BECE 2008 Mathematics Past Questions and Answers

Paper 1: Objectives

1. If 𝐐 = {𝟑, 𝟒, 𝟓, 𝟔, 𝟕, 𝟖} and 𝐑 = {𝟐, 𝟑, 𝟓, 𝟕}, and both 𝐐 and 𝐑 are subsets of 𝐌 = {𝟏, 𝟐, 𝟑, 𝟒, 𝟓, ... , 𝟐𝟎}, find 𝐐 ∩ 𝐑.
   1. A. {𝟑, 𝟓}
   2. B. {𝟓, 𝟕}
   3. C. {𝟑, 𝟓, 𝟕}
   4. D. {𝟐, 𝟑, 𝟓, 𝟕}
   Answer: C

   Intersection (∩) lists elements found in both sets. Elements in both 𝐐 and 𝐑 are {𝟑, 𝟓, 𝟕}.
2. List the members of the set {𝟐 ≤ 𝐱 ≤ 𝟓}.
   1. A. {𝟐, 𝟓}
   2. B. {𝟐, 𝟑, 𝟒}
   3. C. {𝟐, 𝟑, 𝟓}
   4. D. {𝟐, 𝟑, 𝟒, 𝟓}
   Answer: D

   {𝟐 ≤ 𝐱 ≤ 𝟓} includes 𝟐, 𝟑, 𝟒, and 𝟓.
3. Round 𝟖𝟗𝟐𝟏𝟒𝟔𝟓 to the nearest hundred.
   1. A. 𝟖𝟗𝟐𝟏𝟎𝟎𝟎
   2. B. 𝟖𝟗𝟐𝟏𝟒𝟎𝟎
   3. C. 𝟖𝟗𝟐𝟏𝟒𝟔𝟎
   4. D. 𝟖𝟗𝟐𝟏𝟓𝟎𝟎
   Answer: D

   The digit at the hundred's place is rounded up from 𝟒 to 𝟓 as the next digit is 𝟔. Result: 𝟖𝟗𝟐𝟏𝟓𝟎𝟎.
4. Express 𝟗𝟖 as a product of prime factors.
   1. A. 𝟐 × 𝟕
   2. B. 𝟐² × 𝟕
   3. C. 𝟐 × 𝟕²
   4. D. 𝟐³ × 𝟕
   Answer: C

   Prime factors of 𝟗𝟖 = 𝟐 × 𝟕².
5. Evaluate 𝟒(𝟖 - 𝟐) + 𝟓(𝟑 - 𝟖).
   1. A. -𝟑𝟏
   2. B. -𝟏
   3. C. 𝟑𝟕
   4. D. 𝟒𝟗
   Answer: B

   Simplifying: 𝟒(𝟔) + 𝟓(-𝟓) = 𝟐𝟒 - 𝟐𝟓 = -𝟏.
6. Arrange the following in descending order of magnitude: 𝟎.𝟑𝟐, 𝟐/𝟓, 𝟐𝟕%, 𝟏/𝟑.
   1. A. 𝟎.𝟑𝟐, 𝟐/𝟓, 𝟐𝟕%, 𝟏/𝟑
   2. B. 𝟎.𝟑𝟐, 𝟏/𝟑, 𝟐/𝟓, 𝟐𝟕%
   3. C. 𝟐𝟕%, 𝟎.𝟑𝟐, 𝟏/𝟑, 𝟐/𝟓
   4. D. 𝟐/𝟓, 𝟏/𝟑, 𝟎.𝟑𝟐, 𝟐𝟕%
   Answer: D

   As decimals: 𝟐/𝟓 = 𝟎.𝟒, 𝟏/𝟑 ≈ 𝟎.𝟑𝟑𝟑, 𝟎.𝟑𝟐, 𝟐𝟕% = 𝟎.𝟐𝟕. Descending order: 𝟐/𝟓, 𝟏/𝟑, 𝟎.𝟑𝟐, 𝟐𝟕%.
7. The ratio 𝟖 : 𝟏𝟐 is equivalent to 𝑦 : 𝟗. Find 𝑦.
   1. A. 𝟒
   2. B. 𝟓
   3. C. 𝟔
   4. D. 𝟕
   Answer: C

