BECE 2011 Mathematics Past Questions and Answers

Paper 1: Objectives

1. Which of the following is the set of prime factors of 12?
   1. A. {2,3}
   2. B. {1, 2, 3}
   3. C. {1, 2, 4, 6}
   4. D. {2, 3, 4, 6}
   Answer: A

   Prime numbers have only two factors, 1 and itself. 12's prime factors are {2,3}.
2. Expand 3a(a - 4b)
   1. A. 3a - 12ab
   2. B. 3a² - 12ab
   3. C. 3a² + 12b
   4. D. 3a² + 12a
   Answer: B

   3a(a - 4b) = 3a² - 12ab by distributing 3a to each term in the bracket.
3. Express 5 as a percentage of 4.
   1. A. 125%
   2. B. 120%
   3. C. 25%
   4. D. 20%
   Answer: A

   (5/4) x 100% = 125%.
4. Express 2700 as a product of prime numbers.
   1. A. 2³ × 5
   2. B. 2³ × 3⁵
   3. C. 2² × 3³ × 5²
   4. D. 2³ × 5³
   Answer: C

   Prime factorization of 2700: 2² × 3³ × 5².
5. The ratio of mangoes to oranges in a basket is 3:2. If there are 36 mangoes, how many oranges are in the basket?
   1. A. 90
   2. B. 60
   3. C. 24
   4. D. 12
   Answer: C

   36 mangoes correspond to ratio 3, so 2 × (36 / 3) = 24 oranges.
6. Express 0.125 as a fraction in its lowest form.
   1. A. 1/8
   2. B. 1/9
   3. C. 1/12
   4. D. 1/16
   Answer: A

   0.125 = 125/1000 = 1/8 after simplifying.
7. Convert 222 (base 5) to a number in base ten.
   1. A. 30
   2. B. 52
   3. C. 60
   4. D. 62
   Answer: D

   222 (base 5) = 2×25 + 2×5 + 2×1 = 62.
8. If A = {18, 19, 20} and B = {15, 16, 17}, find A ∩ B.
   1. A. {15, 16, 17, 18, 19, 20}
   2. B. {15, 16, 18, 19}
   3. C. {18, 19}
   4. D. {}
   Answer: D

   Intersection (∩) lists elements common in both sets. No common elements in A and B.
9. Simplify 3⁹ ÷ 3³.
   1. A. 3²⁷
   2. B. 3¹²
   3. C. 3⁶
   4. D. 3³
   Answer: C

   Using the law of indices, a^m ÷ a^n = a^(m - n): 3⁹ ÷ 3³ = 3⁹⁻³ = 3⁶.
10. An article which costs GH¢ 25.00 was sold for GH¢ 35.00. Find the percentage profit made.
    1. A. 10%
    2. B. 28%
    3. C. 40%
    4. D. 70%
    Answer: C

    Profit % = (Selling Price - Cost Price) / Cost Price x 100% = 40%.

