BECE 1994 Mathematics Past Questions and Answers

Paper 1: Objectives

1. Which of the following is the set of factors of 12?
   1. A. {12, 6, 4, 3, 2, 1}
   2. B. {12, 6, 4, 3, 2}
   3. C. {12, 6, 4, 2}
   4. D. {6, 4, 2, 1}
   5. E. {6, 4, 3, 2}
   Answer: A

   A factor of a number is a number that divides the given number exactly, leaving no remainder.
2. 
   
   Which of the following describes the relationship between the sets A and B in the Venn diagram below?
   1. A. A ⊆ B
   2. B. A ∩ B = 5
   3. C. A ∩ B = ∅
   4. D. A ∪ B = {1, 2, 3, 4, 5, 6, 7}
   5. E. B ⊆ A
   Answer: C

   The intersection (∩) represents elements found in both sets. Since A ∩ B = ∅, both sets have no common elements.
3. Mark is 30 years old. Yaw is half as old as Mark. Paul is 10 years older than Yaw. How old is Paul?
   1. A. 30 years
   2. B. 25 years
   3. C. 20 years
   4. D. 15 years
   5. E. 10 years
   Answer: B

   Yaw is half as old as Mark, so Yaw is 15 years old. Paul is 10 years older than Yaw, making him 25 years old.
4. How many lines of symmetry does a rectangle have?
   1. A. 1
   2. B. 2
   3. C. 3
   4. D. 9
   5. E. 11
   Answer: B

   A rectangle has 2 lines of symmetry: one through the middle horizontally and one vertically.
5. Which of the following is not a prime number?
   1. A. 3
   2. B. 5
   3. C. 7
   4. D. 9
   5. E. 11
   Answer: D

   9 is not a prime number because it has three divisors: 1, 3, and 9.
6. If x = {1, 2, 3, 4, 5}, find the truth set of 2x + 1 < 7.
   1. A. {1, 2}
   2. B. {2, 3}
   3. C. {1, 2, 3}
   4. D. {3}
   5. E. {2}
   Answer: A

   2x + 1 < 7 implies x < 3, so the truth set is {1, 2}.
7. In how many years will ₵5,000 yield a simple interest of ₵1,000 at a rate of 5% per annum?
   1. A. 4 years
   2. B. 5 years
   3. C. 10 years
   4. D. 25 years
   5. E. 30 years
   Answer: A

   Using the formula I = (P × T × R) / 100, we find that T = 4 years.
8. Make m the subject of the relation $f=\frac{t}{s}-m$.
   1. A. $m=\frac{t}{s}+f$
   2. B. $m=\frac{t}{s}-f$
   3. C. $m=\frac{fs-t}{s}$
   4. D. $m=f-\frac{t}{s}$
   5. E. $m=-f-\frac{t}{s}$
   Answer: B

   $f=\frac{t}{s}-m\Rightarrow m=\frac{t}{s}-f$
9. Which property of arithmetic operations is illustrated by the statement a × (b + c) = ab + ac?
   1. A. Addition
   2. B. Association
   3. C. Commutative
   4. D. Multiplication
   5. E. Distributive
   Answer: E

   This demonstrates the distributive property.
10. Simplify 15².
    1. A. 30
    2. B. 63
    3. C. 225
    4. D. 240
    5. E. 625
    Answer: C

    15² = 225.

