# FUNDAMENTALS OF BUSINESS MATHEMATICS DECEMBER 2021 PAST PAPER

THURSDAY: 16 December 2021.                                                                        Time Allowed: 3 hours.

This paper has three sections. SECTION I has forty (40) multiple choice questions. SECTION II has twenty (20) short response/computational questions. SECTION III has one (1) computational question. All questions  are      compulsory.

Marks allocated to each question are shown at the end of the question.

SECTION 1 – 40 MARKS

1. Which one of this is unaffected by outliers?

(a)            Mean

(b)            Mode

(c)           Standard deviation

(d)           Range                                                                                                                                                                    (1  mark)

1. Since the mode is the most frequently occurring data value in the data distribution, it is:

(a)            Always equal to the mean

(b)            Larger than the mean

(c)           At least two

(d)           Always smaller than the median                                                                                                                            (1 mark)

1. The value of x if 3, 18 and x, 42 are in proportion is:

(a)            6

(b)            54

(c)            7

(d)            3                                                                                                                                                                            (1 mark)

1. Which of the following is true about probability?

(a)            The probability of an impossible event is 0

(b)            Probability can be greater than one

(c)            Probability can be less than zero

(d)            The probability of a sure event is 0                                                                                                                        ( 1 mark)

1. The transpose of a row matrix is a:

(a)            Diagonal matrix

(b)            Zero matrix

(c)            Column matrix

(d)            Identity matrix                                                                                                                                                       ( 1 mark)

1. Which of the following is an inverse of matrix A?

(a)            A’

(b)            A

(c)            Ac

(d)            A                                                                                                                                                                           (1 mark)

1. When we factorise an expression, we write it as a of factors.

(a)            Sum

(b)           Difference

(c)            Product

(d)           Fraction                                                                                                                                                                 ( 1 mark)

8. Which of the following describes the number on top of a fraction?

(a)            Number

(b)            Denominator

(c)            Numerator

(d)            Factor

9. What type of a fraction is 9/7?

(a)            Proper fraction

(b)            Mixed number fraction

(c)            Like fraction

(d)            Improper fraction

10. Which of the following fractions is equivalent to 2/5

(a)            4/8

(b)            5/2

(c)            4/10

(d)             3/15

11. The data below shows marks scored by interviewees in an interview:
54,        80,       65,         75,       96.

Which is the median mark?

(a)            65

(b)            80

(c)            74

(d)            75

12. Mulwa, Mulei and Kingi earned Sh.50,000 in a joint venture business. his share in Sh. was:

(a)             10,000

(b)            15,000

(c)            50,000

(d)            20,000

13. Which one of the following is not a frequency curve?

(a)            Ogive

(b)            Pictogram

(c)            Histogram

(d)            Polygon

14. If two events A and B are mutually exclusive, then

(a)            They must be independent events

(b)            They cannot be compliments

(c)            They cannot happen together

(d)            They can happen together

15. Which one of the following is not a measure of central tendency?

(a)            Variance

(b)            Mode

(c)            Mean

(d)            Median

1. Round off 0.36985 to three decimal places.

(a)            0.369

(b)           0.378

(c)            0.370

(d)           0.37                                                                                                                                                                       (1 mark)

1. Convert a markup of to a margin.

(a)            2/3

(b)            4/5

(c)            2/7

(d)           4/7

( 1 mark)

1. Matrix can be defined as:

(a)            Identity matrix

(b)            Scalar matrix

(c)            Diagonal matrix

(d)           Null matrix                                                                                                                                                            ( 1  mark)

1. Which of the following matrices has an inverse matrix? 1. A vendor bought an item for Sh.80 and later sold it at Sh.100. What was the profit margin as a percentage?

(a)            25%

(b)           20%

(c)            40%

(d)            10%                                                                                                                                                                       ( 1 mark)

1. There are 7 green apples and 5 red apples in a basket. What is the probability of picking a red apple?

(a)             5/7

(b)             5/12

(c)             7/5

(d)             7/12                                                                                                                                                                      (1 mark)

1. In a box, there are 8 red, 7 white and 6 blue balls. If a ball is picked up at random, what is the probability that it is neither red nor blue.

(a)            1/3

(b)            1/2

(c)            2/2

(d)           5/21

1. In a class there are 20 boys and 15 girls. The ratio of boys to girls is:

(a)            3:3

(b)            3:4

(c)           4:5

(d)           None of the above.                                                                                                                                                (1 mark)

1. The probability of two events happening together is referred to as:

(a)            Conditional probability

(b)           Joint probability

(c)           Sure probability

(d)            Equivalent probability                                                                                                                                           (1 mark)

1. You deposit Sh.2,500 today in an account that earns 4% per annum interest compounded quarterly. How much will you have at the end of 10 years’?

(a)            Sh.1,488.90

(b)            Sh.3,700.60

(c)            Sh.3,980.20

(d)            Sh.3,722.20                                                                                                                                                           (1 mark)

1. When 0.36 is written in simplest form, the sum of the numerator and denominator is:

(a)            12

(b)            23

(c)           34

(d)            45                                                                                                                                                                          (1 mark)

1. In a cumulative frequency polygon, frequencies are plotted on:

(a)           Rectangles

(b)            X-axis

(c)            Y-axis

(d)           None of the above                                                                                                                                                 (1 mark)

1. Calculate the simple interest earned in 9 months if a sum of Sh.1,640 is invested in a bank at a rate of interest of 4.5% per annum:

(a)            Sh.36.90

(b)            Sh.55.35

(c)            Sh.73.80

(d)            Sh.16.40                                                                                                                                                                (1 mark)