   Solving: 𝑦 = 𝟔.
8. Express 𝟎.𝟓𝟓 as a fraction in lowest terms.
   1. A. 𝟏𝟏/𝟐𝟎𝟎
   2. B. 𝟏𝟏/𝟐𝟎
   3. C. 𝟏𝟏/𝟐
   4. D. 𝟏𝟏/𝟓
   Answer: B

   𝟎.𝟓𝟓 = 𝟏𝟏/𝟐𝟎 after simplification.
9. 
   
   Which figure can be formed from the given net?
   1. A. Triangular prism
   2. B. Square pyramid
   3. C. Triangular pyramid
   4. D. Cuboid
   Answer: B

   A net with a square base forms a square pyramid.
10. Simplify 𝟓𝑤 + 𝟕𝑝 - 𝟒𝑤 + 𝟑𝑝.
    1. A. 𝟗𝑤 + 𝟏𝟎𝑝
    2. B. 𝑤 + 𝟏𝟎𝑝
    3. C. 𝑤 + 𝟒𝑝
    4. D. 𝟗𝑤 + 𝟒𝑝
    Answer: B

    Combine terms: 𝑤 + 𝟏𝟎𝑝.

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11. Osei bought a hat for ₵𝟓.𝟎𝟎 and sold it with a profit of 𝟐𝟎%. How much did Yaovi pay?
    1. A. ₵𝟒.𝟖𝟎
    2. B. ₵𝟓.𝟓𝟎
    3. C. ₵𝟔.𝟎𝟎
    4. D. ₵𝟕.𝟎𝟎
12. Simplify 𝟐⁹ ÷ 𝟐⁷.
    1. A. 𝟐
    2. B. 𝟐²
    3. C. 𝟐¹²
    4. D. 𝟐²⁷
13. Find the image of -𝟑 under the mapping 𝑥 → 𝟐(𝑥 + 𝟑).
    1. A. 𝟎
    2. B. 𝟐
    3. C. 𝟔
    4. D. 𝟏𝟐
14. A football field is 𝟏𝟐𝟎 𝐦 long and 𝟕𝟓 𝐦 wide. Find the perimeter.
    1. A. 𝟏𝟗𝟓 𝐦
    2. B. 𝟑𝟗𝟎 𝐦
    3. C. 𝟕𝟖𝟎 𝐦
    4. D. 𝟗𝟎𝟎 𝐦
15. A tank holds 𝟐𝟒𝟎 litres when full. How much is 𝟒/𝟓 full?
    1. A. 𝟔𝟎 litres
    2. B. 𝟏𝟑𝟐 litres
    3. C. 𝟏𝟗𝟐 litres
    4. D. 𝟐𝟒𝟎 litres
16. A man has 𝟔𝑥 sheep and 𝟓𝑦 goats. He sells 𝟑𝑥 sheep and 𝟐𝑦 goats. How many animals are left?
    1. A. 𝟑𝑥 - 𝟑𝑦
    2. B. 𝟑𝑥 + 𝟑𝑦
    3. C. 𝟗𝑥 - 𝟓𝑦
    4. D. 𝟗 + 𝟓𝑦
17. The average rainfall in May, June, and July is 𝟐𝟖𝟏, 𝟒𝟓𝟐, and 𝟐𝟔𝟓 mm, respectively. Find the total.
    1. A. 𝟔𝟗𝟔 mm
    2. B. 𝟗𝟑𝟎 mm
    3. C. 𝟗𝟗𝟖 mm
    4. D. 𝟏𝟎𝟐𝟎 mm
18. Find the mean rainfall over six months with a total of 𝟏𝟑𝟖𝟎 mm.
    1. A. 𝟐𝟑𝟎 mm
    2. B. 𝟐𝟖𝟏 mm
    3. C. 𝟑𝟔𝟔 mm
    4. D. 𝟒𝟓𝟐 mm
19. A trader buys pens at ₵𝟒.𝟖𝟎 per dozen and sells them at 𝟒𝟖 GP each. Find her profit percentage.
    1. A. 𝟓%
    2. B. 𝟏𝟎%
    3. C. 𝟏𝟓%
    4. D. 𝟐𝟎%
20. Find the angle through which the minute hand of a clock moves from 5:15 PM to 5:25 PM.
    1. A. 𝟑𝟎°
    2. B. 𝟒𝟓°
    3. C. 𝟔𝟎°
    4. D. 𝟏𝟐𝟎°
21. If E = {prime numbers between 10 and 20} and F = {odd numbers between 0 and 16}, find E ∩ F.
    1. A. {11}
    2. B. {11, 13}
    3. C. {3, 11, 13}
    4. D. {3, 11, 13, 15}
22. Write 17 in base 10 as a base two numeral.
    1. A. 1001
    2. B. 10001
    3. C. 11001
    4. D. 11011
23. What fraction of a revolution is 72°?
    1. A. 1/6
    2. B. 1/5
    3. C. 2/5
    4. D. 5/8
24. Express 6 days is to 3 weeks as a ratio in its simplest form.
    1. A. 1 : 2
    2. B. 2 : 1
    3. C. 2 : 7
    4. D. 7 : 2
25. The letters in the word HIPPOPOTAMUS are placed in a box. What is the probability of taking out a vowel?
    1. A. 1/12
    2. B. 3/12
    3. C. 5/12
    4. D. 7/12
26. 
    
