BECE 2022 Mathematics Past Questions and Answers

Paper 1: Objectives

1. Express 108 as a product of prime factors.
   1. A. 2² × 3³
   2. B. 2³ × 3²
   3. C. 2 × 3⁴
   4. D. 2³ × 3
   Answer: A

   108 = 2 × 54 = 2 × 2 × 27 = 2 × 2 × 3 × 3 × 3 = 2² × 3³.
2. A football match starts at 2:20 p.m. and lasts for 1 hour 50 minutes. At what time will the game end?
   1. A. 3:10 p.m.
   2. B. 4:10 p.m.
   3. C. 5:10 p.m.
   4. D. 6:10 p.m.
   Answer: B

   Adding 1 hour and 50 minutes to 2:20 p.m. brings us to 4:10 p.m.
3. Which of the following is not a quadrilateral?
   1. A. Rhombus
   2. B. Parallelogram
   3. C. Rectangle
   4. D. Triangle
   Answer: D

   A triangle has three sides, unlike quadrilaterals which have four sides.
4. Solve: 5x - (7x - 3) < 9.
   1. A. x > -3
   2. B. x < -3
   3. C. x < -6
   4. D. x < 3
   Answer: A

   Simplifying the inequality gives x > -3.
5. Simplify
   
   
   1. A.
   2. B.
   3. C.
   4. D.
   Answer: D

   After finding a common denominator, the result is 4/7.
6. Given
   
   , what is the negative vector?
   1. A.
   2. B.
   3. C.
   4. D.
   Answer: C

   The negative of AB is BA, as it reverses direction.
7. The point S(4, 3) is reflected in the y-axis. Find the coordinates of the image of S.
   1. A. (-3, 4)
   2. B. (4, -3)
   3. C. (3, -4)
   4. D. (-4, 3)
   Answer: D

   Reflecting across the y-axis changes the x-coordinate, giving (-4, 3).
8. Solve:
   
   
   1. A. x = 4
   2. B.
   3. C.
   4. D. x = 0
   Answer: A

   Clearing the denominators and solving gives x = 4.
9. The longest chord of a circle is the:
   1. A. segment
   2. B. sector
   3. C. circumference
   4. D. diameter
   Answer: D

   The diameter is the longest chord, passing through the center.
10. Factorize completely: xy - xm - my + m².
    1. A. (m - y)(x - m)
    2. B. (x - m)(y - m)
    3. C. (x + m)(y - m)
    4. D. (y - m)(m - x)
    Answer: B

    Group the terms: xy - xm - my + m² = x(y - m) - m(y - m) = (x - m)(y - m).

Answers and solutions for questions 11 to 40 are free in the BECE Past Questions app, with timed practice and offline study.

On an iPhone? Download on the App Store

On Android? Get it on Google Play

11. Given P(3, -2) and Q(-2, 4), find the gradient of the line joining P to Q.
    1. A. -6/5
    2. B. 5/6
    3. C. 6/5
    4. D. -5/6
12. If
    
    , find the value of n.
    1. A. 0.0105
    2. B. 0.105
    3. C. 105
    4. D. 1050
13. The rule of mapping is x -> 2x² - 1. What number does x = 2 map to?
    1. A. 9
    2. B. 8
    3. C. 7
    4. D. 3
14. If
    
    , find x when a = 2, b = -4, and c = -2.
    1. A. 0
    2. B. 8
    3. C. 4
    4. D. 16
15. Arrange the following fractions from lowest to highest:
    
    
    1. A. 1/4, 3/5, 2/3
    2. B. 3/5, 1/4, 2/3
    3. C. 3/4, 1/2, 2/5
    4. D. 1/3, 4/5, 2/5
16. A shop is rented at GHC 9.00 per month. How much is paid in 1 ½ years?
    1. A. GHC 162.00
    2. B. GHC 135.00
    3. C. GHC 6.00
    4. D. GHC 13.00
17. A certain number is subtracted from 12 and the result is multiplied by 3. If the answer is 21, find the number.
    1. A. 6
    2. B. 8
    3. C. 5
    4. D. 4
18. 
    
