BECE 2002 (Paper B) Mathematics Past Questions and Answers

Paper 1: Objectives

1. State the property used in the operation a(b+c) = ab + ac.
   1. A. Associative
   2. B. Distributive
   3. C. Commutative
   4. D. Universal
   Answer: B

   The distributive property states that multiplying the sum of two or more addends by a number is the same as multiplying each addend individually by the number and then adding the products together.
2. Simplify 0.1 x 0.02 x 0.003 (leaving your answer in standard form).
   1. A. 6 x 10⁻⁷
   2. B. 6 x 10⁻⁶
   3. C. 6 x 10⁵
   4. D. 6 x 10⁶
   Answer: B

   0.1 x 0.02 x 0.003 = 6 x 10⁻⁶.
3. Express 1/25 as a decimal fraction.
   1. A. 0.4
   2. B. 0.04
   3. C. 0.004
   4. D. 0.0004
   Answer: B

   1 divided by 25 equals 0.04.
4. In an examination, 25% of the candidates failed to obtain the pass mark. The number of candidates who passed was 150. How many candidates failed?
   1. A. 113
   2. B. 100
   3. C. 50
   4. D. 38
   Answer: C

   If 75% = 150, then 25% = 50.
5. How many faces has a cube?
   1. A. 8
   2. B. 6
   3. C. 5
   4. D. 4
   Answer: B

   
   
   A cube has 6 faces.
6. Simplify 2⁸ ÷ 2³.
   1. A. $2^{24}$
   2. B. $2^{10}$
   3. C. $2^5$
   4. D. $2^3$
   Answer: C

   Using the law of division of indices, 2⁸ ÷ 2³ = 2⁽⁸ ⁻ ³⁾ = 2⁵.
7. 
   
   How many pupils speak both Twi and Ga?
   1. A. 17
   2. B. 11
   3. C. 7
   4. D. 5
   Answer: A

   The intersection represents pupils who speak both Twi and Ga.
8. 
   
   How many pupils speak neither Twi nor Ga?
   1. A. 17
   2. B. 11
   3. C. 7
   4. D. 5
   Answer: D

   The region outside the two circles represents pupils who don't speak any of the two languages.
9. Find the least common multiple (LCM) of the numbers 10, 15, and 25.
   1. A. 30
   2. B. 60
   3. C. 120
   4. D. 150
   Answer: D

   Using prime factorization, LCM = 2 x 3 x 5² = 150.
10. 
    
    Which of the following expression is illustrated on the number line above?
    1. A. x < -3
    2. B. x ≤ -3
    3. C. x > -3
    4. D. x ≥ -3
    Answer: C

    The arrow direction indicates x > -3.

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11. Simplify (2a/3) - (a - b)/2.
    1. A. (a + 3b)/6
    2. B. (a - 3b)/6
    3. C. (a - b)/6
    4. D. (7a - 3b)/6
12. Correct 0.00025 to one significant figure.
    1. A. 0.2
    2. B. 0.003
    3. C. 0.0002
    4. D. 0.0003
13. If y : 28 = 5 : 7, find y.
    1. A. 5
    2. B. 20
    3. C. 31.2
    4. D. 37.5
14. Convert 121 base five to a base ten numeral.
    1. A. 21
    2. B. 35
    3. C. 36
    4. D. 40
15. Find the image of 4 under the following mapping.
    

    x	1	2	3	4	5
    y	4	7	10	k	16

    1. A. 11
    2. B. 12
    3. C. 13
    4. D. 14
16. The point K(3, 4) is rotated through 180° about the origin. Find its image.
    1. A. (-3, 4)
    2. B. (-4, 3)
    3. C. (-3, -4)
    4. D. (3, -4)
17. Arrange the following fractions in descending order of magnitude: 1/2, 17/20, 3/4.
    1. A. 3/4, 17/20, 1/2
    2. B. 17/20, 3/4, 1/2
    3. C. 20/4, 4/20, 2/1
    4. D. 1/2, 3/4, 17/20
18. 
    
    Which of the following best describes the construction shown?
    1. A. Constructing an angle of 60°
    2. B. Constructing the perpendicular bisector of AB
    3. C. Constructing a circle about the midpoint of AB
    4. D. Constructing an angle of 180°
19. Find the image of the point K(3, 5) when it is reflected in the x-axis.
    1. A. (3, 5)
    2. B. (5, 3)
    3. C. (3, -5)
    4. D. (-3, -5)
20. A set of furniture was sold for ₵300,000.00 at a profit of 20%. Find the cost price.
    1. A. ₵250,000
    2. B. ₵240,000
    3. C. ₵200,000
    4. D. ₵180,000
21. Make x the subject of the relation, v² = u² + 2ax.
    1. A. x = (u² + 2av²) / a
    2. B. x = (v² - u²) / a²
    3. C. x = (u² - v²) / 2a
    4. D. x = (v² - u²) / 2a
22. Three baskets contain 95 oranges, x oranges, and 2x oranges. How many oranges are in the three baskets?
    1. A. 96x
    2. B. 95 + 3x
    3. C. 95 + 2x²
    4. D. 98x
23. 
    
    Find the value of the angle marked y in a pie chart with sectors of 80°, 60°, and 120°.
    1. A. 90°
    2. B. 100°
    3. C. 110°
    4. D. 120°
24. 
    
