BECE 1997 Mathematics Past Questions and Answers

Paper 1: Objectives

1. Convert 320 (base five) to a base ten numeral.
   1. A. 25
   2. B. 77
   3. C. 85
   4. D. 86
   5. E. 90
   Answer: C

   320₅ = 3×5² + 2×5¹ + 0×5⁰ = 75 + 10 + 0 = 85.
2. P = {2, 4, 6, 8} and Q = {even counting numbers less than 12}. What is the relationship between P and Q?
   1. A. P=Q
   2. B. P⊂Q
   3. C. P⊆Q
   4. D. Q⊂P
   5. E. P∈Q
   Answer: B

   Q = {2, 4, 6, 8, 10}, so P is a subset of Q.
3. 
   
   In the diagram, P is the set of numbers in the circle, and Q is the set of numbers in the triangle. What is P ∩ Q?
   1. A. {1, 2, 4}
   2. B. {5, 6}
   3. C. {7}
   4. D. {1, 2, 4, 5, 6, 7}
   5. E. {}
   Answer: B

   The intersection is the region where both shapes intersect: {5, 6}.
4. The product 6287 × 543 = 3,413,841. What is the value of 628.7 × 5.43?
   1. A. 3,413,841
   2. B. 342,384.1
   3. C. 34,138.41
   4. D. 3,413.841
   5. E. 341.3841
   Answer: D

   Using decimal adjustment: 628.7 × 5.43 = 3413.841.
5. Express 30 cm as a percentage of 2 m.
   1. A. 0.5%
   2. B. 1.5%
   3. C. 6.7%
   4. D. 15%
   5. E. 66.7%
   Answer: D

   Convert meters to cm: 2 m = 200 cm. So, (30 / 200) × 100% = 15%.
6. 
   
   What solid can be made from the given net?
   1. A. Triangle
   2. B. Rectangular pyramid
   3. C. Triangular prism
   4. D. Rectangular prism
   5. E. Triangular pyramid
   Answer: E

   The base is triangular, so it forms a triangular pyramid.
7. Simplify 3(6b - 9a) + 7(6a - 5b).
   1. A. 17b + 6a
   2. B. -17b + 6a
   3. C. 17b + 48a
   4. D. 15a - 17b
   5. E. 17b - 15a
   Answer: D

   3(6b - 9a) + 7(6a - 5b) = -17b + 15a.
8. Arrange the following fractions in descending order: ⁹⁄₁₆, ⁵⁄₈, 0.62.
   1. A. $\frac{9}{16},0.62,\frac{5}{8}$
   2. B. $0.62,\frac{5}{8},\frac{9}{16}$
   3. C. $\frac{5}{8},\frac{9}{16},0.62$
   4. D. $\frac{5}{8},0.62,\frac{9}{16}$
   5. E. $0.62,\frac{9}{16},\frac{5}{8}$
   Answer: D

   Converted decimals: ⁹⁄₁₆ = 0.5625, ⁵⁄₈ = 0.625. Descending: ⁵⁄₈, 0.62, ⁹⁄₁₆.
9. Find the LCM of 18, 42, and 90.
   1. A. 237
   2. B. 2³×7
   3. C. 2³×5
   4. D. 2³×5×7
   5. E. 2³×3²×5×7
   Answer: E

   The LCM is the product of the highest powers of each prime factor: 2³×3²×5×7.
10. Find the HCF of 18, 42, and 90.
    1. A. 21
    2. B. 18
    3. C. 9
    4. D. 6
    5. E. 3
    Answer: D

    The HCF is the product of the common prime factors in the lowest power: 2×3 = 6.

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11. Simplify $\left(\begin{array}{c}4\\ 5\end{array}\right)+\left(\begin{array}{c}-2\\ 2\end{array}\right)+\left(\begin{array}{c}1\\ 6\end{array}\right)$.
    1. A. $\left(\begin{array}{c}2\\ 13\end{array}\right)$
    2. B. $\left(\begin{array}{c}3\\ 13\end{array}\right)$
    3. C. $\left(\begin{array}{c}5\\ 13\end{array}\right)$
    4. D. $\left(\begin{array}{c}6\\ 13\end{array}\right)$
    5. E. $\left(\begin{array}{c}7\\ 13\end{array}\right)$
12. If R = ½(a + b)k, find k in terms of R, a, and b.
    1. A. a + b / 2R
    2. B. 2R / (a + b)
    3. C. 2R - a / b
    4. D. 2R - b / a
    5. E. R / 2(a + b)
13. 
    
