BECE 2003 Mathematics Past Questions and Answers

Paper 1: Objectives

1. 𝑃 = {3, 6, 9, 12, 15}. Which of the following best describes the set 𝑃?
   1. A. The set of multiples of 3 less than 18
   2. B. The set of multiples of 3
   3. C. The set of odd numbers
   4. D. The set of odd numbers less than 16
   Answer: A

   The elements of 𝑃 are multiples of 3 that are less than 18.
2. If 𝑄 = {2, 4, 6, 7, 8, 10} and 𝑅 = {3, 5, 7, 9, 10, 11}, find 𝑄 ∩ 𝑅.
   1. A. {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
   2. B. {7, 10}
   3. C. {10}
   4. D. {7}
   Answer: B

   Intersection (∩) includes elements in both sets: 𝑄 ∩ 𝑅 = {7, 10}.
3. 
   
   Find the set of missing numbers on the number line above.
   1. A. {−21, −6, 11}
   2. B. {−21, −10, 11}
   3. C. {−25, −6, 15}
   4. D. {−25, −10, 15}
   Answer: D

   The missing numbers fitting the pattern on the number line are {−25, −10, 15}.
4. If 7.2 and 7.9 are two points on a number line, find the number in the middle of these points.
   1. A. 7.35
   2. B. 7.45
   3. C. 7.55
   4. D. 7.65
   Answer: C

   The midpoint is the average: (7.2 + 7.9) ÷ 2 = 7.55.
5. Find the least common multiple (𝐿C𝑀) of 12 and 20.
   1. A. 24
   2. B. 48
   3. C. 60
   4. D. 80
   Answer: C

   Prime factors of 12 (2² × 3) and 20 (2² × 5); 𝐿C𝑀 = 2² × 3 × 5 = 60.
6. Express 72 as a product of prime factors.
   1. A. 2 × 3
   2. B. 2² × 3²
   3. C. 2² × 3³
   4. D. 2³ × 3²
   Answer: D

   Prime factors of 72 = 2 × 2 × 2 × 3 × 3, or 2³ × 3².
7. If 3𝑡 - 2(𝑡 + 12) = 11, find the value of 𝑡.
   1. A. -35
   2. B. -13
   3. C. 13
   4. D. 35
   Answer: D

   Solving: 3𝑡 - 2(𝑡 + 12) = 11; simplifies to 𝑡 = 35.
8. What is the value of the digit 8 in the number 78000?
   1. A. 8 ten thousands
   2. B. 8 thousands
   3. C. 8 hundreds
   4. D. 8 tens
   Answer: B

   In 78000, the value of 8 is 8 thousand.
9. Find the product of 17 and 121.
   1. A. 968
   2. B. 1751
   3. C. 2057
   4. D. 8591
   Answer: C

   17 × 121 = 2057.
10. Araba owes ₵550,000 at the bank. She goes to pay ₵150,000. How much does Araba owe the bank now?
    1. A. ₵700,000
    2. B. ₵600,000
    3. C. ₵500,000
    4. D. ₵400,000
    Answer: D

    Remaining amount = ₵550,000 - ₵150,000 = ₵400,000.

