BECE 2015 Mathematics Past Questions and Answers

Paper 1: Objectives

1. List the members of the set Q = {Prime factors of 30}
   1. A. {2,3,5}
   2. B. {2,6,10}
   3. C. {3,5,15}
   4. D. {3,6,15}
   Answer: A

   Prime factors of 30 = 2 x 3 x 5, so Q = {2,3,5}.
2. Given that set P = {m, n, o, p}, find the number of subsets of P.
   1. A. 4
   2. B. 8
   3. C. 10
   4. D. 16
   Answer: D

   Number of subsets = 2^n, where n = number of elements. P has 4 elements, so 2⁴ = 16.
3. If M = {Multiples of 4 between 10 and 25} and N = {even numbers between 11 and 23}, find M ∪ N.
   1. A. {12,16,20}
   2. B. {14,18,22}
   3. C. {12,14,16,18,22}
   4. D. {12,14,16,18,20,22,24}
   Answer: D

   M = {12,16,20,24} and N = {12,14,16,18,20,22}. Union M ∪ N = {12,14,16,18,20,22,24}.
4. What is the place value of 7 in 24.376?
   1. A. Unit
   2. B. Ten
   3. C. Tenth
   4. D. Hundredth
   Answer: D

   7 is in the hundredth place, which is two places to the right of the decimal.
5. Find the Highest Common Factor of 24, 42, and 72.
   1. A. 4
   2. B. 6
   3. C. 7
   4. D. 12
   Answer: B

   Common prime factors of 24, 42, and 72 are 2 and 3. H.C.F = 2 x 3 = 6.
6. Express 120 (base 5) as a number in base 10.
   1. A. 25
   2. B. 27
   3. C. 32
   4. D. 35
   Answer: D

   120 (base 5) = 1 x 25 + 2 x 5 + 0 = 35 (base 10).
7. If p x q x r = 1197, and p = 19, q = 3, find r.
   1. A. 21
   2. B. 49
   3. C. 57
   4. D. 61
   Answer: A

   r = 1197 / (19 x 3) = 21.
8. How many integers are within the interval -5 < x < 7?
   1. A. 10
   2. B. 11
   3. C. 12
   4. D. 13
   Answer: B

   The integers in the interval -5 < x < 7 are -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, totaling 11.
9. Divide 1.612 by 0.4.
   1. A. 4.3
   2. B. 4.03
   3. C. 0.403
   4. D. 0.43
   Answer: B

   1.612 / 0.4 = 4.03.
10. Arrange the following fractions in ascending order: 5/8, 11/20, 7/10.
    1. A. 5/8, 11/20, 7/10
    2. B. 7/10, 5/8, 11/20
    3. C. 11/20, 5/8, 7/10
    4. D. 8/20, 10/40, 11/30
    Answer: C

    The LCM of denominators (20, 8, 10) is 40. Converted to equivalent fractions, ascending order: 11/20, 5/8, 7/10.

