BECE 2021 Mathematics Past Questions and Answers

Paper 1: Objectives

1. If A = {1, 3, 5, 7, 9, 11, 13, 15} and B = {3, 6, 9, 12, 15}, find n(A ∩ B).
   1. A. 3
   2. B. 5
   3. C. 10
   4. D. 15
   Answer: A

   The intersection (∩) consists of elements found in both sets. Here, A ∩ B = {3, 9, 15}, so n(A ∩ B) = 3.
2. If P = {4, 8, 12, 16, 20}, Q = {16, 4, 12, k, 20} and P = Q, find the value of k.
   1. A. 20
   2. B. 16
   3. C. 8
   4. D. 4
   Answer: C

   Since P and Q are equal, they must contain the same elements. The missing element in Q is 8, so k = 8.
3. Express 7352.4658 correct to three significant figures.
   1. A. 7352465.8
   2. B. 7352.47
   3. C. 7350
   4. D. 735
   Answer: C

   Rounding to three significant figures, 7352.4658 becomes 7350.
4. Find the difference between the values of (2d)² and 2d² when d = 3.
   1. A. 0
   2. B. 18
   3. C. 24
   4. D. 54
   Answer: B

   (2d)² = 36 and 2d² = 18, so the difference is 36 - 18 = 18.
5. Find the image of P(-3, 5) when rotated through 360° about the origin.
   1. A. (5, -3)
   2. B. (-3, -5)
   3. C. (-3, 5)
   4. D. (-5, -3)
   Answer: C

   A 360° rotation brings the point back to its original position, so the image is (-3, 5).
6. The image of P(10, -3) when translated by the vector r is P'(4, 5). Find r.
   1. A.
   2. B.
   3. C.
   4. D.
   Answer: C

   Translation vector r = (-6, 8) to change P(10, -3) to P'(4, 5).
7. Find the next two terms of the sequence: 2, 5, 10, 17, __, __.
   1. A. 24, 35
   2. B. 26, 35
   3. C. 26, 37
   4. D. 27, 38
   Answer: C

   The sequence is quadratic, and the formula is n² + 1. Calculating for n=5 and n=6, the next terms are 26 and 37.
8. Express 134.78 correct to the nearest tenth.
   1. A. 130.0
   2. B. 134.7
   3. C. 134.8
   4. D. 135.0
   Answer: C

   Rounding to the nearest tenth gives 134.8.
9. Kofi and Ama shared an amount of GHC 3000.00 in the ratio 2:3. Find the amount received by Kofi.
   1. A. GHC 1000.00
   2. B. GHC 1200.00
   3. C. GHC 1500.00
   4. D. GHC 1800.00
   Answer: B

   Kofi’s share is (2/5) × 3000 = GHC 1200.00.
10. If 2x - 1 = 5, find the value of x.
    1. A. 3
    2. B. 4
    3. C. 5
    4. D. 6
    Answer: A

    Solving for x gives x = 3.

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11. Solve: (1 - x)/3 < 4.
    1. A. x < -11
    2. B. x > -11
    3. C. x < 11
    4. D. x > 11
12. The area of a rectangle is 18 cm². If one of its sides is 2 cm, find its perimeter.
    1. A. 18 cm
    2. B. 20 cm
    3. C. 22 cm
    4. D. 36 cm
13. A bag contains 5 red and 7 black balls. What is the probability of picking a black ball?
    1. A. 5/7
    2. B. 5/12
    3. C. 7/12
    4. D. 6/12
14. On a map, 1/2 cm represents 5 km. If two towns A and B are 18 cm apart on the map, what is the actual distance?
    1. A. 27 km
    2. B. 30 km
    3. C. 240 km
    4. D. 270 km
15. What is the rule for the above mapping where x values are 1, 2, 3, 4, 5, and y values are 5, 9, 13, 17, 21?
    1. A. y = x + 4
    2. B. y = 3x + 2
    3. C. y = 4x + 1
    4. D. y = 5x + 1
16. 
    
    Find x when y = 37 for the above mapping.
    1. A. 6
    2. B. 7
    3. C. 8
    4. D. 9
17. Esi bought a TV for GHC 1500.00 and sold it at a 20% profit. Find the selling price.
    1. A. GHC 1200.00
    2. B. GHC 1500.00
    3. C. GHC 1750.00
    4. D. GHC 1800.00
18. 
    
