BECE 2013 Mathematics Past Questions and Answers

Paper 1: Objectives

1. If A = {5,10,15,20,25,125} and B = {5,10,15,20,25,625}, list the elements of A ∪ B.
   1. A. {5,25}
   2. B. {10,20,125,625}
   3. C. {5,15,25,125,625}
   4. D. {5,10,15,20,25,125,625}
   Answer: D

   Union (∪) is the list of elements from each set. If an element occurs more than once, it is written only once.
2. Express 1.25 as a percentage.
   1. A. 25%
   2. B. 75%
   3. C. 125%
   4. D. 175%
   Answer: C

   Changing a decimal to a percentage is simply multiplying the decimal by 100. 1.25 x 100 = 125%.
3. Arrange the following in ascending order of magnitude: 0.301, 0.3, 0.33, 0.03.
   1. A. 0.03,0.3,0.301,0.33
   2. B. 0.03,0.301,0.3,0.33
   3. C. 0.33,0.3,0.301,0.03
   4. D. 0.33,0.301,0.3,0.03
   Answer: A

   Place values are compared to order decimals: 0.03, 0.3, 0.301, 0.33.
4. Evaluate 53 - (-7) + (-15).
   1. A. 31
   2. B. 45
   3. C. 61
   4. D. 75
   Answer: B

   Simplify: 53 - (-7) + (-15) = 53 + 7 - 15 = 45.
5. Given that A = {a, e, i, o, u} and B = {r, s, t}, how many elements are in A ∩ B?
   1. A. 0
   2. B. 1
   3. C. 2
   4. D. 3
   Answer: A

   Intersection (∩) is the set of elements in both sets. A ∩ B = {} since no elements are shared.
6. Convert 2114 to a base ten numeral.
   1. A. 194
   2. B. 280
   3. C. 284
   4. D. 300
   Answer: C

   Convert using base 5 powers: 2114_five = 2 × 125 + 1 × 25 + 5 + 4 = 284.
7. Simplify (2² × 3²) / (4² × 3³).
   1. A. 1/12
   2. B. 1/6
   3. C. 1/4
   4. D. 1/3
   Answer: A

   4² = (2²)² = 2⁴, so (2² × 3²)/(2⁴ × 3³) = 2⁻² × 3⁻¹ = 1/4 × 1/3 = 1/12.
8. A car uses 150 litres of petrol in 45 mins. How many litres will it use in 1 hour?
   1. A. 375 litres
   2. B. 230 litres
   3. C. 225 litres
   4. D. 200 litres
   Answer: D

   Convert time to minutes and solve proportionally: (150 × 60) / 45 = 200 litres.
9. Simplify (36a³b²x) / (27ab³y).
   1. A. 4a²x / 3by
   2. B. 4abx / 3y
   3. C. 4a²bx / 3y
   4. D. 4a⁴b⁵x / 3y
   Answer: A

   36/27 = 4/3; a³ ÷ a = a²; b² ÷ b³ = 1/b; so (36a³b²x)/(27ab³y) = 4a²x / 3by.
10. Find the rule of the mapping:
    

    x	1	2	3	4	5
    y	5	8	11	14	17

    1. A. x + 2
    2. B. x + 4
    3. C. 2x + 3
    4. D. 3x + 2
    Answer: D

    y increases by 3 each time x increases by 1, so y = 3x + c. When x = 1, y = 5, so c = 2. The rule is x → 3x + 2.

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11. Given that -1 = 2 - m, find m.
    1. A. -3
    2. B. -1
    3. C. 1
    4. D. 3
12. The perimeter of a rectangle is 48 cm. If the length is 14 cm, find its width.
    1. A. 24 cm
    2. B. 20 cm
    3. C. 10 cm
    4. D. 3.4 cm
13. Make d the subject of the relation n = 2d + 3.
    1. A. d = 3n / 2
    2. B. d = (n + 3) / 2
    3. C. d = (n - 3) / 2
    4. D. d = -3 - n / 2
14. Calculate the gradient of the straight line joining the points A(3,5) and B(-2,3).
    1. A. -5/2
    2. B. -2/5
    3. C. 2/5
    4. D. 5/2
15. 
    
