# FUNDAMENTALS OF BUSINESS MATHEMATICS APRIL 2022 PAST PAPER

TUESDAY: 5 April 2022. Afternoon paper                                                                      Time Allowed: 3 hours.

This paper is made up of a hundred (100) Multiple Choice Questions. Answer ALL questions indicating the letter (a, b, c or d) that represents the correct answer. Do NOT write anything on this paper.

1. Gloria Anyango spends 45% of her income to pay school fees for her children and 15% on rent The rest of her income which amounts to Sh.45,000 is spent on food.

Determine the amount paid as school fees.

(a)           Sh.16,875.

(b)           Sh.112,500.

(c)           Sh.33,750.

(d)           Sh.50,625.                                                                                                                                                       (1 mark)

1. Express 0.084 as a percentage.

(a)           0.00084%.

(b)           8.4%

(c)           84%

(d)           0.84%                                                                                                                                                            (1 mark)

1. Calculate 66 2/3% of 1,200.

(a)            18

(b)           800

(c)          794.76

(d)          80,000                                                                                                                                                             (1 mark)

1. A job is completed 6 persons in 21 days. Determine the number of days 18  persons will  take to complete the same task.

(a)          7 days.

(b)           5.1 days.

(c)           63 days.

(d)           126 days.                                                                                                                                                        ( 1 mark)

1. If the price of an article is increased 25%, the new price is Sh.1,750.

Determine the original price before the price increase.

(a)            Sh.2187.50

(b)           Sh.1,400

(c)           Sh.1,312.50

(d)           Sh.1,725                                                                                                                                                          (1 mark)

1. Convert 60% to a fraction?

(a)           2/3

(b)           2/5

(c)           3/5

(d)           3/10                                                                                                                                                                  (1 mark)

1. Anne, Ben and Carol are operating a partnership business. They share profits in the ratio of 3:5:2. In the year 2021, the partnership made a profit of Sh.2,560,000.

Calculate Anne’s profit share.

(a)          Sh.1,280,000

(b)          Sh.768,000

(c)          Sh.256,000

(d)          Sh.1,024,000                                                                                                                                            (I mark)

1. Round-off 34.478 to the nearest whole number.

(a)          34

(b)          35

(c)          34.5

(d)          36                                                                                                                                                                   ( 1 mark)

1. John Mativo leaves Sh.210,000 inheritance to his two sons, Alfred and Ben so that Ben gets Y4  of what Alfred gets. Calculate the amount received Alfred?

(a)           Sh. I 20,000

(b)           Sh.157,500

(c)           Sh.52,500

(d)           Sh.90,000                                                                                                                                                        ( 1 mark)

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

(a)           Mean

(b)           Mode

(c)           Absolute deviation

(d)           Median                                                                                                                                                          (I mark)

1. Which of the following is not a method of data collection?

(a)           Interview

(b)           Primary data

(c)           Observation

(d)           Questionnaire                                                                                                                                              (1 mark)

1. Which of the following is a discrete data value?

(a)           Number of cars

(b)           Distance

(c)           Length

(d)           Weight                                                                                                                                                             (I mark)

1. is data that has already been collected.

(a)           Secondary data

(b)           Discrete data

(c)           Primary data

(d)           Published data                                                                                                                                             (1 mark)

1. One of the disadvantages of observation method of data collection is that;

(a)           Firsthand information is collected

(b)          Lacks reliability

(c)           Its time consuming

(d)           It is not accurate                                                                                                                                        ( 1 mark)

1. A sampling method in which all items in the population have an equal chance of being selected is referred to as?

(a)            Probabilistic sampling

(b)           Random sampling

(c)           Census

(d)           Stratified sampling                                                                                                                                    (1 mark)

1. From the following data relating to ages of eight women at Faulu College, determine the medium age: 60, 48, 52, 72, 66, 41, 80, 38

(a)          72

(b)          52

(c)          56

(d)          66                                                                                                                                                                   (1 mark)

1. In a final examination in statistics, the mean score of a class of 50 students is found to be 65 marks with a standard deviation of 10 marks.

