw cash from his or her account. This document is used in preparation of a cash book. PAY-IN-SLIP: This is a bank deposit form filled in by depositor and stamped by a teller as evidence of accepting the deposit. WITHDRAW SLIP: This is a document filled by a person withdrawing money from the bank upon being accepted by the bank teller. CASH RECEIPT/ CASH RECEIPT VOUCHER: is the document that acts as proof that cash has been received. Money could be received from customer for cash sale of goods or goods, or cash received when a credit customer settles his or her debt with the business. PAYMENT VOUCHER: is the document that presents evidence that money has been paid. Money might be paid to the supplier for cash purchase of goods or service or settlement of account payable for goods previously bought on credit. PETTY CASH VOUCHER: is the document used by a petty cashier as evidence for making small payment from petty cash fund. This document is used in preparation of Petty Cash Book. STATEMENT OF ACCOUNT: is the document sent by the seller to the buyer at the end of every period (usually each month) acting as a reminder to the buyer to pay the outstanding balance. JOURNAL VOUCHER: is the document that provide evidence of authorization for all transaction other than those which are evidenced by the previously mentioned source documents. This document is used in the preparation of General journal or Journal proper. PREPARATION OF BOOKS OF PRIME ENTRY: As per the accounting cycle or process introduced in chapter one, once transactions are identified they are entered in the books of prime entry, followed by posting the entries to relevant ledgers account. In section, you are going to learn the six special journal and how information from source documents is entered followed by the general journal. CASH BOOK: This is a book where receipts or payments are recorded. This book is both a ledger and a book of prime entry. Receipts and payments entered in on debit side and credit side respectively. Receipt/cheque: are documents which are used to obtain information to prepare Cash book. Moreover, an account has four columns in both Dr and Cr sides of account namely: The format of a Cash account is illustrated below; DR CASH BOOK CR Date Particulars Folio Amount Date Particulars Folio Amount Date column: Is the column used to record the date at which the given transaction took place. Particulars/narration/details: Is the column used to record a short description of the transactions that took place. Folio column: is the column used to record the reference page in books of account. Amount column: is the column used to record the amount of money that used in purchasing or selling the goods. Example 1: Kafuku commenced business on 1st January 2022 with Capital in cash TZS 200,000. Her transactions during the month were as follows: January 2. Purchased goods for cash 40,000 3. Sold goods for cash 10,000 3. Paid rent for cash 60,000 4. Cash purchases 16,000 6. Paid postage charger 1,000 13. Commission received for cash 50,000 17. Paid salaries for cash 9,600 19. Paid adverting expenses for cash 7,000 24. Bought furniture for cash 10,000 28. Paid wages for cash 16,000 Required: Draw up a cash book, balance it and bring down the balance to the following months DR. CASH BOOK CR. Date Particulars Folio Amount Date Particulars Folio Amount 2022 2022 Jan. 1 Capital 2 200,000 Jan. 2 Purchases 3 40,000 3 Sales 4 10,000 3 Rent 5 60,000 13 Commission 7 50,000 4 Purchases 3 16,000 Received 6 Postage 6 1,000 Charges 17 Salaries 8 9,600 19 Advertising 9 7,000 Expenses 24 Furniture 10 10,000 28 Wages 11 16,000 31 Balance c/d 100,400 260,000 260,000 Feb. 1 Balance b/d 100,400 Example 2: Moshi & his Son Islam started business with a capital of Tsh 60000, on 1st September 2022. During the month the following transaction took place: – Sept 2, Purchased of goods for cash Tsh 3000 Sept 4, Paid carriage charge Cash Tsh 2000 Sept 6, Paid Transport charge Cash Tsh 4000 Sept 8, Bought Motor Vehicle for cash Tsh55000 Sept 10, Cash Sales Tsh 44000 Sept 12, Paid Rent for Cash Tsh1500 Sept 15, Paid commission charge Tsh 1000 Required: Records the above transaction into Cash book account and bring down the balance as on 30th September 2022. DR CASH ACCOUNT CR SALES DAY BOOK Sales day book is in which sales made on credit are recorded. It is a book of original entry that contains the list of credit sales made in a business. It is also known as sales journal Sales invoice: is a document prepared and issued by a seller to the buyer containing information about goods sold on credit. This information includes name, quantity and prices of the products sold. Format of the sales day book: The sales day book has six columns which are: Date: this column is used to write the date, month, and the year of the transaction. Generally, it shows when the transaction took place. Particulars: this column gives a short description of the entry for the transaction recorded. Folio: this column records page of reference in books of accounts.it indicates in what ledger and on what page the transaction has been posted. Invoice number: this column records the details of the invoice number which identify the invoice received when a particular transaction was made. Invoice details: this column records the details of the invoice involved in the transaction. Invoice total: this column records the total amount of money being transacted. SALES DAY BOOK Date Particulars Folio Invoice Details Invoice Total Example 1. Co-operative shop made the following purchases during the month of August, 2021. August 1. Credit sales to Mwangomo 100 bags of Rice @ 550/= 50 bags of sugar @ 750/= August 5. Sold to Dons and Sons Ltd. 10 boxes of cooking fat @ 320/= 12 pairs of sandals @ 150/= August 10. Credit sales to Shilabela Traders. 20 pairs of bed sheets @ 170 50 shirts @ 350/= August 15. Sold to Michael and Sons Ltd 2 cartons of Malaika soap @ 500/= Required: Draw up the Sales journal for the months. SALES DAY BOOK/SALES JOURNAL Example 2. On 1stDecember 2022 Mr. Kasoma started the business and the Transaction during the year was as follows: Dec 1stSold the following goods to Kimatah Gilagiza companies 5 Crown colour each Tshs 7,000 11 Cement each Tshs 22,000 4 Cartons of Nyati cola each Tshs 11,000 10th Dec 2022. Said Mrisho Kanyegeli supplier of Mwamgongo village received the following item sold to him. 6 Boxes of cigarette @ 5000 9 Carton of shoes shs 4500 per carton 10 Boxes of Tanga milk shs 9000 @ 16th Dec 2022, Sold the following items to Mwimbe General Supplier 15 Boxes of shoes @ Shs 12,000 60 Crates of Coca-Cola @ 23,00 10 Breads @ 850 and 6 cakes @ 2,500. Required: Enter the above transactions in the Sales Journal Answer Mr. KASOMA SALES JOURNAL PURCHASES DAY BOOK/ PURCHASES JOURNALS This is a book of original entry where credit purchases are recorded before being posted to the ledger. It contains amount of goods are bought on credit. Purchases invoice: is the document that used in preparation of purchases day book. Note: Cash Purchases are not entered in the purchases journal. Format of the purchases journal: The sales day book has six columns which are: Date: this column is used to write the date, month, and the year of the transaction. Generally, it shows when the transaction took place. Particulars: this column gives a short description of the entry for the transaction recorded. Folio: this column records page of reference in books of accounts.it indicates in what ledger and on what page the transaction has been posted. Invoice number: this column records the details of the invoice number which identify the invoice received when a particular transaction was made. Invoice details: this column records the details of the invoice involved in the transaction. Invoice total: this column records the total amount of money being transacted. PURCHASES DAY BOOK, Application of the Double Entry System, The accounting equation Accounting equation is the equation that shows resources owned by a business against those due to others (liabilities). Accounting equation is the equation that show the relationship between assets, capital and liabilities. Assets: are resources that an enterprise controls and uses to conduct its business. Capital or owner equity: is the amount of resources contributed by the owner. Liabilities: are resources in the business supplied by non-owners of the business. They are obligations that a business has to settle by means of transferring resources to other persons or business. At a point when the business has just started, the total value of assets equals the value of capital: When a business has resources supplied by the owner of the business and others who do not own the business, the accounting equation changes as follows: The equation can also be changed or written in words as follows: Example 1. Complete gaps in the following table. S/n Assets TZS Liabilities TZS Capital TZS a) 5000,000 720,000 ? b) 1,120,000 196,000 ? c) 6,720,000 ? 5,000,000 d) 7840,000 ? 6,580,000 e) ? 4,660,000 1,580,000 f) 2,520,000 7,680,00 ? Solution: From the accounting equation which state that Question 1; Complete the following table STATEMENT OF AFFAIRS: is the statement which shows the list of all assets and liabilities (together with their financial value) at a particular date to enable one calculate value of capital. STATEMENT OF AFFAIRS: Is the statement shows the figures of assets and liabilities to determine the amount of capital. This approach is specifically helpful in a situation where one knows the assets and liabilities of the business and wants to calculate the figure if capital. The effects of revenue and expenses on the equity element of accounting can lead to an extended accounting equation which appears as follows Arithmetically, this equation can be re-arranged. Foe ease of understanding the double entry principle, the re-arrangement of the extended accounting equation is as follows: FORMAT OF A STATEMENT OF AFFAIRS: Statement of Affairs as at (date, Month, Year) Example 1. Kyela Business Enterprise has invested in farming activities. They do not keep complete books of accounts. However, the following information is available as at 31st December 2020. Prepare statement of affairs to calculate amount of capital. Example 2. Mr. Salim has the following transaction took place during the year 2023 December 31st. you are required to calculate capital and prepare the initial statement of the affairs. CONCEPT OF DOUBLE ENTRY: The accounting equation is the foundation of the concept of double entry. Double entry deals with the recording and posting of business transactions in the books of accounts. Business transactions are posted to ledger accounts following principle of double entry. Meaning of double entry system: This is the principle which calls for recording each business transactions twice in the books of accounts. The principle of double entry states that, every business transaction should be recorded twice, that is, every debit entry must have its corresponding credit entry of the same amount. Therefore, one side of the account receives while the other side gives depending on the nature of transaction. Double entry is the most commonly used system of book keeping based on the principle that every financial transaction involves the simultaneous receiving and giving of value, and is therefore recorded twice. IMPORTANCE OF DOUBLE ENTRY:, Basic Principles of Book-Keeping, Introduction to Book-Keeping

Topic 7: Basic Financial Statements – Book Keeping Notes Form One New Syllabus

Topic 7: Basic Financial Statements – Book Keeping Notes Form One New Syllabus Introduction ...

