BECE 2005 Mathematics Past Questions and Answers

Paper 1: Objectives

1. 
   
   𝐴 = {𝑏, 𝑑, 𝑖, 𝑜, 𝑢}. 𝐵 has how many members?
   1. A. 𝟸
   2. B. 𝟹
   3. C. 𝟻
   4. D. 𝟽
   Answer: C

   𝐵 has 𝟻 members: {𝑏, 𝑑, 𝑖, 𝑜, 𝑢}.
2. Which of the following is not a factor of 𝟷𝟾?
   1. A. 𝟹
   2. B. 𝟺
   3. C. 𝟼
   4. D. 𝟿
   Answer: B

   A factor divides without remainder. 𝟹, 𝟼, and 𝟿 divide 𝟷𝟾, but 𝟺 does not.
3. Multiply 𝟶.𝟶𝟷𝟺 by 𝟶.𝟸
   1. A. 𝟶.𝟶𝟶𝟶𝟸𝟾
   2. B. 𝟶.𝟶𝟶𝟸𝟾
   3. C. 𝟶.𝟶𝟸𝟾
   4. D. 𝟶.𝟸𝟾
   Answer: B

   𝟶.𝟶𝟷𝟺 × 𝟶.𝟸 = 𝟶.𝟶𝟶𝟸𝟾.
4. If 𝐴 = {𝑏, 𝑐, 𝑖} and 𝐵 = {𝑎, 𝑒, 𝑓, 𝑖}, find 𝐴 ∩ 𝐵.
   1. A. {𝑎, 𝑏, 𝑐, 𝑒, 𝑓, 𝑖}
   2. B. {𝑓, 𝑖}
   3. C. {𝑎}
   4. D. {𝑖}
   Answer: D

   𝐴 ∩ 𝐵 = {𝑖}.
5. If a = 64 and b = 2², find $\frac{a}{b}$.
   1. A. 32
   2. B. 16
   3. C. $\frac{1}{16}$
   4. D. $\frac{1}{32}$
   Answer: B

   b = 2² = 4, so $\frac{a}{b}=\frac{64}{4}=16$.
6. Arrange the following numbers from the highest to the lowest: $\frac{2}{3}$, -7, 0.
   1. A. $-7,0,\frac{2}{3}$
   2. B. $-7,\frac{2}{3},0$
   3. C. $0,\frac{2}{3},-7$
   4. D. $\frac{2}{3},0,-7$
   Answer: D

   𝟸/𝟹 ≈ 𝟶.𝟼𝟽 > 𝟶 > -𝟽.
7. Simplify $2^2\times 3^2\times 2^3\times 3^4$.
   1. A. $2^2\times 3^6$
   2. B. $2^4\times 3^7$
   3. C. $2^5\times 3^6$
   4. D. $2^6\times 3^8$
   Answer: C

   $2^{2+3}\times 3^{2+4}=2^5\times 3^6$
8. In an examination, 𝟺𝟶% failed. If 𝟷𝟾𝟶 passed, how many students failed?
   1. A. 𝟷𝟸𝟶
   2. B. 𝟸𝟽𝟶
   3. C. 𝟹𝟶𝟶
   4. D. 𝟺𝟻𝟶
   Answer: A

   If 𝟼𝟶% = 𝟷𝟾𝟶, then 𝟷𝟸𝟶 students failed (𝟺𝟶%).
9. Evaluate $\frac{1}{3}[(5-1)-(2-7)]$
   1. A. -3
   2. B. -1
   3. C. 1
   4. D. 3
   Answer: D

   $\frac{1}{3}[4-(-5)]=\frac{1}{3}\times 9=3$
10. If 𝟼𝑛 + 𝟺 = 𝟷𝟼, find 𝑛.
    1. A. 𝟸
    2. B. 𝟹
    3. C. 𝟻
    4. D. 𝟼
    Answer: A

    𝟼𝑛 + 𝟺 = 𝟷𝟼 ⟹ 𝑛 = 𝟸.