Determine the coefficient of variation.

(a)            15.38%

(b)           20%

(c)           6.5%

(d)           55%                                                                                                                                                                 (1 mark)

1. From the following data sets, determine the modal value: 12, 14, 12, 16, 18, 16, 20, 18, 20, 14

(a)           20

(b)           16

(c)           None

(d)           All                                                                                                                                                                   (1 mark)

1. In a ready to wear garment shop the most typical shirt size will be determined using?

(a)           Arithmetic mean

(b)           Mode

(c)           Median

(d)           Harmonic mean                                                                                                                                          (1 mark)

1. The distribution of wages paid to foremen is given as follows:

Wages Sh.”000″                 10-20                     20-30                      30 and above

Frequency (t)                     10                           25                            15

Calculate the mean wage paid to the foremen.

(a)           Sh.24,500

(b)           Sh.16,670

(c)          Sh.26,000

(d)           Sh.25,000                                                                                                                                                        (1 mark)

1. Which one of the following measure of central tendency is not rigidly defined?

(a)           Arithmetic mean

(b)           Median

(c)            Mode

(d)           Geometric mean                                                                                                                                         ( I mark)

1. A list of the entire population from which items can be selected to form a sample is called?

(a)            Sampling frame

(b)           Census

(c)           Statistics

(d)           Parameter                                                                                                                                                     ( 1 mark)

1. A sampling technique where every Kth item will be selected to be included in the sample is referred to as?

(a)           Quota sampling

(b)           Stratified sampling

(c)           Multi-stage sampling

(d)           Systematic sampling                                                                                                                                 (1 mark)

1. Which name is given to a smoothed frequency polygon?

(a)            Ogive curve

(b)           Frequency curve

(c)           Frequency histogram

(d)          Relative frequency polygon                                                                                                                    (1 mark)

1. Which of the following statements is true about graphs?

(a)          The independent variable should always be placed on the horizontal axis.

(b)          The dependent variable should always be placed on the horizontal axis.

(c)          The independent variable should always be placed on the vertical axis.

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

1. A trader imported goods from Canada at a cost of 15,000 Canadian dollars. He paid freight charges and insurance in transit of 10% of the purchase value of the goods. He also paid Sh. 200,000 in import duty. Calculate the value of the goods in Shillings.

(1 Canadian Dollar = Sh. 89)

(a)          Sh.1,668,500

(b)          Sh.1,468,500

(c)          Sh.16,500

(d)          Sh. I ,485,000                                                                                                                                             (I mark)

1. A businessman offers a commission of Sh.200 for every sales worth Sh.2,300. Philip Ngeno made sales worth Sh.52,900. Calculate the total commission received Philip Ngeno.

(a)          Sh.2,300

(b)          Sh.10,580,000

(c)          Sh.460,000

(d)          Sh.4,600                                                                                                                                                       (1 mark)

1. An American tourist converted 8,600 dollars to Kenya Shillings at an exchange rate of Ksh.110 per United States dollar. Calculate the amount received the tourist in Kenya shillings.

(a)          Sh.946,000

(b)          Sh. 78.18

(c)          Sh.  100

(d)          Sh.  100,000                                                                                                                                                 (1 mark)

1. A business person imported a car from Japan at a cost of Kenya shillings 3,000,000. If the prevailing exchange rate was Ksh. 80 per Japanese Yen, calculate the cost of the car in Japanese Yen.

(a)          Yen 320,000,000

(b)          Yen 37,500

(c)          Yen 6,400

(d)          Yen 75,000                                                                                                                                                  (1 mark)

1. A manufacturing company pays its workers Sh.1,200 for every unit produced. On a given day Thomas Korir produced 5 units. Calculate the amount paid to Thomas Korir.

