# BUSINESS MATHEMATICS AND STATISTICS DECEMBER 2023 PAST PAPER

TUESDAY: 5 December 2023. Morning 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. Each question is allocated two (2) marks. Do NOT write anything on this paper.

1. Which of the following method of data presentation can be used to estimate the mode of a distribution?

A. Histogram
B. Bar chart
C. Pie chart
D. Cumulative frequency ogive (2 marks)

2. Which of the following is a discount given for prompt payment?

A. Cash discount
B. Loyalty discount
D. Special offer (2 marks)

3. Profit expressed as a percentage of cost is referred to as ____________________.

A. Margin
B. Net profit
C. Discount
D. Mark-up (2 marks)

4. A book seller bought a statistics book for Sh.420. He intends to make a profit margin of 30%. Calculate the selling price of the book.

A. Sh.600
B. Sh.180
C. Sh.240
D. Sh.320 (2 marks)

5. Which of the following is a relative measure of dispersion?

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

6. The profit function of a certain commodity is given by; -Q² +3Q -2. Calculate the profit maximising quantity.

A. -2
B. 1.5
C. 1
D. -1.5 (2 marks)

7. Which of the following is a method of solving simultaneous equations?

B. Matrix method
C. Derivatives
D. Factorisation (2 marks)

8. The probability that an event will not happen is ____________________.

A. 0
B. 1
C. -1
D. (2 marks)

9. A deposit of 20% of marked price is paid if a television set is bought on hire purchase terms. The balance amount plus a 25% interest charge on the balance are paid in 12 equal monthly installments of Sh.8,680 each. When bought on cash basis, a 5% cash discount is provided. Calculate the amount saved when the television set is bought on cash basis and not on hire purchase terms.

A. Sh.104,160
B. Sh.26,040
C. Sh.98,952
D. Sh.124,992 (2 marks)

10. The 7th term of a given geometric progression is 320 and the 12th term is 480. Determine the product of the 5th term and the 10th term.

A. 2,560
B. 204,800
C. 6,553,600
D. 56,002 (2 marks)

11. When computing index numbers, the number of importance assigned to the variable index is referred to as ________.

A. Standard numbers
B. Weight
C. Index
D. Interest (2 marks)

12. Find the inverse of the following matrix:

13. Which of the following defines the matrix below?

A. Scalar matrix
B. Diagonal matrix
C. Identity matrix
D. Null matrix (2 marks)

14. A quadratic function is determined by any _________ point (s) on the graph.

A. 1
B. 2
C. 0
D. 3 (2 marks)

15. All turning points of a curve have a gradient of:

A. 0
B. 2
C. 1
D. -1 (2 marks)

16. The method of data collection where all members of the population are investigated is referred to as:

A. Sampling
B. Population
C. Census
D. Research (2 marks)

17. If the occurrence or non-occurrence of one event does not affect the occurrence or non-occurrence of the other event, then the two events are said to be:

A. Mutually exclusive events
B. Complementary events
C. Independent events
D. Dependent events (2 marks)

18. If the probability of picking a white ball from a bucket is 0.3, how many balls are in the bucket if there are 15 white balls?

A. 20
B. 50
C. 40
D. 35

21. Depreciation is the loss of value of an asset due to________.

A. Accident
B. Misuse
C. Normal usage
D. None of the above (2 marks)

22. Which of the following statement BEST describes a class size in statistics?

A. The difference between the upper-class limit and lower-class limit
B. The difference between the upper-class boundary and the lower-class boundary
C. The difference between the highest observation and the lowest observation in a data distribution
D. The class frequency (2 marks)

23. The grouping of data values into classes with their corresponding frequencies is referred to as__________.

A. Polygon
B. Frequency distribution
C. Histogram
D. Ogive (2 marks)

24. A sales agent is paid a commission of 5% of the total sales made. In the month of June 2023, he earned a commission of Sh.12,000. Calculate the total sales made by the agent.

A. Sh.120,000
B. Sh.480,000
C. Sh.1,200,000
D. Sh.240,000

26. A consultant earns a gross salary of Sh.150,000. He pays 30% of his salary to income tax, Sh.400 to NSSF, Sh.1,800 to NHIF and contributes 10% towards company pension fund. Calculate the net salary for the consultant.

