BECE 2020 Mathematics Past Questions and Answers

Paper 1: Objectives

1. Simplify:
   1. A. 1/3
   2. B. 1/2
   3. C. 1/6
   4. D. 2/3
   Answer: B

   The LCM of 4, 3 and 12 is 12.
   
   3/4 - 1/3 + 1/12 = 9/12 - 4/12 + 1/12 = (9 - 4 + 1)/12 = 6/12 = 1/2.
2. Given that N = {x : x is a factor of 18} and M = {x : x is a multiple of 12}, find N ∩ M.
   1. A. {1,2,3,6}
   2. B. {1,2,3,6,12}
   3. C. {2,3,6,12,18}
   4. D. {}
   Answer: D

   Factors of 18 are {1,2,3,6,9,18}, and multiples of 12 are {12,24,36,...}. The intersection N ∩ M is empty since there are no common elements.
3. Express 4382.93 in standard form.
   1. A. 438293 × 10
   2. B. 43.8293 × 10
   3. C. 4.38293 × 10
   4. D. 4.38293 × 10³
   Answer: D

   Moving the decimal three places to the left gives 4.38293 × 10³ as the standard form.
4. Which property of arithmetic is used in a(x + y) = ax + ay?
   1. A. Associative
   2. B. Commutative
   3. C. Distributive
   4. D. Initiative
   Answer: C

   This is the distributive property, which states that multiplying a sum by a number is the same as multiplying each addend by the number.
5. Subtract (7x - 3) from (5 - 3x).
   1. A. 10x - 8
   2. B. 4x - 8
   3. C. 8 - 10x
   4. D. 2 - 10x
   Answer: C

   Subtracting (7x - 3) from (5 - 3x) gives (5 - 3x) - (7x - 3) = 5 - 3x - 7x + 3 = 8 - 10x.
6. The cost of 12 notebooks is GHC 54.84. Find the cost of one notebook.
   1. A. GHC 5.57
   2. B. GHC 4.67
   3. C. GHC 4.57
   4. D. GHC 3.57
   Answer: C

   Dividing the total cost by the number of notebooks: 54.84 / 12 = 4.57.
7. 
   
   Which of the following inequalities is represented on the number line?
   1. A. -2 > y > 2
   2. B. -2 ≤ y < 2
   3. C. -2 ≥ y > 2
   4. D. -2 < y ≤ 2
   Answer: D

   The number line has a hollow (open) dot at -2 and a solid (shaded) dot at 2, so the inequality is -2 < y ≤ 2.
8. Simplify: (2ab²)² × 3a³b.
   1. A. 6a⁴b⁵
   2. B. 12a³b⁴
   3. C. 12a⁶b⁴
   4. D. 12a⁵b⁵
   Answer: D

   (2ab²)² = 4a²b⁴.
   
   4a²b⁴ × 3a³b = 12a²⁺³b⁴⁺¹ = 12a⁵b⁵.
9. Which of the following polygons does not have a line of symmetry?
   1. A. Kite
   2. B. Isosceles triangle
   3. C. Trapezium
   4. D. Rhombus
   Answer: C

   A trapezium does not have any lines of symmetry unless it is isosceles.
10. A trader sold a radio set for GHC 72.00 making a profit of 8%. Find, correct to the nearest Ghana cedi, the cost of the radio set.
    1. A. GHC 66.00
    2. B. GHC 67.00
    3. C. GHC 77.00
    4. D. GHC 78.00
    Answer: B

    Let CP be the cost price. Using Profit = Selling Price - Cost Price, we solve to get CP ≈ GHC 67.