(a)           Sh.1,200

(b)           Sh.6,000

(c)           Sh.7,200

(d)           Sh.3,600                                                                                                                                                          (1 mark)

1. An employee earns a taxable income of Sh.80,000 per month. The tax rate is 15% per month. Calculate the net pay.

(a)          Sh.I2,000

(b)          Sh.80,000

(c)          Sh.68,000

(d)          Sh.92,000                                                                                                                                                     (1 mark)

1. Juma Barasa bought a piece of land for Sh.850,000. The land is expected to appreciate in value at the rate of 5% per annum. Calculate the value of the land after 3 years.

(a)           Sh.127,500

(b)           Sh.977,500

(e)           Sh.722,500

(d)           Sh.850,000                                                                                                                                                      (1 mark)

1. A manufacturer bought a machine for Sh.250,000. The machine has a useful life of 8 years with no scrap value. Calculate the annual rate of depreciation for the machine.

(a)           10%

(b)          20%

(c)          25%

(d)          12.5%                                                                                                                                                           ( I mark)

1. Duncan Mulwa paid Sh.15,000 to purchase a bicycle after receiving a discount of 20%. What is the gross price of the bicycle?

(a)          Sh.18,000

(b)          Sh.75,000

(c)          Sh.18,750

(d)          Sh. I 2,000                                                                                                                                                   (1 mark)

1. Samuel Mwangi bought an article for Sh.9,600 and later sold it at a loss of 20% of the selling price. Determine the selling price of the article.?

(a)          Sh.7,680

(b)          Sh.11,520

(c)          Sh.11,200

(d)          Sh.8,000                                                                                                                                                       ( I mark)

1. James Olekina sells his products for Sh.30 per unit. He allows his customers a trade discount of 10% and a further cash discount of 7.5% for cash purchase.  Cynthia Kwamboka buys 110 units, calculate the net amount paid Cynthia Kwamboka.

(a)           Sh.2,887.50

(b)          Sh.2,747.25

(c)          Sh.2,970

(d)          Sh.3,059.50                                                                                                                                                 (I mark)

1. An allowance offered to buyers sellers to encourage prompt payment is called?

(b)          Cash discount

(c)          Quantity discount

(d)          Prompt discount                                                                                                                                         ( I mark)

1. Payment earned an agent for selling on behalf of another person is called?

(a)          Discount

(b)          Basic pay

(c)          Commission

(d)          Profit                                                                                                                                                             (1 mark)

1. Sarah Kinyua bought a watch for Sh.1,200 and later sold it for Sh.800. Determine the percentage loss.

(a)          662/3%

(b)          50%

(c)          33 I3%

(d)          50%.                                                                                                                                                              (1 mark)

1. A trader gains 8% selling a product for Sh.2,700. What did the product cost him?

(a)          Sh.2,484

(b)          Sh.2,500

(c)          Sh.2,916

(d)          Sh.216                                                                                                                                                           ( I mark)

1. An article costing Sh.675 is sold at a profit margin of 25%. Find the selling price of the article.

(a)          Sh.900

(b)          Sh.168.75

(c)          Sh.225

(d)          Sh.843.75                                                                                                                                                     (1 mark)

1. Given that mark-up of a product is 2 /3, determine the margin.

(a)            1

(b)           2/5

(e)           3/5

(d)           3

( 1 mark)

1. Matthew Tsofa deposited Sh.150,000 in a bank that paid a simple interest of 15% per annum for 2 years. Calculate the interest receivable after the 2 years.

(a)          Sh. 45,000

(b)          Sh.22,500

(c)          Sh.I95,000

(d)          Sh.  105,000                                                                                                                                                  (1 mark)

1. Compute the compound interest on Sh.20,000 at an interest rate of 8.5% for 2 years.

(a)          Sh.23,544.50

(b)          Sh.3.400

(c)           Sh.3,544.50

(d)          Sh.23,400                                                                                                                                                     ( I mark)

1. Find the principal which amounts to Sh.68,000 at simple interest rate of 12% per annum in 3 years.

(a)           Sh.59,840

(b)          Sh.18,000

(c)          Sh.188,889

(d)          Sh.50,000                                                                                                                                                     (I mark)

1. Find the time in years it will take for a certain amount X invested at a compound rate of interest of 10% per annum to triple.

