BECE 1992 Mathematics Past Questions and Answers

Paper 1: Objectives

1. Find the set of prime factors of 12.
   1. A. {3}
   2. B. {2, 3}
   3. C. {3, 4}
   4. D. {2, 6}
   5. E. {2, 3, 4, 6, 12}
   Answer: B

   Prime factors divide a number exactly without a remainder. The prime factors of 12 are 2 and 3.
2. If P = {7, 11, 13} and Q = {9, 11, 13}, find P ∪ Q.
   1. A. {7}
   2. B. {9}
   3. C. {7, 9}
   4. D. {7, 9, 11}
   5. E. {7, 9, 11, 13}
   Answer: E

   Union (∪) lists each unique element from both sets once. Therefore, P ∪ Q = {7, 9, 11, 13}.
3. 
   
   In the diagram, set Q has 30 members, and set T has 25 members. Q ∩ T has 10 members. Find the number of members of Q ∪ T.
   1. A. 35
   2. B. 45
   3. C. 55
   4. D. 65
   5. E. 75
   Answer: B

   
   
   Using the formula for union: n(Q ∪ T) = 30 + 25 - 10 = 45.
4. Find the value of $\sqrt{6\frac{1}{4}}$.
   1. A. 5.0
   2. B. 4.9
   3. C. 2.5
   4. D. 2.4
   5. E. 1.2
   Answer: C

   Change the fraction: 6 1/4 = 6.25 and calculate its square root to get approximately 2.5.
5. Convert 39₁₀ to a base-five numeral.
   1. A. 100111
   2. B. 1110
   3. C. 234
   4. D. 124
   5. E. 103
   Answer: D

   39 in base 10 is represented as 124 in base 5.
6. Find the least whole number which must be added to 207 to make it divisible by 17.
   1. A. 0
   2. B. 3
   3. C. 13
   4. D. 14
   5. E. 15
   Answer: D

   The next multiple of 17 after 207 is 221. Therefore, 14 must be added.
7. Simplify 2 × (3 1/3 + 1 1/6).
   1. A. 2 1/3
   2. B. 41/4
   3. C. 6 2/3
   4. D. 8
   5. E. 9
   Answer: E

   Simplifying gives 9.
8. If 8.51 ÷ 2.3 = 3.7, find the value of 85.1 ÷ 2.3.
   1. A. 0.037
   2. B. 0.37
   3. C. 3.7
   4. D. 37
   5. E. 370
   Answer: D

   Scaling up by 10 results in 37.
9. Express 0.625 as a fraction in its lowest term.
   1. A. 7/8
   2. B. 3/4
   3. C. 5/8
   4. D. 1/2
   5. E. 1/3
   Answer: C

   0.625 = 5/8.
10. An amount of money is shared between Kofi and Ama in the ratio 3 : 5. If Ama received ₵4,650.00, what is Kofi's share?
    1. A. ₵930.00
    2. B. ₵1,550.00
    3. C. ₵1,743.75
    4. D. ₵2,790.00
    5. E. ₵2,906.25
    Answer: D

    Kofi's share is 3/5 × ₵4650 = ₵2,790.00.

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11. If $1.00 = ₵340.00, what was the cedi value of an article that costs $6.50?
    1. A. ₵6,630.00
    2. B. ₵2,380.00
    3. C. ₵2,210.00
    4. D. ₵346.50
    5. E. ₵333.50
12. Find the simple interest on ₵28,000.00 at 3 1/2% per annum for 6 months.
    1. A. ₵490.00
    2. B. ₵560.00
    3. C. ₵980.00
    4. D. ₵4,000.00
    5. E. ₵5,880.00
13. 
    
    Which village is farthest from the market town?
    1. A. P
    2. B. Q
    3. C. R
    4. D. S
    5. E. T
14. 
    
