BECE 2000 Mathematics Past Questions and Answers

Paper 1: Objectives

1. M = {1, 2, 3, 8, 10} and N = {8, 1, x, 3, 2}. If M is equal to N, what is the value of x?
   1. A. 1
   2. B. 2
   3. C. 3
   4. D. 8
   5. E. 10
   Answer: E

   Two sets A and B are equal if both have the same number of elements and all the elements in A are found in B.
2. 
   
   In the Venn diagram, Q is the set of numbers inside the circle and R is the set of numbers inside the triangle. Find Q ∩ R.
   1. A. {1, 5}
   2. B. {2, 3, 4}
   3. C. {6, 7, 8}
   4. D. {1, 2, 3, 4, 5}
   5. E. {1, 2, 3, 4, 5, 6, 7, 8}
   Answer: A

   Intersection (∩) are elements that can be found in both sets. On a Venn diagram, it is the region where both sets intersect/join/overlap.
3. Simplify: 11 – (11 – 4) + 13.
   1. A. –7
   2. B. –17
   3. C. 9
   4. D. 17
   5. E. 31
   Answer: D

   11 – (11 – 4) + 13 = 11 – 11 + 4 + 13 = 17.
4. What is the value of ‘4’ in the number 2,043,507?
   1. A. Forty
   2. B. Four hundred
   3. C. Four thousand
   4. D. Forty thousand
   5. E. Four hundred thousand
   Answer: D
5. Which of the following is true?
   1. A. {0, 2, 6, 9, 12} is a subset of even numbers.
   2. B. {-1, 0, 2, 3, 5} is a subset of odd numbers.
   3. C. {-2, -1, 1, 3, 9} is a subset of integers.
   4. D. {2, 3, 5, 7, 27} is a subset of prime numbers.
   5. E. {9, 18, 21, 27, 36} is a subset of multiples of 9.
   Answer: C

   An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
6. If (23 × 82) × 79 = 148,994, find the exact value of (2.3 × 82) × 7.9.
   1. A. 1.48994
   2. B. 14.8994
   3. C. 148.994
   4. D. 1489.94
   5. E. 14899.4
   Answer: D

   Express (2.3 × 82) × 7.9 as (23 × 82) × 79 × 10⁻² = 1489.94.
7. Convert 206 to a base five numeral.
   1. A. 411₅
   2. B. 4011₅
   3. C. 3321₅
   4. D. 1311₅
   5. E. 1131₅
   Answer: D

   206₁₀ = 1311₅.
8. 
   
   Which of the following inequalities is represented by the number line?
   1. A. x ≤ -3
   2. B. x ≥ -3
   3. C. x < -3
   4. D. x > -3
   5. E. x = -3
   Answer: D

   The inequality sign should be in the direction of the arrow. The arrow is pointed to the right, hence x > -3.
9. The product of three numbers is 1197. Two of the numbers are 3 and 21. Find the third number.
   1. A. 19
   2. B. 57
   3. C. 63
   4. D. 399
   5. E. 1134
   Answer: A

   Let n = the third number. 3 × 21 × n = 1197. Solve for n to get n = 19.
10. Simplify: $\left(\begin{array}{c}-2\\ 3\end{array}\right)-\left(\begin{array}{c}1\\ 5\end{array}\right)$.
    1. A. $\left(\begin{array}{c}-1\\ 2\end{array}\right)$
    2. B. $\left(\begin{array}{c}-1\\ 8\end{array}\right)$
    3. C. $\left(\begin{array}{c}-3\\ 8\end{array}\right)$
    4. D. $\left(\begin{array}{c}-1\\ -2\end{array}\right)$
    5. E. $\left(\begin{array}{c}-3\\ -2\end{array}\right)$
    Answer: E

    $\left(\begin{array}{c}-2-1\\ 3-5\end{array}\right)=\left(\begin{array}{c}-3\\ -2\end{array}\right)$

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11. A pencil sells at ₵180.00 and an eraser sells at ₵120.00. How much will you pay if you buy three pencils and four erasers?
    1. A. ₵1,020.00
    2. B. ₵1,080.00
    3. C. ₵1,200.00
    4. D. ₵1,280.00
    5. E. ₵2,100.00
12. Simplify: 0.12 × 0.08 ÷ 2.40.
    1. A. 0.4
    2. B. 0.04
    3. C. 0.004
    4. D. 0.0004
    5. E. 0.00004
13. How many lines of symmetry has a square?
    1. A. 2
    2. B. 3
    3. C. 4
    4. D. 6
    5. E. 8
14. 
    