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Partnerships, Topic 9: Manufacturing Account - Book Keeping Form Three, Book-Keeping Form One Notes New Syllabus, Topic 7: Basic Financial Statements - Book Keeping Notes Form One New Syllabus, Trial Balance, Meaning of Books of Prime Entry: Books of prime entry: Are the books in which transactions are recorded before being posted to their respective ledgers. Books of prime entry: Are the books of account that are used to record any transaction for the first time. When a particular transaction has occurred for the first time in a business should be entered into the primary books known as books of prime entry/books of original entry/ subsidiary books/daily books/ journals before being posted to their respective ledger accounts. The word Journal is adopted from a French word which means “daily recording” THE TYPES OF BOOKS OF PRIME ENTRY: There six (06) types of books prime entry which are; Purchases day book (purchases journal) Sales day book (sales journal) Purchases returns day book (Returns outwards journal) Sales returns day book (Returns inwards journal) Cash book Journal proper (General journal) USE OF BOOKS OF PRIME ENTRY: The following are brief descriptions and purpose of each of the book of prime entry: Purchases day book (purchases journal) this journal is used to record details of goods bought by the business with the promise that payment will be made in the future. Purchase returns daybook (purchase returns journal): the purchase returns daybook is used to record transactions related to purchase returns, or returns of goods to suppliers who supplied goods on credit (creditors). Sales day book (sales journal): is the journal used to record details of goods sold on credit with the promise that payment will be received in the future. Sales returns daybook (sales returns journal): this book is used to record details of transactions related to sales returns, or returns of goods from customers to whom goods were sold on credit (debtors). Cash book: is the book used to record transactions related to receipt and payment of cash as well money placed into the bank (bank deposits) and those taken from the bank (bank withdrawals). Cash book is divided into different categories which are Single columns cash book. Two columns’ cash book. Three columns’ cash book. Petty cash book General journal (journal proper) this book of prime entry is used to record transactions related to other items, which according to their nature are not recorded in any other books of prime entry. SOURCE DOCUMENTS/ACCOUNTING INFORMATION: These are documents from which transactions to be recorded in the books of prime entry are extracted. They are documents used in the books of prime entry. These documents are used in the books of prime entry. Source documents can be summarized as follows INVOICE This is a document issued when goods are sold or bought on credit. Sales invoice is issued when goods are sold on credit whereas purchases invoice is issued when credit purchases are made. Invoices are used in preparation of sales day book and purchases day book. DEBIT NOTE is the document prepared and sent by the seller to the buyer to adjust undercharges on the invoice. This document is used by the buyer in preparation of Purchases returns day book/ Returns outwards journal CREDIT NOTE is the document sent by the seller to the buyer to correct an overcharge on an invoice. This document is used in preparation of sales returns day book/ returns inwards journal. CHEQUE: This is a written order by a customer to his/her bank to pay a specified sum of money to the named person at a specific period of time. Is the document used by the drawer to withdraw cash from his or her account. This document is used in preparation of a cash book. PAY-IN-SLIP: This is a bank deposit form filled in by depositor and stamped by a teller as evidence of accepting the deposit. WITHDRAW SLIP: This is a document filled by a person withdrawing money from the bank upon being accepted by the bank teller. CASH RECEIPT/ CASH RECEIPT VOUCHER: is the document that acts as proof that cash has been received. Money could be received from customer for cash sale of goods or goods, or cash received when a credit customer settles his or her debt with the business. PAYMENT VOUCHER: is the document that presents evidence that money has been paid. Money might be paid to the supplier for cash purchase of goods or service or settlement of account payable for goods previously bought on credit. PETTY CASH VOUCHER: is the document used by a petty cashier as evidence for making small payment from petty cash fund. This document is used in preparation of Petty Cash Book. STATEMENT OF ACCOUNT: is the document sent by the seller to the buyer at the end of every period (usually each month) acting as a reminder to the buyer to pay the outstanding balance. JOURNAL VOUCHER: is the document that provide evidence of authorization for all transaction other than those which are evidenced by the previously mentioned source documents. This document is used in the preparation of General journal or Journal proper. PREPARATION OF BOOKS OF PRIME ENTRY: As per the accounting cycle or process introduced in chapter one, once transactions are identified they are entered in the books of prime entry, followed by posting the entries to relevant ledgers account. In section, you are going to learn the six special journal and how information from source documents is entered followed by the general journal. CASH BOOK: This is a book where receipts or payments are recorded. This book is both a ledger and a book of prime entry. Receipts and payments entered in on debit side and credit side respectively. Receipt/cheque: are documents which are used to obtain information to prepare Cash book. Moreover, an account has four columns in both Dr and Cr sides of account namely: The format of a Cash account is illustrated below; DR CASH BOOK CR Date Particulars Folio Amount Date Particulars Folio Amount Date column: Is the column used to record the date at which the given transaction took place. Particulars/narration/details: Is the column used to record a short description of the transactions that took place. Folio column: is the column used to record the reference page in books of account. Amount column: is the column used to record the amount of money that used in purchasing or selling the goods. Example 1: Kafuku commenced business on 1st January 2022 with Capital in cash TZS 200,000. Her transactions during the month were as follows: January 2. Purchased goods for cash 40,000 3. Sold goods for cash 10,000 3. Paid rent for cash 60,000 4. Cash purchases 16,000 6. Paid postage charger 1,000 13. Commission received for cash 50,000 17. Paid salaries for cash 9,600 19. Paid adverting expenses for cash 7,000 24. Bought furniture for cash 10,000 28. Paid wages for cash 16,000 Required: Draw up a cash book, balance it and bring down the balance to the following months DR. CASH BOOK CR. Date Particulars Folio Amount Date Particulars Folio Amount 2022 2022 Jan. 1 Capital 2 200,000 Jan. 2 Purchases 3 40,000 3 Sales 4 10,000 3 Rent 5 60,000 13 Commission 7 50,000 4 Purchases 3 16,000 Received 6 Postage 6 1,000 Charges 17 Salaries 8 9,600 19 Advertising 9 7,000 Expenses 24 Furniture 10 10,000 28 Wages 11 16,000 31 Balance c/d 100,400 260,000 260,000 Feb. 1 Balance b/d 100,400 Example 2: Moshi & his Son Islam started business with a capital of Tsh 60000, on 1st September 2022. During the month the following transaction took place: – Sept 2, Purchased of goods for cash Tsh 3000 Sept 4, Paid carriage charge Cash Tsh 2000 Sept 6, Paid Transport charge Cash Tsh 4000 Sept 8, Bought Motor Vehicle for cash Tsh55000 Sept 10, Cash Sales Tsh 44000 Sept 12, Paid Rent for Cash Tsh1500 Sept 15, Paid commission charge Tsh 1000 Required: Records the above transaction into Cash book account and bring down the balance as on 30th September 2022. DR CASH ACCOUNT CR SALES DAY BOOK Sales day book is in which sales made on credit are recorded. It is a book of original entry that contains the list of credit sales made in a business. It is also known as sales journal Sales invoice: is a document prepared and issued by a seller to the buyer containing information about goods sold on credit. This information includes name, quantity and prices of the products sold. Format of the sales day book: The sales day book has six columns which are: Date: this column is used to write the date, month, and the year of the transaction. Generally, it shows when the transaction took place. Particulars: this column gives a short description of the entry for the transaction recorded. Folio: this column records page of reference in books of accounts.it indicates in what ledger and on what page the transaction has been posted. Invoice number: this column records the details of the invoice number which identify the invoice received when a particular transaction was made. Invoice details: this column records the details of the invoice involved in the transaction. Invoice total: this column records the total amount of money being transacted. SALES DAY BOOK Date Particulars Folio Invoice Details Invoice Total Example 1. Co-operative shop made the following purchases during the month of August, 2021. August 1. Credit sales to Mwangomo 100 bags of Rice @ 550/= 50 bags of sugar @ 750/= August 5. Sold to Dons and Sons Ltd. 10 boxes of cooking fat @ 320/= 12 pairs of sandals @ 150/= August 10. Credit sales to Shilabela Traders. 20 pairs of bed sheets @ 170 50 shirts @ 350/= August 15. Sold to Michael and Sons Ltd 2 cartons of Malaika soap @ 500/= Required: Draw up the Sales journal for the months. SALES DAY BOOK/SALES JOURNAL Example 2. On 1stDecember 2022 Mr. Kasoma started the business and the Transaction during the year was as follows: Dec 1stSold the following goods to Kimatah Gilagiza companies 5 Crown colour each Tshs 7,000 11 Cement each Tshs 22,000 4 Cartons of Nyati cola each Tshs 11,000 10th Dec 2022. Said Mrisho Kanyegeli supplier of Mwamgongo village received the following item sold to him. 6 Boxes of cigarette @ 5000 9 Carton of shoes shs 4500 per carton 10 Boxes of Tanga milk shs 9000 @ 16th Dec 2022, Sold the following items to Mwimbe General Supplier 15 Boxes of shoes @ Shs 12,000 60 Crates of Coca-Cola @ 23,00 10 Breads @ 850 and 6 cakes @ 2,500. Required: Enter the above transactions in the Sales Journal Answer Mr. KASOMA SALES JOURNAL PURCHASES DAY BOOK/ PURCHASES JOURNALS This is a book of original entry where credit purchases are recorded before being posted to the ledger. It contains amount of goods are bought on credit. Purchases invoice: is the document that used in preparation of purchases day book. Note: Cash Purchases are not entered in the purchases journal. Format of the purchases journal: The sales day book has six columns which are: Date: this column is used to write the date, month, and the year of the transaction. Generally, it shows when the transaction took place. Particulars: this column gives a short description of the entry for the transaction recorded. Folio: this column records page of reference in books of accounts.it indicates in what ledger and on what page the transaction has been posted. Invoice number: this column records the details of the invoice number which identify the invoice received when a particular transaction was made. Invoice details: this column records the details of the invoice involved in the transaction. Invoice total: this column records the total amount of money being transacted. PURCHASES DAY BOOK, Application of the Double Entry System, The accounting equation Accounting equation is the equation that shows resources owned by a business against those due to others (liabilities). Accounting equation is the equation that show the relationship between assets, capital and liabilities. Assets: are resources that an enterprise controls and uses to conduct its business. Capital or owner equity: is the amount of resources contributed by the owner. Liabilities: are resources in the business supplied by non-owners of the business. They are obligations that a business has to settle by means of transferring resources to other persons or business. At a point when the business has just started, the total value of assets equals the value of capital: When a business has resources supplied by the owner of the business and others who do not own the business, the accounting equation changes as follows: The equation can also be changed or written in words as follows: Example 1. Complete gaps in the following table. S/n Assets TZS Liabilities TZS Capital TZS a) 5000,000 720,000 ? b) 1,120,000 196,000 ? c) 6,720,000 ? 5,000,000 d) 7840,000 ? 6,580,000 e) ? 4,660,000 1,580,000 f) 2,520,000 7,680,00 ? Solution: From the accounting equation which state that Question 1; Complete the following table STATEMENT OF AFFAIRS: is the statement which shows the list of all assets and liabilities (together with their financial value) at a particular date to enable one calculate value of capital. STATEMENT OF AFFAIRS: Is the statement shows the figures of assets and liabilities to determine the amount of capital. This approach is specifically helpful in a situation where one knows the assets and liabilities of the business and wants to calculate the figure if capital. The effects of revenue and expenses on the equity element of accounting can lead to an extended accounting equation which appears as follows Arithmetically, this equation can be re-arranged. Foe ease of understanding the double entry principle, the re-arrangement of the extended accounting equation is as follows: FORMAT OF A STATEMENT OF AFFAIRS: Statement of Affairs as at (date, Month, Year) Example 1. Kyela Business Enterprise has invested in farming activities. They do not keep complete books of accounts. However, the following information is available as at 31st December 2020. Prepare statement of affairs to calculate amount of capital. Example 2. Mr. Salim has the following transaction took place during the year 2023 December 31st. you are required to calculate capital and prepare the initial statement of the affairs. CONCEPT OF DOUBLE ENTRY: The accounting equation is the foundation of the concept of double entry. Double entry deals with the recording and posting of business transactions in the books of accounts. Business transactions are posted to ledger accounts following principle of double entry. Meaning of double entry system: This is the principle which calls for recording each business transactions twice in the books of accounts. The principle of double entry states that, every business transaction should be recorded twice, that is, every debit entry must have its corresponding credit entry of the same amount. Therefore, one side of the account receives while the other side gives depending on the nature of transaction. Double entry is the most commonly used system of book keeping based on the principle that every financial transaction involves the simultaneous receiving and giving of value, and is therefore recorded twice. IMPORTANCE OF DOUBLE ENTRY:, Basic Principles of Book-Keeping, Introduction to Book-Keeping