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11. Abena spent 3/5 of her money on sweets, 4/35 on provisions, and the rest on gari. What fraction did she spend on gari?
    1. A. 27/35
    2. B. 13/35
    3. C. 8/35
    4. D. 5/35
12. If 5 boys took 14 days to cultivate a piece of land, how long will it take 7 boys working at the same rate?
    1. A. 14 days
    2. B. 12 days
    3. C. 10 days
    4. D. 8 days
13. A man invested GHC800.00 in a bank at a simple interest rate of 5% per annum. Find his total amount in the bank at the end of one year.
    1. A. GHC840.00
    2. B. GHC860.00
    3. C. GHC900.00
    4. D. GHC960.00
14. John sold a car for GHC60,000.00 and made a profit of 20%. What is the cost price of the car?
    1. A. GHC48,000.00
    2. B. GHC50,000.00
    3. C. GHC72,000.00
    4. D. GHC132,000.00
15. What is the value of x if 10ˣ = 1000?
    1. A. 1
    2. B. 2
    3. C. 3
    4. D. 4
16. Express 625.13 in standard form.
    1. A. 6.2513 x 10³
    2. B. 6.2513 x 10¹
    3. C. 6.2513 x 10²
    4. D. 6.2513 x 10⁰
17. Find the median of the numbers 17, 12, 15, 16, 8, 18, 13, and 14.
    1. A. 8
    2. B. 12
    3. C. 14.5
    4. D. 15.5
18. The ages in years of 10 children at a party are 2, 3, 3, 3, 4, 4, 5, 5, 5, and 6. If a child is chosen at random, what is the probability that he or she is not less than 5 years old?
    1. A. 2/3
    2. B. 2/5
    3. C. 3/10
    4. D. 1/2
19. Expand (2x + y)(2x - y).
    1. A. 2x² + y²
    2. B. 4x² - y²
    3. C. 4x² + y²
    4. D. 4 + 4xy - y²
20. Find the value of n, if 25.003 = (2 x 10) + (5 x 1) + (3 x n).
    1. A. 0.001
    2. B. 0.011
    3. C. 0.01
    4. D. 0.1
21. Evaluate (3m) - 3m', when m = 2.
    1. A. 12
    2. B. 18
    3. C. 20
    4. D. 24
22. A wristwatch is priced GHC 2,000.00. A shopkeeper allows a discount of 2% on the cost price. Find the discount on 20 of such wristwatches.
    1. A. GHC 500.00
    2. B. GHC 600.00
    3. C. GHC 800.00
    4. D. GHC 1,000.00
23. Find the value of m if 4(m + 4) = -8.
    1. A. -6
    2. B. -2
    3. C. 2
    4. D. 6
24. Find the rule for the following mapping: x = 1, 2, 3, 4, 5; y = 1, 4, 9, 16, 25.
    1. A. y -> x + 2
    2. B. y -> 2x
    3. C. y -> x²
    4. D. y -> 2x + 2
25. How many vertices does a cuboid have?
    1. A. 6
    2. B. 7
    3. C. 8
    4. D. 14
26. The circumference of a circle is 440 m. Find the area of the circle. [Take π = 22/7]
    1. A. 14,400 m²
    2. B. 15,400 m²
    3. C. 16,400 m²
    4. D. 18,000 m²
27. What name is given to a triangle that has all its sides equal?
    1. A. Isosceles triangle
    2. B. Scalene triangle
    3. C. Equilateral triangle
    4. D. Right-angle triangle
28. At eight o'clock, what is the angle between the hour and minute hands of a clock?
    1. A. 150°
    2. B. 120°
    3. C. 90°
    4. D. 60°
29. A rectangular field 50 m wide and y m long requires 260 m of fencing. Find y.
    1. A. 15 m
    2. B. 40 m
    3. C. 80 m
    4. D. 105 m
30. Which of the following best describes the statement: 'The locus of a point which moves so that its distance from two fixed points are always equal'?
    1. A. Bisector of angle
    2. B. Perpendicular bisector
    3. C. Circle
    4. D. Two parallel lines
31. The point K(1,5) is rotated through 90° anti-clockwise about the origin. Find the coordinates of the image of K.
    1. A. (5,-1)
    2. B. (-5,1)
    3. C. (-1,5)
    4. D. (1,-5)
32. Kwame is facing west. Through how many degrees should he turn anti-clockwise to face north?
    1. A. 90°
    2. B. 180°
    3. C. 270°
    4. D. 360°
33. Given that vectors u = (-3, 5) and v = (2, -3), calculate 2v - u.
    1. A. (1, -1)
    2. B. (-1, 1)
    3. C. (-7, -11)
    4. D. (7, -11)
34. 
    
