BECE 2010 Mathematics Past Questions and Answers

Paper 1: Objectives

1. Which of the following sets is well defined?
   1. A. {Man, Kofi, Red, 14}
   2. B. {Ink, Mango, Green, Nail}
   3. C. {Car, Road, Glass, Book}
   4. D. {Seth, Mary, Jacob, Evelyn}
   Answer: D

   All the sets except {Seth, Mary, Jacob, Evelyn} contain different categories of items. Only {Seth, Mary, Jacob, Evelyn} contains one category: names of people.
2. If set B is a subset of set A, then
   1. A. sets A and B have the same number of elements.
   2. B. some members of set B can be found in set A.
   3. C. no member of set B is in set A.
   4. D. all the members of set B are in set A.
   Answer: D

   All members of a subset can be found in the set it is a subset of.
3. The least common multiple (L.C.M) of 16, 30, and 36 is
   1. A. 3
   2. B. 6
   3. C. 240
   4. D. 720
   Answer: D

   The L.C.M is found by taking the highest powers of all prime factors: 16, 30, and 36 gives 720.
4. The sum of 5 and x divided by 4 is equal to 3.25. Find the value of x.
   1. A. 8
   2. B. 7
   3. C. 2
   4. D. 13
   Answer: A

   Cross multiplying, 100(5 + x) = 4 x 325, solving gives x = 8.
5. The numbers 32, 33, 34, ..., ..., 42 form a sequence in base 5. Find the missing numbers.
   1. A. 35, 36
   2. B. 30, 31
   3. C. 40, 41
   4. D. 31, 41
   Answer: C

   The next sequence in base 5 after 34 is 40, then 41.
6. Write down all the integers in the set A = {-10, -4, 0, 1/4, 2 1/2, 45, 100}
   1. A. {-10, -4, 0, 45, 100}
   2. B. {-10, -4}
   3. C. {0, 45, 100}
   4. D. {1/4, 2 1/2}
   Answer: A

   Integers are numbers without decimal or fractional parts, including negatives and zero.
7. Find the total cost of 25 pens and 75 books if each pen costs GHC 0.20 and each book costs GHC 0.30.
   1. A. GHC 22.50
   2. B. GHC 23.50
   3. C. GHC 27.50
   4. D. GHC 50.00
   Answer: C

   Total cost = (25 x 0.2) + (75 x 0.3) = GHC 27.50.
8. Simplify: -27 + 18 - (10 - 14) - (-2)
   1. A. -3
   2. B. -7
   3. C. -11
   4. D. -35
   Answer: A

   Simplify each term: -27 + 18 - 10 + 14 + 2 = -3.
9. Arrange the following numbers from the lowest to the highest: 0.5, 3, -5, 0.
   1. A. 0, 0.5, -5, 3
   2. B. 0, -5, 0.5, 3
   3. C. -5, 0, 0.5, 3
   4. D. -5, 0.5, 0, 3
   Answer: C

   Arrange numbers on a number line: -5, 0, 0.5, 3.
10. How many pieces of cloth 5m long can be cut from a roll of cloth 121m long?
    1. A. 66½
    2. B. 115½
    3. C. 66
    4. D. 22
    Answer: D

    121 ÷ 5 = 22 full pieces.