Topic 6:  Trial Balance – Book Keeping Notes Form One New Syllabus

Topic 6:  Trial Balance – Book Keeping Notes Form One New Syllabus INTRODUCTION the ...

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Accounts Of Non-Profit Making Organizations, Topic 7: Financial Statements - Book Keeping Form Three, Topic 5: Ledgers - Book Keeping Notes Form One New Syllabus

Topic 5: Ledgers – Book Keeping Notes Form One New Syllabus

Topic 5: Ledgers – Book Keeping Notes Form One New Syllabus Introduction ledgers play ...

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Partnerships, Topic 9: Manufacturing Account - Book Keeping Form Three, Book-Keeping Form One Notes New Syllabus, Topic 7: Basic Financial Statements - Book Keeping Notes Form One New Syllabus, Trial Balance, Meaning of Books of Prime Entry: Books of prime entry: Are the books in which transactions are recorded before being posted to their respective ledgers. Books of prime entry: Are the books of account that are used to record any transaction for the first time. When a particular transaction has occurred for the first time in a business should be entered into the primary books known as books of prime entry/books of original entry/ subsidiary books/daily books/ journals before being posted to their respective ledger accounts. The word Journal is adopted from a French word which means “daily recording” THE TYPES OF BOOKS OF PRIME ENTRY: There six (06) types of books prime entry which are; Purchases day book (purchases journal) Sales day book (sales journal) Purchases returns day book (Returns outwards journal) Sales returns day book (Returns inwards journal) Cash book Journal proper (General journal) USE OF BOOKS OF PRIME ENTRY: The following are brief descriptions and purpose of each of the book of prime entry: Purchases day book (purchases journal) this journal is used to record details of goods bought by the business with the promise that payment will be made in the future. Purchase returns daybook (purchase returns journal): the purchase returns daybook is used to record transactions related to purchase returns, or returns of goods to suppliers who supplied goods on credit (creditors). Sales day book (sales journal): is the journal used to record details of goods sold on credit with the promise that payment will be received in the future. Sales returns daybook (sales returns journal): this book is used to record details of transactions related to sales returns, or returns of goods from customers to whom goods were sold on credit (debtors). Cash book: is the book used to record transactions related to receipt and payment of cash as well money placed into the bank (bank deposits) and those taken from the bank (bank withdrawals). Cash book is divided into different categories which are Single columns cash book. Two columns’ cash book. Three columns’ cash book. Petty cash book General journal (journal proper) this book of prime entry is used to record transactions related to other items, which according to their nature are not recorded in any other books of prime entry. SOURCE DOCUMENTS/ACCOUNTING INFORMATION: These are documents from which transactions to be recorded in the books of prime entry are extracted. They are documents used in the books of prime entry. These documents are used in the books of prime entry. Source documents can be summarized as follows INVOICE This is a document issued when goods are sold or bought on credit. Sales invoice is issued when goods are sold on credit whereas purchases invoice is issued when credit purchases are made. Invoices are used in preparation of sales day book and purchases day book. DEBIT NOTE is the document prepared and sent by the seller to the buyer to adjust undercharges on the invoice. This document is used by the buyer in preparation of Purchases returns day book/ Returns outwards journal CREDIT NOTE is the document sent by the seller to the buyer to correct an overcharge on an invoice. This document is used in preparation of sales returns day book/ returns inwards journal. CHEQUE: This is a written order by a customer to his/her bank to pay a specified sum of money to the named person at a specific period of time. Is the document used by the drawer to withdraw cash from his or her account. This document is used in preparation of a cash book. PAY-IN-SLIP: This is a bank deposit form filled in by depositor and stamped by a teller as evidence of accepting the deposit. WITHDRAW SLIP: This is a document filled by a person withdrawing money from the bank upon being accepted by the bank teller. CASH RECEIPT/ CASH RECEIPT VOUCHER: is the document that acts as proof that cash has been received. Money could be received from customer for cash sale of goods or goods, or cash received when a credit customer settles his or her debt with the business. PAYMENT VOUCHER: is the document that presents evidence that money has been paid. Money might be paid to the supplier for cash purchase of goods or service or settlement of account payable for goods previously bought on credit. PETTY CASH VOUCHER: is the document used by a petty cashier as evidence for making small payment from petty cash fund. This document is used in preparation of Petty Cash Book. STATEMENT OF ACCOUNT: is the document sent by the seller to the buyer at the end of every period (usually each month) acting as a reminder to the buyer to pay the outstanding balance. JOURNAL VOUCHER: is the document that provide evidence of authorization for all transaction other than those which are evidenced by the previously mentioned source documents. This document is used in the preparation of General journal or Journal proper. PREPARATION OF BOOKS OF PRIME ENTRY: As per the accounting cycle or process introduced in chapter one, once transactions are identified they are entered in the books of prime entry, followed by posting the entries to relevant ledgers account. In section, you are going to learn the six special journal and how information from source documents is entered followed by the general journal. CASH BOOK: This is a book where receipts or payments are recorded. This book is both a ledger and a book of prime entry. Receipts and payments entered in on debit side and credit side respectively. Receipt/cheque: are documents which are used to obtain information to prepare Cash book. Moreover, an account has four columns in both Dr and Cr sides of account namely: The format of a Cash account is illustrated below; DR CASH BOOK CR Date Particulars Folio Amount Date Particulars Folio Amount Date column: Is the column used to record the date at which the given transaction took place. Particulars/narration/details: Is the column used to record a short description of the transactions that took place. Folio column: is the column used to record the reference page in books of account. Amount column: is the column used to record the amount of money that used in purchasing or selling the goods. Example 1: Kafuku commenced business on 1st January 2022 with Capital in cash TZS 200,000. Her transactions during the month were as follows: January 2. Purchased goods for cash 40,000 3. Sold goods for cash 10,000 3. Paid rent for cash 60,000 4. Cash purchases 16,000 6. Paid postage charger 1,000 13. Commission received for cash 50,000 17. Paid salaries for cash 9,600 19. Paid adverting expenses for cash 7,000 24. Bought furniture for cash 10,000 28. Paid wages for cash 16,000 Required: Draw up a cash book, balance it and bring down the balance to the following months DR. CASH BOOK CR. Date Particulars Folio Amount Date Particulars Folio Amount 2022 2022 Jan. 1 Capital 2 200,000 Jan. 2 Purchases 3 40,000 3 Sales 4 10,000 3 Rent 5 60,000 13 Commission 7 50,000 4 Purchases 3 16,000 Received 6 Postage 6 1,000 Charges 17 Salaries 8 9,600 19 Advertising 9 7,000 Expenses 24 Furniture 10 10,000 28 Wages 11 16,000 31 Balance c/d 100,400 260,000 260,000 Feb. 1 Balance b/d 100,400 Example 2: Moshi & his Son