    In an isosceles triangle with base angles of 50°, find the angle marked a.
    1. A. 70°
    2. B. 50°
    3. C. 40°
    4. D. 30°
16. 
    
    Use the diagram to find the angle marked b if it’s an isosceles triangle with base angles of 50°.
    1. A. 150°
    2. B. 140°
    3. C. 110°
    4. D. 100°
17. If S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, find the probability that a number selected at random from S is odd.
    1. A. 3/8
    2. B. 1/4
    3. C. 1/2
    4. D. 5/8
18. Find the vector which translates the point (4, -5) to (3, -2).
    1. A. (1, -3)
    2. B. (-1, 3)
    3. C. (1, 3)
    4. D. (-1, -3)
19. Factorize completely the expression 2xy - 6y + 7x - 21.
    1. A. (x - 3)(2y + 7)
    2. B. (x + 3)(2y - 7)
    3. C. (y - 3)(2x + 7)
    4. D. (y + 3)(2x - 7)
20. The area of a circle is 154 cm². Find the diameter. (Take π = 22/7).
    1. A. 7 cm
    2. B. 14 cm
    3. C. 21 cm
    4. D. 49 cm
21. Marne Esi rides her bicycle to school and back everyday. If the distance from her home to the school is 2345 m, how many kilometers does she cover everyday?
    1. A. 4.98 km
    2. B. 4.69 km
    3. C. 3.96 km
    4. D. 3.68 km
22. The length of a rectangular fence is 25 m. The ratio of the length to the width is 5:3. Find the width of the rectangular fence.
    1. A. 9 m
    2. B. 13 m
    3. C. 15 m
    4. D. 16 m
23. Evaluate 20/a - b, if a = 30 and b = 1.
    1. A. -1 2/3
    2. B. -1/3
    3. C. 1/3
    4. D. 1 2/3
24. How many 15Gp Christmas cards can be bought with GHC18.00?
    1. A. 120
    2. B. 150
    3. C. 180
    4. D. 270
25. If u = (6, 9) and v = (4, -5) are column vectors, find u + v.
    1. A. (-2, 2)
    2. B. (2, -4)
    3. C. (10, -14)
    4. D. (10, 4)
26. If 4956 x 25 = 123,900, evaluate 495.6 x 2.5 leaving the answer in standard form.
    1. A. 1.239 x 10⁴
    2. B. 1.239 x 10³
    3. C. 1.239 x 10²
    4. D. 1.239 x 10
27. 
    
    Which of the following expressions is illustrated on the number line?
    1. A. x ≤ -2
    2. B. x < -2
    3. C. x > -2
    4. D. x ≥ -2
28. If 180 oranges were shared among Kwame and Ama in the ratio 7:5, respectively, how many oranges did Ama receive?
    1. A. 45
    2. B. 60
    3. C. 75
    4. D. 90
29. Calculate the simple interest on GH450.00 for 2 years at 12% per annum.
    1. A. GHC 191.00
    2. B. GHC 108.00
    3. C. GHC 54.00
    4. D. GHC 27.00
30. If 15% of the length of a rope is 75 cm, find half of the length of the rope.
    1. A. 500 cm
    2. B. 250 cm
    3. C. 150 cm
    4. D. 100 cm
31. In an office, 2/3 of the telephone bill is paid by Tom, 1/5 by Azuma and the remaining by Tina. What fraction is paid by Tina?
    1. A. 2/15
    2. B. 1/4
    3. C. 1/3
    4. D. 7/15
32. 
    
    Which of the following best describes the construction?
    1. A. Constructing a perpendicular at P
    2. B. Constructing the bisector of line PQ
    3. C. Constructing an angle of 30° at P
    4. D. Constructing an angle of 45° at P
33. Express 0.055 as a common fraction.
    1. A. 11/40
    2. B. 5/18
    3. C. 1/40
    4. D. 11/200
34. The table below shows the distribution of workers in some trades.
    