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. Vera is 11 years old and her brother is 9 years old. They shared 60 oranges in the ratio of their ages. How many more oranges does Vera get?
    1. A. 6
    2. B. 27
    3. C. 34
    4. D. 39
12. If (x - 3)² = 16, find the positive value of x.
    1. A. 1
    2. B. 3
    3. C. 4
    4. D. 7
13. Find the image of the point (-2,3) under a reflection in the y-axis.
    1. A. (2,-3)
    2. B. (-3,2)
    3. C. (2,3)
    4. D. (3,2)
14. What fraction of 3 weeks is 18 days?
    1. A. 2/7
    2. B. 6/7
    3. C. 1/2
    4. D. 1/11
15. What is the median of the following numbers: 4, 16, 13, 18, 3, 20, 6, 7, 15, 2, 10, 12?
    1. A. 7
    2. B. 10
    3. C. 11
    4. D. 12
16. If w/3 = 3(w - 1) - 1, find the value of w.
    1. A. 3/2
    2. B. 3/4
    3. C. 1/2
    4. D. 2/3
17. 
    
    Find the value of x in the diagram below.
    1. A. 68°
    2. B. 75°
    3. C. 112°
    4. D. 124°
18. 
    
    Use the diagram to find the value of y.
    1. A. 68°
    2. B. 75°
    3. C. 112°
    4. D. 124°
19. A car used 8 hours to travel from town A to town B at a speed of 18 km/h. Find the distance traveled.
    1. A. 22.5 km
    2. B. 135 km
    3. C. 140 km
    4. D. 144 km
20. 
    
    The pie chart shows the household budget of a family. Find the angle for INSURANCE AND TAXES.
    1. A. 45°
    2. B. 54°
    3. C. 60°
    4. D. 72°
21. 
    
    If the family's income was GHC 40,000.00, how much was spent on clothing?
    1. A. GHC 1,600.00
    2. B. GHC 2,000.00
    3. C. GHC 3,200.00
    4. D. GHC 4,400.00
22. Two sides of a parallelogram are 5.8 m and 8.2 m long. Find its perimeter.
    1. A. 11.0 m
    2. B. 36.6 m
    3. C. 28.0 m
    4. D. 47.6 m
23. A man earned an interest of GHC 240.00 in 4 years at 20% per annum simple interest. Calculate the principal.
    1. A. GHC 300.00
    2. B. GHC 450.00
    3. C. GHC 480.00
    4. D. GHC 1,200.00
24. A labourer worked for 20½ hours. If he was paid GHC 2.50 per hour, what was his total wage?
    1. A. GHC 51.00
    2. B. GHC 51.25
    3. C. GHC 512.00
    4. D. GHC 512.25
25. If 480 pupils in a school are boys representing 80% of the school's enrolment. Find the total number of pupils in the school.
    1. A. 384
    2. B. 540
    3. C. 600
    4. D. 864
26. 
    
    What is the rule for the mapping x -> y where x = [1, 2, 3, 4] and y = [2, 5, 10, 17]?
    1. A. x -> 3 - 1
    2. B. x -> 5 - 3
    3. C. x -> x² + 1
    4. D. x -> 4x - 2
27. 
    