Islam started business with a capital of Tsh 60000, on 1st September 2022. During the month the following transaction took place: – Sept 2, Purchased of goods for cash Tsh 3000 Sept 4, Paid carriage charge Cash Tsh 2000 Sept 6, Paid Transport charge Cash Tsh 4000 Sept 8, Bought Motor Vehicle for cash Tsh55000 Sept 10, Cash Sales Tsh 44000 Sept 12, Paid Rent for Cash Tsh1500 Sept 15, Paid commission charge Tsh 1000 Required: Records the above transaction into Cash book account and bring down the balance as on 30th September 2022. DR CASH ACCOUNT CR SALES DAY BOOK Sales day book is in which sales made on credit are recorded. It is a book of original entry that contains the list of credit sales made in a business. It is also known as sales journal Sales invoice: is a document prepared and issued by a seller to the buyer containing information about goods sold on credit. This information includes name, quantity and prices of the products sold. Format of the sales day book: The sales day book has six columns which are: Date: this column is used to write the date, month, and the year of the transaction. Generally, it shows when the transaction took place. Particulars: this column gives a short description of the entry for the transaction recorded. Folio: this column records page of reference in books of accounts.it indicates in what ledger and on what page the transaction has been posted. Invoice number: this column records the details of the invoice number which identify the invoice received when a particular transaction was made. Invoice details: this column records the details of the invoice involved in the transaction. Invoice total: this column records the total amount of money being transacted. SALES DAY BOOK Date Particulars Folio Invoice Details Invoice Total Example 1. Co-operative shop made the following purchases during the month of August, 2021. August 1. Credit sales to Mwangomo 100 bags of Rice @ 550/= 50 bags of sugar @ 750/= August 5. Sold to Dons and Sons Ltd. 10 boxes of cooking fat @ 320/= 12 pairs of sandals @ 150/= August 10. Credit sales to Shilabela Traders. 20 pairs of bed sheets @ 170 50 shirts @ 350/= August 15. Sold to Michael and Sons Ltd 2 cartons of Malaika soap @ 500/= Required: Draw up the Sales journal for the months. SALES DAY BOOK/SALES JOURNAL Example 2. On 1stDecember 2022 Mr. Kasoma started the business and the Transaction during the year was as follows: Dec 1stSold the following goods to Kimatah Gilagiza companies 5 Crown colour each Tshs 7,000 11 Cement each Tshs 22,000 4 Cartons of Nyati cola each Tshs 11,000 10th Dec 2022. Said Mrisho Kanyegeli supplier of Mwamgongo village received the following item sold to him. 6 Boxes of cigarette @ 5000 9 Carton of shoes shs 4500 per carton 10 Boxes of Tanga milk shs 9000 @ 16th Dec 2022, Sold the following items to Mwimbe General Supplier 15 Boxes of shoes @ Shs 12,000 60 Crates of Coca-Cola @ 23,00 10 Breads @ 850 and 6 cakes @ 2,500. Required: Enter the above transactions in the Sales Journal Answer Mr. KASOMA SALES JOURNAL PURCHASES DAY BOOK/ PURCHASES JOURNALS This is a book of original entry where credit purchases are recorded before being posted to the ledger. It contains amount of goods are bought on credit. Purchases invoice: is the document that used in preparation of purchases day book. Note: Cash Purchases are not entered in the purchases journal. Format of the purchases journal: The sales day book has six columns which are: Date: this column is used to write the date, month, and the year of the transaction. Generally, it shows when the transaction took place. Particulars: this column gives a short description of the entry for the transaction recorded. Folio: this column records page of reference in books of accounts.it indicates in what ledger and on what page the transaction has been posted. Invoice number: this column records the details of the invoice number which identify the invoice received when a particular transaction was made. Invoice details: this column records the details of the invoice involved in the transaction. Invoice total: this column records the total amount of money being transacted. PURCHASES DAY BOOK, Application of the Double Entry System, The accounting equation Accounting equation is the equation that shows resources owned by a business against those due to others (liabilities). Accounting equation is the equation that show the relationship between assets, capital and liabilities. Assets: are resources that an enterprise controls and uses to conduct its business. Capital or owner equity: is the amount of resources contributed by the owner. Liabilities: are resources in the business supplied by non-owners of the business. They are obligations that a business has to settle by means of transferring resources to other persons or business. At a point when the business has just started, the total value of assets equals the value of capital: When a business has resources supplied by the owner of the business and others who do not own the business, the accounting equation changes as follows: The equation can also be changed or written in words as follows: Example 1. Complete gaps in the following table. S/n Assets TZS Liabilities TZS Capital TZS a) 5000,000 720,000 ? b) 1,120,000 196,000 ? c) 6,720,000 ? 5,000,000 d) 7840,000 ? 6,580,000 e) ? 4,660,000 1,580,000 f) 2,520,000 7,680,00 ? Solution: From the accounting equation which state that Question 1; Complete the following table STATEMENT OF AFFAIRS: is the statement which shows the list of all assets and liabilities (together with their financial value) at a particular date to enable one calculate value of capital. STATEMENT OF AFFAIRS: Is the statement shows the figures of assets and liabilities to determine the amount of capital. This approach is specifically helpful in a situation where one knows the assets and liabilities of the business and wants to calculate the figure if capital. The effects of revenue and expenses on the equity element of accounting can lead to an extended accounting equation which appears as follows Arithmetically, this equation can be re-arranged. Foe ease of understanding the double entry principle, the re-arrangement of the extended accounting equation is as follows: FORMAT OF A STATEMENT OF AFFAIRS: Statement of Affairs as at (date, Month, Year) Example 1. Kyela Business Enterprise has invested in farming activities. They do not keep complete books of accounts. However, the following information is available as at 31st December 2020. Prepare statement of affairs to calculate amount of capital. Example 2. Mr. Salim has the following transaction took place during the year 2023 December 31st. you are required to calculate capital and prepare the initial statement of the affairs. CONCEPT OF DOUBLE ENTRY: The accounting equation is the foundation of the concept of double entry. Double entry deals with the recording and posting of business transactions in the books of accounts. Business transactions are posted to ledger accounts following principle of double entry. Meaning of double entry system: This is the principle which calls for recording each business transactions twice in the books of accounts. The principle of double entry states that, every business transaction should be recorded twice, that is, every debit entry must have its corresponding credit entry of the same amount. Therefore, one side of the account receives while the other side gives depending on the nature of transaction. Double entry is the most commonly used system of book keeping based on the principle that every financial transaction involves the simultaneous receiving and giving of value, and is therefore recorded twice. IMPORTANCE OF DOUBLE ENTRY:, Basic Principles of Book-Keeping, Introduction to Book-Keeping

Topic 3: Recording of Business Transactions – Book Keeping Notes Form One New Syllabus

Topic 3: Recording of Business Transactions – Book Keeping Notes Form One New Syllabus ...