    How much farther is village Q than village R from the market town?
    1. A. 2 km
    2. B. 3 km
    3. C. 4 km
    4. D. 5 km
    5. E. 6 km
15. There are 20 beads in a box. Some are red and some green. The chance that one bead taken at random from the box is red is 1/4. Find the number of red beads in the box.
    1. A. 16
    2. B. 15
    3. C. 10
    4. D. 5
    5. E. 4
16. A bag contains 12 mangoes of which 4 are not ripe. What is the chance of picking a ripe mango at random from the bag?
    1. A. 1/8
    2. B. 1/4
    3. C. 1/3
    4. D. 1/2
    5. E. 2/3
17. Find the value of p² – 6p + 9 when p = -2.
    1. A. 25
    2. B. 9
    3. C. 7
    4. D. 5
    5. E. 3
18. If x = 2, find the value of q in the equation 3x – 4 = x + q
    1. A. 8
    2. B. 1
    3. C. 0
    4. D. -1
    5. E. -8
19. 
    
    Which of the following inequalities is shown on the number line above, where p is a real number?
    1. A. p ≥ 2
    2. B. p > 2
    3. C. p = 2
    4. D. p ≤ 2
    5. E. p < 2
20. Use the mapping below to answer the question.
    
    -2 → y
    -1 → -1
    0 → 1
    2 → 5
    3 → 7
    4 → 9
    ......
    x → 21
    
    Find the value of x.
    1. A. -7
    2. B. 5
    3. C. 6
    4. D. 7
    5. E. 10
21. Use the mapping below to answer the question.
    
    -2 → y
    -1 → -1
    0 → 1
    2 → 5
    3 → 7
    4 → 9
    ......
    x → 21
    
    Find the value of y.
    1. A. 3
    2. B. 1
    3. C. -1
    4. D. -3
    5. E. -5
22. 
    
    Find the bearing of P from Q.
    1. A. 045°
    2. B. 090°
    3. C. 135°
    4. D. 180°
    5. E. 270°
23. A polygon has 10 sides. Which of the following gives the sum of its interior angles?
    1. A. 2 × 180°
    2. B. 4 × 180°
    3. C. 6 × 180°
    4. D. 8 × 180°
    5. E. 10 × 180°
24. 
    
    Using the conversion graph, find the equivalent of 4 miles in kilometers.
    1. A. 2.5
    2. B. 3
    3. C. 3.5
    4. D. 6
    5. E. 6.4
25. 
    
    Express 4 kilometers in miles using the conversion graph.
    1. A. 6.4
    2. B. 6
    3. C. 3.5
    4. D. 3
    5. E. 2.5
26. 
    
    Find |XZ| in the right-angled triangle.
    1. A. 2.4 cm
    2. B. 7 cm
    3. C. 13 cm
    4. D. 17 cm
    5. E. 60 cm
27. 
    
    Find tan ∠YXZ.
    1. A. 5/13
    2. B. 5/12
    3. C. 12/13
    4. D. 12/5
    5. E. 13/5
28. 
    
    Find the vector PQ given the points P and Q in a number plane.
    1. A. [6, 4]
    2. B. [6, -4]
    3. C. [-6, 4]
    4. D. [4, -6]
    5. E. [-4, -6]
29. Find the length of the vector p = [-5, 12].
    1. A. 7
    2. B. 10
    3. C. 13
    4. D. 17
    5. E. 25
30. 
    
    Square P₁Q₁R₁S₁ is an enlargement of PQRS. Given PQRS has area 4 cm² and P₁Q₁R₁S₁ has area 9 cm², find the scale factor.
    1. A. 2/3
    2. B. 4/9
    3. C. 3/2
    4. D. -2/3
    5. E. 2/1
31. The volume of a cube is 27 cm³. Find the area of one face.
    1. A. 3 cm²
    2. B. 6 cm²
    3. C. 9 cm²
    4. D. 18 cm²
    5. E. 54 cm²
32. A cylinder has a height of 3 cm and radius of 2 cm. Find its curved surface area. [Take π = 3.142]
    1. A. 7 cm²
    2. B. 12 cm²
    3. C. 18 cm²
    4. D. 38 cm²
    5. E. 54 cm²
33. 
    
