**November 2021. Time allowed: Two hours**

**This paper has three sections. Section One has forty (40) multiple choice questions. Section Two has twenty (20) short response/computational questions. Section Three has one (1) computational question. All questions are compulsory. The marks allocated to each question are shown at the end of the question.**

**SECTION ONE**

**[40 MARKS] [40 MINUTES]**

1. Which is the best definition of probability? (1 mark)

A. Measure of happenings

B. Measure of Numbers

C. Fraction of happening

D. Measure of likelihood.

2. Which of the following is not a ratio? (1 mark)

A. 4.333

B. 2.847847

C. 5/4

D. 2.115713287.

3. Which of the following is an algebraic expression? (1 mark)

A. x = 3y x 1

B. h + 2m – 3a

C. 5/2

D. 4.

4. Which of the following expression best describe calculus? (1 mark)

A. Study of rates.

B. Study of rate of change.

C. Study of variables

D. Study of changes.

5. Select the equivalent of 4,000 km from the following: (1 mark)

A. 400,000,000 cm

B. 0.0004 cm

C. 40,000 cm

D. 4.0 x 109cm.

6. Select a measure of dispersion from the following: (1 mark)

A. Mean.

B. Mode.

C. Range.

D. Pie chart.

7. Which of the following is equivalent to the ratio: (1 mark)

1/10: 3/10: 4/10: 2/10?

A. 2:7:8:4

B. 1:5:4:2

C. 3:9:12:6

D. 2:5:4:2

8. With regard to matrices, which of the following best describes a property of matrices: (1 mark)

A. AXB = BXA

B. A+B = B+A

C. AXBXC = AXCXB

D. hAB = Hba.

9. Select one of the statements below that best describes mutually exclusive events: (1 mark)

A. Happen at the same time

B. Happen at different times

C. Happening of one excludes happening of the other

D. None of the above.

10. In your opinion, which of the following best represents the income equation: (1 mark)

A. Total Cost – Total Revenue = Income

B. Fixed Costs – Total Revenue = Income

C. Total Revenue – Variable Costs = Income

D. Total Revenue – Total Cost = Income.

11. Name the term used to decide the percentage of profit on sales: (1 mark)

A. Mark-up

B. Gross margin

C. Sales margin

D. Net margin.

12. What indicates boundary points of inequalities of the form: (1 mark)

x>a, or x<b on the number line?

A. Has no effect

B. Doubles the values

C. Changes the sign to its opposite

D. Changes the inequality to an equation.

13. Indicate what best represents the effect of dividing an inequality by a negative number: (1 mark)

A. Has no effect

B. Doubles the values

C. Changes the sign to its opposite

D. Changes the inequality to an equation.

14. From the four expressions below, which one represents the gradient of a polynomial: (1 mark)

15. If events A and B are equiprobable, which of the following is correct: (1 mark)

A. P(A) < P

B. P(A) > P(B)

C. P(A) + P(B) = 1

D. P(A) = P(B).

16. Which of the following tools is used to graphically evaluate the median of a distribution? (1 mark)

A. Cumulative frequency curve

B. Frequency polygon

C. Histogram

D. Stem and leaf diagram.

17. Select the number corrected to 4 significant figures from the following: (1 mark)

A. 52,734

B. 52,730

C. 0.85273

D. 0.5200

18. Which of the following represents 209/264 in its simplest form? (1 mark)

A. 109/264

B. 19/24

C. 19/25

D. 21/24.

19. In any football match. Three outcomes are possible: (1 mark)

A win, a draw or a loss. Given that a win is P(W), a draw P(D) and a loss is P(L).

Which of the following describes the sum of the three: (1 mark)

A. Equiprobable events

B. Conditional events

C. Impossible events

D. Collectively exhaustive events.

20. Which of the following best defines a singular matrix: (1 mark)

A. It’s determinant = 1

B. It’s determinant + Infinity

C. It’s determinant = 0

D. It’s determinant < 0

21. Identify the condition that defines a stationary point from the following: (1 mark)

22. Identify the type of discount that relates to purchases made in bulk from the following: (1 mark)

A. Cash discount

B. Trade discount

C. Loss discount

D. None of the above.

23. Identify the formula for compound interest from the following: (1 marks)

24. Given that the average exchange rate in 2019 was I USD = KES 101.3899, what was the equivalent of KES540 in dollars? (1 mark)

A. 5.032

B. 0.5325

C. 5.326

D. 53.25

25. What is the name given to total possibilities that can happen in a coin tossing experiment? (1 mark)

A. Outcome

B. Sample space

C. Event

D. Tree diagram.

26. Your performance in this examination has no relationship with the performance of a student in Zambia sitting the same examination. Name this type of events: (1 mark)

A. Dependent events

B. Independent events

C. Conditional events

D. Similar events.

27. Which of the following measures of dispersion is the square-root of variance? (1 mark)

A. Standard deviation

B. Mean absolute deviation

C. Mean deviation

D. Mean squared deviation.

28. Which of the following relations represent a symmetrical distribution? (1 mark)

A. Mean < Median < Mode

B. Mean > Median > Mode

C. Mean < Median = Mode

D. Mean = Median = Mode.

29. Identify a depreciation method which charges higher depreciation amounts in the initial years and lower amounts in later years progressively. (1 mark)