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11. What is the next term in {𝟷, 𝟹, 𝟽, 𝟷𝟻, 𝟹𝟷, ... }?
    1. A. 𝟹𝟻
    2. B. 𝟹𝟿
    3. C. 𝟺𝟽
    4. D. 𝟼𝟹
12. Find the mean of: 𝟷𝟶, 𝟷𝟸, 𝟷𝟺, 𝟷𝟼.
    1. A. 𝟷𝟸
    2. B. 𝟷𝟹
    3. C. 𝟷𝟺
    4. D. 𝟷𝟻
13. Simplify $3a^2\times 2ab\times 4bc$
    1. A. $9a^3{b}^{2}c$
    2. B. $12a^2{b}^{2}c$
    3. C. $24a^2{b}^{2}c$
    4. D. $24a^3{b}^{2}c$
14. Expand 𝟹(𝟸𝑎 + 𝟹𝑏)
    1. A. 𝟸𝑎 + 𝟿𝑏
    2. B. 𝟻𝑎 + 𝟼𝑏
    3. C. 𝟼𝑎 + 𝟹𝑏
    4. D. 𝟼𝑎 + 𝟿𝑏
15. Find the area of a circle with diameter 𝟸𝟾 cm. [π = 𝟸𝟸/𝟽]
    1. A. 𝟺𝟺 𝑐𝑚²
    2. B. 𝟾𝟾 𝑐𝑚²
    3. C. 𝟹𝟻𝟸 𝑐𝑚²
    4. D. 𝟼𝟷𝟼 𝑐𝑚²
16. In sharing 95 oranges with Dede, Fofo kept 45 of them and shared the rest equally with Dede. How many oranges did Dede get?
    1. A. 𝟸𝟶
    2. B. 𝟸𝟻
    3. C. 𝟺𝟶
    4. D. 𝟻𝟻
17. If $c=\frac{b^2+4r}{2ar}$, find c when b = 3, r = 4 and a = 5.
    1. A. 𝟷𝟿/𝟺𝟶
    2. B. 𝟷𝟷/𝟸𝟶
    3. C. 𝟹/𝟾
    4. D. 𝟻/𝟾
18. A woman bought a sewing machine for ₵800,000.00 and sold it for ₵920,000.00. Find the percentage profit.
    1. A. 𝟷𝟸%
    2. B. 𝟷𝟹%
    3. C. 𝟷𝟻%
    4. D. 𝟷𝟼.𝟺%
19. Find the rule for the mapping: X: 𝟶, 𝟷, 𝟸, 𝟹, 𝟺; Y: 𝟻, 𝟿, 𝟷𝟹, 𝟷𝟽, 𝟸𝟷.
    1. A. 𝑦 = 𝑥 + 𝟻
    2. B. 𝑦 = 𝟺𝑥 + 𝟻
    3. C. 𝑦 = 𝟻𝑥 + 𝟺
    4. D. 𝑦 = 𝟼𝑥 + 𝟷
20. Find the volume of a cuboid with dimensions 𝟷𝟻 m × 𝟷𝟸 m × 𝟹 m.
    1. A. 𝟹𝟼 m³
    2. B. 𝟺𝟻 m³
    3. C. 𝟷𝟾𝟶 m³
    4. D. 𝟻𝟺𝟶 m³
21. A bag contains 4 blue and 8 red balls. What is the probability of picking a blue ball at random from the bag?
    1. A. 1/3
    2. B. 1/2
    3. C. 2/3
    4. D. 3/4
22. 
    
