BECE 1998 Mathematics Past Questions and Answers

Paper 1: Objectives

1. Two sets which have no common members are known as ________.
   1. A. equal sets
   2. B. equivalent sets
   3. C. empty sets
   4. D. disjoint sets
   5. E. union
   Answer: D
2. P = {0, 2, 4, 6} and Q = {1, 2, 4, 5}. Find P ∩ Q.
   1. A. {0,6}
   2. B. {2,4}
   3. C. {0,4}
   4. D. {0,2,6}
   5. E. {0,1,2,4,5}
   Answer: B

   Intersection (∩) are elements that can be found in both sets, so P ∩ Q = {2, 4}.
3. Evaluate √((4 − 1) − (5 − 6)).
   1. A. -4.0
   2. B. 1.0
   3. C. 2.0
   4. D. 3.0
   5. E. 4.0
   Answer: C

   Simplifying inside the brackets first: √((4 - 1) − (5 - 6)) = √(3 + 1) = √4 = 2.
4. Find the highest (greatest) common factor of 35 and 70.
   1. A. 5
   2. B. 7
   3. C. 10
   4. D. 35
   5. E. 70
   Answer: D

   The HCF of 35 and 70 is 35 (using the prime factors: 5 × 7 for 35 and 2 × 5 × 7 for 70).
5. Write 1101101₂ in base ten.
   1. A. 31
   2. B. 43
   3. C. 108
   4. D. 109
   5. E. 218
   Answer: D

   1101101₂ = 1×2⁶ + 1×2⁵ + 0×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 109.
6. State the property used in the statement: p(q + r) = pq + pr.
   1. A. Associative
   2. B. Commutative
   3. C. Distributive
   4. D. Identity
   5. E. Universal
   Answer: C

   The distributive property states that multiplying the sum of two or more addends by a number is the same as multiplying each addend individually by the number and then adding the products together.
7. If n² + 1 = 50, find n.
   1. A. 7
   2. B. 24.5
   3. C. 25
   4. D. 49
   5. E. 57
   Answer: A

   n² = 50 - 1 = 49. Taking the square root, n = √49 = 7.
8. Evaluate 0.63 × 0.70 ÷ 9.00.
   1. A. 0.0049
   2. B. 0.049
   3. C. 0.49
   4. D. 4.9
   5. E. 49
   Answer: B

   0.63 × 0.70 ÷ 9.00 = 0.049 after removing trailing zeros and dividing.
9. In the relation $\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}$, if $R_1=1$ and $R_2=3$, find R.
   1. A. 1/2
   2. B. 2/3
   3. C. 3/4
   4. D. 3/2
   5. E. 4/3
   Answer: C

   $\frac{1}{R}=\frac{1}{1}+\frac{1}{3}=\frac{4}{3}$, so $R=\frac{3}{4}$.
10. Arrange the following from the highest to the lowest: $\frac{2}{3},-9,\frac{3}{5}$ and 0.
    1. A. $-9,\frac{3}{5},\frac{2}{3}$
    2. B. $-9,0,\frac{3}{5},\frac{2}{3}$
    3. C. $\frac{3}{5},\frac{2}{3},0,-9$
    4. D. $\frac{3}{5},\frac{2}{3},-9,0$
    5. E. $\frac{2}{3},\frac{3}{5},0,-9$
    Answer: E

    $\frac{2}{3}=\frac{10}{15}>\frac{3}{5}=\frac{9}{15}>0>-9$, so the order is $\frac{2}{3},\frac{3}{5},0,-9$.

