BECE 2018 Mathematics Past Questions and Answers

Paper 1: Objectives

1. Which of the following is arranged in ascending order?
   1. A. -25, -64, 4, 17
   2. B. -64, -25, 4, 17
   3. C. -64, -25, 17, 4
   4. D. 17, 4, -25, -64
   Answer: B

   Ascending order means from the lowest to the highest. Thus, -64, -25, 4, 17 is the correct order.
2. If P = {x: x is an even number greater than two and less or equal to twelve}, list the members of P.
   1. A. {2, 4, 2, 8, 10, 12}
   2. B. {3, 4, 6, 8, 10, 12}
   3. C. {2, 4, 6, 8, 10}
   4. D. {4, 6, 8, 10, 12}
   Answer: D

   Even numbers between greater than 2 and up to 12 are {4, 6, 8, 10, 12}.
3. Which of the following is an infinite set?
   1. A. {1, 2, ... , 5, 6, 7}
   2. B. {4, 6, 8, 10, 12}
   3. C. {2, 3, 5, 7, 11, ...}
   4. D. {3, 6, ... , 18, 21, ... 33, 36}
   Answer: C

   Infinite sets go on without end. {2, 3, 5, 7, 11, ...} represents an infinite set.
4. Find the H.C.F. of 18, 36, and 60.
   1. A. 2³ × 3⁵
   2. B. 2² × 3²
   3. C. 2³ × 3 × 5
   4. D. 2 × 3
   Answer: D

   The H.C.F. of 18, 36, and 60 is the product of common prime factors in their lowest powers: 2 × 3.
5. Write two hundred and two million, two thousand, two hundred and two in figures.
   1. A. 202,002,202
   2. B. 202,020,202
   3. C. 202,022,202
   4. D. 202,200,202
   Answer: A

   The correct figure is 202,002,202.
6. Find the least number that can be added to 207 to make the sum divisible by 17.
   1. A. 3
   2. B. 13
   3. C. 14
   4. D. 30
   Answer: C

   The least number is 14, making 207 + 14 = 221, which is divisible by 17.
7. If P = {factors of 36} and Q = {multiples of 4 less than 40}, find the number of subsets in P∩Q.
   1. A. 10
   2. B. 8
   3. C. 6
   4. D. 4
   Answer: B

   P ∩ Q = {4, 12, 36}, which has 3 elements. Number of subsets = 2³ = 8.
8. Find the L.C.M of 10, 15, and 25.
   1. A. 90
   2. B. 120
   3. C. 150
   4. D. 300
   Answer: C

   The L.C.M of 10, 15, and 25 is 150.
9. Evaluate (2/3 - 1/4) ÷ 5/6.
   1. A. 1/2
   2. B. 12/25
   3. C. 5/12
   4. D. 1/5
   Answer: A

   Simplify the bracket first (BODMAS): 2/3 - 1/4 = (8 - 3)/12 = 5/12.
   
   5/12 ÷ 5/6 = 5/12 × 6/5 = 1/2.
10. Arrange 2/3, 4/9, and 3/7 in ascending order.
    1. A. 2/3, 4/9, 3/7
    2. B. 3/7, 2/3, 4/9
    3. C. 4/9, 2/3, 3/7
    4. D. 3/7, 4/9, 2/3
    Answer: D

    Convert all fractions to have a common denominator and arrange in ascending order.

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11. Find the simple interest on GHC 600.00 saved for 2 years 8 months at 5% per annum.
    1. A. GHC 64.00
    2. B. GHC 80.00
    3. C. GHC 84.00
    4. D. GHC 92.00
12. The number of girls in a mixed school is 420. If the ratio of boys to girls in the school is 3:2, how many students are in the school?
    1. A. 1050
    2. B. 1470
    3. C. 1630
    4. D. 1680
13. Mary had a chance to select a number from 1 to 20 randomly. What is the probability that the number is divisible by 3?
    1. A. 3/20
    2. B. 1/5
    3. C. 3/10
    4. D. 7/20
14. Ama bought a pair of sandals for GHC 20.00 and sold it at GHC 24.00. Find the percentage profit.
    1. A. 4%
    2. B. 17%
    3. C. 20%
    4. D. 44%
15. 8 men can do a piece of work in 12 days. How long will 6 men take to do the same work if they work at the same rate?
    1. A. 14 days
    2. B. 16 days
    3. C. 18 days
    4. D. 20 days
16. 
    