    Find the value of t in a right triangle where one side is 5 cm and the hypotenuse is 13 cm.
    1. A. 12
    2. B. 8
    3. C. 4
    4. D. 3
28. Add the following numbers: 2.4, 0.042, 1.12, and 0.342.
    1. A. 2.184
    2. B. 3.904
    3. C. 4.282
    4. D. 6.200
29. Solve: 4^(x/2) = 32.
    1. A. 2½
    2. B. 3½
    3. C. 5
    4. D. 7
30. Find the equation of the straight line passing through the points (-3,5) and (6,8).
    1. A. y = 1/3x
    2. B. y = 1/3x + 6
    3. C. y = 1/3x - 10
    4. D. y = 1/3x + 14
31. There are 15 females in a debating club. If the ratio of females to males is 3:2, how many members are in the club?
    1. A. 6
    2. B. 10
    3. C. 22
    4. D. 25
32. If P'(4,-5) is the image of P(x,y) translated by the vector r = (-2, 3), find the values of x and y.
    1. A. (-6,8)
    2. B. (-6,-8)
    3. C. (6,-8)
    4. D. (6,8)
33. If 2y = 1 - 3x² + 4x, find y when x = -1.
    1. A. -3
    2. B. -1/2
    3. C. 1/2
    4. D. 3
34. Given that p = {1,2,3,4,5,6,7,8,9,10,11,12}, what is the probability of selecting a prime number from the set?
    1. A. 2/3
    2. B. 7/12
    3. C. 1/2
    4. D. 5/12
35. Solve: 3 - (3x + 4) ≤ -4.
    1. A. x ≤ 1
    2. B. x ≥ 1
    3. C. x ≥ 1 2/3
    4. D. x < 1 1/2
36. Two sides of a rectangle are 10 cm and 6 cm. Calculate the area of a square with the same perimeter as that of the rectangle.
    1. A. 16 cm²
    2. B. 30 cm²
    3. C. 60 cm²
    4. D. 64 cm²
37. Make n the subject of the relation y = nx / (x + 1).
    1. A. n = y(x + 1) / x
    2. B. n = x(y + 1)
    3. C. n = y(x - 1) / x
    4. D. n = y - 1 / x
38. Expand and simplify: (a-2)(2a+3).
    1. A. -a + 6
    2. B. 2a² + 7a - 6
    3. C. 2a² - a - 6
    4. D. 2a² - 12a + 6
39. Simplify: 2³ x 2⁷ ÷ 2².
    1. A. 2²
    2. B. 2⁸
    3. C. 2⁹
    4. D. 2¹³
40. If P = {7,11,13} and Q = {9,11,13}, find P ∪ Q.
    1. A. {7,9,11,13}
    2. B. {7,9}
    3. C. {11,13}
    4. D. {9,13}

Paper 2: Theory

1. a) If M = {Prime integers between 1 and 11} and N = {factors of 12}, find:
   
   i) M ∪ N
   
   ii) M ∩ N
   
   b) Simplify 45 ÷ 3 + 2 × 8 - 12 + 42.
   
   c) In the diagram (not drawn to scale), x, y, and z are angles on a straight line. If z:x = 2:3 and y = 80°, find x.
2. a) Simplify 5(6 - ab) + 2(-7 + 3ab).
   
   b) The equation of a straight line is given by 3x - 2y - 6 = 0. Find:
   
   i) the gradient of the line;
   
   ii) the y-intercept.
   
   c) Adwoa received a commission of 20% on bread she sold. In one week, Adwoa's commission was GHC 540.00.
   
   i) How much bread did she sell during that week?
   
   ii) Find her average daily commission.
3. a) Express as a percentage.
   
   b) Factorize ay - y - a + 1.
   
   c) In a fishing community of 9,400 people, the number of women exceeds the number of men by 1,500. Find the ratio of men to women in the community.
4. a) Solve:
   
   b) Multiply 0.03858 by 0.02, leaving the answer in standard form.
   
   c) A cylindrical container of height 28 cm and diameter 18 cm is filled with water. The water is then poured into another container with a rectangular base of length 27 cm and width 11 cm. Calculate the depth of the water in the container. (Take π = 22/7)
5. a) If 11y = 18² - 15², find the value of y.
   
   b) Find the perimeter of a circle with radius 35 cm. (Take π = 22/7).
   
   c) Given that m = (r - s)/(2nr):
   
   i) Make r the subject of the relation.
   
   ii) Find the value of r when s = 117, m = 2, and n = -3.
6. a) Copy and complete the table for y = 12x - 9:
   
   | x | -2 | -1 | 0 | 1 | 2 | 3 | 5 |
   
   |---|----|----|---|---|---|---|---|
   
   | y | | | | | | | |
   
   i) Using a scale of 2 cm to 1 unit on the x-axis and 10 units on the y-axis, draw on a graph sheet two perpendicular axes Ox and Oy.
   
   ii) Using the table, plot all the points of the relation y = 12x - 9 on the graph.
   
   iii) Draw a straight line through the points.
   
   iv) Use the graph to find:
   
   (a) y when x = 2.5;
   
   (b) x when y = 10.
   
   b) List the integers within the interval 7 < x ≤ 14.

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