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11. Factorize completely b² + fb - mb - fm.
    1. A. (bf)(b - m)
    2. B. (b + f)(b - m)
    3. C. (b + f)(m - b)
    4. D. (b + f)(m + b)
12. Simplify: -13 - (-3) + (-10).
    1. A. -26
    2. B. -20
    3. C. -10
    4. D. -6
13. Find the HCF of 3³ × 5² and 3² × 5⁴.
    1. A. 3² × 5²
    2. B. 3³ × 5²
    3. C. 3² × 5⁴
    4. D. 3⁵ × 5⁶
14. State the rule for the mapping x → y in the relation: x = {1, 2, 3, 4}, y = {15, 30, 45, 60}.
    1. A. x → 15x
    2. B. x → 15 + x
    3. C. y → 15x
    4. D. x → 10 + 5x
15. Solve the inequality x - 1/3 ≥ 2/3 - x.
    1. A. x ≤ 1/2
    2. B. x ≤ 2/3
    3. C. x ≥ 1/2
    4. D. x ≥ 2/3
16. Find the area of a square if its perimeter is 28 cm.
    1. A. 784 cm²
    2. B. 196 cm²
    3. C. 49 cm²
    4. D. 14 cm²
17. Simplify: 1/3(1/2 - 1/3) - 1/3(1/3 - 1/2).
    1. A. -1/9
    2. B. -1/18
    3. C. 1/18
    4. D. 1/9
18. Make n the subject of the relation θ = 180 - 360/n.
    1. A. (θ + 180)/2
    2. B. (θ - 180)/2
    3. C. 360/(180 - θ)
    4. D. 360/(180 + θ)
19. If R = h/2 + d²/(8h), find R when d = 8 and h = 6.
    1. A. 3 1/6
    2. B. 4 1/3
    3. C. 4 3/4
    4. D. 4 9/16
20. Eight copies of a book cost GHC 16.00. Find the cost of 5 copies.
    1. A. GHC 2.00
    2. B. GHC 3.20
    3. C. GHC 5.00
    4. D. GHC 10.00
21. Solve the equation 1/5(2 + y) = 1/2(y - 1).
    1. A. -3
    2. B. 3/4
    3. C. 5/3
    4. D. 3
22. The gradient of the straight line that passes through points A(3,2) and B(4,8) is:
    1. A. 1/6
    2. B. 1/2
    3. C. 2
    4. D. 6
23. A car is travelling at 60 km per hour. How far does it travel in 2.5 hours?
    1. A. 30 km
    2. B. 60 km
    3. C. 120 km
    4. D. 150 km
24. 
    
    In the following diagram, RS and WV are parallel lines. The value of the angle marked a is:
    1. A. 38°
    2. B. 52°
    3. C. 58°
    4. D. 64°
25. Given that a = (5, 2n) and b = (2n - 1, 6). If a = b, find the value of n.
    1. A. 6
    2. B. 3
    3. C. 2
    4. D. 1
26. Find the volume of a cube of side 5 cm.
    1. A. 10 cm³
    2. B. 15 cm³
    3. C. 25 cm³
    4. D. 125 cm³
27. 
    
    In the diagram below, AB and CD are two intersecting straight lines. Find the value of the angle marked y.
    1. A. 130°
    2. B. 115°
    3. C. 65°
    4. D. 60°
28. Kwame and Ama shared an amount of money in the ratio 5:4, respectively. If Kwame had GHC 9.00, how much did they share?
    1. A. GHC 16.20
    2. B. GHC 36.00
    3. C. GHC 45.00
    4. D. GHC 81.00
29. 
    
    The area of the trapezium above is:
    1. A. 120 cm²
    2. B. 180 cm²
    3. C. 256 cm²
    4. D. 360 cm²
30. If r = (2, -5) and s = (-2, 5), calculate 2r - 3s.
    1. A. (-10, -25)
    2. B. (-2, -25)
    3. C. (10, -25)
    4. D. (10, 25)
31. There are 10 red and 15 green balls in a bag. Find the probability of selecting at random a red ball from the bag.
    1. A. 3/5
    2. B. 2/5
    3. C. 1/10
    4. D. 1/25
32. The table below gives the distribution of ages of students in a class.
    

    Ages (years)	13	14	15	16	17
    Number of students	3	10	6	7	4

    
    How many students are in the class?
    1. A. 20
    2. B. 30
    3. C. 45
    4. D. 75
33. The table below gives the distribution of ages of students in a class.
    

    Ages (years)	13	14	15	16	17
    Number of students	3	10	6	7	4

    
    What is the modal age?
    1. A. 14
    2. B. 15
    3. C. 16
    4. D. 17
34. The table below gives the distribution of ages of students in a class.
    

    Ages (years)	13	14	15	16	17
    Number of students	3	10	6	7	4

    
    If a student is selected at random from the class, what is the probability that the student is 15 years old?
    1. A. 1/5
    2. B. 1/3
    3. C. 1/2
    4. D. 2/3
35. A ribbon is 16.8 m long. How many ribbons 0.36 m long can be cut from it?
    1. A. 0.46
    2. B. 4.60
    3. C. 46
    4. D. 460
36. A refrigerator was sold for GHC 200.00 at a loss of 10%. Find the cost price.
    1. A. GHC 180.00
    2. B. GHC 190.48
    3. C. GHC 220.00
    4. D. GHC 222.22
37. 
    
