BECE 2017 Mathematics Past Questions and Answers

Paper 1: Objectives

1. If Q = {1,3,5,7,9,10,11,13,15} and T = {1,2,3,5,6,7,10,11,12}, find Q U T.
   1. A. {1,2,3,5,7,10,11}
   2. B. {1,3,5,7,9,11,13,15}
   3. C. {1,2,3,4,5,6,7,8,9,10,11,12,13}
   4. D. {1,2,3,5,6,7,9,10,11,12,13,15}
   Answer: D

   Union is obtained by listing each item in both sets in ascending order without repeating any items. Q U T = {1,2,3,5,6,7,9,10,11,12,13,15}.
2. If 21:2x = 7:12, find the value of x.
   1. A. 10
   2. B. 12
   3. C. 15
   4. D. 18
   Answer: D

   Convert the ratio to fractions: 21/2x = 7/12. Cross-multiply to get 2x × 7 = 21 × 12. Solving, x = 18.
3. Given that 1/2p = 1/8, find the value of p.
   1. A. 4
   2. B. 3
   3. C. 2
   4. D. 1
   Answer: A

   Cross-multiply to solve: 2p × 1 = 1 × 8, then p = 4.
4. Simplify 3q x 12pq.
   1. A. 15pq²
   2. B. 15p²q
   3. C. 36pq²
   4. D. 36p²q
   Answer: C

   Using the law of indices, 3q × 12pq = 3 × 12 × p × q¹⁺¹ = 36pq².
5. If A = {2,6,8} and B = {4,6,8,10}, which of the following statements is true?
   1. A. A ⊂ B
   2. B. A ∩ B = {2,6,8}
   3. C. A U B = {2,4,6,8,10}
   4. D. A ⊇ B
   Answer: C

   Union is obtained by listing all items from both sets in ascending order without repetition. A U B = {2,4,6,8,10}.
6. Find the product of 4x and x²yz.
   1. A. 4x²yz
   2. B. 4x³yz
   3. C. 4xy²z
   4. D. 4x²y³z
   Answer: B

   Applying the law of multiplication of indices, 4x × x²yz = 4x³yz.
7. The sum of the interior angles of a regular polygon with 10 sides is
   1. A. 1449°
   2. B. 900°
   3. C. 1440°
   4. D. 1800°
   Answer: C

   Sum of interior angles = (n-2) × 180°, where n = number of sides. For 10 sides: (10-2) × 180° = 1440°.
8. Solve 2 + x/3 = 1 - 2x
   1. A. -1 2/7
   2. B. -3/7
   3. C. 3/7
   4. D. 1 2/7
   Answer: B

   Multiply each term by 3: 6 + x = 3 - 6x -> x + 6x = 3 - 6 -> 7x = -3 -> x = -3/7.
9. The ages of the members of a social club are 20 years, 55 years, 60 years, and 25 years. Find the mean age of the members of the club.
   1. A. 20 years
   2. B. 30 years
   3. C. 40 years
   4. D. 50 years
   Answer: C

   Mean = Sum of numbers / No. of numbers. Total = 160, Mean = 160 / 4 = 40 years.
10. Evelyn saved GHC 35.48 every month for 8 months. How much did she save?
    1. A. GHC 183.60
    2. B. GHC 280.63
    3. C. GHC 283.20
    4. D. GHC 283.84
    Answer: D

    Total amount saved = Amount per month × Months = 35.48 × 8 = GHC 283.84.

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11. Evaluate 0.00492 / 0.041
    1. A. 0.012
    2. B. 0.12
    3. C. 1.2
    4. D. 12.0
12. A woman deposited GHC 50,000.00 at a bank for 2 years at a rate of 20% per annum. Find the simple interest.
    1. A. GHC 1,000.00
    2. B. GHC 2,000.00
    3. C. GHC 10,000.00
    4. D. GHC 20,000.00
13. What is the total cost of x shirts at GHC 5.00 each and y shirts at GHC 1.50 each?
    1. A. 5x + 1.5y
    2. B. 5y + 1.5x
    3. C. 5(x + 1.5y)
    4. D. 1.5(5x + y)
14. At a meeting attended by 23 people, the females were 7 more than the males. How many males were there?
    1. A. 8
    2. B. 15
    3. C. 16
    4. D. 30
15. 
    
