BECE 2019 Mathematics Past Questions and Answers

Paper 1: Objectives

1. Given that A = {2,4,6,8,10} and B = {4,8,12}, find A ∪ B.
   1. A. {4,8}
   2. B. {2,8,12}
   3. C. {4,6,8,12}
   4. D. {2,4,6,8,10,12}
   Answer: D

   The union of two sets is a set containing all elements in both sets without repetition. Hence A ∪ B = {2,4,6,8,10,12}.
2. Express 0.000344 in standard form.
   1. A. 3.44 x 10^-6
   2. B. 3.44 x 10^-5
   3. C. 3.44 x 10^-4
   4. D. 3.44 x 10^-3
   Answer: C

   The first non-zero digit is 3. Moving the decimal point four places to the right gives 3.44 x 10^-4.
3. Which of the following numbers is the largest?
   1. A. -70
   2. B. -50
   3. C. -3
   4. D. -2
   Answer: D

   The lower the negative value, the larger it is. Thus, -2 is the largest.
4. Correct 0.024561 to three significant figures.
   1. A. 0.03
   2. B. 0.025
   3. C. 0.0245
   4. D. 0.0246
   Answer: D

   The first three significant figures are 2, 4, and 6. Rounding up gives 0.0246.
5. Simplify: (75 x 73) ÷ 76
   1. A. 79
   2. B. 74
   3. C. 73
   4. D. 72
   Answer: D

   (75 x 73) = 75+3 = 78, and 78 ÷ 76 = 78 - 6 = 72.
6. How many lines of symmetry has a square?
   1. A. 0
   2. B. 1
   3. C. 2
   4. D. 4
   Answer: D

   A square has 4 lines of symmetry.
7. Solve the equation 10 - (x+3)/2 = 8.
   1. A. -9
   2. B. -3
   3. C. 1
   4. D. 15
   Answer: C

   Solving by isolating x, we get x = 1.
8. Factorize: kx+2xt-4k-8t.
   1. A. (k-2t)(x+4)
   2. B. (k+2t)(x+4)
   3. C. (k+t)(x-4)
   4. D. (k+2t)(x-4)
   Answer: D

   Grouping terms, factor out (k+2t) and (x-4).
9. There are 12 boys and 18 girls in a class. Find the fraction of boys in the class.
   1. A. 2/5
   2. B. 3/5
   3. C. 2/3
   4. D. 3/4
   Answer: A

   Fraction of boys = 12/(12+18) = 2/5.
10. Express 30% as a fraction in its lowest term.
    1. A. 7/10
    2. B. 3/20
    3. C. 7/20
    4. D. 3/10
    Answer: D

    30% = 30/100 = 3/10.

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. Make k the subject of the relation ky - k = y².
    1. A. k = y² / (y -1)
    2. B. k = y² / y + 1
    3. C. k = y² - y
    4. D. k = y(y -1)
12. The mean of the numbers 5, 2x,4 and 3 is 5. Find the value of x.
    1. A. 3
    2. B. 4
    3. C. 5
    4. D. 8
13. Find the rule of the mapping.
    
    

    x	1	2	3	4	5
    y	3	1	-1	-3	-5

    1. A. y = 2x + 2
    2. B. y = -2x + 2
    3. C. y = 4x
    4. D. y = -2x + 5
14. The two sides of a parallelogram are 4.8 m and 7.2 m long. Find its perimeter.
    1. A. 48.0 m
    2. B. 34.6 m
    3. C. 24.0 m
    4. D. 17.3 m
15. A tank in the form of a cuboid has length 6 m and breadth 4 m. If the volume of the tank is 36 m³, find the height.
    1. A. 0.67 m
    2. B. 1.5 m
    3. C. 1.8 m
    4. D. 5.0 m
16. If the bearing of A from B is 240°, find the bearing of B from A.
    1. A. 040°
    2. B. 060°
    3. C. 120°
    4. D. 300°
17. Find the truth set of the inequality 2y + 5 < 4y - 5.
    1. A. {y: y > 5}
    2. B. {y: y < 5}
    3. C. {y: y > 1}
    4. D. {y: y > 0}
18. Find the gradient of the straight line which passes through the points (-3,4) and (3,-2).
    1. A. 2
    2. B. 1
    3. C. -2
    4. D. -1
19. If 6:8 = r:48, find the value of r.
    1. A. 36
    2. B. 34
    3. C. 14
    4. D. 12
20. 
    
    Find ∠QPS in the diagram.
    1. A. 70°
    2. B. 40°
    3. C. 35°
    4. D. 20°
21. A man travelled a distance of 8 km in an hour. How long will it take him to cover a distance of 12 km, travelling at the same speed?
    1. A. 1⅓ hrs
    2. B. 1½ hrs
    3. C. 1¾ hrs
    4. D. 2 hrs
22. A number is selected at random from: 25,26,27,28,...,35. Find the probability that the number selected is a prime number.
    1. A. 6/11
    2. B. 3/11
    3. C. 2/11
    4. D. 1/11
23. Express 12/25 in decimal fraction.
    1. A. 0.0408
    2. B. 0.048
    3. C. 0.408
    4. D. 0.48
24. Find the diameter of a circle whose circumference is 88 cm. [Take π = 22/7]
    1. A. 14 cm
    2. B. 22 cm
    3. C. 28 cm
    4. D. 82 cm
25. When twelve is subtracted from three times a certain number and the result is divided by four, the answer is eighteen. Find the number.
    1. A. 84
    2. B. 40
    3. C. 28
    4. D. 20
26. 
    