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Partnerships, Topic 9: Manufacturing Account - Book Keeping Form Three, Book-Keeping Form One Notes New Syllabus, Topic 7: Basic Financial Statements - Book Keeping Notes Form One New Syllabus, Trial Balance, Meaning of Books of Prime Entry: Books of prime entry: Are the books in which transactions are recorded before being posted to their respective ledgers. Books of prime entry: Are the books of account that are used to record any transaction for the first time. When a particular transaction has occurred for the first time in a business should be entered into the primary books known as books of prime entry/books of original entry/ subsidiary books/daily books/ journals before being posted to their respective ledger accounts. The word Journal is adopted from a French word which means “daily recording” THE TYPES OF BOOKS OF PRIME ENTRY: There six (06) types of books prime entry which are; Purchases day book (purchases journal) Sales day book (sales journal) Purchases returns day book (Returns outwards journal) Sales returns day book (Returns inwards journal) Cash book Journal proper (General journal) USE OF BOOKS OF PRIME ENTRY: The following are brief descriptions and purpose of each of the book of prime entry: Purchases day book (purchases journal) this journal is used to record details of goods bought by the business with the promise that payment will be made in the future. Purchase returns daybook (purchase returns journal): the purchase returns daybook is used to record transactions related to purchase returns, or returns of goods to suppliers who supplied goods on credit (creditors). Sales day book (sales journal): is the journal used to record details of goods sold on credit with the promise that payment will be received in the future. Sales returns daybook (sales returns journal): this book is used to record details of transactions related to sales returns, or returns of goods from customers to whom goods were sold on credit (debtors). Cash book: is the book used to record transactions related to receipt and payment of cash as well money placed into the bank (bank deposits) and those taken from the bank (bank withdrawals). Cash book is divided into different categories which are Single columns cash book. Two columns’ cash book. Three columns’ cash book. Petty cash book General journal (journal proper) this book of prime entry is used to record transactions related to other items, which according to their nature are not recorded in any other books of prime entry. SOURCE DOCUMENTS/ACCOUNTING INFORMATION: These are documents from which transactions to be recorded in the books of prime entry are extracted. They are documents used in the books of prime entry. These documents are used in the books of prime entry. Source documents can be summarized as follows INVOICE This is a document issued when goods are sold or bought on credit. Sales invoice is issued when goods are sold on credit whereas purchases invoice is issued when credit purchases are made. Invoices are used in preparation of sales day book and purchases day book. DEBIT NOTE is the document prepared and sent by the seller to the buyer to adjust undercharges on the invoice. This document is used by the buyer in preparation of Purchases returns day book/ Returns outwards journal CREDIT NOTE is the document sent by the seller to the buyer to correct an overcharge on an invoice. This document is used in preparation of sales returns day book/ returns inwards journal. CHEQUE: This is a written order by a customer to his/her bank to pay a specified sum of money to the named person at a specific period of time. Is the document used by the drawer to withdraw cash from his or her account. This document is used in preparation of a cash book. PAY-IN-SLIP: This is a bank deposit form filled in by depositor and stamped by a teller as evidence of accepting the deposit. WITHDRAW SLIP: This is a document filled by a person withdrawing money from the bank upon being accepted by the bank teller. CASH RECEIPT/ CASH RECEIPT VOUCHER: is the document that acts as proof that cash has been received. Money could be received from customer for cash sale of goods or goods, or cash received when a credit customer settles his or her debt with the business. PAYMENT VOUCHER: is the document that presents evidence that money has been paid. Money might be paid to the supplier for cash purchase of goods or service or settlement of account payable for goods previously bought on credit. PETTY CASH VOUCHER: is the document used by a petty cashier as evidence for making small payment from petty cash fund. This document is used in preparation of Petty Cash Book. STATEMENT OF ACCOUNT: is the document sent by the seller to the buyer at the end of every period (usually each month) acting as a reminder to the buyer to pay the outstanding balance. JOURNAL VOUCHER: is the document that provide evidence of authorization for all transaction other than those which are evidenced by the previously mentioned source documents. This document is used in the preparation of General journal or Journal proper. PREPARATION OF BOOKS OF PRIME ENTRY: As per the accounting cycle or process introduced in chapter one, once transactions are identified they are entered in the books of prime entry, followed by posting the entries to relevant ledgers account. In section, you are going to learn the six special journal and how information from source documents is entered followed by the general journal. CASH BOOK: This is a book where receipts or payments are recorded. This book is both a ledger and a book of prime entry. Receipts and payments entered in on debit side and credit side respectively. Receipt/cheque: are documents which are used to obtain information to prepare Cash book. Moreover, an account has four columns in both Dr and Cr sides of account namely: The format of a Cash account is illustrated below; DR CASH BOOK CR Date Particulars Folio Amount Date Particulars Folio Amount Date column: Is the column used to record the date at which the given transaction took place. Particulars/narration/details: Is the column used to record a short description of the transactions that took place. Folio column: is the column used to record the reference page in books of account. Amount column: is the column used to record the amount of money that used in purchasing or selling the goods. Example 1: Kafuku commenced business on 1st January 2022 with Capital in cash TZS 200,000. Her transactions during the month were as follows: January 2. Purchased goods for cash 40,000 3. Sold goods for cash 10,000 3. Paid rent for cash 60,000 4. Cash purchases 16,000 6. Paid postage charger 1,000 13. Commission received for cash 50,000 17. Paid salaries for cash 9,600 19. Paid adverting expenses for cash 7,000 24. Bought furniture for cash 10,000 28. Paid wages for cash 16,000 Required: Draw up a cash book, balance it and bring down the balance to the following months DR. CASH BOOK CR. Date Particulars Folio Amount Date Particulars Folio Amount 2022 2022 Jan. 1 Capital 2 200,000 Jan. 2 Purchases 3 40,000 3 Sales 4 10,000 3 Rent 5 60,000 13 Commission 7 50,000 4 Purchases 3 16,000 Received 6 Postage 6 1,000 Charges 17 Salaries 8 9,600 19 Advertising 9 7,000 Expenses 24 Furniture 10 10,000 28 Wages 11 16,000 31 Balance c/d 100,400 260,000 260,000 Feb. 1 Balance b/d 100,400 Example 2: Moshi & his Son Islam started business with a capital of Tsh 60000, on 1st September 2022. During the month the following transaction took place: – Sept 2, Purchased of goods for cash Tsh 3000 Sept 4, Paid carriage charge Cash Tsh 2000 Sept 6, Paid Transport charge Cash Tsh 4000 Sept 8, Bought Motor Vehicle for cash Tsh55000 Sept 10, Cash Sales Tsh 44000 Sept 12, Paid Rent for Cash Tsh1500 Sept 15, Paid commission charge Tsh 1000 Required: Records the above transaction into Cash book account and bring down the balance as on 30th September 2022. DR CASH ACCOUNT CR SALES DAY BOOK Sales day book is in which sales made on credit are recorded. It is a book of original entry that contains the list of credit sales made in a business. It is also known as sales journal Sales invoice: is a document prepared and issued by a seller to the buyer containing information about goods sold on credit. This information includes name, quantity and prices of the products sold. Format of the sales day book: The sales day book has six columns which are: Date: this column is used to write the date, month, and the year of the transaction. Generally, it shows when the transaction took place. Particulars: this column gives a short description of the entry for the transaction recorded. Folio: this column records page of reference in books of accounts.it indicates in what ledger and on what page the transaction has been posted. Invoice number: this column records the details of the invoice number which identify the invoice received when a particular transaction was made. Invoice details: this column records the details of the invoice involved in the transaction. Invoice total: this column records the total amount of money being transacted. SALES DAY BOOK Date Particulars Folio Invoice Details Invoice Total Example 1. Co-operative shop made the following purchases during the month of August, 2021. August 1. Credit sales to Mwangomo 100 bags of Rice @ 550/= 50 bags of sugar @ 750/= August 5. Sold to Dons and Sons Ltd. 10 boxes of cooking fat @ 320/= 12 pairs of sandals @ 150/= August 10. Credit sales to Shilabela Traders. 20 pairs of bed sheets @ 170 50 shirts @ 350/= August 15. Sold to Michael and Sons Ltd 2 cartons of Malaika soap @ 500/= Required: Draw up the Sales journal for the months. SALES DAY BOOK/SALES JOURNAL Example 2. On 1stDecember 2022 Mr. Kasoma started the business and the Transaction during the year was as follows: Dec 1stSold the following goods to Kimatah Gilagiza companies 5 Crown colour each Tshs 7,000 11 Cement each Tshs 22,000 4 Cartons of Nyati cola each Tshs 11,000 10th Dec 2022. Said Mrisho Kanyegeli supplier of Mwamgongo village received the following item sold to him. 6 Boxes of cigarette @ 5000 9 Carton of shoes shs 4500 per carton 10 Boxes of Tanga milk shs 9000 @ 16th Dec 2022, Sold the following items to Mwimbe General Supplier 15 Boxes of shoes @ Shs 12,000 60 Crates of Coca-Cola @ 23,00 10 Breads @ 850 and 6 cakes @ 2,500. Required: Enter the above transactions in the Sales Journal Answer Mr. KASOMA SALES JOURNAL PURCHASES DAY BOOK/ PURCHASES JOURNALS This is a book of original entry where credit purchases are recorded before being posted to the ledger. It contains amount of goods are bought on credit. Purchases invoice: is the document that used in preparation of purchases day book. Note: Cash Purchases are not entered in the purchases journal. Format of the purchases journal: The sales day book has six columns which are: Date: this column is used to write the date, month, and the year of the transaction. Generally, it shows when the transaction took place. Particulars: this column gives a short description of the entry for the transaction recorded. Folio: this column records page of reference in books of accounts.it indicates in what ledger and on what page the transaction has been posted. Invoice number: this column records the details of the invoice number which identify the invoice received when a particular transaction was made. Invoice details: this column records the details of the invoice involved in the transaction. Invoice total: this column records the total amount of money being transacted. PURCHASES DAY BOOK, Application of the Double Entry System, The accounting equation Accounting equation is the equation that shows resources owned by a business against those due to others (liabilities). Accounting equation is the equation that show the relationship between assets, capital and liabilities. Assets: are resources that an enterprise controls and uses to conduct its business. Capital or owner equity: is the amount of resources contributed by the owner. Liabilities: are resources in the business supplied by non-owners of the business. They are obligations that a business has to settle by means of transferring resources to other persons or business. At a point when the business has just started, the total value of assets equals the value of capital: When a business has resources supplied by the owner of the business and others who do not own the business, the accounting equation changes as follows: The equation can also be changed or written in words as follows: Example 1. Complete gaps in the following table. S/n Assets TZS Liabilities TZS Capital TZS a) 5000,000 720,000 ? b) 1,120,000 196,000 ? c) 6,720,000 ? 5,000,000 d) 7840,000 ? 6,580,000 e) ? 4,660,000 1,580,000 f) 2,520,000 7,680,00 ? Solution: From the accounting equation which state that Question 1; Complete the following table STATEMENT OF AFFAIRS: is the statement which shows the list of all assets and liabilities (together with their financial value) at a particular date to enable one calculate value of capital. STATEMENT OF AFFAIRS: Is the statement shows the figures of assets and liabilities to determine the amount of capital. This approach is specifically helpful in a situation where one knows the assets and liabilities of the business and wants to calculate the figure if capital. The effects of revenue and expenses on the equity element of accounting can lead to an extended accounting equation which appears as follows Arithmetically, this equation can be re-arranged. Foe ease of understanding the double entry principle, the re-arrangement of the extended accounting equation is as follows: FORMAT OF A STATEMENT OF AFFAIRS: Statement of Affairs as at (date, Month, Year) Example 1. Kyela Business Enterprise has invested in farming activities. They do not keep complete books of accounts. However, the following information is available as at 31st December 2020. Prepare statement of affairs to calculate amount of capital. Example 2. Mr. Salim has the following transaction took place during the year 2023 December 31st. you are required to calculate capital and prepare the initial statement of the affairs. CONCEPT OF DOUBLE ENTRY: The accounting equation is the foundation of the concept of double entry. Double entry deals with the recording and posting of business transactions in the books of accounts. Business transactions are posted to ledger accounts following principle of double entry. Meaning of double entry system: This is the principle which calls for recording each business transactions twice in the books of accounts. The principle of double entry states that, every business transaction should be recorded twice, that is, every debit entry must have its corresponding credit entry of the same amount. Therefore, one side of the account receives while the other side gives depending on the nature of transaction. Double entry is the most commonly used system of book keeping based on the principle that every financial transaction involves the simultaneous receiving and giving of value, and is therefore recorded twice. IMPORTANCE OF DOUBLE ENTRY:, Basic Principles of Book-Keeping, Introduction to Book-Keeping