A. Declining balance method

B. Straight line method

C. Revaluation method

D. None of the above.

30. Select a non-statutory deduction from the following: (1 mark)

A. NSSF

B. Bank loan

C. NHIF

D. Income tax.

31. What is the main distinction between fixed and variable costs? (1 mark)

A. Fixed costs remain fixed with increase in output.

B. Variable costs vary according to period length to which they relate.

C. Fixed costs are also variable costs in the long run.

D. Fixed costs and variable costs are the same.

32. In computing a mark-up, what is the denominator? (1 mark)

A. Total sales

B. Total expenses

C. Total cost

D. Net profit.

33. Given a matrix of the form , which of the following expressions represents the determinant of A?

A. bc – ad

B. ab – cd

C. ac – bd

D. ad – bc (1 mark)

34. The number line contains natural numbers N, Whole numbers W, Rational number Q and Irrational number Qc . Identify a natural number from the following: (1 mark)

A. 2.1

B. 2/5

C. –7/15

D. 4

35. What is the shape formed by the area between equations y = 3x + 5 and y = 3x + 9 from x = 0 to x = 5

A. Trapezium

B. Pararellogram

C. Circle

D. Square. (1 mark)

36. Which of the following terms describes the rate of change? (1 mark)

37. Simplify the term: (x + 3y) (2x – 1) (1 mark)

(1 – 2x) (3x + 9y)

A. 2/3

B. 1/3

C. –1/3

D. –3

38. Which of the following is a method of solving simultaneous equations? (1 mark)

A. Matrix method

B. Factorisation

C. Expansion

D. Addition.

39. Which of the laws of probability applies when possibility of an event reduces? (1 mark)

A. Division law

B. Addition law

C. Subtraction law

D. Multiplication law.

40. What expression best represents the solution to the expression (2x)? (1 mark)

**SECTION TWO**

**[40 MARKS] [1 Hour]**

41. In your view, do you agree that substitution is one of the methods of solving a simultaneous equation? (2 marks)

42. Expand and simplify 2y(3x + 1) – 6yx + 9x. (2 marks)

43. What is the name given to a value that represents a sample (usually calculated from a sample)? (2 marks)

44. Solve the following set of simultaneous equations:

3x + 1⁄2y = 4

2y – 4x = 0 (2 marks)

45. When Salim sells up to KES75,000 worth of sales, he receives 30% commission on sales. When he sells up to KES150,000, he receives 5% commission on sales. What is his sales commission when he sells KES120,000? (2 marks)

46. Five men can off-load a truck in 2 hours. How long will 8 men take to off-load the same truck? (2 marks)

47. Given that 3x + 2(5 – x) < 7, solve for x. (2 marks)

48. Four exercise books and 3 pens cost KES255. What is the cost of 1 exercise book and 2 pens, given that 3 exercise books and 1 pen costs KES160? (2 marks)

49. Convert the fraction 5/9 into a percentage correct to 2 decimal places. (2 marks)

50. Indicate whether this definition is true or false:

Standard deviation is the square-root of mean squared deviations from mean. (2 marks)

51. Given that profit of a firm is = 8 + q – q2 where q, is the quantity sold in thousands, find q for maximum profit. (2 marks)

52. Write 3.4.5 as a fraction. (2 marks)

53. Given

Find A + 2B (2 marks)

54. Ali Mohamed deposited KES200,000 in a bank that compounds interest half yearly. What interest accrued in 3 years? (2 marks)

55. Without graphing, how do you distinguish between a minimum stationary point from a maximum stationary point?

56. Work out the determinant of

(2 marks)

57. The book value of a machine depreciates to 90% of its value at the beginning of the year. What is its book value after 3 years in terms of its original value? (2 marks)

58. Use these five deviations to work out standard deviation 3, –1, –2, 1 –1 (2 marks)

59. What is plotted on the x – axis of a cumulative frequency curve? (2 marks)

60. What is the sum of year’s digits method used for? (2 marks)

**(Total: 20 marks)**

**SECTION THREE**

**[20 MARKS] [20 MINUTES]**

61. Peta Limited produces product P and Q. At the current levels of production of 200 units of P and 250 units of Q, a sale of 2 units of P and 3 units of Q yields a profit of KES 7,500; while a sale of 1 unit of P and 2 units of Q yields a profit of KES4,400.

**Required:**

(a) Profit per unit of products P and Q at the current production levels of 200 units of P and 250 units of Q. (6 marks)

(b) Production level of products P and Q that yields maximum profit. (8 marks)

(c) Maximum profit at the production levels in (b) above for both products P and Q. (4 marks)

(d) Additional units to the current production level to attain the level that maximizes profit for both products P and Q. (2 marks)

**(Total: 20 marks)**