    What is the name of the figure above?
    1. A. Cuboid
    2. B. Kite
    3. C. Triangle
    4. D. Pyramid

35. 13	12	17
    E	F	10
    11	16	G

    
    Use the magic square above to find the value of F if the sum of each row is 42.
    1. A. 14
    2. B. 15
    3. C. 18
    4. D. 23

36. 13	12	17
    E	F	10
    11	16	G

    
    Use the magic square above to find the value of E if the sum of each row is 42.
    1. A. 14
    2. B. 15
    3. C. 18
    4. D. 23

37. 13	12	17
    E	F	10
    11	16	G

    
    Evaluate E + G using the values from the magic square above where each row sums to 42.
    1. A. 29
    2. B. 30
    3. C. 33
    4. D. 38
38. The hypotenuse and a side of a right-angled triangle are 13 cm and 5 cm respectively. Find the length of the third side.
    1. A. 8 cm
    2. B. 9 cm
    3. C. 12 cm
    4. D. 17 cm
39. Find the missing number in the sequence 11, 16, 22, 29, ..., 46, 56.
    1. A. 30
    2. B. 36
    3. C. 37
    4. D. 39
40. A hall 20 m long is represented on a diagram as 10 cm long. What is the scale of the diagram?
    1. A. 1:200
    2. B. 1:250
    3. C. 1:400
    4. D. 1:500

Paper 2: Theory

1. (a) In a class of 70 students, 40 belong to the Red Cross Society, 27 belong to the Girls' Guide Society, and 12 belong to both the Red Cross Society and the Girls' Guide Society. The remaining students do not belong to any of the two societies.
   
   (i) Illustrate the information on a Venn diagram.
   
   (ii) How many students belong to the Red Cross Society only?
   
   (iii) How many students do not belong to any of the two societies?
   
   (b) A farmer uses 1/3 of his land to plant cassava, 2/5 of the remaining land to plant maize, and the rest for vegetables. If vegetables cover an area of 10 acres, what is the total area of the farmer's land?
2. (a) Solve for x: 2/5 - x/3 < 4/3
   
   (b) At a rally attended by 520 people, 30% were Fantes, 25% Ewes, 15% Nzemas, 20% Gas, and the rest Gonjas.
   
   (i) How many Gonjas were at the rally?
   
   (ii) How many more Fantes than Nzemas were at the rally?
   
   (iii) Draw a pie chart to illustrate the information.
3. (a) Mr. Mensah's farm is 20 km from his house. He uses his car to travel y km of the distance from his house and then walks 1 1/2 hours at the rate of 3 km per hour to get to his farm. Find y.
   
   (b) The perimeter of a square field is the same as that of a rectangular field. If the length of the rectangular field is 8 km and the width is 5 km, calculate the area of the square field.
   
   (c) Find the gradient of the line which passes through the points M(2, -1) and K(-3, 6).
4. (a) Using a ruler and a pair of compasses only, construct triangle PST with ∠PST = 30°, [ST] = 9 cm, and [PS] = 12 cm.
   
   (b) With T as the center, draw a circle of radius 6 cm.
   
   (c) Construct the perpendicular bisector (mediator) of line PS.
   
   (d) Label the intersections of the circle and the mediator Q₁ and Q₂.
   
   (e) (i) Measure [Q₁Q₂].
   
   (ii) Measure ∠Q₁TQ₂.
5. (a) Anita bought 51 tubers of yam at 3 for GHC10.00. If she sold them and made a loss of 40%, how much did she sell each tuber of yam?
   
   (b) The volume of a cylinder closed at one end is 1056 cm³. If its height is 21 cm, find its:
   
   (i) Diameter
   
   (ii) Total surface area. [Take π = 22/7]
6. (a) (i) Copy and complete the following mapping:
   
   X = {1, 2, 3, 4, 5, 6, 7}
   
   Y = {5, 7, 9, 11, 13, 15, 17}
   
   (ii) Determine the rule for the mapping.
   
   (b) Draw two perpendicular axes Ox and Oy on a graph sheet.
   
   (c) Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis, mark the x-axis from 0 to 8 and the y-axis from 0 to 20.
   
   (d) Plot the point for each ordered pair (x, y) and join them with a straight line.
   
   (e) Find:
   
   (i) y when x = 0;
   
   (ii) x when y = 14.

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