A. Sh.60,000
B. Sh.62,200
C. Sh.105,000
D. Sh.87,800 (2 marks)

27. Jacob, Celestine and Talie are in partnership business. They share profits in the ratio of 2:5:3. Calculate the amount earned by Talie if the partnership earns Sh.2,300,000 in profits.

A. Sh.1,380,000
B. Sh.1,150,000
C. Sh.460,000
D. Sh.690,000 (2 marks)

28. A sales woman is paid a commission of 2% on sales worth up to Sh.200,000. She gets an additional 1.5% on sales above this. She is also paid a monthly salary of Sh.22,000. In the month of August 2023, she sold 400 handbags at Sh.1,500 each. Calculate the total earnings made by the sales woman that month.

A. Sh.86,000
B. Sh.32,000
C. Sh.10,000
D. Sh.12,000 (2 marks)

29. The demand function of product Zed is given by a straight line of the form P = a + bx where P is the price and x are the units sold. Determine the demand function if the number of units sold when the price is Sh.10 are 60 units and 10 units when the price is Sh.20.

A. P = 22 + 0.2x
B. P = 22 – 0.2x
C. P = 20 – 0.2x
D. P = 20 + 0.2x (2 marks)

30. The data value that has the highest frequency is referred to as _____________.

A. Mean
B. Mode
C. Median
D. Range (2 marks)

The table below shows the number of companies in the manufacturing industry earning a given range of profits:

Use the table above to answer questions 31 to question 35.

31. Calculate the arithmetic mean profit.

A. Sh.173.5
B. Sh.383.25
C. Sh.100
D. Sh.17.35 (2 marks)

32. Calculate the standard deviation of the profit.

A. Sh.9.07
B. Sh.81,49
C. Sh.17.35
D. Sh.384 (2 marks)

33. Calculate the coefficient of variation.

A. 90.7%
B. 52.26%
C. 17.25%
D. 47.74% (2 marks)

34. Calculate the modal value.

A. 25
B. 20
C. 21.2
D. 21.5 (2 marks)

35. Calculate the median profit.

A. Sh.15
B. Sh.21.2
C. Sh.22.22
D. Sh.17.22 (2 marks)

36. An importer imported goods worth 50,000 United States Dollars (USD). The prevailing exchange rate at the time was 1USD=Ksh.145. Calculate the value of the goods in Ksh.

A. Sh.7,250,000
B. Sh.344,830
C. Sh.725,000
D. Sh.7,500,000 (2 marks)

37. A trader bought a pick-up for Sh.1,800,000 which has an estimated useful life of 5 years. Calculate the rate of depreciation per annum.

A. Sh.720,000
B. Sh.360,000
C. Sh.540,000
D. Sh.180,000

39. Two matrices can be added or subtracted if and only if:

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

40. Alice Aloo borrowed a loan of Sh.5,000,000 at a simple interest rate of 8% per annum. Calculate the interest paid after 3 years.

A. Sh.1,200,000
B. Sh.400,000
C. Sh.3,800,000
D. Sh.6,200,000 (2 marks)

Use the table above to answer questions 43 to question 46.

43. Calculate the Laspeyre’s price index.

A. 100
B. 138.46
C. 72.22
D. 38.46 (2 marks)

44. Calculate the Paasche’s price index.

A. 138.71
B. 38.56
C. 72.09
D. 100 (2 marks)

45. Calculate the Marshall’s edge-worth price index.

A. 139
B. 176
C. 138.71
D. 138.81 (2 marks)

46. Calculate the Fisher’s ideal price index.

A. 137.00
B. 138.58
C. 137.58
D. 38.71

49. Which of the following BEST describes the complement of a set?

A. This is the set of all elements under consideration
B. This is a set of elements shared among two or more sets
C. This is a set of elements in the universal set but not members of a given set
D. None of the above (2 marks)

50. What type of a set is A={2,4,6,…n}?

A. Finite set
B. Infinite set
C. Union of a set
D. Universal set (2 marks)

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