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11. If $\frac{1}{x}=1\frac{1}{2}$, find x.
    1. A. $3\frac{1}{2}$
    2. B. $\frac{3}{2}$
    3. C. $\frac{4}{3}$
    4. D. $\frac{2}{3}$
    5. E. $\frac{1}{3}$
12. Calculate the size of an exterior angle of a regular pentagon.
    1. A. 72°
    2. B. 90°
    3. C. 108°
    4. D. 360°
    5. E. 540°
13. Factorize $x^2-5x+6$.
    1. A. (x + 3)(x - 2)
    2. B. (x - 2)(x - 3)
    3. C. (x + 1)(x - 6)
    4. D. (x + 2)(x + 3)
    5. E. (x + 6)(x - 1)
14. Kwame, Atsu, and Kojo shared a profit of ₵500,000 in the ratio 1:4:3 respectively. How much did Atsu get?
    1. A. ₵62,500
    2. B. ₵125,000
    3. C. ₵187,500
    4. D. ₵250,000
    5. E. ₵312,500
15. Use the identity a² - b² = (a + b)(a - b) to evaluate 83² - 17².
    1. A. 660
    2. B. 6,600
    3. C. 7,178
    4. D. 7,600
    5. E. 8,317
16. What is the probability of obtaining a prime number when a fair die is thrown once?
    1. A. 2/3
    2. B. 1/2
    3. C. 1/3
    4. D. 1/6
    5. E. 5/6
17. The following are the scores obtained by girls in a beauty contest: 12, 16, 19, 14, 17, 8, 11, 19. What is the probability of obtaining a score of 19?
    1. A. 1/9
    2. B. 1/8
    3. C. 1/4
    4. D. 19/53
    5. E. 19/108
18. Express 25 as a percentage of 75.
    1. A. 300%
    2. B. 100%
    3. C. 50%
    4. D. 33.3%
    5. E. 25%
19. Find the value of m given that $m=(3^6÷3^4)\times 27$.
    1. A. $3^1$
    2. B. $3^2$
    3. C. $3^5$
    4. D. $3^6$
    5. E. $3^{13}$
20. Express 0.0043216 in standard form.
    1. A. 4.3216 × 10
    2. B. 4.3216 × 10⁻³
    3. C. 4.3216 × 10⁵
    4. D. 4.3216 × 10⁻⁵
    5. E. 4.3216 × 10⁰
21. Given that a = 2 and b = 3, evaluate (2a + b)(a - 2b).
    1. A. 28
    2. B. 8
    3. C. -7
    4. D. -8
    5. E. -28
22. 
    
    Which of the following is illustrated on the number line?
    1. A. $-1<x<\frac{3}{2}$
    2. B. $-1\le x<\frac{3}{2}$
    3. C. $-1\le x\le \frac{3}{2}$
    4. D. $-1<x\le \frac{3}{2}$
    5. E. $\frac{3}{2}\le x\le -1$
23. 
    
    A is the center of the circle with radius 20 cm. If angle BAC is 90°, find the perimeter of the shaded sector. [Use π = 22/7]
    1. A. 31.4 cm
    2. B. 31.8 cm
    3. C. 40.0 cm
    4. D. 51.4 cm
    5. E. 71.4 cm
24. 
    
    In triangle ABC, [AB] = [BC] = 5 cm, and [AC] = 8 cm. Find [BD].
    1. A. 3 cm
    2. B. 4 cm
    3. C. 9 cm
    4. D. 33 cm
    5. E. 41 cm
25. Write ₵35,632.00 correct to the nearest thousand cedis.
    1. A. ₵40,000.00
    2. B. ₵36,000.00
    3. C. ₵35,600.00
    4. D. ₵35,000.00
    5. E. ₵30,000.00
26. Solve for x if 2x + 5 = 3x - 7.
    1. A. 12
    2. B. 2
    3. C. $\frac{2}{3}$
    4. D. -2
    5. E. -12
27. Evaluate $(\frac{2}{3}-\frac{1}{4})÷\frac{5}{6}$.
    1. A. $\frac{1}{2}$
    2. B. $\frac{1}{5}$
    3. C. $\frac{2}{3}$
    4. D. -2
    5. E. -12
28. A boy walked 7 km on a bearing of 060°. Which of the following diagrams shows his direction?
    1. A.
    2. B.
    3. C.
    4. D.
    5. E.
29. 
    