    Trade	Shoe making	Mining	Road transport	Agriculture	Manufacturing goods
    Number of workers	300,000	25,000	160,000	225,000	165,000

    
    Which trade employed the most number of workers?
    1. A. Agriculture
    2. B. Manufacturing
    3. C. Shoe making
    4. D. Road transport
35. The table below shows the distribution of workers in some trades.
    

    Trade	Shoe making	Mining	Road transport	Agriculture	Manufacturing goods
    Number of workers	300,000	25,000	160,000	225,000	165,000

    
    How many people are employed under all the trades?
    1. A. 325,000
    2. B. 485,000
    3. C. 650,000
    4. D. 875,000
36. Ama bought a carton of fish at GHC 80.00 and sold it at a profit of GHC 13.60. Find the selling price.
    1. A. GHC 66.40
    2. B. GHC 93.60
    3. C. GHC 103.60
    4. D. GHC 144.00
37. 
    
    If the two figures ABCD and PQRS are similar, find the value of b.
    1. A. 60 cm
    2. B. 40 cm
    3. C. 33 cm
    4. D. 30 cm
38. A man shared an amount of money between his two children, Esi and Ato in the ratio 2:3 respectively. If Ato received GHC 45.00, what was the total amount shared?
    1. A. GHC 18.00
    2. B. GHC 27.50
    3. C. GHC 75.00
    4. D. GHC 112.50
39. How many edges does a cuboid have?
    1. A. 16
    2. B. 12
    3. C. 8
    4. D. 4
40. Two sets whose intersection is an empty set are:
    1. A. disjoint sets
    2. B. equivalent sets
    3. C. finite sets
    4. D. empty sets

Paper 2: Theory

1. a) Fifty students in a class took an examination in French and Mathematics. If 14 of them passed French only, 23 passed in both French and Mathematics, and 5 of them failed in both subjects, find:
   
   (i) the number of students who passed in French.
   
   (ii) the probability of selecting a student who passed in Mathematics.
   
   b) Solve the inequality 2x - 1 > 5x - 6.
2. a) Convert 444₅ to a base two numeral.
   
   b) A man had three GHC50.00, seven GHC20.00, and five GHC10.00 notes in his pocket. If he bought a bicycle for GHC150.00 and two mobile phones at GHC80.00 each, how many GHC20.00 and GHC10.00 notes did he have left?
3. a) Using a ruler and a pair of compasses only:
   
   (i) Construct a triangle XYZ with length XY = 7 cm, length YZ = 5 cm, and angle XYZ = 45°.
   
   (ii) Measure and write down the length of XZ.
   
   b) Given that the circumference of a circle is 44 cm, find:
   
   (i) the radius of the circle.
   
   (ii) the area of the circle.
4. The table shows the distribution of marks of students in a class test.
   
   Marks: 1, 2, 3, 4, 5, 6.
   
   Frequency: 5, 6, 5, 3, 4, 2.
   
   (a) Using a graph sheet, draw a bar chart for the distribution.
   
   (b) Calculate the mean mark of the distribution correct to the nearest whole number.
5. a) Simplify: 6(3 1/4 - 1 1/3).
   
   b) Copy and complete the magic square so that the sum of numbers in each row, column, or diagonal is 18:
   
   .
   
   c) Find the sum of all the factors of 24.
   
   d) Given vectors , find m + n + r.
6. a) Copy and complete the table for the relation y = 2x + 5.
   
   

   x	-3	-2	-1	0	1	2	3	4
   y	-1	1		5				13

   
   
   b) (i) Using a scale of 2 cm to 2 units on both axes, draw two perpendicular axes OX and OY on a graph sheet.
   
   (ii) Mark the x-axis from -6 to 10 and the y-axis from -6 to 14.
   
   (iii) Using the table, plot all the points of the relation y = 2x + 5 on the graph.
   
   (iv) Draw a straight line through the points.
   
   c) Use the graph to find:
   
   (i) y when x = 1.6.
   
   (ii) x when y = 10.

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