BECE 2001 Mathematics Past Questions and Answers

Paper 1: Objectives

1. R = {1, 3, 5, 7} and S = {2, 4, 6, 8}. Find R ∪ S.
   1. A. {}
   2. B. {1, 2, 3, 5, 6, 8}
   3. C. {1, 2, 3, 4, 5, 7, 8}
   4. D. {1, 2, 3, 4, 5, 6, 7, 8}
   5. E. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
   Answer: D

   Union is simply listing each of the elements from both sets. If an element appeared in both sets, it is listed only once. R ∪ S = {1, 2, 3, 4, 5, 6, 7, 8}
2. Find the missing members in the set {5, 10, 15, _, 25, _, _, 40}.
   1. A. 20 and 30
   2. B. 30 and 35
   3. C. 20 and 35
   4. D. 20, 30 and 35
   5. E. 30, 35 and 45
   Answer: D

   The set is a list of multiples of 5 less than 45. The set is {5, 10, 15, 20, 25, 30, 35, 40}
3. What property of addition is defined by (a + b) + c = a + (b + c)?
   1. A. Union
   2. B. Inverse
   3. C. Commutative
   4. D. Distributive
   5. E. Associative
   Answer: E

   The associative property states that it doesn't matter how we group the numbers in addition or multiplication. (a + b) + c = a + (b + c)
4. Find the highest (greatest) common factor of 63 and 81.
   1. A. 3
   2. B. 7
   3. C. 9
   4. D. 21
   5. E. 27
   Answer: C

   The HCF of 63 and 81 is 9, found by taking the common factors in their lowest power.
5. Change 124₅ to a base ten numeral.
   1. A. 24
   2. B. 35
   3. C. 39
   4. D. 42
   5. E. 55
   Answer: C

   124₅ = 1×5² + 2×5 + 4 = 25 + 10 + 4 = 39
6. Kofi bought 4 books at an average price of ₵2,500.00. If the total cost of 3 of the books was ₵6,500.00, find the cost of the fourth book.
   1. A. ₵3,500.00
   2. B. ₵4,000.00
   3. C. ₵4,500.00
   4. D. ₵6,500.00
   5. E. ₵10,000.00
   Answer: A

   The total cost is ₵10,000. Fourth book cost = ₵10,000 - ₵6,500 = ₵3,500.00
7. Find the sum of all even numbers between 70 and 80.
   1. A. 200
   2. B. 223
   3. C. 280
   4. D. 300
   5. E. 375
   Answer: D

   Even numbers between 70 and 80 are {72, 74, 76, 78}. Their sum is 300.
8. By how much is $\frac{5}{6}$ greater than $\frac{3}{4}$?
   1. A. 1/12
   2. B. 1/6
   3. C. 5/12
   4. D. 2/3
   5. E. 4/5
   Answer: A

   $\frac{5}{6}-\frac{3}{4}=\frac{10-9}{12}=\frac{1}{12}$
9. Evaluate 0.25 × 0.006, correct to three decimal places.
   1. A. 0.001
   2. B. 0.002
   3. C. 0.015
   4. D. 0.075
   5. E. 0.105
   Answer: B

   0.25 × 0.006 = 0.002 (rounded to three decimal places).
10. Express 5/8 as a decimal fraction.
    1. A. 0.125
    2. B. 0.375
    3. C. 0.625
    4. D. 0.750
    5. E. 0.875
    Answer: C

    5/8 as a decimal is 0.625.