    In the diagram, triangle G,OH, is an enlargement of triangle GOH with scale factor k. If [GG,] = 5 cm, [GO] = 2 cm and [GH] = 1 cm, what is the value of k?
    1. A. -5
    2. B. -3/2
    3. C. -2
    4. D. -2/3
    5. E. -3
30. If 14_x = 9_ten, find x.
    1. A. Nine
    2. B. Eight
    3. C. Seven
    4. D. Six
    5. E. Five
31. How many faces does a cuboid have?
    1. A. 6
    2. B. 8
    3. C. 12
    4. D. 16
    5. E. 32
32. Which of the following is a factor of the expression ac -2bc + ad - 2bd?
    1. A. c-d
    2. B. a-2b
    3. C. a+b
    4. D. a+2b
    5. E. c+2d
33. Three boys weeded a piece of land in 4 hours. How long would it take 18 boys to weed the same piece of land weeding at the same rate?
    1. A. $\frac{2}{3}$ hour
    2. B. $3\frac{1}{3}$ hours
    3. C. $4\frac{2}{3}$ hours
    4. D. 22 hours
    5. E. 24 hours
34. 
    
    Find the size of the angle marked a in the diagram.
    1. A. 30°
    2. B. 60°
    3. C. 90°
    4. D. 120°
    5. E. 180°
35. Which of the following is the net of a cube?
    1. A.
    2. B.
    3. C.
    4. D.
    5. E.
36. Use the mapping below to answer the question.
    
    5 → 10_five
    10 → 20_five
    20 → 40_five
    40 → x_five
    y → 310_five
    
    Find the value of x.
    1. A. 30_five
    2. B. 100_five
    3. C. 110_five
    4. D. 120_five
    5. E. 130_five
37. 
    
    In the diagram, find the size of the angle marked e°.
    1. A. 52°
    2. B. 56°
    3. C. 72°
    4. D. 108°
    5. E. 128°
38. 
    
    If the area of the figure above is 60 cm², find x.
    1. A. 8 cm
    2. B. 9 cm
    3. C. 12 cm
    4. D. 16 cm
    5. E. 20 cm
39. The mean of the numbers 4, 3, 3, x is 5. Find x.
    1. A. 20
    2. B. 10
    3. C. 5
    4. D. 4
    5. E. 3
40. If a number is selected at random from the table below, what is the probability that the number is 5?
    

    Number	1	3	5	7	9
    Frequency	25	15	8	10	2

    1. A. 8/25
    2. B. 4/25
    3. C. 1/12
    4. D. 2/15
    5. E. 5/8

Paper 2: Theory

1. a) Multiply (a-b) by (2b - a)
   
   b) Find the truth set of 2x - 6 < 5(3 - x). Illustrate your answer on a number line.
   
   c) Simplify -1(u + (1/3)v - (2/3))
2. a) A ladder leans against a wall. The end of the ladder touches the wall 12 m from the ground. The foot of the ladder is 9 m away from the foot of the wall.
   
   (i) What is the length of the ladder?
   
   (ii) Calculate the angle that the ladder makes with the ground.
   
   b) Given that π = 3.14 and g = 20, find the value of F in the relation F = (πg²)/4.
3. Using a ruler and a pair of compasses only:
   
   a) Construct triangle PQR in which |PQ| = 8 cm, ∠QPR = 45° and ∠PQR = 90°. Measure |QR|.
   
   b) Construct the mediator of line PQ to meet line PR at the point S.
   
   c) With S as the centre and radius 3 cm, construct a circle.
4. Using a scale of 2 cm to 1 unit on both axes, draw two perpendicular lines OX and OY on a graph sheet. Mark the x-axis from -5 to 5 and the y-axis from -6 to 6. Mark the origin O.
   
   (i) Draw on the same graph sheet, indicating in each case, the coordinates of all the vertices of square ABCD where A(1, 2), B(4, 2), C(4, 5), and D(1, 5) are the respective points.
   
   (ii) Using the y-axis as a mirror line, draw the image A'B'C'D' of square ABCD.
   
   (iii) Draw an enlargement A''B''C''D'' of the square ABCD with scale factor -1 from O.
   
   (iv) What single transformation maps A''B''C''D'' onto the square A'B'C'D'?
5. The following table gives the distribution of sales of soft drinks sold by the Jatokrom JSS canteen in one week:
   
   Soft Drink | Number of Bottles Sold:
   
   Fanta: 13
   
   Pepsi Cola: 21
   
   Mirinda: 14
   
   Coca-Cola: 17
   
   Sprite: 7.
   
   Draw a pie chart to illustrate the sales.

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