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11. The total number of goals scored each month by a football team are: 3, 4, 8, 2, 4, 6, 4, 8, 7 and 6. What is the mode?
    1. A. 2
    2. B. 4
    3. C. 5
    4. D. 6
    5. E. 8
12. A trader sold 90 oranges at 3 for ₵50.00. How much did she get from selling all the oranges?
    1. A. ₵1,500.00
    2. B. ₵4,500.00
    3. C. ₵6,000.00
    4. D. ₵15,000.00
    5. E. ₵45,000.00
13. A man bought a car for ₵5.5 million and sold it for ₵6.5 million. Find the percentage gain.
    1. A. 1.54%
    2. B. 1.82%
    3. C. 15.38%
    4. D. 18.18%
    5. E. 84.44%
14. On a map, two towns P and Q are 15.5 cm apart. The scale of the map is 1 cm : 4 km. Calculate the actual distance between P and Q.
    1. A. 15.5 km
    2. B. 31 km
    3. C. 46 km
    4. D. 60 km
    5. E. 62 km
15. Expand the expression 2(3a + 2b).
    1. A. 6a + 2b
    2. B. 5a + 4b
    3. C. 6a + 4b
    4. D. 10ab
    5. E. 12ab
16. Mansah obtained 150 marks out of 240 marks in an English test. What was her percentage score?
    1. A. 33.33%
    2. B. 37.5%
    3. C. 41.67%
    4. D. 62.5%
    5. E. 79.1%
17. The marks obtained by six boys in a test are: 14, 20, 25, 15, 28, and 16. Find the mean mark.
    1. A. 19.67
    2. B. 22.00
    3. C. 23.20
    4. D. 26.40
    5. E. 28.00
18. Which of the following is equivalent to 2³ × 3²?
    1. A. 2³⁰
    2. B. 2³ × 3³
    3. C. 2³ × 3⁰
    4. D. 2³
    5. E. 2³ × 3²
19. Kwaku had 300 mangoes. He sold 240 of them. What is the percentage of mangoes left?
    1. A. 8%
    2. B. 20%
    3. C. 25%
    4. D. 26%
    5. E. 80%
20. A bag contains 5 black and 6 white balls. What is the probability of picking a white ball?
    1. A. ¹⁄₁₁
    2. B. ¹⁄₆
    3. C. ¹⁄₅
    4. D. ⁵⁄₁₁
    5. E. ⁶⁄₁₁
21. Solve for h in the equation 15 − 2h = 6
    1. A. -10.5
    2. B. -9.0
    3. C. -4.5
    4. D. 4.5
    5. E. 10.5
22. What is the image of 3 in the mapping x → 3x + 7?
    1. A. 10
    2. B. 13
    3. C. 16
    4. D. 24
    5. E. 34
23. How many faces has a closed cylindrical object?
    1. A. 1
    2. B. 2
    3. C. 3
    4. D. 4
    5. E. 34
24. 
    
    Find the gradient of the line AB
    1. A. 1
    2. B. 2
    3. C. 3
    4. D. 4
    5. E. 5
25. 
    
    Find the coordinates of the point at which the line cuts the x-axis.
    1. A. (1, 0)
    2. B. (0, 1)
    3. C. (-1, 0)
    4. D. (0, -1)
    5. E. (0, 0)
26. A man deposited an amount of C50,000.00 at a bank for 2 years at a rate of 20%. Find the simple interest.
    1. A. C1,000.00
    2. B. C2,000.00
    3. C. C10,000.00
    4. D. C20,000.00
    5. E. C200,000.00
27. Kofi received C800.00 commission on sales made. This commission is 20% of his sales. Calculate his total sales for the day.
    1. A. C1,200.00
    2. B. C2,400.00
    3. C. C3,200.00
    4. D. C4,000.00
    5. E. C4,800.00
28. 
    
    Calculate the bearing of town P from town K.
    1. A. 005°
    2. B. 085°
    3. C. 095°
    4. D. 265°
    5. E. 275°
29. 
    
    In the diagram below, PQR is an isosceles triangle with PQ = PR and ∠QPR = 40°. Find angle PRS.
    1. A. 40°
    2. B. 70°
    3. C. 100°
    4. D. 110°
    5. E. 140°
30. Factorize completely the expression 2xy - 8x + 5y - 20.
    1. A. (2x + 5)(y - 4)
    2. B. (2x - 5)(y + 4)
    3. C. (2x - 5)(y - 4)
    4. D. (x + 5)(y - 4)
    5. E. (2x + 5)(y + 4)
31. Ama is facing east. Through how many degrees should she turn clockwise to face north?
    1. A. 90°
    2. B. 135°
    3. C. 180°
    4. D. 225°
    5. E. 270°
32. 
    
    In triangle RST, ∠RST is 90°, [RS]= 4 cm, [ST]= 3 cm. What is the length of RT?
    1. A. 2 cm
    2. B. 3 cm
    3. C. 4 cm
    4. D. 5 cm
    5. E. 7 cm
33. How many lines of symmetry does a rhombus have?
    1. A. 2
    2. B. 3
    3. C. 4
    4. D. 5
    5. E. 6
34. Given that $\mathbf{a}=\left(\begin{array}{c}-3\\ 4\end{array}\right)$ and $\mathbf{b}=\left(\begin{array}{c}1\\ 2\end{array}\right)$, find $\mathbf{b}-\mathbf{a}$.
    1. A. $\left(\begin{array}{c}-2\\ 6\end{array}\right)$
    2. B. $\left(\begin{array}{c}-4\\ 2\end{array}\right)$
    3. C. $\left(\begin{array}{c}-3\\ 8\end{array}\right)$
    4. D. $\left(\begin{array}{c}-2\\ 2\end{array}\right)$
    5. E. $\left(\begin{array}{c}4\\ -2\end{array}\right)$
35. If $\mathbf{u}=\left(\begin{array}{c}3\\ -1\end{array}\right)$ and $\mathbf{v}=\left(\begin{array}{c}6\\ 1\end{array}\right)$, find $2\mathbf{u}+\mathbf{v}$.
    1. A. $\left(\begin{array}{c}12\\ 0\end{array}\right)$
    2. B. $\left(\begin{array}{c}12\\ -1\end{array}\right)$
    3. C. $\left(\begin{array}{c}6\\ 1\end{array}\right)$
    4. D. $\left(\begin{array}{c}6\\ 0\end{array}\right)$
    5. E. $\left(\begin{array}{c}6\\ -1\end{array}\right)$
36. The volume of water in a cuboid is 9m³. The length of the cuboid is 3 m, and the breadth is 2 m. Calculate the depth of water in the cuboid.
    1. A. 0.15 m
    2. B. 0.18 m
    3. C. 1.5 m
    4. D. 1.8 m
    5. E. 6.0 m
37. 
    