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11. The following are angles at the center of a circle: 30°, 70°, 120°, 2x, and 5x. Find the value of x.
    1. A. 20
    2. B. 40
    3. C. 70
    4. D. 100
    5. E. 140
12. On a map, 1 cm represents 4.5 km. What is the actual distance between two towns 4 cm apart on the map?
    1. A. 9 km
    2. B. 16 km
    3. C. 18 km
    4. D. 19 km
    5. E. 21 km
13. If 2y = 6 - 3x, find y when x = 0.
    1. A. -3
    2. B. -2
    3. C. 0
    4. D. 2
    5. E. 3
14. How many lines of symmetry does an isosceles triangle have?
    1. A. 1
    2. B. 2
    3. C. 3
    4. D. 4
    5. E. 5
15. Kofi's age in the next ten years will be four times his age five years ago. How old is Kofi now?
    1. A. 5
    2. B. 6
    3. C. 10
    4. D. 15
    5. E. 20
16. A point P (3, 4) is rotated 90° anticlockwise about the origin. Find the image P'.
    1. A. (3, -4)
    2. B. (4, -3)
    3. C. (-3, 4)
    4. D. (-4, 3)
    5. E. (-4, -3)
17. Which of the following is not a quadrilateral?
    1. A. Square
    2. B. Rectangle
    3. C. Rhombus
    4. D. Triangle
    5. E. Parallelogram
18. Express 2345 in standard form.
    1. A. 2.345 × 10¹
    2. B. 2.345 × 10
    3. C. 2.345 × 10³
    4. D. 2.345 × 10²
    5. E. 2.345 × 10⁴
19. Solve the inequality 3(x - 1) ≤ 12.
    1. A. x ≤ -5
    2. B. x ≤ -3
    3. C. x ≤ 3
    4. D. x ≤ 5
    5. E. $x\le \frac{13}{3}$
20. Kofi and Ama shared an amount of money in the ratio 3 : 2 respectively. If Kofi had ₵60,000.00, how much was shared?
    1. A. ₵36,000.00
    2. B. ₵40,000.00
    3. C. ₵90,000.00
    4. D. ₵100,000.00
    5. E. ₵120,000.00
21. Workers are required to pay 4½ % of their salaries into an educational fund. A worker's salary is ₵120,000.00. How much does he pay into the educational fund?
    1. A. ₵5,332.00
    2. B. ₵5,400.00
    3. C. ₵6,000.00
    4. D. ₵10,800.00
    5. E. ₵11,500.00
22. Araba bought an electric cooker for ₵540,000.00 at a discount of 10%. Find the actual price of the electric cooker.
    1. A. ₵469,000.00
    2. B. ₵496,000.00
    3. C. ₵594,000.00
    4. D. ₵600,000.00
    5. E. ₵605,000.00
23. Given that a = p × q, find the value of a if p = 13 and q = 15.
    1. A. 28
    2. B. 175
    3. C. 195
    4. D. 247
    5. E. 494
24. A mapping is defined by n → 2n − 3. What is the image of −2 under the mapping?
    1. A. -1
    2. B. -5
    3. C. -7
    4. D. 7
    5. E. 1
25. Simplify 4p + 6p - 2p + 2p
    1. A. 2p + 8p
    2. B. 6p + 8p
    3. C. 2p - 8
    4. D. 6p - 8p
    5. E. -4 + 10p
26. Make q the subject of the relation w = n / (q + 1)
    1. A. q = -n - 1 / w
    2. B. q = -n + 1 / w
    3. C. q = (n + 2) / (1 + w)
    4. D. q = (n / w) - 1
    5. E. q = n / (w - 1)
27. Given that E = ½mc², find E when m = 10 and c = 4
    1. A. 20
    2. B. 40
    3. C. 60
    4. D. 80
    5. E. 160
28. The scores obtained by 8 pupils in a test are 2, 3, 4, 5, 7, 8, 8, and 9. What is the median score?
    1. A. 3
    2. B. 5
    3. C. 6
    4. D. 7
    5. E. 8
29. The scores obtained by 8 pupils in a test are 2, 3, 4, 5, 7, 8, 8, and 9. Find the mean score.
    1. A. 4.50
    2. B. 5.75
    3. C. 6.00
    4. D. 8.75
    5. E. 10.00
30. The scores obtained by 8 pupils in a test are 2, 3, 4, 5, 7, 8, 8 and 9. What is the probability that a pupil chosen at random scores 8 marks?
    1. A. $\frac{1}{8}$
    2. B. $\frac{4}{23}$
    3. C. $\frac{1}{4}$
    4. D. $\frac{1}{3}$
    5. E. $\frac{1}{2}$
31. 
    
    Determine the value of x when y is 3 using the line graph.
    1. A. ½
    2. B. ⅔
    3. C. 2
    4. D. 3
    5. E. 8
32. 
    
    Find the gradient of the line MN on the graph.
    1. A. -2
    2. B. -1
    3. C. 1
    4. D. 3/2
    5. E. 2
33. State the rule of the following mapping: x = {1, 2, 3, 4, 5}, y = {1, 4, 9, 16, 25}
    1. A. x → x
    2. B. x → 2x
    3. C. x → x³
    4. D. x → x²
    5. E. x → x + 2
34. The area of a rectangle is 18 cm². One of its sides is 9 cm long. Find its perimeter.
    1. A. 11 cm
    2. B. 18 cm
    3. C. 22 cm
    4. D. 36 cm
    5. E. 54 cm
35. 
    