    How many more students offered science subjects than Arts subjects given that the angles for science and arts are 120° and 80° in a 720-student pie chart?
    1. A. 40
    2. B. 80
    3. C. 160
    4. D. 240
25. Kofi is two years older than Ama. If the sum of their ages is 16, find Ama's age.
    1. A. 7 years
    2. B. 9 years
    3. C. 14 years
    4. D. 18 years
26. Given J = ½mv², if v = 4 and J = 12, find m.
    1. A. 1.5
    2. B. 3.0
    3. C. 3.6
    4. D. 6.3
27. 
    
    PQR is a right-angled triangle with area 6 cm² and |QR| = 3 cm. Find |PR|.
    1. A. 2 cm
    2. B. 3 cm
    3. C. 5 cm
    4. D. 6 cm
28. 
    
    A rectangle has a length of 8 cm and a breadth of 6 cm. How long is its diagonal?
    1. A. 10 cm
    2. B. 14 cm
    3. C. 28 cm
    4. D. 50 cm
29. Simplify $\frac{1}{3}(2\frac{2}{3}+\frac{5}{6})$.
    1. A. 13/4
    2. B. 7/6
    3. C. 13/18
    4. D. 31/18
30. A man divided his 360 cattle among his three sons in the ratio 7 : 6 : 5. How many cattle did the one with the smallest share receive?
    1. A. 100
    2. B. 120
    3. C. 140
    4. D. 160
31. The marks obtained by 9 students are 3, 3, 4, 5, 6, 7, 7, 7, 8. Find the median.
    1. A. 4
    2. B. 5
    3. C. 6
    4. D. 7
32. The marks obtained by 9 students are 3, 3, 4, 5, 6, 7, 7, 7, 8. What is the mode?
    1. A. 3
    2. B. 4
    3. C. 6
    4. D. 7
33. What is the fifth term of the sequence 1/3, 2/5, 7/15 ...?
    1. A. 4/9
    2. B. 5/11
    3. C. 6/13
    4. D. 3/5
34. 30 men dig a pit in 21 days. How many days will 14 men take?
    1. A. 20
    2. B. 25
    3. C. 30
    4. D. 45
35. A bag contains 6 white and 8 red balls. What is the probability of picking a white ball?
    1. A. 1/7
    2. B. 3/7
    3. C. 4/7
    4. D. 6/7
36. 
    
    Find the area of the face PQRV of a cuboid with dimensions x, y, and z.
    1. A. xy cm²
    2. B. yz cm²
    3. C. x² cm²
    4. D. xz cm²
37. A rod 200 cm long is broken into two parts. The shorter part is one-quarter of the rod. Express the shorter part as a percentage of the longer part.
    1. A. 25%
    2. B. 30%
    3. C. 33.33%
    4. D. 66.67%
38. 
    
    MN and PQ are straight lines. Find the value of the angle marked x.
    1. A. 65°
    2. B. 75°
    3. C. 85°
    4. D. 155°
39. Find the value of x in the equation x/4 = 2.
    1. A. 2
    2. B. 4
    3. C. 6
    4. D. 8
40. The circumference of a circular track is 15.4 m. Find the diameter. [Take π = 22/7]
    1. A. 4.9 m
    2. B. 22 m
    3. C. 24 m
    4. D. 24.5 m

Paper 2: Theory

1. a) Simplify 2 3/4 ÷ 3 3/8 - 1 1/2.
   
   b) There are 50 pupils in a class. Out of this number, 1/10 speak French only and 4/5 of the remainder speak both French and English. If the rest speak English only:
   
   (i) Find the number of students who speak:
   
   (α) both French and English
   
   (β) only English.
   
   (ii) Draw a Venn diagram to illustrate the above information.
2. A shop sells a pencil at ₵500.00 and a pen at ₵2,000.00:
   
   a) If Afua bought 8 pencils and 5 pens, how much did she pay together for them?
   
   b) The price of a pencil is increased by 20% and a pen by 10%. Find how much she will pay for 10 pencils and 8 pens.
3. Using a ruler and a pair of compasses only:
   
   a) Construct:
   
   (i) Triangle ABC such that AB = 12 cm, AC = 8 cm, and ∠BAC = 30°.
   
   (ii) A perpendicular from C to meet AB at M.
   
   b) Measure:
   
   (i) Angle ABC.
   
   (ii) |CM|.
   
   c) Calculate the area of triangle ABC.
4. a) Solve the inequality: (5x/6 - 3/4) - (2x/4 - 4/6) < 2.
   
   b) (i) Copy and complete the table of values for the relation y = 2x + 1:
   
   | x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
   
   | y | -5 | -3 | | 1 | 3 | | 7 | 9 |
   
   (ii) Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis, plot the ordered pairs (x, y) on a graph sheet.
   
   (iii) Use a ruler to join the points plotted.
   
   (iv) Use your graph to find:
   
   (α) x when y = 4.
   
   (β) y when x = -2.5.
5. The table shows the number of students in a JSS class who prepared various dishes for their practical:
   
   | Dish | No. of students |
   
   |-----------------------------|------------------|
   
   | Fufu and light soup | 5 |
   
   | Banku and Okro stew | 20 |
   
   | Fried rice | 30 |
   
   | Fried plantain and beans | 25 |
   
   | Boiled yam and palaver sauce | 10 |
   
   a) (i) Draw a pie chart for the distribution above.
   
   (ii) What dish was prepared most?
   
   (iii) What percentage of students prepared fried rice?
   
   b) What is the probability that a student chosen at random cooked fried plantain and beans?

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