    In the diagram, line MN is parallel to line TU, line TS cuts line MN at O and ∠MOS = 115°. Find ∠OTU.
    1. A. 65°
    2. B. 55°
    3. C. 45°
    4. D. 25°
27. Given that r = (-3, -5) and t = (3, -5), find r + t.
    1. A.
    2. B.
    3. C.
    4. D.
28. A trader sold 90 oranges at 3 for GH₵ 0.75. How much did she get from selling all the oranges?
    1. A. GH₵ 22.50
    2. B. GH₵ 67.50
    3. C. GH₵ 75.00
    4. D. GH₵ 225.50
29. Express 72 as a product of prime factors.
    1. A. 2³ × 3²
    2. B. 2² × 3³
    3. C. 2² × 3²
    4. D. 2 × 3
30. Simplify: 3a × 24ab.
    1. A. 27ab²
    2. B. 27a²b
    3. C. 72ab²
    4. D. 72a²b
31. Simplify:
    1. A.
    2. B.
    3. C.
    4. D.
32. Multiply 247 by 32.
    1. A. 6916
    2. B. 7804
    3. C. 7904
    4. D. 1235
33. Evaluate: (0.07 × 0.02) ÷ 14.
    1. A. 0.01
    2. B. 0.001
    3. C. 0.0001
    4. D. 0.00001
34. In a class of 23 students, the girls were 7 more than the boys. How many boys were in the class?
    1. A. 8
    2. B. 15
    3. C. 16
    4. D. 30
35. Express 30 minutes as a percentage of 3 hours 20 minutes.
    1. A. 12.5%
    2. B. 15%
    3. C. 16⅔%
    4. D. 20%
36. Find the Least Common Multiple (L.C.M) of 2, 3 and 5.
    1. A. 6
    2. B. 12
    3. C. 24
    4. D. 30
37. The simple interest on GH₵ 450.00 for 4 years is GH₵ 45.00, find the rate of interest.
    1. A. 2.5%
    2. B. 10%
    3. C. 25%
    4. D. 6.5%
38. Find the median of the following numbers: 46, 68, 34, 37, 76, and 81.
    1. A. 35.5
    2. B. 57
    3. C. 67
    4. D. 68
39. 
    
    In the Venn diagram M and N are the subsets of the universal set U. Find M ∩ N.
    1. A. {7}
    2. B. {2,7}
    3. C. {3,5,8}
    4. D. {1,2,3,4,5,6,7,8,9}
40. In the Venn diagram M and N are the subsets of the universal set U. How many members are in the set N?
    1. A. 2
    2. B. 3
    3. C. 4
    4. D. 6

Paper 2: Theory

1. a) Given that X = {whole numbers from 4 to 13} and Y = {multiples of 3 between 2 and 20}, find X ∩ Y.
   
   b) Find the Least Common Multiple (L.C.M) of the following numbers: 3, 5, and 9.
   
   c) If (p + 2q)/p = 7/5, find the value of q/p.
2. a) Solve (4x + 5)/5 + (x - 3)/4 = -1.
   
   b) The ratio of boys to girls in a school is 12:25. If there are 120 boys:
   
   (i) How many girls are in the school?
   
   (ii) What is the total number of boys and girls in the school?
   
   c) Simplify: (8x²y³)(⅜xy⁴).
3. a) In an examination, 60 candidates passed Integrated Science or Mathematics. If 15 passed both subjects and 9 more passed Mathematics than Integrated Science, find:
   
   (i) The number of candidates who passed in each subject.
   
   (ii) The probability that a candidate passed exactly one subject.
   
   b) Factorize: xy + 6x + 3y + 18.
4. a) Express 250% as a fraction in its lowest term.
   
   
   
   b) Use the diagram to find the value of x.
   
   c) Simplify: 2 ÷ (15/64 + 6/7).
   
   d) If q = (7, -1) and r = (4, -5), find q + r.
5. a) The mapping shows the relationship between x and y:
   
   x = {1, 2, 3, 4, 5}, y = {0, 3, 6, 9, 12}.
   
   i) 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 for 1 ≤ x ≤ 5 and 0 ≤ y ≤ 14.
   
   ii) Plot the points for each ordered pair, (x, y).
   
   iii) Join the points with a straight line.
   
   iv) Using the graph, find the gradient of the line.
   
   v) Use the graph to find the equation of the line.
   
   b) Simplify: 32 × 8 × 4 × 2, leaving the answer in the form 2ⁿ.
6. The marks obtained by students in a class test were:
   
   4, 8, 7, 6, 7, 2, 1, 7, 4, 7, 3, 7, 6, 4, 3, 7, 5, 2, 7, 2, 5, 4, 8, 3, 2.
   
   a) Construct a frequency distribution table for the data.
   
   b) Find:
   
   (i) The mode of the distribution.
   
   (ii) The median mark of the test.
   
   (iii) The mean mark.

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