(a)           11.52 years

(b)          3 years

(c)          2.72 years

(d)          3.3 years                                                                                                                                                       (1 mark)

1. A father leaves an estate to be divided among his three sons Ali, Baba and Chacha. All gets I /3 of the estate, Babu gets 1/4 while Chacha receives 1/, of the remainder. What is the total value of the estate if Chacha’s share amounted to Sh.240,000.

(a)          Sh.576,000

(b)          Sh.1,000,000

(c)          Sh.1,152,000

(d)          Sh.411,429                                                                                                                                                  (1 mark)

1. Determine the value of y given that 2,8 and 32, y are in proportion.

(a)          8

(b)          256

(c)          320

(d)          128                                                                                                                                                                (1 mark)

1. The factorisation of 6x + 18y is.

(a)          3 (2x + 6y)

(b)          6(x + 9y)

(c)          6(x + 3y)

(d)          3 (2x + 9y)                                                                                                                                                   (1 mark)

1. The factorisation of 6xy +4x + 6- 9x is.

(a)          (3x-2)(2y-3)

(b)          (3x+2)(2y -3)

(c)          (3x+2)(2y +3)4

(d)          (3x-2)(2y +3)                                                                                                                                             (1 mark)

1. A box contains 3 yellow balls and 5 green balls. 1 ball is selected at random from the box. What is the probability that the ball is yellow?                                                                                                          ( I mark)

1. Differentiate the following function: Y=4×3 + x2 +6x+10 with respect to x.

(a)             12×2+2x+6

(b)            4×2+2x+6x

(c)             12×2+2x+6x

(d)            12×2+2x+16                                                                                                                                                  (1 mark)

1. Find the inverse of the following matrix;

(1 mark)

1. Define the following notation as used in matrices; A-1

(a)           Inverse of a matrix

(b)           Compliment of a matrix

(c)           Equality of a matrix

(d)           None of the above                                                                                                                                            (1 mark)

1. Two matrices can be added or subtracted if and only if

(a)          They are of the same size.

(b)          The number of columns in the first matrix is equal to the rows in the second matrix

(c)          The number of rows in the first matrix is equal to the columns in the second matrix

(d)          The number of columns in the second matrix is equal to the rows in the first matrix          (1 mark)

1. If the probability of picking a blue pen from a pack is 0.25, how many pens are in the pack if there are 20 blue pens?

(a)          45

(b)          80

(c)           60

(d)          40                                                                                                                                                                    (1 mark)

1. A column vector matrix is a matrix which;

(a)          Has no columns

(b)          Has one row

(c)          Has no rows

(d)          Has one column                                                                                                                                          ( I mark)

1. A minima turning point has a gradient of;

(a)            1

(b)           cc

(c)           0

(d)           -1                                                                                                                                                                     (1 mark)

1. Which of the following is not a form of a turning point?

(a)           Minima

(b)           Point of infraction

(c)           Maxima

1. Integrate the following function 4×3 .

(a)           4×4+ e

(b)           4X4

(c)           X4 + C

(d)           12X2                                                                                                                                                                (1 mark)

1. Convert a profit margin of 20% to markup.

(a)           40%

(b)           25%

(c)            10%

(d)           33.33%                                                                                                                                                             (1 mark)

1. How many terms are there in the expression 5xy2-F6x-4y+10?

(a)           2

(b)           1

(c)           4

(d)           5                                                                                                                                                                      (I mark)

1. The coefficient of 9×3 is?

(a)           3

(b)           27

(c)           6

(d)           9                                                                                                                                                                      (1 mark)