Topic 3: Application of the Double Entry System – Book Keeping Notes Form One New Syllabus

Topic 3: Application of the Double Entry System – Book Keeping Notes Form One ...

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Partnerships, Topic 9: Manufacturing Account - Book Keeping Form Three, Book-Keeping Form One Notes New Syllabus, Topic 7: Basic Financial Statements - Book Keeping Notes Form One New Syllabus, Trial Balance, Meaning of Books of Prime Entry: Books of prime entry: Are the books in which transactions are recorded before being posted to their respective ledgers. Books of prime entry: Are the books of account that are used to record any transaction for the first time. When a particular transaction has occurred for the first time in a business should be entered into the primary books known as books of prime entry/books of original entry/ subsidiary books/daily books/ journals before being posted to their respective ledger accounts. The word Journal is adopted from a French word which means “daily recording” THE TYPES OF BOOKS OF PRIME ENTRY: There six (06) types of books prime entry which are; Purchases day book (purchases journal) Sales day book (sales journal) Purchases returns day book (Returns outwards journal) Sales returns day book (Returns inwards journal) Cash book Journal proper (General journal) USE OF BOOKS OF PRIME ENTRY: The following are brief descriptions and purpose of each of the book of prime entry: Purchases day book (purchases journal) this journal is used to record details of goods bought by the business with the promise that payment will be made in the future. Purchase returns daybook (purchase returns journal): the purchase returns daybook is used to record transactions related to purchase returns, or returns of goods to suppliers who supplied goods on credit (creditors). Sales day book (sales journal): is the journal used to record details of goods sold on credit with the promise that payment will be received in the future. Sales returns daybook (sales returns journal): this book is used to record details of transactions related to sales returns, or returns of goods from customers to whom goods were sold on credit (debtors). Cash book: is the book used to record transactions related to receipt and payment of cash as well money placed into the bank (bank deposits) and those taken from the bank (bank withdrawals). Cash book is divided into different categories which are Single columns cash book. Two columns’ cash book. Three columns’ cash book. Petty cash book General journal (journal proper) this book of prime entry is used to record transactions related to other items, which according to their nature are not recorded in any other books of prime entry. SOURCE DOCUMENTS/ACCOUNTING INFORMATION: These are documents from which transactions to be recorded in the books of prime entry are extracted. They are documents used in the books of prime entry. These documents are used in the books of prime entry. Source documents can be summarized as follows INVOICE This is a document issued when goods are sold or bought on credit. Sales invoice is issued when goods are sold on credit whereas purchases invoice is issued when credit purchases are made. Invoices are used in preparation of sales day book and purchases day book. DEBIT NOTE is the document prepared and sent by the seller to the buyer to adjust undercharges on the invoice. This document is used by the buyer in preparation of Purchases returns day book/ Returns outwards journal CREDIT NOTE is the document sent by the seller to the buyer to correct an overcharge on an invoice. This document is used in preparation of sales returns day book/ returns inwards journal. CHEQUE: This is a written order by a customer to his/her bank to pay a specified sum of money to the named person at a specific period of time. Is the document used by the drawer to withdraw cash from his or her account. This document is used in preparation of a cash book. PAY-IN-SLIP: This is a bank deposit form filled in by depositor and stamped by a teller as evidence of accepting the deposit. WITHDRAW SLIP: This is a document filled by a person withdrawing money from the bank upon being accepted by the bank teller. CASH RECEIPT/ CASH RECEIPT VOUCHER: is the document that acts as proof that cash has been received. Money could be received from customer for cash sale of goods or goods, or cash received when a credit customer settles his or her debt with the business. PAYMENT VOUCHER: is the document that presents evidence that money has been paid. Money might be paid to the supplier for cash purchase of goods or service or settlement of account payable for goods previously bought on credit. PETTY CASH VOUCHER: is the document used by a petty cashier as evidence for making small payment from petty cash fund. This document is used in preparation of Petty Cash Book. STATEMENT OF ACCOUNT: is the document sent by the seller to the buyer at the end of every period (usually each month) acting as a reminder to the buyer to pay the outstanding balance. JOURNAL VOUCHER: is the document that provide evidence of authorization for all transaction other than those which are evidenced by the previously mentioned source documents. This document is used in the preparation of General journal or Journal proper. PREPARATION OF BOOKS OF PRIME ENTRY: As per the accounting cycle or process introduced in chapter one, once transactions are identified they are entered in the books of prime entry, followed by posting the entries to relevant ledgers account. In section, you are going to learn the six special journal and how information from source documents is entered followed by the general journal. CASH BOOK: This is a book where receipts or payments are recorded. This book is both a ledger and a book of prime entry. Receipts and payments entered in on debit side and credit side respectively. Receipt/cheque: are documents which are used to obtain information to prepare Cash book. Moreover, an account has four columns in both Dr and Cr sides of account namely: The format of a Cash account is illustrated below; DR CASH BOOK CR Date Particulars Folio Amount Date Particulars Folio Amount Date column: Is the column used to record the date at which the given transaction took place. Particulars/narration/details: Is the column used to record a short description of the transactions that took place. Folio column: is the column used to record the reference page in books of account. Amount column: is the column used to record the amount of money that used in purchasing or selling the goods. Example 1: Kafuku commenced business on 1st January 2022 with Capital in cash TZS 200,000. Her transactions during the month were as follows: January 2. Purchased goods for cash 40,000 3. Sold goods for cash 10,000 3. Paid rent for cash 60,000 4. Cash purchases 16,000 6. Paid postage charger 1,000 13. Commission received for cash 50,000 17. Paid salaries for cash 9,600 19. Paid adverting expenses for cash 7,000 24. Bought furniture for cash 10,000 28. Paid wages for cash 16,000 Required: Draw up a cash book, balance it and bring down the balance to the following months DR. CASH BOOK CR. Date Particulars Folio Amount Date Particulars Folio Amount 2022 2022 Jan. 1 Capital 2 200,000 Jan. 2 Purchases 3 40,000 3 Sales 4 10,000 3 Rent 5 60,000 13 Commission 7 50,000 4 Purchases 3 16,000 Received 6 Postage 6 1,000 Charges 17 Salaries 8 9,600 19 Advertising 9 7,000 Expenses 24 Furniture 10 10,000 28 Wages 11 16,000 31 Balance c/d 100,400 260,000 260,000 Feb. 1 Balance b/d 100,400 Example 2: Moshi & his Son Islam started business with a capital of Tsh 60000, on 1st September 2022. During the month the following transaction took place: – Sept 2, Purchased of goods for cash Tsh 3000 Sept 4, Paid carriage charge Cash Tsh 2000 Sept 6, Paid Transport charge Cash Tsh 4000 Sept 8, Bought Motor Vehicle for cash Tsh55000 Sept 10, Cash Sales Tsh 44000 Sept 12, Paid Rent for Cash Tsh1500 Sept 15, Paid commission charge Tsh 1000 Required: Records the above transaction into Cash book account and bring down the balance as on 30th September 2022. DR CASH ACCOUNT CR SALES DAY BOOK Sales day book is in which sales made on credit are recorded. It is a book of original entry that contains the list of credit sales made in a business. It is also known as sales journal Sales invoice: is a document prepared and issued by a seller to the buyer containing information about goods sold on credit. This information includes name, quantity and prices of the products sold. Format of the sales day book: The sales day book has six columns which are: Date: this column is used to write the date, month, and the year of the transaction. Generally, it shows when the transaction took place. Particulars: this column gives a short description of the entry for the transaction recorded. Folio: this column records page of reference in books of accounts.it indicates in what ledger and on what page the transaction has been posted. Invoice number: this column records the details of the invoice number which identify the invoice received when a particular transaction was made. Invoice details: this column records the details of the invoice involved in the transaction. Invoice total: this column records the total amount of money being transacted. SALES DAY BOOK Date Particulars Folio Invoice Details Invoice Total Example 1. Co-operative shop made the following purchases during the month of August, 2021. August 1. Credit sales to Mwangomo 100 bags of Rice @ 550/= 50 bags of sugar @ 750/= August 5. Sold to Dons and Sons Ltd. 10 boxes of cooking fat @ 320/= 12 pairs of sandals @ 150/= August 10. Credit sales to Shilabela Traders. 20 pairs of bed sheets @ 170 50 shirts @ 350/= August 15. Sold to Michael and Sons Ltd 2 cartons of Malaika soap @ 500/= Required: Draw up the Sales journal for the months. SALES DAY BOOK/SALES JOURNAL Example 2. On 1stDecember 2022 Mr. Kasoma started the business and the Transaction during the year was as follows: Dec 1stSold the following goods to Kimatah Gilagiza companies 5 Crown colour each Tshs 7,000 11 Cement each Tshs 22,000 4 Cartons of Nyati cola each Tshs 11,000 10th Dec 2022. Said Mrisho Kanyegeli supplier of Mwamgongo village received the following item sold to him. 6 Boxes of cigarette @ 5000 9 Carton of shoes shs 4500 per carton 10 Boxes of Tanga milk shs 9000 @ 16th Dec 2022, Sold the following items to Mwimbe General Supplier 15 Boxes of shoes @ Shs 12,000 60 Crates of Coca-Cola @ 23,00 10 Breads @ 850 and 6 cakes @ 2,500. Required: Enter the above transactions in the Sales Journal Answer Mr. KASOMA SALES JOURNAL PURCHASES DAY BOOK/ PURCHASES JOURNALS This is a book of original entry where credit purchases are recorded before being posted to the ledger. It contains amount of goods are bought on credit. Purchases invoice: is the document that used in preparation of purchases day book. Note: Cash Purchases are not entered in the purchases journal. Format of the purchases journal: The sales day book has six columns which are: Date: this column is used to write the date, month, and the year of the transaction. Generally, it shows when the transaction took place. Particulars: this column gives a short description of the entry for the transaction recorded. Folio: this column records page of reference in books of accounts.it indicates in what ledger and on what page the transaction has been posted. Invoice number: this column records the details of the invoice number which identify the invoice received when a particular transaction was made. Invoice details: this column records the details of the invoice involved in the transaction. Invoice total: this column records the total amount of money being transacted. PURCHASES DAY BOOK, Application of the Double Entry System, The accounting equation Accounting equation is the equation that shows resources owned by a business against those due to others (liabilities). Accounting equation is the equation that show the relationship between assets, capital and liabilities. Assets: are resources that an enterprise controls and uses to conduct its business. Capital or owner equity: is the amount of resources contributed by the owner. Liabilities: are resources in the business supplied by non-owners of the business. They are obligations that a business has to settle by means of transferring resources to other persons or business. At a point when the business has just started, the total value of assets equals the value of capital: When a business has resources supplied by the owner of the business and others who do not own the business, the accounting equation changes as follows: The equation can also be changed or written in words as follows: Example 1. Complete gaps in the following table. S/n Assets TZS Liabilities TZS Capital TZS a) 5000,000 720,000 ? b) 1,120,000 196,000 ? c) 6,720,000 ? 5,000,000 d) 7840,000 ? 6,580,000 e) ? 4,660,000 1,580,000 f) 2,520,000 7,680,00 ? Solution: From the accounting equation which state that Question 1; Complete the following table STATEMENT OF AFFAIRS: is the statement which shows the list of all assets and liabilities (together with their financial value) at a particular date to enable one calculate value of capital. STATEMENT OF AFFAIRS: Is the statement shows the figures of assets and liabilities to determine the amount of capital. This approach is specifically helpful in a situation where one knows the assets and liabilities of the business and wants to calculate the figure if capital. The effects of revenue and expenses on the equity element of accounting can lead to an extended accounting equation which appears as follows Arithmetically, this equation can be re-arranged. Foe ease of understanding the double entry principle, the re-arrangement of the extended accounting equation is as follows: FORMAT OF A STATEMENT OF AFFAIRS: Statement of Affairs as at (date, Month, Year) Example 1. Kyela Business Enterprise has invested in farming activities. They do not keep complete books of accounts. However, the following information is available as at 31st December 2020. Prepare statement of affairs to calculate amount of capital. Example 2. Mr. Salim has the following transaction took place during the year 2023 December 31st. you are required to calculate capital and prepare the initial statement of the affairs. CONCEPT OF DOUBLE ENTRY: The accounting equation is the foundation of the concept of double entry. Double entry deals with the recording and posting of business transactions in the books of accounts. Business transactions are posted to ledger accounts following principle of double entry. Meaning of double entry system: This is the principle which calls for recording each business transactions twice in the books of accounts. The principle of double entry states that, every business transaction should be recorded twice, that is, every debit entry must have its corresponding credit entry of the same amount. Therefore, one side of the account receives while the other side gives depending on the nature of transaction. Double entry is the most commonly used system of book keeping based on the principle that every financial transaction involves the simultaneous receiving and giving of value, and is therefore recorded twice. IMPORTANCE OF DOUBLE ENTRY:, Basic Principles of Book-Keeping, Introduction to Book-Keeping