    In the diagram, AB is parallel to DE, angle ABC = 81° and angle DCE = 20°. What is the value of x?
    1. A. 20°
    2. B. 61°
    3. C. 81°
    4. D. 101°
19. 
    
    In the diagram, AB is parallel to DE, angle ABC = 81° and angle DCE = 20°. Find the value of y.
    1. A. 20°
    2. B. 81°
    3. C. 79°
    4. D. 101°
20. Adjoa traveled 12 km due north and 5 km due east. How far was she from her starting point?
    1. A. 60 km
    2. B. 17 km
    3. C. 13 km
    4. D. 7 km
21. Which of the following is the largest set?
    1. A. {Whole numbers}
    2. B. {Composite}
    3. C. {Natural numbers}
    4. D. {Integers}
22. Write 1930.54 in standard form.
    1. A. 1.93054 x 10³
    2. B. 1.93054 x 10²
    3. C. 1.93054 x 10⁻²
    4. D. 1.93054 x 10
23. Expand: (2a - b)(a - b)
    1. A. 2a² + 3ab - b²
    2. B. 2a² - 3ab
    3. C. 2a² + 3ab + b²
    4. D. 2a² - 3ab + b²
24. The stem and leaf plot shows the weights (kg) of cocoa bags weighed in a week.
    

    Stem	Leaf
    4	0, 5, 7, 9
    5	1, 3, 4, 5, 7, 8
    6	0, 2, 3, 4, 4, 4, 4, 5, 6, 8
    7	1, 2, 3, 4, 5, 8, 8, 9
    8	2, 3, 5, 6, 9
    9	4, 5

    
    How many bags of cocoa were weighed in the week?
    1. A. 35
    2. B. 29
    3. C. 6
    4. D. 41
25. The stem and leaf plot shows the weights (kg) of cocoa bags weighed in a week.
    

    Stem	Leaf
    4	0, 5, 7, 9
    5	1, 3, 4, 5, 7, 8
    6	0, 2, 3, 4, 4, 4, 4, 5, 6, 8
    7	1, 2, 3, 4, 5, 8, 8, 9
    8	2, 3, 5, 6, 9
    9	4, 5

    
    What is the median weight of the bags of cocoa?
    1. A. 62 kg
    2. B. 65 kg
    3. C. 61 kg
    4. D. 68 kg
26. The stem and leaf plot shows the weights (kg) of cocoa bags weighed in a week.
    

    Stem	Leaf
    4	0, 5, 7, 9
    5	1, 3, 4, 5, 7, 8
    6	0, 2, 3, 4, 4, 4, 4, 5, 6, 8
    7	1, 2, 3, 4, 5, 8, 8, 9
    8	2, 3, 5, 6, 9
    9	4, 5