1. The value of 3×2 — 2x + 3 when x-3 is?

(a)           3

(b)           24

(c)           21

(d)           -24                                                                                                                                                                   (1 mark)

1. The number — 10.36 lies on which side of the number line?

(a)           Center

(b)           Left

(c)           Right

(d)           Either side.                                                                                                                                                       (1 mark)

1. The number line for natural numbers

(a)           Extends indefinitely on both sides

(b)           Extends indefinitely to the left from zero

(c)           Extends indefinitely to the right from zero

(d)           Lies between -1 and 1                                                                                                                                      (1 mark)

1. -1 0 is than 10 and -12 is  than -8.

(a)           Greater and greater

(b)           Smaller and greater

(c)           Smaller and smaller

(d)           Greater and smaller.                                                                                                                                         (1 mark)

1. Expand (x + I) (x – 2).

(a)               -x+2

(b)          x2- x – 2

(c)          x2 + x – 2

(d)          x2+ x + 2                                                                                                                                                      ( I mark)

1. Factorise x2 – 5x + 6.

(a)          (x + 2) (x + 3)

(b)          (x – 2) (x + 3)

(c)          (x – 2)(x – 3)

(d)          (x + 2) (x – 3)                                                                                                                                             (1 mark)

1. Simplify (x + 6)2 + (2x -1)1

(a)          4x – I 1

(b)          4x + 11

(c)           11

(d)          4x + 13                                                                                                                                                          (1 mark)

71.                                                                                                                                                              (I mark)

1. The profit equation of a food processing plants described as J1=16x 2×2- 14 in Sh. “000”. What is the initial cost of the project?

(a)          Sh.0

(b)          Sh.I4,000

(c)          Sh. I 6,000

(d)          -Sh.2,000                                                                                                                                                      (1 mark)

1. Find the derivative of 3/2 x2 -1.

(a)          9/2 x3- lx

(b)          3x

(c)          3x- 1

(d)          3x – x                                                                                                                                                             ( I mark)

1. Find the range of values of x which satisfy the following inequality. -3x -4 > 2.

(a)          x > -2

(b)          x > -2/3

(c)          x < -2

(d)          x < -2/3                                                                                                                                                         (1 mark)

1. Find the range of values of x which satisfy the following inequality ’15- x-/4> 2.

(a)          x < – 40

(b)          x <40

(c)          x > – 40

(d)          x > 40                                                                                                                                                            (1 mark)

1. A quadratic equation can be solved using any of the following approaches except?

(a)          Graphical approach

(b)          By factorising

(c)          By substitution method

(d)          By completing the square method                                                                                                         ( I mark)

1. The profit function of a certain production process is expressed as y = 11 Oq — q2 — 1000. Determine the number of units required to maximize profit.

(a)           55 units

(b)           10 units

(c)            100 units

(d)           110 units                                                                                                                                                         (1 mark)

1. Solve the following simultaneous equations.

12x + 8y = 48

16x— 12y =-4

(a)           x = 4

y = 0

(b)           x = 2

y= 3

(c)           x = 3

y = 2

(d)           x = 0

y = 6                                                                                                                                                                (1 mark)

1. A teacher is twice as old as his student. In twenty years time, he will be 1.5 times as old. What is the difference in their ages today?

(a)            10

(b)           40

(c)           20

(d)           30                                                                                                                                                                    (1 mark)

1. Determine the equation of the straight line which passes through points A (1,6) and B (2, 10).

(a)           y = 5.75 + 0.25x

(b)           y = 2 + 4x

(c)           y = 2     4x

(d)           y = 4.4 + 1.6x                                                                                                                                                  (1 mark)

1. A worker is paid Sh.500 for each day he worked. A penalty of Sh.250 is imposed for each day the worker is absent. The worker was paid Sh.7,750 after 20 days. For how many days was he absent?