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11. Find the value of 124.3 + 0.275 + 74.06, correcting your answer to one decimal place.
    1. A. 198.6
    2. B. 198.7
    3. C. 892.0
    4. D. 892.4
12. Esi and Kwasi are 12 and 8 years old respectively. They share 60 mangoes in the ratio of their ages. How many mangoes does Esi get?
    1. A. 42
    2. B. 40
    3. C. 36
    4. D. 18
13. It takes 6 students 1 hour to sweep their school compound. How long will it take 15 students to sweep the same compound?
    1. A. 24 minutes
    2. B. 12 minutes
    3. C. 3 hours
    4. D. 2 hours
14. A housing agent makes a commission of GHC 103,500 when he sells a house for GHC 690,000. Calculate the percentage of his commission.
    1. A. 15.0%
    2. B. 10.0%
    3. C. 7.5%
    4. D. 5.0%
15. A simple interest of GHC 37,500.00 is earned on an amount of GHC 500,000.00 for 3 years. Calculate the percentage rate.
    1. A. 20.0%
    2. B. 10.0%
    3. C. 5.0%
    4. D. 2.5%
16. Simplify: (8x²y³)(3/8 xy⁴)
    1. A. 3x³y⁷
    2. B. 3x²y⁷
    3. C. 3x³y⁴
    4. D. 3xy
17. The scores of 10 students in an examination are: 45, 12, 75, 81, 54, 51, 24, 67, 19, and 39. What is the median of the scores?
    1. A. 39
    2. B. 48
    3. C. 51
    4. D. 54
18. A pie chart is drawn from the data: Cassava 20%, Yam 17%, Plantain 28%, Maize 35%. What will be the angle of the sector for maize?
    1. A. 126.0°
    2. B. 100.8°
    3. C. 72.0°
    4. D. 61.2°
19. Nineteen cards are numbered from 11 to 29. If one card is chosen at random, what is the probability that it contains the digit 2?
    1. A. 3/9
    2. B. 7/18
    3. C. 5/9
    4. D. 11/19
20. Find the value of x if x/4 + 1 = 5.
    1. A. 24
    2. B. 20
    3. C. 19
    4. D. 16
21. Factorize: xy + 5x + 2y + 10.
    1. A. (x + 5)(2y + 10)
    2. B. (x + 2)(6y + 10)
    3. C. (x + 5)(y + 2)
    4. D. (x + 2)(y + 5)
22. If x ∈ {2, 3, 4, 5}, find the truth set of 2x + 1 < 8.
    1. A. {2, 3, 4}
    2. B. {2, 3}
    3. C. {3, 4}
    4. D. {4, 5}
23. Solve the inequality: 7x - (10x + 3) ≥ -9.
    1. A. x ≥ 2
    2. B. x < 4
    3. C. x ≥ 4
    4. D. x ≤ 2
24. Find the rule of the mapping:
    

    1	2	3	4	5	...	x
    ↓	↓	↓	↓	↓		↓
    7	11	15	19	23	...	y

    1. A. x → 4x - 3
    2. B. x → 3 - 4x
    3. C. x → 4x + 3
    4. D. x → 4x + 5
25. Find the circumference of a circle whose area is equal to 64π cm².
    1. A. 32π cm
    2. B. 16π cm
    3. C. 8π cm
    4. D. 4π cm
26. Which of the following geometric figures is the plane shape of a cube?
    1. A. Circle
    2. B. Rectangle
    3. C. Square
    4. D. Triangle
27. How many lines of symmetry does a rectangle have?
    1. A. 4
    2. B. 3
    3. C. 2
    4. D. 1
28. A rectangular box has length 20 cm, width 6 cm, and height 4 cm. How many cubes of size 2 cm will fit into the box?
    1. A. 120
    2. B. 60
    3. C. 30
    4. D. 15
29. The interior angle of a regular polygon is 120°. How many sides does the polygon have?
    1. A. 3
    2. B. 4
    3. C. 5
    4. D. 6
30. 
    
    In the diagram, length of PS = Length of SQ and angle SQR = 112°. Find the value of x.
    1. A. 68°
    2. B. 56°
    3. C. 46°
    4. D. 44°
31. 
    
    XYZ is a right-angled triangle with length of sides as shown. Which of the following equations gives the value of z²?
    1. A. (x + y)²
    2. B. (x - y)²
    3. C. x² + y²
    4. D. (x² - y²)
32. Express 7 minutes 30 seconds as a percentage of 1 hour.
    1. A. 2.5%
    2. B. 7.5%
    3. C. 11.7%
    4. D. 12.5%
33. The point (4, 5) is translated to the point (3, 1). What is the translation vector?
    1. A. (1, 4)
    2. B. (-1, 4)
    3. C. (1, -4)
    4. D. (-1, -4)
34. 
    
