BECE 2004 Mathematics Past Questions and Answers

Paper 1: Objectives

1. If the set A = {1, 2, 3, 4, 5} and the set B = {2, 4, 6}, find the number of members in the set A ∪ B.
   1. A. 8
   2. B. 6
   3. C. 5
   4. D. 2
   Answer: B

   A ∪ B = {1, 2, 3, 4, 5, 6}. The number of members in A ∪ B is 6.
2. How many faces does a cuboid have?
   1. A. 3
   2. B. 4
   3. C. 5
   4. D. 6
   Answer: D

   
   
   A cuboid has 6 faces.
3. Evaluate 0.036 ÷ 0.02.
   1. A. 0.018
   2. B. 0.18
   3. C. 1.8
   4. D. 18.0
   Answer: C

   0.036 ÷ 0.02 = 1.8.
4. The angle formed by one complete revolution is equivalent to:
   1. A. one right angle
   2. B. two right angles
   3. C. three right angles
   4. D. four right angles
   Answer: D

   One complete revolution is 360°, which is four right angles (4 × 90° = 360°).
5. If the set P = {1, 2, 3, 4, 5}, which of the following statements best describes P?
   1. A. Set of whole numbers up to 6
   2. B. Set of counting numbers less than 6
   3. C. Set of counting numbers greater than 6
   4. D. Set of integers less than 6
   Answer: B

   The set P contains counting numbers less than 6.
6. Which of the following numbers is the next prime number greater than 23?
   1. A. 17
   2. B. 24
   3. C. 25
   4. D. 29
   Answer: D

   29 is the next prime number greater than 23.
7. Simplify -35 - (-15) + (-30).
   1. A. 17
   2. B. -50
   3. C. 50
   4. D. -20
   Answer: B

   -35 - (-15) + (-30) = -35 + 15 - 30 = -50.
8. Round 78910 to the nearest thousand.
   1. A. 70,000
   2. B. 78,000
   3. C. 79,000
   4. D. 80,000
   Answer: C

   Rounding 78910 to the nearest thousand gives 79,000.
9. Simplify $\frac{2^{10}\times 3^2}{3^6\times 2^8}$
   1. A. $\frac{2^2}{3^4}$
   2. B. $\frac{3^4}{2^2}$
   3. C. $3^3\times 2^4$
   4. D. $\frac{2^4}{3^4}$
   Answer: A

   $\frac{2^{10}\times 3^2}{3^6\times 2^8}=2^{10-8}\times 3^{2-6}=\frac{2^2}{3^4}$
10. 
    
    Which of the following inequalities is represented on the number line?
    1. A. -2 < x < 3
    2. B. -2 ≤ x < 3
    3. C. -2 ≤ x ≤ 3
    4. D. -2 < x ≤ 3
    Answer: D

    The circle at -2 is not shaded (<) and the circle at 3 is shaded (≤), so -2 < x ≤ 3.

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11. Factorize completely the expression 4xy - 16x + 10y - 40.
    1. A. (y + 4)(4x - 10)
    2. B. (y - 4)(4x + 10)
    3. C. (4 - y)(10 - 4x)
    4. D. (y + 4)(4x + 10)
12. What is the image of 2 in the mapping x ↦ 2x + 5?
    1. A. 7
    2. B. 9
    3. C. 12
    4. D. 20
13. Simplify 3a⁵ × 4ab.
    1. A. 12a⁶b
    2. B. 7a⁵b
    3. C. 4a⁵b
    4. D. 7a⁶b
14. Find the solution set of 2x + 1 < 5 in the domain {-1, 0, 1, 2, 3}.
    1. A. {-1, 1, 3}
    2. B. {-1, 0, 1}
    3. C. {-1, 1, 2}
    4. D. {0, 1, 2}
15. Find the highest common factor (HCF) of 48, 60, and 96.
    1. A. 12
    2. B. 24
    3. C. 36
    4. D. 48
16. P = {odd numbers between 20 and 30} and Q = {23, 29}. Which of the following is true?
    1. A. P ⊆ Q
    2. B. Q ⊆ P
    3. C. P = Q
    4. D. P ≠ Q
17. Find the rule for the following mapping: X: {0, 1, 2, 3, 4} -> Y: {-1, 1, 3, 5, 7}.
    1. A. y = 2x + 1
    2. B. y = 2x - 1
    3. C. y = x - 1
    4. D. y = x + 1
18. Simplify (2a⁴)(3b)(2a⁻¹b²).
    1. A. 6a⁵b³
    2. B. 12a³b³
    3. C. 6ab
    4. D. 4a⁶b
19. 
    