(a)           9

(b)           5

(c)           3

(d)           15                                                                                                                                                                    (1 mark)

1. A maximum turning point on a curve may be determined using?

(a)          Integration

(b)          Differentiation

(d)          Factorisation                                                                                                                                                (I mark)

1. Given that x = 3 and y = 2.

Evaluate x2 — x3y + 6.

(a)           – 45

(b)           – 39

(c)           – 51

(d)           – 3                                                                                                                                                                    (1 mark)

1. A matrix B [3       1           is such that determinant is I. Find out the value of y.

2      y

(a)           — 1/3

(b)           3

(c)           5

(d)           1                                                                                                                                                                      (1 mark)

1. Given that

Which of these matrices is compatible for multiplication?

(a)           B x A

(b)          B x C

(c)           A x B

(d)          C x B                                                                                                                                                              (1 mark)

1. A matrix obtained interchanging the rows and columns of a matrix is known as?

(a)          Inverse of a matrix

(b)          Transpose of a matrix

(c)          Square matrix

(d)          Diagonal matrix                                                                                                                                          ( I mark)

1. A square diagonal matrix with all elements in the primary diagonal being equal is called?

(a)          A scalar

(b)          Column vector

(c)          Null matrix

(d)          Row vector                                                                                                                                                   (1 mark)

1. What is the probability of success if the probability of failure is 0.05?

(a)          0.45

(b)          0.50

(c)          0.95

(d)          1.05                                                                                                                                                               (1 mark)

1. Which of the following is not a probability value?

(a)          0

(b)          -1

(c)          0.456

(d)            1                                                                                                                                                                      (I mark)

1. What is the probability of a sure event?

(a)           I

(b)          2

(c)          0

(d)          00                                                                                                                                                                    (1 mark)

1. Two events are said to be independent if;

(a)          The two events cannot happen together.

(b)          The two event can happen together.

(c)          The occurrence or non-occurrence of one event affects the occurrence or non-occurrence of the other.

(d)          The occurrence or non-occurrence of one event does not affects the occurrence or non-occurrence of the other.                                                                                                                                                           ( 1 mark)

1. Two events are said to be mutually exclusive if;.

(a)          The two events cannot happen together.

(b)          The two events can happen together.

(c)          The occurrence or non-occurrence of one event affects the occurrence or non-occurrence of the other.

(d)          The occurrence or non-occurrence of one event does not affect the occurrence or non-occurrence of the other.                                                                                                                     ( 1 mark)

1. The probability of producing a defective unit machine A is 0.15. If the machine produces 760 units, how many defective units will be produced?

(a)           646

(b)            15

(c)            85

(d)            114                                                                                                                                                                  (1 mark)

1. The number of units in a sample are referred to as.

(a)           Outcomes

(b)          Sample events

(c)           Sample space

(d)          Probability space                                                                                                                                        (I mark)

1. Under the additional rule of probability, the events must be

(a)           Dependent

(b)          Equally likely

(c)           Mutually exclusive

(d)          Collectively exhaustive                                                                                                                            ( I mark)

1. Probability can assume any value between

(a)           0 and 1

(b)          -1 and  1

(c)           I and 2

(d)          -1 and 0                                                                                                                                                        (1 mark)

1. The probability of an event A happening given that event B has already happened is referred to as?

(a)           Joint probability

(b)          Conditional probability

(c)           Equally likely probability

(d)          Impossible probability                                                                                                                             (1 mark)

1. Two events are said to be equally likely if;

(a)           They can happen together

(b)          They have to occur

(c)          They have the same probability of occurrence

(d)          They cannot happen together.                                                                                                                 (1 mark)

1. Three unbiased coins are tossed simultaneously. Find the sample space.

(a)           6

(b)          9

(c)          8

(d)          3                                                                                                                                                                      (1 mark)

1. A single possible outcome of an experiment is called?

(a)          Simple event

(b)          Compound event

(c)          Equally likely event

(d)          Mutually exclusive event                                                                                                                         (1 mark)

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