    Find the perimeter of a kite with side lengths 16 cm and 22 cm.
    1. A. 38 cm
    2. B. 64 cm
    3. C. 76 cm
    4. D. 88 cm
27. Illustrate 3 < x < 5 on the number line, where x ∈ {rational numbers}.
    1. A.
    2. B.
    3. C.
    4. D.
28. How many lines of symmetry does an equilateral triangle have?
    1. A. 1
    2. B. 2
    3. C. 3
    4. D. 4
29. If p = (4, 3) and q = (-2, 7), find 4p - 2q.
    1. A. (12, -2)
    2. B. (12, 2)
    3. C. (20, -2)
    4. D. (20, 2)
30. Which of the following is not a quadrilateral?
    1. A. Hexagon
    2. B. Kite
    3. C. Rectangle
    4. D. Trapezium
31. 
    
    In a straight line, if 4x + 5x = 180°, find x.
    1. A. 20°
    2. B. 30°
    3. C. 40°
    4. D. 50°
32. 
    
    Given the triangle with angles 3x, 4x, and f, find the value of f.
    1. A. 10°
    2. B. 20°
    3. C. 40°
    4. D. 80°
33. Solve for k in 4k / 9 = 12.
    1. A. 23
    2. B. 25
    3. C. 27
    4. D. 29
34. Expand (a + 4)(a + 6).
    1. A. 2a + 24
    2. B. a² + 6a + 10
    3. C. a² + 10a + 10
    4. D. a² + 10a + 24
35. Find 12½% of GHC 80.00.
    1. A. GHC 8.00
    2. B. GHC 10.00
    3. C. GHC 12.00
    4. D. GHC 12.50
36. Write the number 34.1 in standard form.
    1. A. 3.41 × 10⁻²
    2. B. 3.41 × 10⁻¹
    3. C. 3.41 × 10⁰
    4. D. 3.41 × 10
37. Simplify 30 ÷ [5 × (-2)]
    1. A. -10
    2. B. -6
    3. C. -3
    4. D. 3
38. Find the highest common factor of 15 and 21.
    1. A. 1
    2. B. 3
    3. C. 5
    4. D. 7
39. The difference between two numbers is 168. If the smaller number is 113, find the other number.
    1. A. 223
    2. B. 271
    3. C. 281
    4. D. 291
40. If r = (2, 5) and t = (-2, -3), evaluate r + t.
    1. A. (0, -2)
    2. B. (0, 2)
    3. C. (4, 2)
    4. D. (4, 8)

Paper 2: Theory

1. a) E and F are subsets of the universal set U such that:
   
   U = {natural numbers less than 15}
   
   E = {even numbers between 1 and 15}
   
   F = {multiples of 4 between 9 and 15}
   
   (i) List the elements of U, E, and F.
   