    Find the area of the parallelogram PQRS with base 12 cm and height 4 cm.
    1. A. 20 cm²
    2. B. 21 cm²
    3. C. 48 cm²
    4. D. 60 cm²
    5. E. 240 cm²
34. If one-third of a number is added to one-fifth of the same number, the result is 8. Find the number.
    1. A. 3
    2. B. 5
    3. C. 15
    4. D. 40
    5. E. 45
35. If 1 : x is equivalent to 6¼ : 25, find x.
    1. A. 4
    2. B. 5
    3. C. 6.25
    4. D. 24
    5. E. 100
36. Express ³⁄₈ as a percentage.
    1. A. 0.373%
    2. B. 12%
    3. C. 25%
    4. D. 37.5%
    5. E. 40%
37. Akosua buys 480 pineapples for ₵24,000.00 and sells them for ₵28,000.00. Find her profit percentage.
    1. A. 13.9%
    2. B. 16.7%
    3. C. 20%
    4. D. 40%
    5. E. 83.3%
38. How many edges does a cuboid have?
    1. A. 4
    2. B. 6
    3. C. 8
    4. D. 10
    5. E. 12
39. 
    
    Find the area of the plot with corn on a farm of 250 hectares using the pie chart.
    1. A. 48.6
    2. B. 55.3
    3. C. 62.5 ha
    4. D. 83.3 ha
    5. E. 125.0 ha
40. 
    
    What fraction of the farm is planted with pepper?
    1. A. 1/3
    2. B. 1/4
    3. C. 1/5
    4. D. 2/9
    5. E. 7/32

Paper 2: Theory

1. a) Solve 5 – 2x > x + 2, where x is a real number. Illustrate your result on the number line.
   
   b) Find the truth set of the equation: (2(3y - 1) / 3) - ((y + 2) / 3) = 1.
   
   c) Factorize completely: mp + np – mt – nt.
   
   d) Make t the subject of the relation v = u + at.
2. A landlady rented out her house for ₵240,000.00 for one year. During the year, she paid 15% of the rent as income tax, 25% as property tax, and spent ₵10,000.00 on repairs.
   
   a) Calculate the landlady's total expenses.
   
   b) Find the remainder of the rent after the landlady's expenses.
   
   c) Determine the percentage of the rent spent on repairs.
3. a) Using a scale of 2 cm to 1 unit on both axes, draw perpendicular lines OX and OY on a graph sheet.
   
   b) Mark the x-axis from -5 to 5 and the y-axis from -6 to 6.
   
   c) Plot the points A(1, 1), B(4, 3), and C(2, 5) on the graph and join them to form a triangle.
   
   d) Using the y-axis as the mirror line, draw the image A1B1C1 of the triangle ABC such that A → A1, B → B1, and C → C1. Write the coordinates of A1, B1, and C1.
   
   e) Using the x-axis as the mirror line, draw the image A2B2C2 of the triangle ABC such that A → A2, B → B2, and C → C2.
4. The table below gives the frequency distribution of marks obtained in a class test by a group of 64 pupils:
   
   Marks (Out of ten): 2, 3, 4, 5, 6, 7, 8, 9
   
   Frequency: 9, 14, 13, 10, 5, 8, 2, 3
   
   a) Draw a bar chart for the distribution.
   
   b) A pupil is chosen at random from the class. What is the probability that the pupil obtained 7 marks?
5. Using a ruler and a pair of compasses only:
   
   a) Draw |PQ| = 9 cm.
   
   b) Construct a perpendicular to PQ at Q.
   
   c) Construct angle QPS = 60° at the point P on PQ such that |PS| = 6.5 cm.
   
   d) Construct a line parallel to PQ through S. Let the perpendicular through Q and the parallel through S meet at R. Measure |PR|.

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