    In the diagram, MNO is a right-angled triangle. |MO| = 13 cm and |MN| = 5 cm. Find the value of x.
    1. A. 3
    2. B. 4
    3. C. 8
    4. D. 12
    5. E. 18
15. Amina spends 17/35 of her pocket money on transport and food. If she spends 2/7 on transport only, what fraction does she spend on food?
    1. A. 1/4
    2. B. 1/5
    3. C. 5/7
    4. D. 15/28
    5. E. 18/35
16. If x → 3x – 4, what is the image of -2?
    1. A. -10
    2. B. -2
    3. C. -1
    4. D. 2
    5. E. 10
17. Simplify: (2ab²)(3a²b).
    1. A. 5a²b²
    2. B. 6a²b²
    3. C. 5a²b³
    4. D. 6a³b²
    5. E. 6a³b³
18. It takes 15 men 48 days to weed a plot of land. How many men can weed the same plot in 16 days?
    1. A. 5
    2. B. 18
    3. C. 32
    4. D. 45
    5. E. 48
19. The ratio 9 : x is equivalent to 36 : 20. What is the value of x?
    1. A. 4
    2. B. 5
    3. C. 6
    4. D. 8
    5. E. 10
20. In an enlargement, PQ → P′Q′. |PQ| = 3 cm and |P′Q′| = 15 cm. Calculate the scale factor.
    1. A. 1/5
    2. B. 2/3
    3. C. 5
    4. D. 10
    5. E. 45
21. Simplify: 7a - 3(b - a)
    1. A. 4a - 3b
    2. B. 6a - 3b
    3. C. 8a - 3b
    4. D. 10a - 3b
    5. E. 10a + 3b
22. A man deposited an amount of money in his savings account for 5 years. The rate of interest was 14% per annum. If the interest was ₵35,000.00, find the amount deposited.
    1. A. ₵85,000.00
    2. B. ₵50,000.00
    3. C. ₵39,900.00
    4. D. ₵24,500.00
    5. E. ₵15,000.00
23. Arrange the following fractions from the lowest to the highest: 3/4, 2/3, and 3/5
    1. A. 3/5, 2/3, 3/4
    2. B. 3/4, 3/5, 2/3
    3. C. 5/4, 3/5, 2/3
    4. D. 3/3, 2/5, 4/5
    5. E. 4/5, 2/3, 3/4
24. The marked price of a radio set is ₵450,000. A discount of 5% of the marked price is allowed. What is the selling price of the radio set?
    1. A. ₵427,000
    2. B. ₵427,500
    3. C. ₵428,571
    4. D. ₵472,500
    5. E. ₵473,684
25. If 60% of the pupils in a school is 240, find the total enrolment in the school.
    1. A. 144
    2. B. 160
    3. C. 360
    4. D. 384
    5. E. 400
26. If a × b = 2a - b, evaluate 4 × 3
    1. A. 1
    2. B. 2
    3. C. 3
    4. D. 4
    5. E. 5
27. 
    
    What is the modal mark in the test distribution?
    1. A. 4
    2. B. 5
    3. C. 6
    4. D. 7
    5. E. 8
28. 
    
    How many pupils took the test?
    1. A. 5
    2. B. 20
    3. C. 25
    4. D. 29
    5. E. 30
29. A school has a population of 600. Out of this, 120 are girls. What is the probability of meeting a pupil who is a boy?
    1. A. ¼
    2. B. ⅕
    3. C. ⅗
    4. D. ⅘
    5. E. 12/25
30. If 1/k = 1/k₁ + 1/k₂, find k when k₁ = 1 and k₂ = 2.
    1. A. ½
    2. B. ⅔
    3. C. ⅗
    4. D. ⅖
    5. E. 3
31. Solve the equation 13x - 2(3x + 4) = 22.
    1. A. 2
    2. B. 4
    3. C. 18/7
    4. D. 26/7
    5. E. 30/7
32. A rectangular tank is 4 m long, 3 m wide and 2.5 m high. What is the volume of the tank?
    1. A. 24 m³
    2. B. 30 m³
    3. C. 36 m³
    4. D. 48 m³
    5. E. 60 m³
33. Write the rule for the mapping where x = {1, 2, 3, 4} and y = {1, 3, 5, 7}.
    1. A. x → 2x + 1
    2. B. x → 2x - 1
    3. C. x → 2(x + 1)
    4. D. x → 2(x - 1)
    5. E. x → x² - 1
34. If r = (2, -1) and s = (-3, 2), calculate 2r - 3s.
    1. A. (-5, 12)
    2. B. (-5, -8)
    3. C. (13, -3)
    4. D. (13, -8)
    5. E. (13, 8)
35. 
    