1. Under the straight line method of providing depreciation, the cost of an item;

(a)            Decreases every year

(b)            Remains constant every year

(c)            Increases every year

(d)           None of the above                                                                                                                                                  (1 mark)

1. The probability of getting two tails when two coins are tossed is:

(a)            1/6

(b)            1/2

(c)            1/3

(d)            1/4                                                                                                                                                                          (1 mark)

1. Depreciation occurs due to:

(a)            Losses

(b)           Wear and tear

(c)            Accident

(d)           None of the above                                                                                                                                                 (1 mark)

1. In a class there are 20 boys and 15 girls. The ratio of boys to girls is:

(a)            3:3

(b)           3:4

(c)            4:5

(d)           None of the above.                                                                                                                                                (1 mark)

1. The probability of two events happening together is referred to as:

(a)            Conditional probability

(b)           Joint probability

(c)            Sure probability

(d)            Equivalent probability                                                                                                                                           ( 1 mark)

1. You deposit Sh.2,500 today in an account that earns 4% per annum interest compounded quarterly. How much will you have at the end of 10 years?

(a)            Sh.1,488.90

(b)            Sh.3,700.60

(c)            Sh.3,980.20

(d)            Sh.3,722.20                                                                                                                                                           (1 mark)

1. When 0.36 is written in simplest form, the sum of the numerator and denominator is:

(a)            12

(b)           23

(c)            34

(d)           45                                                                                                                                                                          (1 mark)

1. In a cumulative frequency polygon, frequencies are plotted on:

(a)            Rectangles

(b)          X-axis

(c)            Y-axis

(d)           None of the above                                                                                                                                                 ( I mark)

1. Calculate the simple interest earned in 9 months if a sum of Sh.1,640 is invested in a bank at a rate of interest of 4.5% per annum:

(a)            Sh.36.90

(b)            Sh.55.35

(c)            Sh.73.80

(d)            Sh.16.40                                                                                                                                                               (1 mark)

1. Under the straight line method of providing depreciation, the cost of an item;

(a)            Decreases every year

(b)           Remains constant every year

(c)            Increases every year

(d)           None of the above                                                                                                                                                 (1 mark)

1. The probability of getting two tails when two coins are tossed is:

(a)            1/6

(b)            1/2

(c)            1/3

(d)            1/4                                                                                                                                                                         ( 1 mark)

1. Depreciation occurs due to:

(a)            Losses

(b)           Wear and tear

(c)            Accident

(d)           None of the above                                                                                                                                                 (I mark)

SECTION II – 40 MARKS

1. Differentiate the following function.

Y = -32.4 + x3 + x2+ x                                                                                                                                                 (2 marks)

1. The data below shows the time taken in minutes by ten athletes to complete a race:

60, 50, 52, 38, 58, 34, 52, 57, 44

State the mode of the distribution.                                                                                                                            (2 marks)

1. Three business partners, Abel, Anitta and Angela share their profit in the ratio of 4:5:1.

If Angela received sh.25,000, what was the total profit earned.                                                                       (2 marks)

1. Evaluate

-1 (2+6) – 12 – 5 + 5

-2 x 4 + -3x-5                                                                                                                                                                 (2 marks)

1. The cost of a car in Japan is 25,000 Japanese Yen.

determine the cost of the car in Kenya shillings (Sh.) if 1 Japanese Yen = Kenya sh.127                       (2 marks)

1. The number of female students in State college is 2,100. If the probability of selecting a female student at random from the college is – , calculate the number of male students in the college.                                               (2 marks)

1. Grace bought a calculator at a cost of sh.600 and later sold it at sh.900

Calculate the profit markup on the sale of the calculator.                                                                                  (2 marks)

1. James bought a car at an initial cost of sh. 5,000,000. The car depreciates at the rate of 12% per annum on a straight line basis.

Required:

Find the net book value of the car after 4 years.                                                                                                   (2 marks)

1. Convert 3/8 to a percentage.                                                                                                                                          (2 marks)

50.Round off 23.386521 to three decimal places. (2 marks)

1. Given 50, 64, 25, 76, calculate the arithmetic mean. (2 marks)

1. Dave deposited sh.80,000 in a fixed deposit account. After four years, the amount in the account was Sh.144,000.

Calculate the simple rate of interest.                                                                                                                         (2 marks)

1. Use indices to find the value of x. (2 marks)

1. Integrate 4×3 – 6×2 + 8x – 5 with respect to x. (2 marks)

1. Solve the following simultaneous equations.

6x + 2y = 102

4x + 3y = 98                                                                                                                                                                     (2 marks)

1. A manufacturer sold an item to a wholesaler at a 20% profit markup. The wholesaler sold the item to a retailer at Sh.3,600 at a 25% markup.

Calculate the cost of manufacturing the item.                                                                                                        (2 marks)

1. Factorise; 12y2-20y + 3 (2 marks)

58. Expand; (x + 4) (x — 2) (2 marks)

1. The marked price of a business mathematics book is sh. 800. The seller offers a cash discount of 5%. Determine the price of the book after the discount.                                                                                                                  (2 marks)

1. Solve the following equation 2Y x 2y+2 = 16            (2 marks)

SECTION III – 20 MARKS

1. The table below shows the profit earned by Small and Medium Size Enterprises (SMSEs) in Kenya.

Profit Sh.`million’                             Number of companies

10 – 20                                                         10

20 – 30                                                         8

30 – 40                                                         5

40 – 50                                                         22

50 – 60                                                         15

60 – 70                                                         12

70 – 80                                                         8

Required:

The arithmetic mean profit.                                                                                                                        (5 marks)

The median profit.                                                                                                                                         (5 marks)

The modal profit.                                                                                                                                           (5 marks)

The standard deviation of the profit.                                                                                                        (5 marks)

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