Topic 2: Basic Principles of Book-Keeping – Book Keeping Notes Form One New Syllabus

Topic 2: Basic Principles of Book-Keeping – Book Keeping Notes Form One New Syllabus ...

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Partnerships, Topic 9: Manufacturing Account - Book Keeping Form Three, Book-Keeping Form One Notes New Syllabus, Topic 7: Basic Financial Statements - Book Keeping Notes Form One New Syllabus, Trial Balance, Meaning of Books of Prime Entry: Books of prime entry: Are the books in which transactions are recorded before being posted to their respective ledgers. Books of prime entry: Are the books of account that are used to record any transaction for the first time. When a particular transaction has occurred for the first time in a business should be entered into the primary books known as books of prime entry/books of original entry/ subsidiary books/daily books/ journals before being posted to their respective ledger accounts. The word Journal is adopted from a French word which means “daily recording” THE TYPES OF BOOKS OF PRIME ENTRY: There six (06) types of books prime entry which are; Purchases day book (purchases journal) Sales day book (sales journal) Purchases returns day book (Returns outwards journal) Sales returns day book (Returns inwards journal) Cash book Journal proper (General journal) USE OF BOOKS OF PRIME ENTRY: The following are brief descriptions and purpose of each of the book of prime entry: Purchases day book (purchases journal) this journal is used to record details of goods bought by the business with the promise that payment will be made in the future. Purchase returns daybook (purchase returns journal): the purchase returns daybook is used to record transactions related to purchase returns, or returns of goods to suppliers who supplied goods on credit (creditors). Sales day book (sales journal): is the journal used to record details of goods sold on credit with the promise that payment will be received in the future. Sales returns daybook (sales returns journal): this book is used to record details of transactions related to sales returns, or returns of goods from customers to whom goods were sold on credit (debtors). Cash book: is the book used to record transactions related to receipt and payment of cash as well money placed into the bank (bank deposits) and those taken from the bank (bank withdrawals). Cash book is divided into different categories which are Single columns cash book. Two columns’ cash book. Three columns’ cash book. Petty cash book General journal (journal proper) this book of prime entry is used to record transactions related to other items, which according to their nature are not recorded in any other books of prime entry. SOURCE DOCUMENTS/ACCOUNTING INFORMATION: These are documents from which transactions to be recorded in the books of prime entry are extracted. They are documents used in the books of prime entry. These documents are used in the books of prime entry. Source documents can be summarized as follows INVOICE This is a document issued when goods are sold or bought on credit. Sales invoice is issued when goods are sold on credit whereas purchases invoice is issued when credit purchases are made. Invoices are used in preparation of sales day book and purchases day book. DEBIT NOTE is the document prepared and sent by the seller to the buyer to adjust undercharges on the invoice. This document is used by the buyer in preparation of Purchases returns day book/ Returns outwards journal CREDIT NOTE is the document sent by the seller to the buyer to correct an overcharge on an invoice. This document is used in preparation of sales returns day book/ returns inwards journal. CHEQUE: This is a written order by a customer to his/her bank to pay a specified sum of money to the named person at a specific period of time. Is the document used by the drawer to withdraw cash from his or her account. This document is used in preparation of a cash book. PAY-IN-SLIP: This is a bank deposit form filled in by depositor and stamped by a teller as evidence of accepting the deposit. WITHDRAW SLIP: This is a document filled by a person withdrawing money from the bank upon being accepted by the bank teller. CASH RECEIPT/ CASH RECEIPT VOUCHER: is the document that acts as proof that cash has been received. Money could be received from customer for cash sale of goods or goods, or cash received when a credit customer settles his or her debt with the business. PAYMENT VOUCHER: is the document that presents evidence that money has been paid. Money might be paid to the supplier for cash purchase of goods or service or settlement of account payable for goods previously bought on credit. PETTY CASH VOUCHER: is the document used by a petty cashier as evidence for making small payment from petty cash fund. This document is used in preparation of Petty Cash Book. STATEMENT OF ACCOUNT: is the document sent by the seller to the buyer at the end of every period (usually each month) acting as a reminder to the buyer to pay the outstanding balance. JOURNAL VOUCHER: is the document that provide evidence of authorization for all transaction other than those which are evidenced by the previously mentioned source documents. This document is used in the preparation of General journal or Journal proper. PREPARATION OF BOOKS OF PRIME ENTRY: As per the accounting cycle or process introduced in chapter one, once transactions are identified they are entered in the books of prime entry, followed by posting the entries to relevant ledgers account. In section, you are going to learn the six special journal and how information from source documents is entered followed by the general journal. CASH BOOK: This is a book where receipts or payments are recorded. This book is both a ledger and a book of prime entry. Receipts and payments entered in on debit side and credit side respectively. Receipt/cheque: are documents which are used to obtain information to prepare Cash book. Moreover, an account has four columns in both Dr and Cr sides of account namely: The format of a Cash account is illustrated below; DR CASH BOOK CR Date Particulars Folio Amount Date Particulars Folio Amount Date column: Is the column used to record the date at which the given transaction took place. Particulars/narration/details: Is the column used to record a short description of the transactions that took place. Folio column: is the column used to record the reference page in books of account. Amount column: is the column used to record the amount of money that used in purchasing or selling the goods. Example 1: Kafuku commenced business on 1st January 2022 with Capital in cash TZS 200,000. Her transactions during the month were as follows: January 2. Purchased goods for cash 40,000 3. Sold goods for cash 10,000 3. Paid rent for cash 60,000 4. Cash purchases 16,000 6. Paid postage charger 1,000 13. Commission received for cash 50,000 17. Paid salaries for cash 9,600 19. Paid adverting expenses for cash 7,000 24. Bought furniture for cash 10,000 28. Paid wages for cash 16,000 Required: Draw up a cash book, balance it and bring down the balance to the following months DR. CASH BOOK CR. Date Particulars Folio Amount Date Particulars Folio Amount 2022 2022 Jan. 1 Capital 2 200,000 Jan. 2 Purchases 3 40,000 3 Sales 4 10,000 3 Rent 5 60,000 13 Commission 7 50,000 4 Purchases 3 16,000 Received 6 Postage 6 1,000 Charges 17 Salaries 8 9,600 19 Advertising 9 7,000 Expenses 24 Furniture 10 10,000 28 Wages 11 16,000 31 Balance c/d 100,400 260,000 260,000 Feb. 1 Balance b/d 100,400 Example 2: Moshi & his Son Islam started business with a capital of Tsh 60000, on 1st September 2022. During the month the following transaction