    In the diagram, QP is parallel to ST, angle QPR = 68 and angle SRT = 40°. Find the value of angle PQR.
    1. A. 40°
    2. B. 68°
    3. C. 72°
    4. D. 108°
17. 
    
    In the diagram, QP is parallel to ST, angle QPR = 68 and angle SRT = 40. Find the value of angle TSR.
    1. A. 40°
    2. B. 68°
    3. C. 72°
    4. D. 112°
18. A train is travelling at a speed of 60 km/h. What distance will it cover from 10.45 am to 12.15 pm?
    1. A. 75 km
    2. B. 87 km
    3. C. 90 km
    4. D. 150 km
19. The perimeter of a rectangle is 26 cm. If its length is 10 cm, find its area.
    1. A. 30 cm²
    2. B. 60 cm²
    3. C. 130 cm²
    4. D. 160 cm²
20. Find the slope of the line 3x - 6y = 33.
    1. A. -3
    2. B. -1/2
    3. C. 1/2
    4. D. 3
21. If y = c + bx², find y when c = 14/5, b = 4/5 and x = 2.
    1. A. 3
    2. B. 4
    3. C. 6
    4. D. 7
22. The volume of a cylinder is 20π cm³. If the height of the cylinder is 5 cm, find the base radius.
    1. A. 1 cm
    2. B. 2 cm
    3. C. 3 cm
    4. D. 4 cm
23. 
    
    In the diagram, PQR is a right-angled triangle with [PR] = 15 cm and [QR] = 12 cm. Find the length PQ.
    1. A. 3.0 cm
    2. B. 8.0 cm
    3. C. 9.0 cm
    4. D. 19.2 cm
24. How many edges does a triangular prism have?
    1. A. 3
    2. B. 5
    3. C. 6
    4. D. 9
25. Make m the subject of the relation: 3q = (m + n)h.
    1. A. m = 3q - n / h
    2. B. m = 3q - hn
    3. C. m = 3q + hn
    4. D. m = 3q - 4h
26. Simplify 16² × 8².
    1. A. 2¹⁰
    2. B. 2¹⁴
    3. C. 2¹⁵
    4. D. 2¹⁶
27. Simplify: 4a - 9b - 2(2a - 3b).
    1. A. 8a + 3b
    2. B. 8a - 3b
    3. C. -15b
    4. D. -3b
28. If u = (3, 1) and v = (-2, 1), evaluate 6v + 2u.
    1. A. (-1, 3)
    2. B. (-6, 8)
    3. C. (1, 3)
    4. D. (6, 8)
29. Find the image of the point (2,5) under the transformation (x - 2, y).
    1. A. (2, -3)
    2. B. (2, 2)
    3. C. (2, 3)
    4. D. (2, 7)
30. Find the image of Q(-4,5) when rotated anticlockwise through 90° about the origin.
    1. A. (4,5)
    2. B. (-5, -4)
    3. C. (4, -5)
    4. D. (-5, 4)
31. The following data show the marks of students in a test: 10,4,1,4,3,3,2,1,1,7,8. How many students scored more than the pass mark of 4?
    1. A. 1
    2. B. 2
    3. C. 3
    4. D. 4
32. The following data show the marks of students in a test: 10,4,1,4,3,3,2,1,1,7,8. Find the mean mark.
    1. A. 3
    2. B. 4
    3. C. 7
    4. D. 8
33. How many lines of symmetry does a rhombus have?
    1. A. 2
    2. B. 3
    3. C. 4
    4. D. 5
34. In an enlargement, length AB = 3 cm and length of image A1B1 = 15 cm. Calculate the scale factor.
    1. A. 1/5
    2. B. 2/3
    3. C. 5
    4. D. 12
35. Find the rule of the mapping: X = 0, 3, 6, 9, 12; Y = -2, 4, 10, 16, 22.
    1. A. y -> x/2
    2. B. y -> x - 2
    3. C. y -> x² - 2
    4. D. y -> 2x - 2
36. Solve the inequality: 1/2(3x - 1) + 1 ≤ 7 + 2x.
    1. A. x ≥ -14
    2. B. x ≤ -14
    3. C. x ≥ -13
    4. D. x ≤ -13
37. If 4 - x = 3(4x + 5), find the value of x.
    1. A. 11/13
    2. B. 6/13
    3. C. -1/6
    4. D. -11/13
38. In a class, there are 12 girls and 48 boys. Find the percentage of boys in the class.
    1. A. 20%
    2. B. 40%
    3. C. 60%
    4. D. 80%
39. The bearing of P from Q is 060°. Find the bearing of Q from P.
    1. A. 120°
    2. B. 150°
    3. C. 210°
    4. D. 240°
40. 
    
