BECE 2007 Mathematics Past Questions and Answers

Paper 1: Objectives

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

   Factors are numbers that divide 𝟑𝟎 without a remainder. Odd factors are {𝟏, 𝟑, 𝟓, 𝟏𝟓}.
2. 𝐌 = {𝑔, 𝑜, 𝑞, 𝑠} and 𝐖 = {ℎ, 𝑝, 𝑟, 𝑡}. Find 𝐖 ∪ 𝐌.
   1. A. {𝑞, 𝑟, 𝑠, 𝑡}
   2. B. {𝑔, ℎ, 𝑜, 𝑞, 𝑟}
   3. C. {𝑔, ℎ, 𝑜, 𝑞, 𝑟, 𝑡}
   4. D. {𝑔, ℎ, 𝑜, 𝑝, 𝑞, 𝑟, 𝑠, 𝑡}
   Answer: D

   Union (∪) lists elements from both sets without duplicates: {𝑔, ℎ, 𝑜, 𝑝, 𝑞, 𝑟, 𝑠, 𝑡}.
3. 
   
   Name the geometrical figure shown in the diagram.
   1. A. Cuboid
   2. B. Cone
   3. C. Pyramid
   4. D. Sphere
   Answer: B

   The shape is a cone.
4. Express 𝟓/𝟏𝟔 as a decimal fraction.
   1. A. 𝟎.𝟑𝟑𝟑𝟑
   2. B. 𝟎.𝟑𝟏𝟐𝟓
   3. C. 𝟎.𝟐𝟔𝟔𝟕
   4. D. 𝟎.𝟐𝟓𝟎𝟎
   Answer: B

   Dividing 𝟓 by 𝟏𝟔 yields 𝟎.𝟑𝟏𝟐𝟓.
5. If 𝑦 = -𝑥 + 𝟔, find 𝑦 when 𝑥 = 𝟒.
   1. A. -𝟐
   2. B. 𝟐
   3. C. 𝟒
   4. D. 𝟖
   Answer: C

   Substitute 𝑥 = 𝟒: 𝑦 = -𝟒 + 𝟔 = 𝟒.
6. The marks obtained by 𝟏𝟑 candidates are {𝟓, 𝟕, 𝟐, 𝟗, 𝟏𝟏, 𝟏𝟎, 𝟐, 𝟏𝟐, 𝟐, 𝟗, 𝟑, 𝟏𝟖, 𝟐}. What is the mode?
   1. A. 𝟐
   2. B. 𝟓
   3. C. 𝟗
   4. D. 𝟏𝟖
   Answer: A

   The mode is the score appearing most frequently: 𝟐 appears 𝟒 times.
7. Find the median of {𝟓, 𝟕, 𝟐, 𝟗, 𝟏𝟏, 𝟏𝟎, 𝟐, 𝟏𝟐, 𝟐, 𝟗, 𝟑, 𝟏𝟖, 𝟐}.
   1. A. 𝟗
   2. B. 𝟕
   3. C. 𝟓
   4. D. 𝟐
   Answer: B

   Ordered list: {𝟐, 𝟐, 𝟐, 𝟐, 𝟑, 𝟓, 𝟕, 𝟗, 𝟗, 𝟏𝟎, 𝟏𝟏, 𝟏𝟐, 𝟏𝟖}. The middle number is 𝟕.
8. 
   
   Find the angle marked 𝐗° in the pie chart showing 𝟑𝟔𝟎 pupils.
   1. A. 𝟑𝟎°
   2. B. 𝟒𝟎°
   3. C. 𝟏𝟎𝟎°
   4. D. 𝟏𝟓𝟎°
   Answer: B

   𝟏𝟓𝟎° + 𝟕𝟎° + 𝐗° + 𝟏𝟎𝟎° = 𝟑𝟔𝟎°; 𝐗° = 𝟒𝟎°.
9. 
   
   How many more students are in Yellow House than Blue House?
   1. A. 𝟑𝟎
   2. B. 𝟒𝟎
   3. C. 𝟕𝟎
   4. D. 𝟏𝟎𝟎
   Answer: A

   Yellow House: 𝟏𝟎𝟎; Blue House: 𝟕𝟎; Difference: 𝟏𝟎𝟎 - 𝟕𝟎 = 𝟑𝟎.
10. Express 𝟐𝟒𝟐 as a product of prime factors.
    1. A. 𝟐² × 𝟏𝟏²
    2. B. 𝟐 × 𝟏𝟏 × 𝟏𝟏
    3. C. 𝟐³ × 𝟏𝟏
    4. D. 𝟐⁴ × 𝟏𝟏
    Answer: B

    Prime factors of 𝟐𝟒𝟐 = 𝟐 × 𝟏𝟏 × 𝟏𝟏.