    Find the value of x in the diagram.
    1. A. 28°
    2. B. 30°
    3. C. 34°
    4. D. 60°
16. How many lines of symmetry does a rhombus have?
    1. A. 2
    2. B. 3
    3. C. 4
    4. D. 5
17. In 1995, 215 boys and 185 girls were admitted into a school. Find the percentage of girls admitted.
    1. A. 46%
    2. B. 47%
    3. C. 53%
    4. D. 54%
18. Simplify (2(u -v)(2u + 3v)) / (4u + 6v).
    1. A. (u - v)(2u + v) / (u + v)
    2. B. (u - v)(u + v) / (u + 2v)
    3. C. 1/2 (u - v)
    4. D. (u - v)
19. Solve 25x + 450 < 3000.
    1. A. x > 102
    2. B. x > 138
    3. C. x < 102
    4. D. x < 138
20. Given that a = 3 and b = -3, find a + b.
    1. A. 0
    2. B. -1
    3. C. 3
    4. D. -6
21. Mr. Agyekum has 11 of the GHC 20.00 notes, 15 of the GHC 10.00 notes and 6 of the GHC 5.00 notes. How much does Mr. Agyekum have altogether?
    1. A. GHC 280.00
    2. B. GHC 320.00
    3. C. GHC 360.00
    4. D. GHC 400.00
22. A man travelled a distance of 1.5 km in 30 minutes. What distance can he cover in 50 minutes, travelling at the same speed?
    1. A. 2.2 km
    2. B. 2.5 km
    3. C. 2.8 km
    4. D. 3.2 km
23. 
    
    In the diagram, UVW is an isosceles triangle. [UV] = [UW] and angle VUW = 70°. Find angle UVW.
    1. A. 70°
    2. B. 60°
    3. C. 55°
    4. D. 35°
24. Arrange the following in descending order: 7/20, 7/25, 37/100, 1/4.
    1. A. 37/100, 7/20, 7/25, 1/4
    2. B. 1/4, 7/25, 7/20, 37/100
    3. C. 37/100, 7/20, 1/4, 7/25
    4. D. 7/25, 1/4, 7/20, 37/100
25. The point D(4,3) is reflected in the y-axis. Find the coordinates of its image.
    1. A. (-4, -3)
    2. B. (-3, 4)
    3. C. (-4, 3)
    4. D. (3, -4)
26. Simplify: 7 1/2 × (1/4 ÷ 1/2) - 1/4
    1. A. 7/2
    2. B. 11/16
    3. C. 7/32
    4. D. 1/2
27. Divide 64.5 by 0.015, leaving the answer in standard form.
    1. A. 4.3 x 10
    2. B. 4.3 x 10³
    3. C. 4.3 x 10⁴
    4. D. 4.3 x 10⁵
28. The point Q(-2,3) is rotated anticlockwise about the origin through an angle of 90°. Find the coordinates of its image.
    1. A. (-3, -2)
    2. B. (-3, 2)
    3. C. (3, -2)
    4. D. (3, 2)
29. Elias bought five books. Their mean price was GHC 3.25. The total cost for four of the books was GHC 11.75. What was the cost of the fifth book?
    1. A. GHC 3.50
    2. B. GHC 4.00
    3. C. GHC 4.20
    4. D. GHC 4.50
30. Tins of milk each of volume 77 cm³ and weight 170 g were packed into an empty carton of volume 1540 cm³ and weight 500 g. How many tins of milk can be packed to fill the carton?
    1. A. 2
    2. B. 3
    3. C. 20
    4. D. 22
31. What is the weight of the carton when packed with the tins of milk?
    1. A. 2.06 kg
    2. B. 2.94 kg
    3. C. 3.90 kg
    4. D. 8.50 kg
32. A piece of cloth is 8.4 m long. If 30 cm is needed to sew a napkin, how many napkins can be sewn from this piece of cloth?
    1. A. 20
    2. B. 25
    3. C. 28
    4. D. 30
33. Express 10/32 as a decimal fraction.
    1. A. 0.3200
    2. B. 0.3125
    3. C. 0.3676
    4. D. 0.3222
34. A match box contains 40 sticks. If 15 of them are spoilt, find the probability that a stick chosen at random is not spoilt.
    1. A. 3/5
    2. B. 3/8
    3. C. 5/8
    4. D. 5/5
35. The number of pupils who attended hospital from eight classes on a particular day are: 1,5,3,1,7,5,1,1. Find the median number.
    1. A. 1
    2. B. 2
    3. C. 3
    4. D. 4
36. The number of pupils who attended hospital from eight classes on a particular day are: 1,5,3,1,7,5,1,1. What is the modal number?
    1. A. 1
    2. B. 4
    3. C. 5
    4. D. 7
37. The number of pupils who attended hospital from eight classes on a particular day are: 1,5,3,1,7,5,1,1. Calculate the mean.
    1. A. 2
    2. B. 3
    3. C. 4
    4. D. 5
38. The distance from the centre of a circle to any point on it is called
    1. A. circumference
    2. B. diameter
    3. C. radius
    4. D. sector
39. Express 1352 as a product of prime factors.
    1. A. 2 × 13
    2. B. 2³ × 13²
    3. C. 2² × 13³
    4. D. 2³ × 13³
40. Which of the following statements about sets is true?
    1. A. Every set is a subset of the null set.
    2. B. The universal set is the subset of the null set.
    3. C. The intersection of two sets is always null set.
    4. D. The universal set is the union of all its subsets.