    Find the size of the angle marked y in the diagram.
    1. A. 35°
    2. B. 45°
    3. C. 55°
    4. D. 90°
23. An equilateral triangle has side 16 cm. A square has the same perimeter as the equilateral triangle. What is the area of the square?
    1. A. 48 cm²
    2. B. 96 cm²
    3. C. 144 cm²
    4. D. 256 cm²
24. Kofi deposited ₵500,000.00 with a bank for 2 years at a rate of 10% per annum. Find the simple interest.
    1. A. ₵10,000.00
    2. B. ₵20,000.00
    3. C. ₵50,000.00
    4. D. ₵100,000.00
25. Make T the subject of the relation $l^2=\frac{4{\pi }^{2}T}{g}$.
    1. A. $T=\frac{gl}{2\pi }$
    2. B. $T=\frac{g{l}^2}{2\pi }$
    3. C. $T=\frac{l^2}{4g{\pi }^2}$
    4. D. $T=\frac{g{l}^2}{4{\pi }^2}$
26. Evaluate 0.54 × 0.7 / 9
    1. A. 0.0042
    2. B. 0.042
    3. C. 0.42
    4. D. 4.2
27. Eric and Ebo are to share an amount of ₵800,000.00 in the ratio 5 : 3 respectively. What will be Ebo's share?
    1. A. ₵30,000.00
    2. B. ₵50,000.00
    3. C. ₵300,000.00
    4. D. ₵500,000.00
28. How many faces has a rectangular pyramid?
    1. A. 4
    2. B. 5
    3. C. 6
    4. D. 7
29. The perimeter of a rectangle is 24 cm. If the breadth of the rectangle is 4 cm, find the area of the rectangle.
    1. A. 32 cm²
    2. B. 48 cm²
    3. C. 64 cm²
    4. D. 144 cm²
30. Factorize $4a{b}^2-20b{a}^2$.
    1. A. $4a(b^2-5b)$
    2. B. $4b(b-5a)$
    3. C. $4ab(b-5a)$
    4. D. $4ab(a-5b)$
31. Solve the equation $\frac{2}{3}(x-3)=\frac{5}{6}(x+6)$.
    1. A. -42
    2. B. -12
    3. C. 18
    4. D. 42
32. Kofi had 100 mangoes and sold 80 of them. What is the percentage of mangoes left?
    1. A. 12.5%
    2. B. 18%
    3. C. 20%
    4. D. 25%
33. Find the median of the following marks: 2, 4, 10, 3, 6, 12.
    1. A. 4
    2. B. 5
    3. C. 6
    4. D. 10
34. In a class of 20 pupils, 8 pupils read Mathematics, 13 read English, and 3 read both Mathematics and English. How many pupils read English only?
    1. A. 2
    2. B. 3
    3. C. 5
    4. D. 10
35. How many pupils do not read either Mathematics or English?
    1. A. 2
    2. B. 3
    3. C. 5
    4. D. 7
36. Calculate 82.5 ÷ 0.25, expressing the answer in standard form.
    1. A. 3.3 × 10^-3
    2. B. 3.3 × 10
    3. C. 3.3 × 10²
    4. D. 3.3 × 10³
37. The price of a gas cooker costing ₵450,000.00 was increased by 10%. Find its new price.
    1. A. ₵45,000.00
    2. B. ₵49,000.00
    3. C. ₵405,000.00
    4. D. ₵495,000.00
38. What is the number of all possible outcomes of tossing a die?
    1. A. 2
    2. B. 3
    3. C. 4
    4. D. 6
39. 
    
    In the diagram, QRS is a triangle. Angle QRS = 50° and angle RST = 120°. Find angle RQS.
    1. A. 60°
    2. B. 65°
    3. C. 70°
    4. D. 80°
40. Which of the following dimensions form the sides of a right-angled triangle?
    1. A. 3 cm, 4 cm, 6 cm
    2. B. 3 cm, 5 cm, 7 cm
    3. C. 5 cm, 12 cm, 13 cm
    4. D. 5 cm, 13 cm, 17 cm

Paper 2: Theory

1. a) A boy has enough money to buy 14 pencils at C450.00 each. How many erasers costing C300.00 each can he buy with the same amount of money?
   
   b) A circle has a circumference of 44 cm. Calculate its radius if π = 22/7.
   
   c) Simplify 2 3/4 - 1 5/8 + 7/16.
   
   d) Solve 5(n + 6) = n.
2. a) Copy and complete the table for x + y = 180:
   
   | x | 0 | 30 | 60 | 90 | 120 | 150 | 180 |
   
   | y | | | | | | | |
   
   b) Using a scale of 2 cm to 20 units on both axes:
   
   (i) Draw two perpendicular axes OX and OY.
   
   (ii) Mark both axes from 0 to 180.
   
   (iii) Plot all the seven points and join them with a ruler.
   
   c) Using your graph, find:
   
   (i) y when x = 100;
   
   (ii) x when y = 70.
3. a) There are 30 boys in a sporting club. 20 of them play hockey and 15 play volleyball. Each boy plays at least one of the two games:
   
   (i) Illustrate the information on a Venn diagram.
   
   (ii) How many boys play volleyball only?
   
   b) Factorize xy + 3x + 6y + 18.
   
   c) Multiply (3 + x) by (5 - 2x).
4. A woman borrowed C2,000,000.00 from a bank at a rate of 15% per annum simple interest for 2 years:
   
   a) Find:
   
   (i) The interest for the 2 years.
   
   (ii) How much she paid in all to the bank after the 2 years.
   
   b) She used the C2,000,000.00 to purchase a fridge and sold it at a profit of 45%. Find the selling price of the fridge.
   
   c) If she used the amount raised from the sale of the fridge to pay for the bank loan and interest, find how much money is left.
5. The following marks were obtained by pupils in a test:
   
   6, 4, 8, 2, 8, 6, 8, 8, 8, 10, 8, 9, 8, 6, 10, 2, 2, 6, 6, 6.
   
   a) Construct a frequency distribution table for the data.
   
   b) What is the modal mark?
   
   c) Calculate the mean mark.
   
   d) How many pupils scored more than 6 marks?
   
   e) What is the probability that a student chosen at random obtained 2 marks?

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