    Which of the following statements best describes the construction below?
    1. A. Construction of line AB from P.
    2. B. Construction of perpendicular from P to meet line AB.
    3. C. Construction of an arc of a circle with center P.
    4. D. Construction of the bisector of line AB.

Paper 2: Theory

1. (a) Solve the inequality 5x - 3 ≥ (15x - 11)/2 and represent the answer on a number line.
   
   (b) Given that t = (-1, 3) and k = (2, -4), find 2t + k.
   
   (c) The sides of a triangle are in the ratio 6:8:10. If the perimeter of the triangle is 288 cm, find the:
   
   (i) longest side
   
   (ii) shortest side
   
   (iii) difference between the longest and shortest sides.
2. (a) An English textbook costs GHC 25.00. The author of the book agreed to take 20% of the cost of each book sold. If 1,702 copies were sold, calculate the author's share.
   
   (b) Simplify: (2/15 + 2/5) + (9/10 × 4/3) + (1/5 ÷ 1/4).
   
   
   
   (c) In the diagram, [MN] = 13 cm, [MP] = 15 cm, [MS] = 12 cm, and MS is perpendicular to NP. Calculate length NP.
3. (a) Simplify 0.084 × 0.81 / 0.027 × 0.04, leaving the answer in standard form.
   
   (b) (i) Make r the subject of the relation y = (x - r)/(x + r).
   
   (ii) From (b)(i), find the value of r when y = 3 and x = 10.
   
   (c) Juliet bought 1,756 kg of frozen chicken, 675 g of vegetables, and 95 g of corn oil from a shopping mall. What is the total weight of the items she bought in kilograms?
4. (a) The sum of the interior angles of a regular polygon is 900°. Find the number of sides of the polygon.
   
   (b) Using a ruler and a pair of compasses only, construct:
   
   (i) Triangle XYZ such that length XY = 10 cm, ∠XYZ = 30°, and length YZ = 9 cm.
   
   (ii) Perpendicular from Z to meet line XY at P.
   
   (iii) Measure the:
   
   (I) Length PZ
   
   (II) Angle XZY.
   
   (iv) Calculate, correct to the nearest whole number, the area of triangle XYZ.
5. (a) A property worth GHC 10,480.00 is shared between a widow and her 10 children in the ratio 1:4 respectively. The children shared their portion equally. Find each child's share.
   
   (b) The data shows the distribution of marks in a class test:
   
   27, 55, 19, 65, 69, 46, 38, 42, 14, 57, 11, 13, 14, 67, 22, 10, 25, 17, 45, 39, 61, 52, 43, 24, 28, 63, 56, 49, 64, 32.
   
   (i) Make a stem-and-leaf plot of the data.
   
   (ii) How many students scored more than 10 marks and less than 20 marks?
   
   (iii) What is the probability of a student scoring less than 20 marks?
6. (a) An aeroplane left Kotoka International Airport on Wednesday at 7:26 pm and reached its destination after nine hours thirty minutes. Find the day and time the aeroplane reached its destination.
   
   (b) (i) Using a scale of 2 cm to 2 units on both axes, draw two perpendicular axes Ox and Oy for -10 ≤ x ≤ 10 and -12 ≤ y ≤ 12.
   
   (ii) Draw on this graph indicating the coordinates of all vertices, the quadrilateral ABCD with vertices A(0, 10), B(-6, -2), C(-3, -11), and D(4, 3).
   
   (iii) Draw the line x = -2 to meet AB at P and CD at Q.
   
   (iv) Measure angles BPQ and PQD.
   
   (v) State the relationship between:
   
   (I) Angles BPQ and PQD
   
   (II) Lines AB and CD.

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