Paper 2: Theory

1. a) In a class of 30 girls, 17 play football, 12 play hockey, and 4 play both games.
   
   i) Draw a Venn diagram to illustrate the given information.
   
   ii) How many girls play:
   
   1) one or two of the games;
   
   2) none of the two games?
   
   
   
   b) In the diagram, ABCD is a circle of radius 14 cm and center O. Line BO is perpendicular to line AC.
   
   Calculate the total area of the shaded portions. [Take π = 22/7]
2. a) Two consecutive odd numbers are such that seven times the smaller, subtracted from nine times the bigger, gives 144. Find the two numbers.
   
   b) A paint manufacturing company has a machine that fills 24 tins with paint in 5 minutes.
   
   i) How many tins will the machine fill in 1 minute, correct to the nearest whole number?
   
   ii) How many tins will the machine fill in 1 hour?
   
   iii) How many hours will it take to fill 1440 tins?
   
   c) Given that s = n/2[2a + (n-1)d], where a = 3, d = 4, and n = 10, find the value of s.
3. a) Using a ruler and a pair of compasses only, construct:
   
   i) a triangle ABC with [BC] = 9 cm, [AC] = 8 cm, and [AB] = 6 cm;
   
   ii) the perpendicular bisector of line BC;
   
   iii) the bisector of angle ACB.
   
   b) Label the point of intersection of the two bisectors as Y.
   
   c) Draw a line to join B and Y.
   
   d) Measure:
   
   i) [BY];
   
   ii) [YC];
   
   iii) the base angles of triangle BYC.
   
   e) What type of triangle is BYC?
4. a) The table below shows the ages of students admitted in a hospital:
   
   | Age (years) | 10 | 11 | 12 | 13 | 14 | 15 |
   
   |-------------|----|----|----|----|----|----|
   
   | No. of students | 5 | 1 | 7 | 10 | 3 | 4 |
   
   i) What is the modal age?
   
   ii) Calculate the mean age of the students, correct to two decimal places.
   
   b) Rice is sold at GHC 56.00 per bag of 50 kg. A trader bought some bags of rice and paid GHC 1,344.00.
   
   i) How many bags of rice did the trader buy?
   
   ii) If the trader retailed the bags of rice at GHC 1.40 per kg, how much profit was made on 1 kg of rice?
5. a) Using a scale of 2 cm to 1 unit on both axes, draw on a graph sheet two perpendicular axes Ox and Oy for -5 ≤ x ≤ 5 and -5 ≤ y ≤ 5. Plot and indicate the coordinates of:
   
   i) Points A(2, 3) and B(-3, 4). Draw a straight line passing through points A and B.
   
   ii) Points C(4, 2) and D(-2, -3). Draw a straight line passing through points C and D to meet line AB.
   
   b) Using the graphs in (a):
   
   i) Find the values of y when x = -2.
   
   ii) Measure the angle between lines AB and CD.
6. a) If m = (2x + 1, 2 - 3y), n = (6, -8) and (m + n) = (9, -12), find the:
   
   i) values of x and y;
   
   ii) components of m.
   
   b) Solve the inequality:
   
   (3/4)(x + 1) + 1 ≤ (1/2)(x - 2) + 5.
   
   i) Illustrate the answer on a number line.
   
   
   
   c) In the diagram, AB is parallel to CD.
   
   i) Find the value of x.
   
   ii) Find the value of y.

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