    Calculate the area of figure PQRST
    1. A. 112.5 cm²
    2. B. 135.0 cm²
    3. C. 180.0 cm²
    4. D. 215.0 cm²
    5. E. 315.0 cm²
36. In an enlargement with scale factor k, which statement is not true?
    1. A. Each length is multiplied by k
    2. B. Each angle remains the same
    3. C. The shape of the figure does not change
    4. D. The size of the figure does not change
    5. E. Corresponding lines are parallel
37. 
    
    Find the angle MON in the diagram.
    1. A. 48°
    2. B. 52°
    3. C. 58°
    4. D. 65°
    5. E. 75°
38. 
    
    Angle MON and PMO are
    1. A. Alternate angles
    2. B. Vertically opposite angles
    3. C. Corresponding angles
    4. D. Adjacent angles
    5. E. Complementary angles
39. If $\mathbf{u}=\left(\begin{array}{c}1\\ 3\end{array}\right)$ and $\mathbf{v}=\left(\begin{array}{c}4\\ -2\end{array}\right)$, find $2\mathbf{u}+3\mathbf{v}$.
    1. A. $\left(\begin{array}{c}5\\ 1\end{array}\right)$
    2. B. $\left(\begin{array}{c}11\\ 5\end{array}\right)$
    3. C. $\left(\begin{array}{c}11\\ 13\end{array}\right)$
    4. D. $\left(\begin{array}{c}14\\ 0\end{array}\right)$
    5. E. $\left(\begin{array}{c}14\\ 12\end{array}\right)$
40. 
    
    Which best describes the construction in the diagram?
    1. A. Construction of a horizontal line CD
    2. B. Construction of a line parallel to AB
    3. C. Construction of the bisector of AB
    4. D. Construction of a top line
    5. E. Construction of a vertical line

Paper 2: Theory

1. (a) M is a set consisting of all positive integers between 1 and 10. P and Q are subsets of M such that P = {factors of 6}, Q = {multiples of 2}.
   
   (i) List the elements of M, P, and Q.
   
   (ii) Represent M, P, and Q on a Venn diagram.
   
   (iii) Find P ∩ Q.
   
   (b) (i) Solve the inequality (2x - 2)/4 < (2x - 1)/3.
   
   (ii) Illustrate your answer on the number line.
2. (a) Express 131₅ as a binary numeral.
   
   (b) Three children, Kwabena, Esi, and Yaw, were given 160 oranges to share. Kwabena gets 1/4 of the oranges. Esi and Yaw share the remainder in the ratio 3:2 respectively.
   
   (i) Find how many oranges Esi received.
   
   (ii) How many more oranges did Yaw receive than Kwabena?
3. (a) Using a ruler and a pair of compasses only, construct triangle XYZ such that |XY| = 6 cm, |XZ| = 8 cm, and |YZ| = 10 cm.
   
   (b) (i) Construct the mediator of line YZ.
   
   (ii) Construct the mediator of line XZ.
   
   (iii) Locate O, the point of intersection of the mediators of lines YZ and XZ.
   
   (iv) With center O and radius OY, draw a circle.
   
   (c) Measure the radius of the circle you have drawn in (b)(iv) above and hence calculate the circumference of the circle. [Take π = 3.14].
4. (a) (i) Using a scale of 2 cm to 1 unit on both axes, draw two perpendicular axes OX and OY on a graph sheet.
   
   (ii) On the same graph sheet, mark the x-axes from -5 to 5 and the y-axis from -6 to 6.
   
   (b) On the same graph sheet, plot the points A(2, 5), B(4, 3), and C(1, 1). Join the points A, B, and C to form a triangle.
   
   (c) Reflect triangle ABC in the y-axis such that A → A₁, B → B₁, and C → C₁. Label the vertices of triangle A₁B₁C₁.
   
   (d) Translate triangle A₁B₁C₁ by the vector (-1, -2) such that A₁ → A₂, B₁ → B₂, and C₁ → C₂. Label the vertices of triangle A₂B₂C₂.
   
   (e) Join the vertices A₂B₂B₁ and C₂. Name the figure formed.
5. (a) A cylinder closed at one end has radius 7 cm and height 20 cm.
   
   (i) Find its total surface area.
   
   (ii) If the cylinder is filled with water to a depth of 5 cm, calculate the volume of the water in it. [Take π = 22/7].
   
   (b) Evaluate (0.07 × 0.6) ÷ (0.014 × 0.03), leaving your answer in standard form.

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