    
    What is the modal weight of the bags of cocoa?
    1. A. 68 kg
    2. B. 60 kg
    3. C. 64 kg
    4. D. 65 kg
27. If a = [2,-3] and b = [-2,3], find a + b.
    1. A.
    2. B.
    3. C.
    4. D.
28. For what value of x is 3^x = 81?
    1. A. 2
    2. B. 27
    3. C. 4
    4. D. 9
29. Simplify: -15 - (-20) + (-10).
    1. A. -45
    2. B. -5
    3. C. -25
    4. D. 5
30. Express 3/8 as a decimal fraction.
    1. A. 0.429
    2. B. 0.375
    3. C. 0.365
    4. D. 0.625
31. What is the length of the side of a square of area 225 cm²?
    1. A. 15.00 cm
    2. B. 12.00 cm
    3. C. 112.50 cm
    4. D. 56.25 cm
32. What is the probability that a number greater than 5 shows up when a die is thrown?
    1. A. 5/6
    2. B. 1/6
    3. C. 2/3
    4. D. 1/3
33. Given that 117(12 + 18) = 117(15 + k), find the value of k.
    1. A. 15
    2. B. -15
    3. C. -30
    4. D. 30
34. A mother has GHC 5.00 and gives each of her 3 children GHC 1.50 as pocket money. How much is left for her?
    1. A. GHC 3.50
    2. B. GHC 4.50
    3. C. GHC 0.15
    4. D. GHC 0.50
35. A car travels 36 kilometres in an hour. Find its speed in metres per second.
    1. A. 10 m/s
    2. B. 100 m/s
    3. C. 20 m/s
    4. D. 200 m/s
36. Peter had GHC 200.00 and spent GHC 83.00. What percentage of the money is left?
    1. A. 29.06%
    2. B. 70.94%
    3. C. 58.50%
    4. D. 41.50%
37. If a trader made a profit of 10% in selling a shirt for GHC 44.00, find the cost price.
    1. A. GHC 39.60
    2. B. GHC 38.50
    3. C. GHC 48.40
    4. D. GHC 40.00
38. Express 15 : 12 in the form 1 : n.
    1. A. 1 : 0.8
    2. B. 1 : 12
    3. C. 1 : 15
    4. D. 1 : 1.2
39. The ratio of farmers to children in a village is 13 : 11. If there were 312 farmers in the village, how many children were there?
    1. A. 264
    2. B. 143
    3. C. 48
    4. D. 169
40. The volume of a cylinder is 40π cm³. If the height of the cylinder is 10 cm, find the base radius.
    1. A. 1 cm
    2. B. 4 cm
    3. C. 2 cm
    4. D. 3 cm

Paper 2: Theory

1. a) Given that P = {factors of 36} and Q = {factors of 54},
   
   (i) List the members in the sets P and Q.
   
   (ii) Find:
   
   A) P ∩ Q
   
   B) n(P ∩ Q)
   
   C) The Highest Common Factor (HCF) of 36 and 54.
   
   b) Write down the next two terms of the sequence 1, 4, 9, ..., ....
   
   c) The median of the ordered set of observations 2, 3, (4m-3), (3m+1), 11, and 13 in ascending order is 6. Find the value of m.
2. a) Simplify: (5/12 ÷ 2/5) + 1/24.
   
   b) Find the product of (2x-3) and (2x+3).
   
   c) In the diagram, ABC is an equilateral triangle. Find the value of (x + y) if AB = BC = CA = 11 and AB = 3x + 2, BC = 2y + 3.
3. a) Given the relation L = ,
   
   (i) Simplify L.
   
   (ii) Find the value of L when m = 2 and n = 3.
   
   b) Solve: .
   
   c) A salesman gets a commission of 5 ½% of the value of items he sells. He sells 12 textbooks at GHC25 each, 3 scientific calculators at GHC50 each, and 8 packets of pens at GHC50 each. Calculate the salesman's commission.
4. a) Fred is (x-1) years old now. Find:
   
   (i) His age 4 years ago.
   
   (ii) His age 8 years from now.
   
   (iii) His current age if in 8 years he will be 3 times his age 4 years ago.
   
   b) The perimeter of a rectangular cocoa farm is 497 km. The length of the farm is 2 ½ times the width. Find:
   
   (i) The width.
   
   (ii) The length.
5. a) Factorize: (x-y)(3m+n)-(x-y)(m-2n).
   
   b) Given that 2-3x = 6 and -2y = 8, find the value of (x + y).
   
   c) (i) Solve x-1/2 < 1/2 + x.
   
   (ii) Illustrate the solution on a number line.
   
   
6. a) Copy and complete the table for the relation y = 5-2x for -3 ≤ x ≤ 4.
   
   b) Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis, draw the graph.
   
   c) (i) Plot all points of the relation.
   
   (ii) Draw a straight line through all the points.
   
   d) Using the graph, find:
   
   (i) The value of y when x = -2.6.
   
   (ii) The value of x when y = -2.8.
   
   (iii) The gradient of the line.

Worked solutions to the theory questions are free in the app.

On an iPhone? Download on the App Store

On Android? Get it on Google Play