BECE 2016 Mathematics Past Questions and Answers

Paper 1: Objectives

1. Which of the following is a finite set?
   1. A. {2,4,6,8,...}
   2. B. {1,2,3,4,...}
   3. C. {...,2,3,5,7}
   4. D. {3,6,9,12}
   Answer: D

   Finite sets have a countable number of elements. Only {3,6,9,12} has a finite number of elements.
2. Given that M = {a, b, c}, find the number of subsets of M.
   1. A. 3
   2. B. 4
   3. C. 6
   4. D. 8
   Answer: D

   Number of subsets = 2^n where n = 3. Therefore, subsets = 2³ = 8.
3. If P = {2,3,4,6,8} and Q = {1,2,3,4}, find P ∩ Q.
   1. A. {2,3,4}
   2. B. {7,9,10}
   3. C. {2,3,4,6,8}
   4. D. {1,2,3,4,6,8}
   Answer: A

   Intersection includes elements in both sets. P ∩ Q = {2,3,4}.
4. A boy bought 3 pairs of socks at GHC17.50 per pair and paid with two GHC50.00 notes. How much change was he given?
   1. A. GHC27.50
   2. B. GHC37.50
   3. C. GHC47.50
   4. D. GHC48.50
   Answer: C

   Cost for socks = 3 x GHC17.50 = GHC52.5. Payment = GHC100. Change = GHC100 - GHC52.5 = GHC47.5.
5. Find the Least Common Multiple (LCM) of the numbers 5, 10, and 12.
   1. A. 2 × 3 × 5
   2. B. 2 × 3² × 5
   3. C. 2² × 3 × 5
   4. D. 2² × 3² × 5²
   Answer: C

   5 = 5, 10 = 2 × 5, 12 = 2² × 3. LCM is the product of each prime factor in its highest power: LCM = 2² × 3 × 5 = 60.
6. Correct 48,947.2547 to the nearest hundred.
   1. A. 490
   2. B. 48,900
   3. C. 48,950
   4. D. 49,000
   Answer: B

   Rounding to the nearest hundred: the digit in tens is 4, so round down. Result: 48,900.
7. Simplify: 16 + 5.6 + 0.681
   1. A. 2.2281
   2. B. 22.281
   3. C. 222.81
   4. D. 2228.1
   Answer: B

   Addition result: 16 + 5.6 + 0.681 = 22.281.
8. Evaluate: 4/5 - 1/3 + 2/9
   1. A. 5/11
   2. B. 11/45
   3. C. 31/45
   4. D. 41/45
   Answer: C

   LCM of 5, 3, and 9 is 45. Convert each fraction: 36/45 - 15/45 + 10/45 = 31/45.
9. Arrange the following integers from least to highest: -4, 9, -10, -7, and 2.
   1. A. -10, -7, -4, 2, 9
   2. B. -10, 9, -7, -4, 2
   3. C. -4, -7, -10, 2, 9
   4. D. 2, -4, -7, 9, -10
   Answer: A

   Order of integers from least to highest: -10, -7, -4, 2, 9.
10. Simplify: (46 x 102) + (102 x 54)
    1. A. 1,020
    2. B. 10,200
    3. C. 102,000
    4. D. 1,020,000
    Answer: B

    Factor out 102: 102(46 + 54) = 102 x 100 = 10,200.

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. Correct 5178.3426 to two decimal places.
    1. A. 5178.00
    2. B. 5178.30
    3. C. 5178.34
    4. D. 5178.35
12. Find the simple interest on GHC120,000.00 for 5 months at 12% per annum.
    1. A. GHC6,000.00
    2. B. GHC7,200.00
    3. C. GHC50,000.00
    4. D. GHC72,000.00
13. Fifteen boys took 12 hours to weed a plot of land. If nine boys work at the same rate, how long will it take them?
    1. A. 6 hours
    2. B. 7.5 hours
    3. C. 11.5 hours
    4. D. 20 hours
14. A car costs GHC12,500.00. A discount of 9% is given for cash payment. What is the cash price?
    1. A. GHC10,250.00
    2. B. GHC11,250.00
    3. C. GHC11,375.00
    4. D. GHC13,625.00
15. Simplify: 5² × 2² × 5² × 2
    1. A. 2² × 5²
    2. B. 2² × 5⁴
    3. C. 2³ × 5²
    4. D. 2³ × 5⁴
16. The table shows the marks of some students in a test.
    