    In the diagram, AEFG is an enlargement of rectangle ABCD with AB = 5 cm and AE = 15 cm. What is the scale factor?
    1. A. 1/3
    2. B. 2/3
    3. C. 2
    4. D. 3
    5. E. 10
38. 
    
    Calculate the area of the shaded region in a circle with angle 300°.
    1. A. πr²
    2. B. 5πr²
    3. C. 3πr²
    4. D. (5/6)πr²
    5. E. (1/2)πr²
39. Which best describes: 'The locus of points 6 cm from a fixed point O?'
    1. A. A parallel line 6 cm from O
    2. B. A vertical line 6 cm from point O
    3. C. A horizontal line 6 cm from point O
    4. D. An equilateral triangle of side 6 cm
    5. E. A circle with centre O and radius 6 cm
40. 
    
    In trapezium OPQR, PQ is parallel to OR, |PQ| = 30 cm and the height is 20 cm. The perpendiculars from P and Q divide OR into parts of 20 cm, 30 cm and 16 cm. What is the area of the trapezium?
    1. A. 460 cm²
    2. B. 600 cm²
    3. C. 920 cm²
    4. D. 960 cm²
    5. E. 1000 cm²

Paper 2: Theory

1. (a) Simplify the expression 3 + 6xy - 3 + 4 + 8xy + 2
   
   (b) (i) Solve 3x - 9 ≥ 12(x - 3)
   
   (ii) Illustrate your answer on the number line.
   
   (c) If p = 7, a = 16, b = 4, and c = 3, evaluate p × (a²b ÷ c).
2. (a) Using a ruler and a pair of compasses only:
   
   (i) Construct a triangle PQR such that |PQ| = 8 cm, ∠RPQ = 90°, and ∠PQR = 30°. Measure |RQ|.
   
   (ii) Construct the perpendicular bisector (mediator) of RQ. Let it meet RQ at O.
   
   (b) With O as center and radius OP, draw a circle. Measure |OP|.
   
   (c) What is the special name for the chord RQ?
3. (a) A man traveled from Bakwa to Pabam. The distance between the two towns is 510 km. At Pabam, he covered an additional 40 km on official duties. He returned to Bakwa the next day.
   
   (i) Find the total distance covered by the man.
   
   (ii) If the car used one liter of petrol to cover 20 km, find the amount of petrol used for the whole journey.
   
   (iii) If a liter of petrol costs ₵522.00, calculate the total cost of petrol used for the whole journey.
   
   (b) A woman sold an article for ₵200,000.00. She made a profit of 25%. Find the cost price of the article.
4. 
   
   (a) The pie chart shows angles representing the number of candidates who applied for admission into four programmes at a senior secondary school: Technical 64°, General Programme 156°, Business (a right angle) and Vocational x°. The total number of applicants was 1080. Find:
   
   (i) the angle x° representing the Vocational programme.
   
   (ii) the number of candidates who applied for the Business programme.
   
   (iii) correct to the nearest whole number, the percentage of the number of applicants who applied for the General Programme.
   
   (b) The data below shows the distribution of the masses of pupils in a school. On a graph paper, draw a bar chart for the distribution.
   

   Mass (kg)	19	20	21	22	23	24
   Frequency	5	9	19	25	18	4

5. (a) Using a scale of 2 cm to 2 units on both axes, draw two perpendicular axes OX and OY on a graph sheet. Mark the x-axis from -8 to 8 and the y-axis from -8 to 8.
   
   (i) Plot P(-2, 3) and Q(6, 4). Join PQ.
   
   (ii) Draw the image P'Q' of PQ under an anticlockwise rotation through 90° about the origin, where P → P' and Q → Q'. Indicate clearly all the coordinates.
   
   (iii) Draw the image P"Q" of PQ under a clockwise rotation through 90° about the origin where P → P" and Q → Q". Indicate clearly all the coordinates.
   
   (b) The base radius of a closed cylinder is 4 m. The height of the cylinder is 7 m. Calculate its total surface area. [Take π = 22/7].

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