    Name the geometrical figure shown in the diagram below.
    1. A. Parallelogram
    2. B. Triangle
    3. C. Cone
    4. D. Tetrahedron
    5. E. Pyramid
36. A car travels 72 kilometers in an hour. Find its speed in meters per second.
    1. A. 5 ms⁻¹
    2. B. 20 ms⁻¹
    3. C. 50 ms⁻¹
    4. D. 200 ms⁻¹
    5. E. 1200 ms⁻¹
37. The circumference of a circular track is 154 m. Find the diameter of the track. [π = 22/7]
    1. A. 22.0 m
    2. B. 24.5 m
    3. C. 49.0 m
    4. D. 242.0 m
    5. E. 484.0 m
38. 
    
    Find the value of the angle marked y in the diagram.
    1. A. 35°
    2. B. 43°
    3. C. 67°
    4. D. 78°
    5. E. 137°
39. 
    
    Which of the following best describes the construction in the diagram?
    1. A. Constructing a 30° angle
    2. B. Constructing a 60° angle
    3. C. Bisecting a line segment
    4. D. Bisecting a given angle
    5. E. Drawing a perpendicular from a given point
40. Ama is N years old now. How old will she be in 10 years?
    1. A. (N - 10) years
    2. B. (N + 10) years
    3. C. (10 - N) years
    4. D. 10N years
    5. E. 10 / N years

Paper 2: Theory

1. a) Simplify: 2/3 of 6 3/4 ÷ 2 4/15 - 1 2/3.
   
   b) Solve the equation 1/3(x + 3) - 2/3(x - 5) = 41.
   
   c) If 3y = 2x² - 3x + 7, find y when x = 5.
2. 
   
   a) In the diagram, PADQ and RBCS are parallel lines. │BD│ = │DC│, ∠ADB = 65°, and ∠ABR = 50°.
   
   (i) Calculate the angle BDC.
   
   (ii) Calculate angle ABD.
   
   (iii) Find angle BAD.
   
   (iv) What type of triangle is triangle ABD?
   
   b) Using a ruler and a pair of compasses only, construct triangle XYZ with |YZ| = 8 cm, ∠XYZ = 60°, and |XY| = 9 cm.
   
   (i) Measure angle YZX.
   
   (ii) Measure |XZ|.
3. Ama was granted a loan of ₵800,000.00 by a bank. The rate of interest was 42% per annum.
   
   a) Calculate:
   
   (i) The interest at the end of the year.
   
   (ii) The total amount Ama had to pay at the end of the year.
   
   b) Ama was able to pay only ₵700,000.00 at the end of the year.
   
   (i) Find how much Ama still owed the bank.
   
   (ii) Express the amount Ama owed after paying ₵700,000.00 as a percentage of the loan she took from the bank.
4. The following is a record of scores obtained by 30 JSS form 2 pupils in a test marked out of 5:
   
   5, 3, 2, 4, 5, 2, 4, 3, 1, 1, 3, 4, 2, 3, 4, 5, 3, 4, 3, 2, 4, 3, 1, 2, 2, 3, 3, 2, 4, 3.
   
   a) Copy and complete the table:
   
   | Score (x) | Tally | Frequency (f) | fx |
   
   |-----------|--------------|----------------|----|
   
   | 1 | || | 3 | 3 |
   
   | 2 | |||| | 6 | 12 |
   
   | 3 | |||||||||| | 10 | 30 |
   
   | 4 | ||||| | 7 | 28 |
   
   | 5 | || | 4 | 20 |
   
   b) Find the mean of the distribution.
   
   c) If a pupil is selected at random, what is the probability that he/she scored 4 marks?
5. The diagram shows a running track ABCDEFA. AB and ED are the straight sides. The ends AFE and BCD are semicircular shapes. |AB| = |ED| = 90 m and |AE| = |BD| = 70 m.
   
   a) Find the total length of the two semicircular ends, AFE and BCD.
   
   b) Find the perimeter of the running track ABCDEFA.
   
   c) Find the total area of the running track ABCDEF. (Take π = 22/7).

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