took place: – Sept 2, Purchased of goods for cash Tsh 3000 Sept 4, Paid carriage charge Cash Tsh 2000 Sept 6, Paid Transport charge Cash Tsh 4000 Sept 8, Bought Motor Vehicle for cash Tsh55000 Sept 10, Cash Sales Tsh 44000 Sept 12, Paid Rent for Cash Tsh1500 Sept 15, Paid commission charge Tsh 1000 Required: Records the above transaction into Cash book account and bring down the balance as on 30th September 2022. DR CASH ACCOUNT CR SALES DAY BOOK Sales day book is in which sales made on credit are recorded. It is a book of original entry that contains the list of credit sales made in a business. It is also known as sales journal Sales invoice: is a document prepared and issued by a seller to the buyer containing information about goods sold on credit. This information includes name, quantity and prices of the products sold. Format of the sales day book: The sales day book has six columns which are: Date: this column is used to write the date, month, and the year of the transaction. Generally, it shows when the transaction took place. Particulars: this column gives a short description of the entry for the transaction recorded. Folio: this column records page of reference in books of accounts.it indicates in what ledger and on what page the transaction has been posted. Invoice number: this column records the details of the invoice number which identify the invoice received when a particular transaction was made. Invoice details: this column records the details of the invoice involved in the transaction. Invoice total: this column records the total amount of money being transacted. SALES DAY BOOK Date Particulars Folio Invoice Details Invoice Total Example 1. Co-operative shop made the following purchases during the month of August, 2021. August 1. Credit sales to Mwangomo 100 bags of Rice @ 550/= 50 bags of sugar @ 750/= August 5. Sold to Dons and Sons Ltd. 10 boxes of cooking fat @ 320/= 12 pairs of sandals @ 150/= August 10. Credit sales to Shilabela Traders. 20 pairs of bed sheets @ 170 50 shirts @ 350/= August 15. Sold to Michael and Sons Ltd 2 cartons of Malaika soap @ 500/= Required: Draw up the Sales journal for the months. SALES DAY BOOK/SALES JOURNAL Example 2. On 1stDecember 2022 Mr. Kasoma started the business and the Transaction during the year was as follows: Dec 1stSold the following goods to Kimatah Gilagiza companies 5 Crown colour each Tshs 7,000 11 Cement each Tshs 22,000 4 Cartons of Nyati cola each Tshs 11,000 10th Dec 2022. Said Mrisho Kanyegeli supplier of Mwamgongo village received the following item sold to him. 6 Boxes of cigarette @ 5000 9 Carton of shoes shs 4500 per carton 10 Boxes of Tanga milk shs 9000 @ 16th Dec 2022, Sold the following items to Mwimbe General Supplier 15 Boxes of shoes @ Shs 12,000 60 Crates of Coca-Cola @ 23,00 10 Breads @ 850 and 6 cakes @ 2,500. Required: Enter the above transactions in the Sales Journal Answer Mr. KASOMA SALES JOURNAL PURCHASES DAY BOOK/ PURCHASES JOURNALS This is a book of original entry where credit purchases are recorded before being posted to the ledger. It contains amount of goods are bought on credit. Purchases invoice: is the document that used in preparation of purchases day book. Note: Cash Purchases are not entered in the purchases journal. Format of the purchases journal: The sales day book has six columns which are: Date: this column is used to write the date, month, and the year of the transaction. Generally, it shows when the transaction took place. Particulars: this column gives a short description of the entry for the transaction recorded. Folio: this column records page of reference in books of accounts.it indicates in what ledger and on what page the transaction has been posted. Invoice number: this column records the details of the invoice number which identify the invoice received when a particular transaction was made. Invoice details: this column records the details of the invoice involved in the transaction. Invoice total: this column records the total amount of money being transacted. PURCHASES DAY BOOK, Application of the Double Entry System, The accounting equation Accounting equation is the equation that shows resources owned by a business against those due to others (liabilities). Accounting equation is the equation that show the relationship between assets, capital and liabilities. Assets: are resources that an enterprise controls and uses to conduct its business. Capital or owner equity: is the amount of resources contributed by the owner. Liabilities: are resources in the business supplied by non-owners of the business. They are obligations that a business has to settle by means of transferring resources to other persons or business. At a point when the business has just started, the total value of assets equals the value of capital: When a business has resources supplied by the owner of the business and others who do not own the business, the accounting equation changes as follows: The equation can also be changed or written in words as follows: Example 1. Complete gaps in the following table. S/n Assets TZS Liabilities TZS Capital TZS a) 5000,000 720,000 ? b) 1,120,000 196,000 ? c) 6,720,000 ? 5,000,000 d) 7840,000 ? 6,580,000 e) ? 4,660,000 1,580,000 f) 2,520,000 7,680,00 ? Solution: From the accounting equation which state that Question 1; Complete the following table STATEMENT OF AFFAIRS: is the statement which shows the list of all assets and liabilities (together with their financial value) at a particular date to enable one calculate value of capital. STATEMENT OF AFFAIRS: Is the statement shows the figures of assets and liabilities to determine the amount of capital. This approach is specifically helpful in a situation where one knows the assets and liabilities of the business and wants to calculate the figure if capital. The effects of revenue and expenses on the equity element of accounting can lead to an extended accounting equation which appears as follows Arithmetically, this equation can be re-arranged. Foe ease of understanding the double entry principle, the re-arrangement of the extended accounting equation is as follows: FORMAT OF A STATEMENT OF AFFAIRS: Statement of Affairs as at (date, Month, Year) Example 1. Kyela Business Enterprise has invested in farming activities. They do not keep complete books of accounts. However, the following information is available as at 31st December 2020. Prepare statement of affairs to calculate amount of capital. Example 2. Mr. Salim has the following transaction took place during the year 2023 December 31st. you are required to calculate capital and prepare the initial statement of the affairs. CONCEPT OF DOUBLE ENTRY: The accounting equation is the foundation of the concept of double entry. Double entry deals with the recording and posting of business transactions in the books of accounts. Business transactions are posted to ledger accounts following principle of double entry. Meaning of double entry system: This is the principle which calls for recording each business transactions twice in the books of accounts. The principle of double entry states that, every business transaction should be recorded twice, that is, every debit entry must have its corresponding credit entry of the same amount. Therefore, one side of the account receives while the other side gives depending on the nature of transaction. Double entry is the most commonly used system of book keeping based on the principle that every financial transaction involves the simultaneous receiving and giving of value, and is therefore recorded twice. IMPORTANCE OF DOUBLE ENTRY:, Basic Principles of Book-Keeping, Introduction to Book-Keeping

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