    In the figure, triangle M′ON′ is an enlargement of triangle MON with centre O. Find the scale factor of the enlargement.
    1. A. 9
    2. B. 3
    3. C. 2
    4. D. -2
    5. E. -3
14. 
    
    Find OM if the scale factor is ⁶⁄₃.
    1. A. 9
    2. B. 6
    3. C. 4.5
    4. D. 3
    5. E. 1.5
15. Find the image of the point (6, 3) when translated by the vector $\left(\begin{array}{c}-4\\ -1\end{array}\right)$.
    1. A. (-2, -2)
    2. B. (2, -2)
    3. C. (-2, 2)
    4. D. (2, 2)
    5. E. (10, 4)
16. A student spends $\frac{17}{35}$ of his pocket money on transport and fruits. He spends $\frac{5}{6}$ of the remainder on sweets. What fraction of his pocket money does he spend on sweets?
    1. A. $\frac{4}{7}$
    2. B. $\frac{3}{7}$
    3. C. $\frac{17}{35}$
    4. D. $\frac{18}{35}$
    5. E. $\frac{17}{42}$
17. 
    
    In the diagram, PQ is parallel to RS and |PR| = |QR|. What is angle a?
    1. A. 29°
    2. B. 46°
    3. C. 75°
    4. D. 88°
    5. E. 134°
18. 
    
    In the diagram, PQ is parallel to RS and |PR| = |QR|. Find angle b.
    1. A. 29°
    2. B. 46°
    3. C. 88°
    4. D. 92°
    5. E. 105°
19. 
    
    In the diagram, PQ is parallel to RS and |PR| = |QR|. Find angle c.
    1. A. 29°
    2. B. 46°
    3. C. 75°
    4. D. 88°
    5. E. 105°
20. If p = 7, q = 5 and r = 3, find the value of p² + q - r³.
    1. A. 10
    2. B. 27
    3. C. 51
    4. D. 57
    5. E. 81
21. Simplify $35x^5{y}^3÷7x{y}^2$
    1. A. $5x^6{y}^5$
    2. B. $5x^{4}y$
    3. C. $5x^{6}y$
    4. D. $5x^4{y}^5$
    5. E. $5x^{5}y$
22. The sum of two numbers is 240. If one of them is y, find the other number.
    1. A. 120y
    2. B. 240 + y
    3. C. 240 - y
    4. D. 240y
    5. E. 240/y
23. Make n the subject of the relation 2n + 5 = 7a
    1. A. n = 1/2 (7a + 5)
    2. B. n = 1/2 (7a - 5)
    3. C. n = 2(7a + 5)
    4. D. n = 2(7a - 5)
    5. E. n = 7a - 5
24. 
    
    Find the bearing of Q from P in the diagram above.
    1. A. 030°
    2. B. 060°
    3. C. 070°
    4. D. 090°
    5. E. 150°
25. 
    
    Find the area of the figure above, which consists of a rectangle of 8 cm by 6 cm and a triangle with a base of 6 cm and a height of 3 cm.
    1. A. 33 cm²
    2. B. 48 cm²
    3. C. 51 cm²
    4. D. 57 cm²
    5. E. 66 cm²
26. The marks obtained by 10 boys in a test are 0, 1, 3, 3, 5, 7, 8, 9, 9, 9. Find the median score.
    1. A. 3
    2. B. 5
    3. C. 6
    4. D. 7
    5. E. 8
27. Calculate the mean score of the marks: 0, 1, 3, 3, 5, 7, 8, 9, 9, 9.
    1. A. 4.4
    2. B. 5.4
    3. C. 6.0
    4. D. 6.4
    5. E. 9.0
28. What is the probability that a boy chosen at random scored 3?
    1. A. 1/2
    2. B. 1/18
    3. C. 1/10
    4. D. 1/5
    5. E. 1/3
29. Express 57 in base two (binary) numeral.
    1. A. 101011₂
    2. B. 100111₂
    3. C. 110101₂
    4. D. 110111₂
    5. E. 111001₂
30. The scale of a map is 1 : 100,000. What is the distance (in km) between two towns 4 cm apart on the map?
    1. A. 0.04
    2. B. 0.4
    3. C. 4.0
    4. D. 40
    5. E. 400
31. If 22% of a rope is 55 m long, find the full length of the rope.
    1. A. 12.1 m
    2. B. 25 m
    3. C. 121 m
    4. D. 250 m
    5. E. 2500 m
32. Adwoa and Ama share an amount of C6,000.00 in the ratio 3 : 2. Find Adwoa's share.
    1. A. C2,000.00
    2. B. C2,400.00
    3. C. C3,000.00
    4. D. C3,600.00
    5. E. C4,000.00
33. Find the truth set of 5x - 8 < 2x + 4.
    1. A. {x > 4}
    2. B. {x > -4}
    3. C. {x < 4}
    4. D. {x < -4}
    5. E. {x = 4}
34. 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
    5. E. 2464 cm²
35. If $\mathbf{a}=\left(\begin{array}{c}3\\ 3\end{array}\right)$ and $\mathbf{b}=\left(\begin{array}{c}5\\ -5\end{array}\right)$, find $\mathbf{a}+\mathbf{b}$.
    1. A. $\left(\begin{array}{c}2\\ 8\end{array}\right)$
    2. B. $\left(\begin{array}{c}8\\ 8\end{array}\right)$
    3. C. $\left(\begin{array}{c}2\\ 2\end{array}\right)$
    4. D. $\left(\begin{array}{c}8\\ -8\end{array}\right)$
    5. E. $\left(\begin{array}{c}8\\ -2\end{array}\right)$

