BECE 2014 Mathematics Past Questions and Answers

Paper 1: Objectives

1. If set N is a subset of set M, then
   1. A. sets M and N have the same number of elements.
   2. B. some members of set N can be found in set M
   3. C. no member of set N is in set M.
   4. D. all members of set N are in set M.
   Answer: D

   All members of a subset are found in the main set.
2. 
   
   The Venn diagram shows the number of pupils who offer Mathematics (M) and/or English (E) in a class. How many pupils offer Mathematics?
   1. A. 10
   2. B. 18
   3. C. 25
   4. D. 28
   Answer: C

   Mathematics is the region in M. Number of pupils who offer Mathematics = 18 + 7 = 25.
3. 
   
   The Venn diagram shows the number of pupils who offer Mathematics (M) and/or English (E) in a class. How many pupils offer only one subject?
   1. A. 3
   2. B. 7
   3. C. 18
   4. D. 21
   Answer: D

   Only one subject is the region outside the intersection (7). Only one subject = 18 + 3 = 21.
4. Simplify: 12 - 7 - (-5)
   1. A. -10
   2. B. -2
   3. C. 0
   4. D. 10
   Answer: D

   Simplify using the rule: -(-) = +. 12 - 7 - (-5) = 12 - 7 + 5 = 10.
5. Express 72 as a product of its prime factors.
   1. A. 2 x 3³
   2. B. 2³ x 3
   3. C. 2 x 3²
   4. D. 2³ x 3²
   Answer: D

   Prime factors of 72 are 2 x 2 x 2 x 3 x 3 = 2³ x 3².
6. Find the smallest number which is divisible by 16 and 20.
   1. A. 40
   2. B. 80
   3. C. 120
   4. D. 160
   Answer: B

   The LCM of 16 and 20 is 80.
7. Convert 243 (base 5) to a base ten numeral.
   1. A. 40
   2. B. 43
   3. C. 45
   4. D. 73
   Answer: D

   243 (base 5) = 2 x 25 + 4 x 5 + 3 x 1 = 73 (base 10).
8. A pineapple bought for GHC1.00 was sold at GHC1.30. Calculate the profit percent.
   1. A. 10%
   2. B. 20%
   3. C. 23%
   4. D. 30%
   Answer: D

   Profit % = (Profit / Cost Price) x 100 = (0.3 / 1) x 100 = 30%.
9. Simplify 35x⁵y³ ÷ 7xy².
   1. A. 5x⁴y
   2. B. 5x⁴y⁵
   3. C. 5x⁶y
   4. D. 5x⁶y⁵
   Answer: A

   35 ÷ 7 = 5; x⁵ ÷ x = x⁴; y³ ÷ y² = y. So 35x⁵y³ ÷ 7xy² = 5x⁴y.
10. Two bells P and Q ring at intervals of 3 hours and 4 hours, respectively. After how many hours will the two bells first ring simultaneously?
    1. A. 6 hours
    2. B. 8 hours
    3. C. 12 hours
    4. D. 24 hours
    Answer: C

    The LCM of 3 and 4 is 12.

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11. A boy scores 17/25 in a French test. Express his score as a percentage.
    1. A. 17%
    2. B. 34%
    3. C. 68%
    4. D. 85%
12. Arrange the following fractions in ascending order: 2/5, 5/12, 3/4.
    1. A. 2/5, 3/4, 5/12
    2. B. 2/5, 5/12, 3/4
    3. C. 5/12, 2/5, 3/4
    4. D. 3/4, 2/5, 5/12
13. Kofi paid rent of GHC1,800.00 each year. If the rent is 0.3 of his annual income, find his annual income.
    1. A. GHC600.00
    2. B. GHC5,400.00
    3. C. GHC6,000.00
    4. D. GHC18,000.00
14. I gave a storekeeper a GHC10.00 note for goods I bought. He asked for another 15Gp for ease of change. If he then gave me 50Gp, how much did I pay for the goods?
    1. A. GHC9.35
    2. B. GHC9.45
    3. C. GHC9.65
    4. D. GHC10.65
15. Kojo can buy 15 shirts at GHC4.00 each. If the price increases to GHC5.00, how many shirts can he buy?
    1. A. 12
    2. B. 15
    3. C. 19
    4. D. 20
16. A hall 8 m long is represented as 4 cm on a diagram. What is the scale of the diagram?
    1. A. 1:200
    2. B. 1:250
    3. C. 1:400
    4. D. 1:800
17. Jane arrived at work at 7:55 a.m and left at 4:15 p.m. For how long was she at work?
    1. A. 7 hr 20 min
    2. B. 7 hr 45 min
    3. C. 8 hr 20 min
    4. D. 8 hr 40 min
18. Given that (3.14 x 18) x 17.5 = 3.14 x (3p x 17.5). Find the value of p.
    1. A. 3.0
    2. B. 5.8
    3. C. 6.0
    4. D. 9.0
19. 
    