    Marks	0	1	2	3	4	5	6	7	8	9	10
    Number of students	3	4	5	4	5	4	7	3	4	2	2

    
    Use the information to find the modal mark.
    1. A. 2
    2. B. 5
    3. C. 6
    4. D. 10
17. The table shows the marks of some students in a test.
    

    Marks	0	1	2	3	4	5	6	7	8	9	10
    Number of students	3	4	5	4	5	4	7	3	4	2	2

    
    How many students failed if the pass mark was 4?
    1. A. 4
    2. B. 6
    3. C. 16
    4. D. 21
18. What is the probability of obtaining 4 when a fair die is tossed once?
    1. A. 1/6
    2. B. 1/2
    3. C. 2/3
    4. D. 5/6
19. Make P the subject of the relation R = (P + Q)/2.
    1. A. P = Q - 2R
    2. B. P = 2R - Q
    3. C. P = 2R + Q
    4. D. P = 2Q + R
20. Given t = p² + 1, find p when t = 10.
    1. A. 3.0
    2. B. 4.5
    3. C. 11.0
    4. D. 81.0
21. Simplify: 4(x + 2) - 3(x + 1).
    1. A. x + 5
    2. B. x + 11
    3. C. 7x + 5
    4. D. 7x + 11
22. When a number is doubled and the result is decreased by 9, the answer is 19. Find the number.
    1. A. 5
    2. B. 7
    3. C. 14
    4. D. 16
23. Solve the inequality 2x + 10 ≥ (7/2)x - 5.
    1. A. x ≥ 10
    2. B. x ≤ 10
    3. C. x ≤ 40
    4. D. x ≥ 40
24. Find the image of 5, under the mapping x -> 4x - 7.
    1. A. 3
    2. B. 13
    3. C. 20
    4. D. 27
25. An angle which is greater than 180 but less than 360 is
    1. A. a right angle
    2. B. an acute angle
    3. C. an obtuse angle
    4. D. a reflex angle
26. How many lines of symmetry does a rectangle have?
    1. A. 1
    2. B. 2
    3. C. 3
    4. D. 4
27. The perimeter of an isosceles triangle is 45 cm. Find the length of the third side, if each of the equal sides is 14 cm.
    1. A. 11 cm
    2. B. 14 cm
    3. C. 17 cm
    4. D. 31 cm
28. Find the area of a circle whose diameter is 7 cm. [Take π = 22/7]
    1. A. 1 cm²
    2. B. 38 cm²
    3. C. 44 cm²
    4. D. 54 cm²
29. The mean of three numbers is 12. If two of the numbers are 14 and 16, find the third number.
    1. A. 6
    2. B. 12
    3. C. 30
    4. D. 36
30. The sum of the interior angles of a regular polygon is 540°. Find the number of sides of the polygon.
    1. A. 7
    2. B. 6
    3. C. 5
    4. D. 4
31. 
    
    The figure QPR is an equilateral triangle. If angle PRS = (2x - 10)°, find the value of x.
    1. A. 55
    2. B. 65
    3. C. 85
    4. D. 95
32. The diagonal of a rectangle is 10 cm long. If the length of the rectangle is 8 cm, find its breadth.
    1. A. 2 cm
    2. B. 3 cm
    3. C. 5 cm
    4. D. 6 cm
33. In an enlargement, XY = XY'. If [XY] = 24 cm and [Y'] = 8 cm, calculate the scale factor of the enlargement.
    1. A. 1/32
    2. B. 1/24
    3. C. 1/8
    4. D. 1/3
34. Study the triangle of odd numbers below.
    

    13	b	c	19
    7	9	a
    3	5
    1

    
    Evaluate: 13 + b + c + 19.
    1. A. 62
    2. B. 64
    3. C. 74
    4. D. 76
35. Study the triangle of odd numbers below.
    