    In the diagram, line AB is parallel to line PD. Find the value of x.
    1. A. 20°
    2. B. 80°
    3. C. 100°
    4. D. 120°
19. Make h the subject of the relation V = πr²h.
    1. A.
    2. B.
    3. C.
    4. D.
20. Find the simple interest on GHC 600.00 saved for 8 months at 5% per annum.
    1. A. GHC 20.00
    2. B. GHC 40.00
    3. C. GHC 45.00
    4. D. GHC 240.00
21. Priscila's age is k years while Mary's age is b years. If Mary is 15 years older than Priscila, which of the following statements is correct?
    1. A. 2k + b = 15
    2. B. b - k = 15
    3. C. k - b = 15
    4. D. 2b + k = 15
22. What is the Highest Common Factor (HCF) of 24, 32, and 64?
    1. A. 4
    2. B. 6
    3. C. 8
    4. D. 16
23. Factorize: 3ax + 6a - x - 2.
    1. A. (3a + 1)(x + 2)
    2. B. (3a + 1)(x - 2)
    3. C. 3a(x - 2)
    4. D. (3a - 1)(x + 2)
24. A car covered a distance of 150 km at a speed of 18 km/h. Find the time taken.
    1. A. 7 hours 33 minutes
    2. B. 7 hours 53 minutes
    3. C. 8 hours 13 minutes
    4. D. 8 hours 20 minutes
25. Simplify 3y - (2y - 3)/4.
    1. A. 10y + 3
    2. B. 10y - 3
    3. C. (10y - 3)/4
    4. D. (10y + 3)/4
26. Divide 0.5445 by 0.09.
    1. A. 5.05
    2. B. 6.05
    3. C. 6.50
    4. D. 60.50
27. If the median of the numbers 9, 10, 12, x, 20, and 25 is 14, find the value of x.
    1. A. 14
    2. B. 16
    3. C. 18
    4. D. 22
28. Expand (7r - 5)(3r + 4).
    1. A. 21r² + 13r - 20
    2. B. 21r² - 13r - 20
    3. C. 21r² - 43r - 20
    4. D. 21r² + 43r - 20
29. Find the gradient of the line that joins the points A(-3,5) and B(7,-2).
    1. A. 10/7
    2. B. 5/12
    3. C. -7/10
    4. D. -12/5
30. The area of a trapezium is 36 cm². If the parallel sides are 10.5 cm and 9.5 cm, calculate the distance between the two parallel sides.
    1. A. 1.0 cm
    2. B. 1.8 cm
    3. C. 3.2 cm
    4. D. 3.6 cm
31. If the average of 5, 6, 7, and x is 8, find the value of x.
    1. A. 12
    2. B. 14
    3. C. 16
    4. D. 24
32. An amount of GHC 375,000.00 was needed to build a clinic for a community of twelve towns. Each community contributed GHC 25,000.00. If the District Assembly also contributed GHC 30,500.00, how much more is needed?
    1. A. GHC 44,500.00
    2. B. GHC 45,500.00
    3. C. GHC 35,500.00
    4. D. GHC 75,000.00
33. Which property of arithmetic is shown in the equation (6 + x) + 5 = 6 + (x + 5)?
    1. A. Commutative
    2. B. Associative
    3. C. Closure
    4. D. Distributive
34. A trader bought 100 tubers of yam for GHC n each. All the yams were sold at GHC m each. Find the profit.
    1. A. GHC 100(m - n)
    2. B. GHC 100(m + n)
    3. C. GHC 100(n - m)
    4. D. GHC 100(nm)
35. A box can take 12 pencils. If 156 pencils are packed into such boxes, how many boxes will be fully packed?
    1. A. 10
    2. B. 11
    3. C. 12
    4. D. 13
36. Given that x = 4, y = 7, evaluate 2xy + 3(x + y).
    1. A. 79
    2. B. 89
    3. C. 99
    4. D. 109
37. Simplify:
    
    
    1. A. -1
    2. B. 0
    3. C. 1
    4. D. 1/2
38. Given that x = 8, what type of angle is (9x + 8)?
    1. A. Straight angle
    2. B. Obtuse angle
    3. C. Acute angle
    4. D. Right angle
39. Express 0.725 as a fraction in its lowest term.
    1. A.
    2. B.
    3. C.
    4. D.
40. Simplify 3(5a² + 2c) - 2a(1 - 3a) - 6c.
    1. A. 21a² - 2a - 6c
    2. B. 13a² - 2a - 12c
    3. C. 13a² - 2a
    4. D. 21a² - 2a

Paper 2: Theory

1. (a)In the Venn diagram, M and N are intersecting sets in the universal set µ.
   
   Express n(M) and n(N) in terms of x.
   
   (b) Given that n(M) = n(N), find the:
   
   (i) Value of x
   
   (ii) n(µ)
   
   (c) Simplify: 2⁰ + 2² - 2.
2. (a) Factorize the expression 5ay - by + 15a - 3b.
   
   (b) Solve: 6/(4p - 1) = 4/[3(p + 4)].
   
   (c) Esi and Kofi shared an amount of GHC 21,000.00 in the ratio of 2:5 respectively. How much more did Kofi receive than Esi?
3. (a) If r = -4/5 and m = -1/2, find p given p = r - m.
   
   (b) The sum of two numbers is 81. If the second number is twice the first, find the second number.
   
   (c) The floor of a rectangular hall is of length 9 m and width 4 m. How many tiles of 20 cm by 30 cm can be used to cover the floor completely?
4. (a) Antwiwaa bought 25 mangoes, 7 of which were unripe. What percentage of the mangoes were ripe?
   
   (b) The mapping shows the relationship between x and y:
   
   
   
   Find the:
   
   (i) Rule for the mapping
   
   (ii) Values of m and n
   
   (c) A bus left town X at 6:30 am and arrived at town Y at 1:00 pm. If the bus traveled at an average speed of 100 km/h, calculate the distance from town X to town Y.
5. (a) Simplify: (4x + 2)(x - 2) - 3
   
   (b) The following are the angles formed at the center of a circle: 40°, 60°, 100°, 3x, and 5x. Find the value of x.
   
   (c) The cost (C) in Ghana Cedis of producing a book of x pages is given by C = 25 + 0.6x.
   
   (i) Find the cost of producing a book with 220 pages.
   
   (ii) How many pages are in a book produced at a cost of GHC 145.00?
6. (a) Complete the table:
   
   Number of marbles (x): 1, 2, 3, 4, 5, 6
   
   Number of students (f): 4, 5, 14, 9, 6, 2
   
   (b) How many:
   
   (i) Students were in the class?
   
   (ii) Marbles were brought altogether?
   
   (iii) Marbles did most of the students bring?
   
   (c) Calculate, correct to the nearest whole number, the mean number of marbles brought for the lesson.

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