    The diagram above is the net of a:
    1. A. Cone
    2. B. Cuboid
    3. C. Rectangular prism
    4. D. Pyramid
38. What is the value of 7 in the number 832713?
    1. A. Seven thousand
    2. B. Seven hundred
    3. C. Seventy
    4. D. Seven
39. Write 3560 in standard form.
    1. A. 3.56 x 10
    2. B. 3.56 x 10²
    3. C. 3.56 x 10³
    4. D. 3.56 x 10⁴
40. Correct 0.02751 to three decimal places.
    1. A. 0.027
    2. B. 0.028
    3. C. 0.03
    4. D. 0.28

Paper 2: Theory

1. a) In a school of 255 students, 80 of them study Arabic only and 125 study French only. Each student studies at least one of the two subjects.
   
   (i) Draw a Venn diagram to represent the information.
   
   (ii) How many students study:
   
   (a) both subjects?
   
   (b) French?
   
   b) Make h the subject of v = -nπr²h.
   
   c) A bookseller bought 80 copies of books at GHC 3.50 per copy. He sold each of them at GHC 4.20. Find:
   
   (i) the total cost price;
   
   (ii) his percentage profit.
2. a) The pie chart below shows the distribution of exercise books to six schools A, B, C, D, E, and F in a town. School D was given 8,000 exercise books.
   
   
   
   (i) How many exercise books were given to each of the rest of the schools?
   
   (ii) What is the average number of exercise books given to the schools?
   
   (iii) How many schools had less than the average number of exercise books?
   
   b) Solve the inequality (1/3)x + 1 ≥ (1/2)x + (1/4)(2 - x) and illustrate the answer on a number line.
3. a) Using a ruler and a pair of compasses only:
   
   (i) Construct triangle ABC such that AB = 8 cm, ∠CBA = 45°, and ∠CAB = 60°.
   
   (ii) Draw the bisector of ∠CBA to meet AB at T.
   
   b) Measure:
   
   (i) [CT];
   
   (ii) ∠CTB.
   
   c) A boy spent 3/8 of his money and had GHC 15.00 left. How much did he have?
4. a) The perimeter of a rectangular plot of land whose length is (2x + 5) m and width (x - 10) m is 80 m. Find:
   
   (i) the value of x;
   
   (ii) the area of the plot;
   
   (iii) the cost of weeding the plot at GHC 0.24 per m².
   
   b) Find the value of x and w in the diagram below if [AB] = [BC].
   
   
5. a) Given that a = (-3, 3) and b = (4, -6), calculate:
   
   (i) a + 2b;
   
   (ii) 1/2(2a - b).
   
   b) The number of pupils in a primary school is given in the table below:
   
   | Class | One | Two | Three | Four | Five | Six |
   
   |-------|------|------|-------|-------|------|-----|
   
   | Pupils | 24 | 35 | 35 | 20 | 21 | 45 |
   
   (i) Find the number of pupils in the school.
   
   (ii) What is the mean number of pupils in a class?
   
   (iii) What percentage of pupils are in class six?
   
   c) Convert 312₅ to base 10 numeral.
6. a) Copy and complete the table for the relation y = x/20, where y is the cost (in Ghana cedis) and x is the weight (in grammes) of rice sold in a market.
   
   | x (grammes) | 50 | 100 | 150 | 200 | 250 | 300 |
   
   |-------------|------|------|------|------|------|------|
   
   | y (GHC) | | | | | | |
   
   b)
   
   (i) On a graph sheet, draw two perpendicular axes OX and OY.
   
   (ii) Using a scale of 2 cm to 50 grammes on the x-axis and 2 cm to GHC 2.00 on the y-axis, draw the graph of the relation y = x/20.
   
   c) Using the graph, find:
   
   (i) the cost of 175 grammes of rice;
   
   (ii) the weight of rice that can be bought with GHC 14.00.

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