    13	b	c	19
    7	9	a
    3	5
    1

    
    Evaluate: a + b + c.
    1. A. 24
    2. B. 29
    3. C. 36
    4. D. 43
36. Simplify: (-3, 5) + (2, -7)
    1. A. (-1, 2)
    2. B. (-5, 12)
    3. C. (-1, -2)
    4. D. (-5, -12)
37. The bearing of X from Y is 196°. What is the bearing of Y from X?
    1. A. 16°
    2. B. 74°
    3. C. 106°
    4. D. 244°
38. If a = -4 and b = 3, evaluate (3a + 2b)/(ab).
    1. A. 3/2
    2. B. 1
    3. C. 1/2
    4. D. -3/2
39. The point P(-3, 7) is reflected in the x-axis. Find its image.
    1. A. (-3, -7)
    2. B. (-3, 7)
    3. C. (-7, 3)
    4. D. (3, -7)
40. The instrument used to measure the angle between two lines that meet at a point is known as a
    1. A. pair of compasses
    2. B. set-square
    3. C. protractor
    4. D. pair of dividers

Paper 2: Theory

1. a) In an examination, 50 candidates sat for either Mathematics or English Language. 60% passed in Mathematics and 48% passed in English Language. If each candidate passed in at least one of the subjects, how many candidates passed in:
   
   (i) Mathematics?
   
   (ii) English Language?
   
   b) Illustrate the information given in (a) on a Venn diagram.
   
   c) Using the Venn diagram, find the number of candidates who passed in:
   
   (i) both subjects;
   
   (ii) Mathematics only.
   
   d) If and are equal vectors, find the values of x and y.
2. a) The cost (P), in Ghana cedis, of producing n items is given by the formula P = (3/4)n + 1800. Find:
   
   (i) the cost of producing 2,000 items;
   
   (ii) the number of items that will be produced with GHC2,400.00;
   
   (iii) the cost when no items are produced.
   
   b) A passenger traveling by air is allowed a maximum of 20 kg luggage. A man has four bags weighing 3.5 kg, 15 kg, 2 kg, and 1.5 kg.
   
   (i) Find the excess weight of his luggage.
   
   (ii) Express the excess weight as a percentage of the maximum weight allowed.
3. a) A doctor treated 2,000 patients over a period of time. If he worked for 5 hours a day and spent 15 minutes on each patient, how many days did the doctor spend to treat all the patients?
   
   b) The pie chart shows the distribution of textbooks to six classes A, B, C, D, E, and F in a school:
   
   .
   
   (i) If class D was given 720 textbooks, how many textbooks were distributed to each of the remaining classes?
   
   (ii) What is the average number of textbooks distributed to the classes?
   
   (iii) How many classes had less than the average number of textbooks distributed?
4. a) Using a scale of 2 cm to 1 unit on both axes, draw on a graph sheet two perpendicular axes Ox and Oy for -5 < x < 5 and -5 < y < 5.
   
   (i) Plot, indicating the coordinates of all points P(1, 1), Q(1, 2), R(2, 2), and S(2, 1) on the graph sheet. Join the points to form square PQRS.
   
   (ii) Draw and indicate clearly all coordinates, the image P'Q'R'S' of square PQRS under an enlargement from the origin with a scale factor of 2.
   
   (iii) Draw and indicate clearly all coordinates, the image P"Q"R"S" of square PQRS under a reflection in the x-axis.
   
   b) Using the graph in (a), find the gradient of line RS.
5. a) Given that u = 4, t = 5, a = 10, and s = ut + (1/2)at², find the value of s.
   
   b) The selling price of a gas cooker is GHC450.00. If a customer is allowed a discount of 20%, calculate:
   
   (i) the discount;
   
   (ii) the amount paid by the customer.
   
   c) A crate of minerals containing 10 bottles of Coca-Cola and 14 bottles of Fanta was given to some children for a birthday party. If a child chose a drink at random from the crate, find the probability that it was Fanta.
6. a) Using a ruler and a pair of compasses only, construct:
   
   (i) triangle XYZ with [XY] = 9 cm, [YZ] = 12 cm, and [XZ] = 8 cm.
   
   (ii) the perpendicular bisector of line XY.
   
   (iii) the perpendicular bisector of line XZ.
   
   b) (i) Label the point of intersection of the two bisectors as T.
   
   (ii) With point T as center, draw a circle of radius 6 cm.
   
   c) Measure:
   
   (i) [TX];
   
   (ii) angle XYZ.

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