# FUNDAMENTALS OF BUSINESS MATHEMATICS  DECEMBER 2022 PAST PAPER

TUESDAY: 6 December 2022.     Afternoon Paper.        Time Allowed: 2 hours.

This paper is made up of fifty (50) Multiple Choice Questions. Answer ALL questions by indicating the letter (A, B, C or D) that represents the correct answer. Do NOT write anything on this paper.

1. Round off 562 to the nearest number of hundreds.

A. 500
B. 550
C. 560
D. 600 (2 marks)

2. Round off 23.89543 to two decimal places.

A. 23.00
B. 23.89
C. 23.90
D. 23.91 (2 marks)

3. What type of fraction is 103/7?

A. Improper fraction
B. Mixed fraction
C. Proper fraction
D. Whole number (2 marks)

4. Convert 55/8 into a percentage?

A. 62.5%
B. 500%
C. 562.5%
D. 600% (2 marks)

5. A construction company hired 40 workers to construct and complete a project in 200 days. However, due to heavy rains there was a delay of 40 days in starting the work. Determine the number of extra workers to be hired in order to complete the work on time after the delay.

A. 8
B. 10
C. 160
D. 200 (2 marks)

6. During drought, 1⁄5 of the animals in a certain village died and 1,200 were left. Determine the number of animals that died?

A. 300
B. 1,500
C. 4,800
D. 6,000   15. Differentiation is used to determine the____________________________ of a function.

A. y intercept
C. Value
D. Range (2 marks) 17. Two matrices can be multiplied if and only if:

A. The number of columns in the first matrix is equal to the number of rows in the second matrix
B. They are of the same order
C. The number of rows in the first matrix is equal to the number of columns in the second matrix
D. Has equal number of rows and columns (2 marks)

18. A square matrix in which all elements in the principal diagonal are the same, but all other elements are zero is referred to as:

A. Square matrix
B. Diagonal matrix
C. Null matrix
D. Scalar matrix (2 marks) 21. Convert a margin of 3/10 to a mark-up.

A. 3/13
B. 3/7
C. 3/5
D. 7/10 (2 marks)

22. Noah sells X watches at a total price of Sh.2,016,000. He makes a profit of 40% on cost price of all the watches. If the cost per watch is Sh.4,000, determine the number of watches that Noah sold.

A. 202
B. 302
C. 360
D. 504 (2 marks)

23. Bella bought a pick-up for Sh.2,000,000. The pick-up depreciated at the rate of 20% per annum on a straight line basis. It has a residual value of Sh.400,000. Calculate the value of the pick-up after 3 years.

A. Sh.800,000
B. Sh.960,000
C. Sh.1,040,000
D. Sh.1,200,000 (2 marks)

Use the information below to answer question 24 to 26.
Mr Mutie bought a machine for Sh.3,600,000. After using it for 150,000 hours, he can sell it for Sh.2,100,000.

24. What is the rate of depreciation of the machine per hour?

A. Sh.10
B. Sh.14
C. Sh.24
D. Sh.38 (2 marks)

25. What is the linear depreciation equation in terms of hours worked by the machine?

A. r = 2,100,000 – 10t
B. r = 3,600,000 – 24t
C. r = 3,600,000 – 10t
D. r = 3,600,000 – 14t (2 marks)

26. What is the book value of the machine after running for 240,000 hours?

A. Sh.240,000
B. Sh.1,200,000
C. Sh.2,400,000
D. Sh.3,360,000 (2 marks)

27. A business imported goods worth 123,500 US Dollars, the prevailing exchange rate was 1 US Dollar = Ksh.110. Calculate the value of the goods in Kenya Shillings.

A. Ksh.12,350
B. Ksh.1,235,000
C. Ksh.1,358,500
D. Ksh.13,585,000 (2 marks)

28. John Kitavi bought a car from a Japanese friend for 5,640,000 Yen. Given that 100 Japanese Yen = 83 Kenya Shillings, determine the amount in Kenya Shillings that John Kitavi paid for the car.

A. Ksh.56,400
B. Ksh.67,952
C. Ksh.4,681,200
D. Ksh.6,795,181 (2 marks)

29. An employee earns a taxable income of Sh.80,000. If the rate of tax is 15% for the first Sh.20,000 and 25% for any amount above Sh.20,000, calculate his net income.

A. Sh.18,000
B. Sh.62,000
C. Sh.65,000
D. Sh.77,000 (2 marks)

30. An employee is paid Sh.250 per hour for a 40 hours week. He then earns overtime at time-and-a-half. During a certain week, his total weekly wage was Sh.13,000. How many hours of overtime did he work?