    The pie chart shows how Kwaku spends his monthly salary. Find the value of x.
    1. A. 65°
    2. B. 75°
    3. C. 85°
    4. D. 100°
20. 
    
    Kwaku earns GHC630.00 a month. How much of this does he spend on food?
    1. A. GHC140.00
    2. B. GHC157.00
    3. C. GHC210.00
    4. D. GHC350.00
21. 
    
    What percentage of Kwaku's salary does he spend on rent and utilities?
    1. A. 12.1%
    2. B. 12.5%
    3. C. 22.2%
    4. D. 33.3%
22. In an enlargement with scale factor 2, which of the following statements is not true?
    1. A. Each length is multiplied by 2.
    2. B. Each angle remains the same.
    3. C. The shape of the figure does not change.
    4. D. The size of the figure does not change.
23. Kofi, Kojo, and Ama shared GHC480,000.00 in the ratio 3:5:4. How much did Ama receive?
    1. A. GHC160,000.00
    2. B. GHC200,000.00
    3. C. GHC218,181.81
    4. D. GHC342,859.14
24. If w = 12, x = 5, y = 6, and z = 4, find the value of wx - yz.
    1. A. 18
    2. B. 27
    3. C. 36
    4. D. 84
25. A man was 24 years old when his son was born. Now he is three times as old as his son. Find the age of the son.
    1. A. 6 years
    2. B. 12 years
    3. C. 18 years
    4. D. 36 years
26. There are 20 identical balls in a box. Twelve are blue, and the rest are green. If one ball is taken at random from the box, find the probability that the ball is green.
    1. A. 1/20
    2. B. 2/5
    3. C. 3/5
    4. D. 4/5
27. Using the following mapping, find the missing numbers p and q where y values are 3, 5, p, 9, 11, q for x values of 1, 2, 3, 4, 5, 6.
    1. A. p=6, q=12
    2. B. p=6, q=13
    3. C. p=7, q=12
    4. D. p=7, q=13
28. The perimeter of a rectangle is 24 cm. If the length is 7 cm, find its width.
    1. A. 3 cm
    2. B. 5 cm
    3. C. 10 cm
    4. D. 12 cm
29. A boy walks on a bearing of 070°. Which of the following diagrams shows his direction?
    1. A.
    2. B.
    3. C.
    4. D.
30. How many faces does a cube have?
    1. A. 4
    2. B. 6
    3. C. 8
    4. D. 12
31. The diameter of a circular tray is 28 cm. Find the area of the tray. [Take π = 22/7]
    1. A. 44 cm²
    2. B. 88 cm²
    3. C. 154 cm²
    4. D. 616 cm²
32. Calculate the volume of a cylinder with radius 7 cm and height 10 cm. [Take π = 22/7]
    1. A. 220 cm³
    2. B. 440 cm³
    3. C. 1,540 cm³
    4. D. 3,080 cm³
33. 
    
    Find the value of e in the diagram provided with angles PRQ = 50° and PQR = 38°.
    1. A. 38°
    2. B. 40°
    3. C. 88°
    4. D. 92°
34. 
    