    Find the value of x in a pentagon where the sum of the angles is 540° and angles are 2x, 4x, x, 5x, and 3x.
    1. A. 12°
    2. B. 36°
    3. C. 60°
    4. D. 72°
20. An article costs C60,000.00. The price was increased by 10%. Find the new price.
    1. A. €54,000.00
    2. B. €61,000.00
    3. C. €66,000.00
    4. D. €70,000.00
21. Solve for x in the equation 15 - 2x = 6.
    1. A. -10.5
    2. B. --4.5
    3. C. 4.5
    4. D. 10.5
22. The population of Ghana was 5,000,000 in 1957. The population in 1998 was estimated to be 17,000,000. Find the percentage increase in population from 1957 to 1998.
    1. A. 2.4%
    2. B. 24%
    3. C. 240%
    4. D. 2400%
23. The angles of a triangle are in the ratio 3 : 2 : 1. Find the value of the smallest angle.
    1. A. 30°
    2. B. 45°
    3. C. 60°
    4. D. 90°
24. Find the least common multiple (LCM) of 4, 6 and 10.
    1. A. 10
    2. B. 24
    3. C. 30
    4. D. 60
25. Convert 134 (base-5) to a base-10 numeral.
    1. A. 16
    2. B. 40
    3. C. 44
    4. D. 220
26. A circle has radius 7 cm; find its area. [Take π = 22/7]
    1. A. 22 cm²
    2. B. 44 cm²
    3. C. 145 cm²
    4. D. 154 cm²
27. Simplify $\frac{1}{2}-\frac{2}{3}+\frac{3}{4}$
    1. A. $\frac{11}{12}$
    2. B. $\frac{7}{12}$
    3. C. $\frac{1}{6}$
    4. D. $\frac{5}{12}$
28. Solve for x, if $\frac{1}{2}x-4x>20$
    1. A. $x<-13\frac{1}{3}$
    2. B. $x<-5\frac{5}{7}$
    3. C. $x>5\frac{5}{7}$
    4. D. $x>13\frac{1}{3}$
29. Which of the following is equivalent to $2^2\times 6^3$?
    1. A. $2^6\times 3^3$
    2. B. $2^5\times 3^3$
    3. C. $2^4\times 3$
    4. D. $2^3\times 3^3$
30. The volume of water in a rectangular tank is 30 cm³. The length of the tank is 5 cm and its breadth is 2 cm. Calculate the depth of water in the tank.
    1. A. 4.0 cm
    2. B. 3.0 cm
    3. C. 5.0 cm
    4. D. 6.0 cm
31. The temperatures recorded in 10 cities in Europe were -4, 5, 2, 0, -6, -4, 3, -6, -4, and 7. Find the modal temperature.
    1. A. 2°C
    2. B. -4°C
    3. C. 0°C
    4. D. 6°C
32. The ratio of the ages of two sisters is 4:3. The elder sister is 3 years older than the younger one. How old is the younger sister?
    1. A. 9 years
    2. B. 12 years
    3. C. 15 years
    4. D. 18 years
33. If n² + 4 = 40, find n.
    1. A. 6
    2. B. 18
    3. C. 22
    4. D. 44
34. An angle which is more than 90° but less than 180° is called?
    1. A. an acute angle
    2. B. a right angle
    3. C. an obtuse angle
    4. D. a reflex angle
35. Arrange the following fractions in ascending order: 4/7, 1/4, 4/9.
    1. A. 1/4 < 4/9 < 4/7
    2. B. 4/9 < 1/4 < 4/7
    3. C. 4/7 < 4/9 < 1/4
    4. D. 4/7 < 1/4 < 4/9
36. Prices of items in a shop were reduced by 10% during a sale. If a customer bought an electric fan for C81,000.00, what was its original price?
    1. A. €72,900.00
    2. B. C73,900.00
    3. C. €89,100.00
    4. D. €90,000.00
37. The marks scored by 8 pupils in a science test are: 3, 7, 8, 8, 5, 4, 8, 4. What is the median mark?
    1. A. 5
    2. B. 6
    3. C. 7
    4. D. 8
38. The marks scored by 8 pupils in a science test are: 3, 7, 8, 8, 5, 4, 8, 4. What is the probability that a pupil chosen at random scored 4 marks?
    1. A. 1/2
    2. B. 1/4
    3. C. 1/8
    4. D. 1/47
39. If $y=k+a{x}^2$, find y when $k=\frac{14}{5}$, $a=\frac{4}{5}$ and $x=2$.
    1. A. 30
    2. B. $7\frac{3}{5}$
    3. C. 6
    4. D. 4
40. Which of the following dimensions of a triangle form the sides of a right angled triangle?
    1. A. 3cm, 4cm, 6cm
    2. B. 3cm, 5cm, 7cm
    3. C. 5cm, 12cm, 13cm
    4. D. 5cm, 13cm, 17cm

Paper 2: Theory

1. a) (i) Factorize completely the expression 2xy - 8x + 3y - 12.
   
   (ii) Evaluate the expression in (i) if x = 5 and y = 7.
   
   b) Make q the subject of the equation t = (q/p) + (1/p).
   
   c) Simplify (7/4) - (3/8) + (5/2).
2. a) Ama and Kofi shared the profit earned from their business in the ratio 3:4. The profit was ₵1,743,000.00.
   
   (i) Find how much of the profit each person received.
   
   (ii) Kofi lent out his share of the profit at a rate of 20% per annum for 2 years. Find the interest on his share.
   
   (iii) What will be Kofi's total amount at the end of the 2 years?
   
   b) Change 243₅ to a base ten numeral.
3. a) Using a ruler and a pair of compasses only,
   
   (i) Construct triangle PQR such that |PQ| = 8 cm, angle QPR = 60° and angle PQR = 45°.
   
   (ii) Measure |QR|.
   
   b) A rectangular water tank has length 60 cm, width 45 cm, and height 50 cm.
   
   (i) Find the total surface area of the tank when closed.
   
   (ii) Find the volume of the tank.
   
   (iii) Find the height of the water in the tank if the tank contains 81,000 cm³ of water.
4. a) A car runs on average at 45 km for 5 liters of fuel. Calculate how many liters of fuel are required for a journey of 117 km.
   
   b) (i) Solve for x in the inequality 2x + 5 < 8 ⅔.
   
   (ii) Illustrate the solution on the number line.
   
   c) A factory increased its production by 22 ½% and produced 49,000 tonnes. How many tonnes was it producing before?
5. a) The following are the ages in years of members of a group: 8, 11, 8, 10, 6, 7, 3x, 11, 11. If the mean age is 9 years, find:
   
   (i) x
   
   (ii) The modal age
   
   (iii) The median age.
   
   b) Draw a bar chart for the distribution.

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