A. 4 hours
B. 8 hours
C. 12 hours
D. 44 hours (2 marks)

31. Monthly taxable pay Rate of tax per month

1 – 24,000 10%
24,000 – 32,333 25%
Excess over 32,333 30%

From the above table, compute the total tax payable by an employee earning Sh.56,000 in a month.
A. Sh.4,483.25
B. Sh.7,100.1
C. Sh.11,583.35
D. Sh.16,800 (2 marks)

32. A company pays its salesmen Sh.8,000 per month as basic pay plus a commission of X% on the gross sales monthly. In the month of November, one salesman earned Sh.298,460 after making gross sales of Sh.2,420,500.

Determine the rate of commission as a percentage.
A. 0.12%
B. 0.13%
C. 12%
D. 13% (2 marks)

33. Grace borrowed a loan of Sh.1,200,000 at a compound interest rate of 8% per annum. Calculate the interest paid after 5 years.

A. Sh.480,000
B. Sh.563,193.69
C. Sh.1,763,193.69
D. Sh.2,963,193.69 (2 marks)

34. Simple interest is calculated based on__________________________________.

A. Accumulated interest
B. The principal amount
C. The principal amount plus accumulated interest
D. The principal amount minus the accumulated interest (2 marks)

35. Mary Muinde invested Sh.55,000 for 18 months at a simple interest rate of 11.5% per annum. Find the maturity value of the principal.

A. Sh.9,487.5
B. Sh.64,487.5
C. Sh.113,850
D. Sh.168,850 (2 marks)

Use the following data to answer question 36 to 38.

The earnings per share (EPS) for 5 companies are tabulated below:
Company Earnings per share (EPS) (Sh.)
A 2.5
B 4
C 2.5
D 3
E 3.25

36. What is the arithmetic mean earning per share?

A. Sh.2.5
B. Sh.3
C. Sh.3.05
D. Sh.3.25 (2 marks)

37. What is the median earning per share?

A. Sh.2.5
B. Sh.3
C. Sh.3.25
D. Sh.4 (2 marks)

38. Given that the standard deviation for the earning per share is 0.56. Calculate the percentage coefficient of variation.

A. 17.2%
B. 18.36%
C. 18.61%
D. 22.4% (2 marks)

39. Which of the following variables is discrete?

A. Share price
B. Shares sold
C. Weight
D. Volume (2 marks)

40. Which of the following tools can be used to estimate the mode of a distribution?

A. Frequency
B. Lorenz curve
C. Pie chart
D. Z – chart (2 marks)

41. The average squared deviation of the data points from their mean is known as:

A. Coefficient of variation
B. Mean deviation
C. Standard deviation
D. Variance (2 marks)

42. A variable which can assume at most a countable number of values is called?

A. Continuous variable
B. Discrete variable
C. Integer
D. Random variable (2 marks)

43. The probability of an event B occurring given that event A has already occurred is referred to as:

A. Conditional probability
B. Joint probability
C. Marginal probability
D. Simple probability (2 marks)

44. The total of all possible outcomes in an experiment is referred to as_____________________.

A. Event
B. Sample point
C. Sample space
D. Outcome (2 marks)

Use the data below to answer question 45 and 46.
A cross tabulation of students in a singing competition by gender and by singing voice is given below: A student is selected at random, what is the probability that the student selected is:

45. Tenor or male

A. 609/836
B. 95/836
C. 490/836
D. 514/836 (2 marks)

46. An alto given that the student is male.

A. 145/395
B. 145/298
C. 145/836
D. 693/836 (2 marks)

47. The count of data points in a class divided by the total number of data points is called?

A. Class mid-point
B. Cumulative frequency
C. Frequency
D. Relative frequency (2 marks)

48. The probability rule for compliments is stated as:

A. P(Ā) = P(A) – 1
B. P(Ā) = P(Ā) + P(A)
C. P(Ā) = 1 – P(A)
D. P(Ā) = 1 + P(A) (2 marks)

49. Mary and John are operating a partnership business where they share profit or loss in the ratio of 5:7 respectively. If Mary earned Sh.200,000 from the partnership, calculate the total profit earned from the partnership.

A. Sh.117,000
B. Sh.280,000
C. Sh.480,000
D. Sh.672,000 (2 marks)

50. An investor wishes to have an amount of Sh.440,000 on maturity in 30 months’ time. He can invest his money at a simple interest rate of 8.5% per annum. How much money should he invest now in order to achieve his aim?

A. Sh.16,603.77
B. Sh.17,254.90
C. Sh.140,800
D. Sh.362.886.60 (2 marks)

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