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11. Evaluate 37 × 7 ÷ (100 × 10).
    1. A. 0.259
    2. B. 2.590
    3. C. 25.900
    4. D. 259.000
12. Express 1.25 as a mixed fraction in its lowest form.
    1. A. $1\frac{1}{25}$
    2. B. $1\frac{4}{25}$
    3. C. $1\frac{1}{4}$
    4. D. $\frac{3}{4}$
13. The total number of match sticks in 6 match boxes was 270. Find the total number of sticks in 20 similar boxes.
    1. A. 710
    2. B. 800
    3. C. 810
    4. D. 900
14. A car travels at an average speed of 45 km per hour. What distance does it cover in 12 hours?
    1. A. 450 km
    2. B. 480 km
    3. C. 500 km
    4. D. 540 km
15. Calculate the simple interest on ₵130,000 for 2½ years at 12% per annum.
    1. A. ₵78,000
    2. B. ₵39,000
    3. C. ₵36,000
    4. D. ₵31,200
16. Express ⅖ as a percentage.
    1. A. 20%
    2. B. 25%
    3. C. 40%
    4. D. 80%
17. Kwame gets a commission of 20% on bread sold. In one week, Kwame's commission was ₵45,000. How much bread did he sell during that week?
    1. A. ₵205,000
    2. B. ₵220,000
    3. C. ₵225,000
    4. D. ₵235,000
18. Write 83000 in standard form.
    1. A. 8.3 × 10¹
    2. B. 8.3 × 10²
    3. C. 8.3 × 10⁰
    4. D. 8.3 × 10⁴
19. What is the mode of the marks 2, 3, 5, 2, 3, 4, 2, 3, 5, 3?
    1. A. 2
    2. B. 3
    3. C. 4
    4. D. 5
20. Calculate the mean of the marks 2, 3, 5, 2, 3, 4, 2, 3, 5, 3.
    1. A. 3.0
    2. B. 3.2
    3. C. 4.0
    4. D. 4.2
21. There are 12 red and 8 blue balls in a bag. If a ball is selected at random, what is the probability that it is red?
    1. A. 2∕5
    2. B. 2∕3
    3. C. 3∕5
    4. D. 4∕5
22. If y = (x - 2) ∕ 3, express x in terms of y.
    1. A. x = 3y - 2
    2. B. x = 3y + 2
    3. C. x = (y + 2) ∕ 3
    4. D. x = 3y ∕ 2
23. Simplify $6a^2\times 4a^2{b}^2$.
    1. A. $10a^4{b}^2$
    2. B. $24a^2{b}^2$
    3. C. $24a^4{b}^2$
    4. D. $24a^2{b}^4$
24. Change 17 in base ten to base two.
    1. A. 101
    2. B. 1001
    3. C. 1000
    4. D. 10001
25. Which of the following statements is true?
    1. A. 8 + 4 < 10
    2. B. 7 + 4 < 10
    3. C. 6 + 4 < 10
    4. D. 5 + 4 < 10
26. Find the set of integers within the interval -2 < x < 2.
    1. A. {-2, -1, 2}
    2. B. {-2, -1, 0}
    3. C. {-1, 0, 1}
    4. D. {-1, 1, 2}
27. What is the rule for this mapping given x = 1, 2, 3, 4, 5 and y = -4, -2, 0, 2, m?
    1. A. x → 2(x - 3)
    2. B. x → 2(x - 1)
    3. C. x → 2(x - 2)
    4. D. x → 2x - 3
28. Find m if x = 1, 2, 3, 4, 5 and y = -4, -2, 0, 2, m.
    1. A. -4
    2. B. 4
    3. C. 6
    4. D. 8
29. Which of the following represents the net of a pyramid?
    1. A.
    2. B.
    3. C.
    4. D.
30. A rectangular tank has dimensions 2.5 m by 4 m by 5 m. If 35 m³ of water is used, how much water is left?
    1. A. 50 m³
    2. B. 35 m³
    3. C. 25 m³
    4. D. 15 m³
31. 
    
    In the triangle XYZ, angle XZY = 90°, XY = 13 cm, and YZ = 5 cm. Find XZ.
    1. A. 4 cm
    2. B. 8 cm
    3. C. 12 cm
    4. D. 13 cm
32. How many lines of symmetry does an equilateral triangle have?
    1. A. 1
    2. B. 2
    3. C. 3
    4. D. 4
33. The value of an obtuse angle lies between:
    1. A. 0° and 90°
    2. B. 90° and 180°
    3. C. 90° and 270°
    4. D. 180° and 360°
34. 
    