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11. Convert 𝟏𝟏𝟎𝟎𝟏𝟏 from binary (base 𝟐) to decimal (base 𝟏𝟎).
    1. A. 𝟓𝟏
    2. B. 𝟓𝟎
    3. C. 𝟒𝟖
    4. D. 𝟑𝟐
12. A die is thrown once. What is the probability of getting the number 𝟒?
    1. A. 𝟏/𝟔
    2. B. 𝟏/𝟑
    3. C. 𝟏/𝟐
    4. D. 𝟓/𝟔
13. Arrange the fractions 𝟓/𝟔, 𝟒/𝟓, and 𝟒/𝟕 in descending order.
    1. A. 𝟓/𝟔, 𝟒/𝟕, 𝟒/𝟓
    2. B. 𝟒/𝟕, 𝟒/𝟓, 𝟓/𝟔
    3. C. 𝟓/𝟔, 𝟒/𝟓, 𝟒/𝟕
    4. D. 𝟒/𝟓, 𝟓/𝟔, 𝟒/𝟕
14. Solve the inequality 𝟑𝑥 + 𝟔 < 𝟓𝑥 - 𝟐.
    1. A. 𝑥 < 𝟐
    2. B. 𝑥 ≤ 𝟐
    3. C. 𝑥 < 𝟒
    4. D. 𝑥 > 𝟒
15. If 𝟖𝑥 - 𝟑(𝟐𝑥 - 𝟒) = 𝟒, find the value of 𝑥.
    1. A. -𝟖
    2. B. -𝟒
    3. C. 𝟒
    4. D. 𝟖
16. 
    
    Find the size of angle 𝑦 in the diagram.
    1. A. 𝟕𝟓°
    2. B. 𝟖𝟎°
    3. C. 𝟏𝟎𝟎°
    4. D. 𝟏𝟎𝟓°
17. 
    
    Angles 𝐍𝐓𝐙 and 𝐐𝐙𝐓 are
    1. A. alternate angles
    2. B. corresponding angles
    3. C. complementary angles
    4. D. supplementary angles
18. Factorize 𝑝² + 𝑝𝑥
    1. A. 𝑝(𝑥 + 𝟐)
    2. B. 𝑝(𝑝 + 𝑥)
    3. C. 𝑝²(𝑥 + 𝟏)
    4. D. 𝑝(𝑥 + 𝟏)
19. Jojo and Fiifi share money in a 𝟑:𝟒 ratio. If Fiifi has ₵𝟏𝟒𝟎,𝟎𝟎𝟎, find the total amount shared.
    1. A. ₵𝟐𝟎𝟎,𝟎𝟎𝟎
    2. B. ₵𝟐𝟐𝟎,𝟎𝟎𝟎
    3. C. ₵𝟐𝟒𝟓,𝟎𝟎𝟎
    4. D. ₵𝟐𝟖𝟎,𝟎𝟎𝟎
20. Simplify 𝟔(𝟕𝑎 + 𝟒) - 𝟑(𝟖𝑎 + 𝟗)
    1. A. 𝟏𝟖𝑎 - 𝟑
    2. B. 𝟏𝟖𝑎 + 𝟓𝟏
    3. C. 𝟒𝟐𝑎 - 𝟐𝟕
    4. D. 𝟔𝟔𝑎 - 𝟑
21. A man invested ₵500,000.00 at 15% simple interest per annum for 2 years. Calculate the amount at the end of the period.
    1. A. ₵350,000.00
    2. B. ₵650,000.00
    3. C. ₵750,000.00
    4. D. ₵800,000.00
22. Make m the subject of p = 3m + 1 / m
    1. A. m = 3p + 1
    2. B. m = p - 3
    3. C. m = 1 / (p - 3)
    4. D. m = (3p + 1) / (p - 3)
23. Simplify 200 × 0.01 × 372, leaving your answer in standard form.
    1. A. 7.44 × 10¹
    2. B. 74.4 × 10¹
    3. C. 7.44 × 10²
    4. D. 7.44 × 10³
24. What percentage of 5 is 0.25?
    1. A. 4%
    2. B. 5%
    3. C. 20%
    4. D. 25%
25. 
    
    Calculate the area of the figure ABCD above with lengths 12 cm and 18 cm and height 6 cm.
    1. A. 72 cm²
    2. B. 90 cm²
    3. C. 108 cm²
    4. D. 126 cm²
26. In which of the following constructions is P equidistant from the points A and B?
    1. A.
    2. B.
    3. C.
    4. D.
27. If a : 27 = 6 : 18, find a.
    1. A. 4
    2. B. 9
    3. C. 51
    4. D. 81
28. 
    