   (ii) Draw a Venn diagram to show the sets U, E, and F.
   
   b) In a school, 7/10 of the pupils like Mathematics. Half of those pupils who like Mathematics are girls. If there are 240 pupils altogether in the school, how many girls like Mathematics?
   
   c) A typist charges 28 Gp for the first five sheets and 8 Gp for each additional sheet she types. How much will she earn if she types 36 sheets?
2. 
   
   a) The diagram AEBCD shows the shape of Mr. Awuah's garden, which is made up of a rectangular portion ABCD and a triangular portion AEB:
   
   AB = DC = 90 m, AD = BC = 70 m, AE = 48.5 m, and EB = 50 m. The height of the triangle is 20 m. Find:
   
   (i) The area of ABCD.
   
   (ii) The area of AEB.
   
   (iii) The total area of the garden.
   
   (iv) The perimeter of the garden.
   
   b) Find the value of x if (3x - 2)/5 is greater than (1 - 4x)/10 by 5.
3. a) A traffic survey gave the results shown in the table below:
   
   | Vehicle | Frequency |
   
   |----------|-----------|
   
   | Car | 15 |
   
   | Lorry | 12 |
   
   | Bus | 8 |
   
   | Bicycle | 25 |
   
   (i) Represent the information on a pie chart.
   
   (ii) What percentage of the vehicles were lorries?
   
   b) Akosua was granted a loan of GHC 96.00. The interest rate was 24% per annum. Calculate:
   
   (i) The interest at the end of the year.
   
   (ii) The total amount she had to pay at the end of the year.
   
   (iii) The amount she still owes if Akosua was able to pay only GHC 60.00 at the end of the year.
4. a) Copy and complete the table of values for the relations y₁ = 2x + 5 and y₂ = 3 - 2x for x from -4 to 3.
   
   

   x	-4	-3	-2	-1	0	1	2	3
   y₁ = 2x + 5	-3			3		7		11
   y₂ = 3 - 2x	11	9		5

   
   
   b) (i) Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis, draw two perpendicular axes OX and OY on a graph sheet.
   
   (ii) On the same graph sheet, draw the graphs of the relations y₁ = 2x + 5 and y₂ = 3 - 2x.
   
   c) Find the coordinates of the point where y₁ and y₂ meet.
   
   d) The vectors p = (2, 3), q = (2, 5) and r = 1/2(q + p). Find the vector r.
5. a) Using a ruler and a pair of compasses only:
   
   (i) Construct triangle ABC with sides AB = 7 cm, BC = 8 cm, and AC = 9 cm.
   
   (ii) Draw the perpendicular bisectors of the three sides.
   
   (iii) Locate the point of intersection, O, of the perpendicular bisectors.
   
   (iv) With center O and radius OA, draw a circle to pass through the vertices of the triangle.
   
   b) Measure and write down the radius of the circle you have drawn in (a)(iv).
   
   c) Find the product of (2x - 3) and (x - 1).
6. a) The marks obtained by 20 pupils in a test were:
   
   4, 8, 7, 6, 2, 1, 7, 4, 3, 7, 6, 4, 7, 5, 2, 7, 5, 4, 8, 3.
   
   (i) Construct a frequency distribution table for this data.
   
   (ii) What is the mode of the distribution?
   
   (iii) Calculate the mean mark.
   
   (iv) What percentage of the pupils passed if the pass mark is 6?
   
   (v) What is the probability that a pupil selected at random scored not more than 5 marks?
   
   b) Simplify 7 1/3 - 4 1/6 + 2 5/8.

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