    In the diagram, AB is parallel to CD. Angles x and y are:
    1. A. Alternate angles
    2. B. Corresponding angles
    3. C. Vertically opposite angles
    4. D. Co-interior angles
35. If $\mathbf{a}=\left(\begin{array}{c}2\\ 1\end{array}\right)$ and $\mathbf{b}=\left(\begin{array}{c}3\\ -4\end{array}\right)$, find $2\mathbf{a}+\mathbf{b}$.
    1. A. $\left(\begin{array}{c}7\\ -2\end{array}\right)$
    2. B. $\left(\begin{array}{c}5\\ -3\end{array}\right)$
    3. C. $\left(\begin{array}{c}8\\ -7\end{array}\right)$
    4. D. $\left(\begin{array}{c}3\\ -4\end{array}\right)$
36. 
    
    Find the size of the angle marked f in the diagram.
    1. A. 56°
    2. B. 72°
    3. C. 108°
    4. D. 128°
37. The dimensions of a cuboid are 2 cm, P cm and 5 cm. Which of the following is an expression for the volume of the cuboid?
    1. A. 7P cm³
    2. B. (7 + P) cm³
    3. C. 10P cm³
    4. D. (10 + P) cm³
38. Simplify 5(3t + 1) - 6(t - 1).
    1. A. 9t + 11
    2. B. 9t + 7
    3. C. 9t + 1
    4. D. 9t - 5
39. Simplify: $(\frac{2}{3}-\frac{1}{2})÷\frac{1}{6}$
    1. A. $\frac{1}{36}$
    2. B. $\frac{1}{12}$
    3. C. 1
    4. D. 6
40. The point P moves in a plane such that it is always at equal distance from two fixed points, A and B in the same plane. Which of these is the locus of the point P?
    1. A. The bisector of angle PAB
    2. B. A circle center B and radius AB
    3. C. A circle with AB as the diameter
    4. D. The perpendicular bisector of line AB

Paper 2: Theory

1. S = {1, 2, 3, ..., 18}, A = {Prime numbers}, B = {Odd numbers greater than 3}
   
   (a) If A and B are subsets of the universal set S, list the members of A and B.
   
   (b) Find the set (i) A ∩ B; (ii) A ∪ B.
   
   (c) (i) Illustrate A and B on a Venn diagram. (ii) Shade the region for prime factors of 18 on the Venn diagram.
2. (a) If 2n - 5m + 10 = 0, find (i) m when n = 2; (ii) n when m = 5.
   
   (b) Simplify 6.4 × 0.25 × 16 ÷ (0.8 × 0.5), leaving your answer in standard form.
   
   (c) A number of sweets were shared among 8 children, and each child received 30. If 12 children shared the same number of sweets, how many will each receive?
3. The table shows the distribution of the ages (in years) of children in a nursery school.
   
   Age (years): {1, 2, 3, 4, 5}
   
   Number of children: {6, 4, 2, 3, 5}
   
   (a) (i) Find the modal age.
   
   (ii) Find the mean age.
   
   (b) Draw a bar chart for the distribution.
   
   (c) What is the probability that a child chosen at random from the school is 4 years old?
4. (a) p = (-3, 4), q = (5, -4), r = (-3, 7). Find p + 2q + r.
   
   (b) Solve the inequality (x - 4)/5 ≤ -1, if the domain is the set {-2, -1, 0, 1, 2}.
   
   (c) A rectangular sheet of metal has length 44 cm and breadth 10 cm. It is folded to form a cylinder with the breadth becoming the height.
   
   (i) Calculate the radius of the cylinder formed.
   
   (ii) Calculate the volume of the cylinder. [Take π = 22/7].
5. (a) Using a pair of compasses and a ruler only:
   
   (i) Construct triangle ABC with |AB| = 8 cm, |BC| = 8 cm and |AC| = 7 cm.
   
   (ii) Bisect angle ABC and let the bisector meet AC at D. Produce [BD] to P such that |BD| = |DP|. Join AP and CP.
   
   (b) Measure (i) angle ADB; (ii) |AP|.
   
   (c) What kind of quadrilateral is ABCP?

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