    In the circle with center O, what is the name given to the shaded region if A and B are points on the circle?
    1. A. Chord
    2. B. Segment
    3. C. Sector
    4. D. Arc
29. An amount of ₵5,400.00 is shared among three sisters in the ratio of their ages 10, 6, and 2 years. Find the share of the youngest sister.
    1. A. ₵300.00
    2. B. ₵600.00
    3. C. ₵1,200.00
    4. D. ₵1,800.00
30. Find the Least Common Multiple (L.C.M) of 4, 5, and 6.
    1. A. 20
    2. B. 24
    3. C. 30
    4. D. 60
31. Expand (a + 2b)(a - 2b).
    1. A. a² - 4ab - 4b²
    2. B. a² + 4ab - 4b²
    3. C. a² - 4b²
    4. D. a² + 4
32. If a woman was paid ₵180,000 for working 45 days, how much would she be paid for one day?
    1. A. ₵40,000.00
    2. B. ₵45,000.00
    3. C. ₵54,000.00
    4. D. ₵81,000.00
33. Express 0.68 as a fraction in its lowest terms.
    1. A. ⁷/₂₅
    2. B. ¹⁷/₂₅
    3. C. ³/₅
    4. D. ⁷/₁₅
34. Write down all integers within the interval 21 < y ≤ 27.
    1. A. {21, 22, 23, 24, 25, 26, 27}
    2. B. {22, 23, 24, 25, 26, 27}
    3. C. {21, 22, 23, 24, 25, 26}
    4. D. {22, 23, 24, 25, 26}
35. Simplify (2⁶ × 3³) ÷ (2⁴ × 3²).
    1. A. 2²3¹
    2. B. 2³3¹
    3. C. 3²
    4. D. 2⁶3⁰
36. 
    
    Which of the following is represented by vector AB in the diagram?
    1. A. (5 cm, 045°)
    2. B. (5 cm, 135°)
    3. C. (5 cm, 180°)
    4. D. (5 cm, 225°)
37. Solve for y, if 3 + 3y = 1 - 13y.
    1. A. -¹/₈
    2. B. -¹/₄
    3. C. ¹/₈
    4. D. ¹/₄
38. Convert 37 base ten to a base two numeral.
    1. A. 100101
    2. B. 100111
    3. C. 101101
    4. D. 110101
39. The length of a rectangular playing field is 5 metres longer than its width. If the perimeter of the field is 150 metres, find its width.
    1. A. 30 metres
    2. B. 35 metres
    3. C. 40 metres
    4. D. 45 metres
40. Given vector a = (3, 2) and vector b = (1, -2), find 2a - b.
    1. A. (0, 2)
    2. B. (6, 2)
    3. C. (6, -2)
    4. D. (5, 6)

Paper 2: Theory

1. a) In a class of 39 students, 19 offer French and 25 offer Ga. Five students do not offer any of the two languages. How many students offer only French?
   
   b)
   In the diagram above, AC is parallel to DG, angle EFG = 118° and angle ABE = 83°. Find the value of:
   
   (i) angle CBF;
   
   (ii) x.
   
   c) A fair die is thrown once.
   
   (i) Write down the set of all possible outcomes.
   
   (ii) Find the probability of obtaining a multiple of 2.
   
   (iii) What is the probability of obtaining a prime number?
2. a) A water tank in the form of a cuboid of height 22 cm and a rectangular base of length 7 cm and width 5 cm is filled with water. The water is then poured into a cylindrical container of diameter 14 cm. Calculate the height of the water in the cylindrical container. [Take π = 22/7]
   
   b) A trader is given a 15% discount on goods bought from a factory. If the original price of an item in the factory is ₵45,000,000, calculate:
   
   (i) the discount on the item.
   
   (ii) the amount the trader paid for the item.
   
   c) Solve -3/5x ≤ 4x and illustrate your answer on the number line.
3. Using a ruler and a pair of compasses only:
   
   a) Construct triangle PQR such that |PQ| = 10 cm, angle QPR = 90° and angle PQR = 30°. Measure the length of |PR|.
   
   b) Bisect the angle QRP to meet PQ at M.
   
   c) With M as center, and radius MP, draw a circle.
   
   d) Measure the radius of the circle.
4. Marks scored in a class test:
   
   
   
   (a) (i) Write down the frequency table for the distribution.
   
   (ii) Use the table to find the mean mark.
   
   (b) If the pass mark is 4, how many pupils failed the test?
5. a) Mr. Jones used 173 units of electricity last month. If the charge for the first 110 units was ₵150 per unit and ₵200 per unit for the rest, calculate the total bill for Mr. Jones.
   
   b) Express 4 hours in seconds leaving your answer in standard form.
   
   c) Given the vectors r = (3, -5) and p = (-7, -9) and q = 2p - r, find q.

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