    Find the angle marked d in the diagram with angle RTS = 48° and angle PRQ = 92°.
    1. A. 38°
    2. B. 40°
    3. C. 48°
    4. D. 88°
35. A 3.6 m long string is to be cut into pieces, each of length 40 cm. How many pieces can be cut from the string?
    1. A. 4
    2. B. 6
    3. C. 8
    4. D. 9
36. Solve the inequality 2x + 10 ≥ 7x/2 - 5.
    1. A. x ≤ 10
    2. B. x ≥ 10
    3. C. x ≤ 40
    4. D. x ≥ 40
37. The point P(5,4) is reflected in the y-axis. Find its image.
    1. A. (-5,4)
    2. B. (5,-4)
    3. C. (-4,5)
    4. D. (4,-5)
38. Solve the equation x - 3 = 4 and find x.
    1. A. -1
    2. B. 1
    3. C. 7
    4. D. 12
39. Find the gradient of the line that passes through points M(-1,2) and N(6,-3).
    1. A. -5/7
    2. B. -7/5
    3. C. 5/7
    4. D. 7/5
40. Find the next two terms in the sequence 11, 7, 3, -1, ..., ...
    1. A. 5, 9
    2. B. 3, 7
    3. C. -4, -9
    4. D. -5, -9

Paper 2: Theory

1. a) P = {Factors of 30}
   
   Q = {Multiples of 5 less than 40}
   
   Find P ∩ Q.
   
   b) A trader saved GHC 200.00 for 3 years at 12% simple interest per annum. What will be the total amount in the trader's account at the end of the 3 years?
   
   c) Evaluate 4.56 × 3.6 and leave your answer in standard form.
2. a) i) Ama scored 82, 74, and 90 in three tests. What mark should she score in the fourth test so that her average mark for the four tests would be 85?
   
   ii) What was her median score in the four tests?
   
   
   
   b) In the diagram, AD is parallel to EG, angle CFG = 40° and triangle BCF is isosceles. Find the value of:
   
   i) angle CBF;
   
   ii) angle DCF;
   
   iii) x.
3. a) Solve for x if (1/3)x + 1 2/3 < -(3/4)x - 1/2
   
   b) The following shows the distribution of marks of students in an examination:
   
   Marks: {6, 43, 26, 18, 27, 42, 8, 22, 31, 39, 55, 44, 37, 47, 59, 10, 12, 36, 53, 48}
   
   i) Make a stem-and-leaf plot of the marks above.
   
   ii) Find the probability of selecting a student who scored between 40 and 50.
   
   iii) Find the number of students who passed the examination if the pass mark was 30.
4. a) A box has length 8.0 cm, width 5.0 cm, and height 10.0 cm. Find:
   
   i) total surface area of the box;
   
   ii) volume of the box.
   
   b) i) Plot the points A(0, 3), B(2, 3), and C(4, 5) to form triangle ABC.
   
   ii) Draw the image A'B'C' of triangle ABC under a translation by the vector (-1, -1).
   
   iii) Draw the image A''B''C'' of triangle ABC under a reflection in the x-axis.
5. a) Using a ruler and compass only:
   
   i) Construct triangle PQR such that [PR] = 8 cm, [PQ] = 6 cm, and [QR] = 5 cm.
   
   ii) Construct the perpendicular bisector of [PR] and label it l₁.
   
   iii) Construct the perpendicular bisector of [QR] and label it l₂.
   
   iv) Label the point of intersection of l₁ and l₂ as N.
   
   v) With N as center and radius equal to NP, draw a circle.
   
   b) i) Measure the radius of the circle.
   
   ii) Calculate the circumference of the circle, correct to 3 significant figures. [Take π = 3.14]
6. a) Factorize completely: 6xy - 3y + 4x - 2.
   
   b) The diagram shows a ladder AB leaning against a vertical wall PQ at B. If [PB] = 8 m and the other end of the ladder is 6 m away from the foot of the wall (at P), find the length of the ladder (AB).
   
   c) Kojo had 1,800 bags of rice in stock for sale. In January, he sold 2/3 of it. In February, he sold 3/4 of what was left.
   
   i) What fraction of the stock of rice did he sell:
   
   (a) in February?
   
   (b) in January and February?
   
   ii) How many bags of rice were left unsold by the end of February?

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