36. x	0	1	2	3	4
    y	0	1	4	9	16

    
    What is the rule for the mapping above?
    1. A. x → x + 3
    2. B. x → x + 1
    3. C. x → x - 1
    4. D. x → x + 2
    5. E. x → x²
37. If 50 oranges cost C2,500.00 how many oranges can be bought for C15,000.00?
    1. A. 3
    2. B. 30
    3. C. 60
    4. D. 300
    5. E. 360
38. A farmer has 1853 pineapple suckers. He plants 17 pineapples in a row. How many rows can he plant?
    1. A. 17
    2. B. 19
    3. C. 91
    4. D. 109
    5. E. 190
39. 
    
    In triangle PQR, [PQ = QR], and angle PQR = 90°. Find x.
    1. A. 30°
    2. B. 45°
    3. C. 60°
    4. D. 90°
    5. E. 180°
40. If a × b × c = 1197 and a = 21, b = 3, find c.
    1. A. 19
    2. B. 49.9
    3. C. 57
    4. D. 63
    5. E. 399

Paper 2: Theory

1. a) If p = 4, a = 16, b = -5 and c = 3, evaluate $p^2-\frac{a-b}{c}$.
   
   b) Solve the inequality $5x-3(x-1)\ge 39$. Illustrate your answer on the number line.
   
   c) If $\mathbf{x}=\left(\begin{array}{c}-3\\ 2\end{array}\right)$ and $\mathbf{y}=\left(\begin{array}{c}4\\ -1\end{array}\right)$, find (i) $\mathbf{x}+2\mathbf{y}$; (ii) $3\mathbf{x}-\mathbf{y}$.
2. Using a ruler and a pair of compasses only:
   
   a) (i) Construct a triangle ABC such that |AB| = 8 cm, ∠ABC = 60°, and |BC| = 8 cm.
   
   (ii) What type of triangle is triangle ABC?
   
   b) Construct the bisector of angle BAC to meet BC at D. Measure |AD|.
   
   c) Construct the perpendicular bisector of |BA| to meet |AD| at O.
   
   d) Using O as the center and radius OD, draw a circle to touch the three sides of the triangle.
3. a) If 2y - 5x + 10 = 0, find:
   
   (i) y, when x = 2
   
   (ii) x, when y = 5
   
   b) (i) Using a scale of 2 cm to 1 unit on both axes, draw two perpendicular lines OX and OY on a graph sheet.
   
   (ii) Mark the x-axis from -5 to 5 and the y-axis from -6 to 6.
   
   (iii) Plot the points A(0, -5) and B(4, 5). Join AB using a ruler.
   
   (iv) Find the gradient of the line AB.
   
   (v) Measure the acute angle that the line AB makes with the x-axis using a protractor.
4. a) The table below shows the distribution of the ages (in years) of children treated in a clinic in a day:
   
   | Age (years) | Frequency |
   
   |-------------|-----------|
   
   | 1 | 6 |
   
   | 2 | 4 |
   
   | 3 | 2 |
   
   | 4 | 3 |
   
   | 5 | 5 |
   
   Find:
   
   (i) The mean age
   
   (ii) The modal age
   
   b) Draw a bar chart for the distribution.
5. a) The volume of a cylinder is 220 cm³. The radius of the cross-section is 2.5 cm. Find the height of the cylinder. (Take π = 22/7).
   
   b) Each interior angle of a regular polygon is 140°. How many sides does it have?

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