    In the diagram below, triangle QRT is the enlargement of QST. Which side of triangle QRT corresponds to side QT of triangle QST?
    1. A. TS
    2. B. TR
    3. C. QR
    4. D. SR
35. 
    
    In the diagrams above Fig. I is an enlargement of Fig. II. Find the side EF of Fig. II.
    1. A. 20 cm
    2. B. 5 cm
    3. C. 4 cm
    4. D. 3 cm
36. Express 4037 in standard form.
    1. A. 4.037 x 10⁻⁴
    2. B. 4.037 x 10⁻³
    3. C. 4.037 x 10³
    4. D. 4.037 x 10⁴
37. 
    
    Which of the following angles can be constructed by using the arcs at point C in the diagram?
    1. A. 30°
    2. B. 45°
    3. C. 60°
    4. D. 75°
38. Given that vector a = (-5, 12) and b = (10x, 12), find the value of x if a = b.
    1. A. -2
    2. B. -1/2
    3. C. 1/2
    4. D. 2
39. 
    
    In the diagram, the bearing of point B from A is:
    1. A. 340°
    2. B. 220°
    3. C. 140°
    4. D. 50°
40. Ama is 9 years older than Kwame. If Kwame is 18 years old, find the ratio of Kwame’s age to Ama's age.
    1. A. 3:2
    2. B. 1:3
    3. C. 2:3
    4. D. 2:1

Paper 2: Theory

1. a) Factorize (m + n)(2x - y) - x(m + n).
   
   b) A and B are subsets of a universal set U = {1, 2, 3, ..., 18} such that A = {even numbers} and B = {multiples of 3}.
   
   (i) List the elements of the sets A, B, (A ∩ B), (A ∪ B), and (A ∪ B)'.
   
   (ii) Illustrate the information in (i) on a Venn diagram.
   
   c) Find the values of x and y in the vector equation:
   
   (5, 3) + 2(x, y) - (1, -7) = 0.
2. a) Find the sum of 2,483.65, 701.532, and 102.7, giving your answer to one decimal place.
   
   b) In the quadrilateral ABCD, [AB] = 3 cm, [BC] = 4 cm, [CD] = 12 cm, and angles ABC and ACD are 90°. Calculate:
   
   (i) the perimeter of ABCD.
   
   (ii) the area of ABCD.
3. a) Evaluate (2⁷ × 3⁴ × 5³)/(2³ × 3² × 5²), leaving your answer in standard form.
   
   b) Kwame rode a bicycle for a distance of x km and walked for 1/2 hour at a rate of 6 km per hour. If the total distance covered was 10 km, find the distance x he covered by bicycle.
   
   c) A rectangular tank of dimensions 22 cm × 9 cm × 16 cm is filled with water. The water is poured into a cylindrical container of radius 6 cm. Calculate:
   
   (i) the volume of the rectangular tank.
   
   (ii) the depth of water in the cylindrical container.
4. a) Simplify: 7 - 4² + 2³ ÷ 8.
   
   b) The area of a trapezium is 31.5 cm². If the parallel sides are 7.3 cm and 5.3 cm, calculate the perpendicular distance between them.
   
   c) The marks scored by four students in a Mathematics test are: Esi = 92, Seth = 85, Mary = 65, Efe = X.
   
   (i) Write an expression for the mean of the marks.
   
   (ii) If the mean is less than 80, write a linear inequality for the information.
   
   (iii) Find the possible marks Efe scored in the test.
5. a) Solve: (4x - 3)/2 = (8x - 10)/8 + 2.
   
   b) Using a scale of 2 cm to 1 unit on both axes, draw two perpendicular lines OX and OY on a graph sheet for the x-axis from -5 to 5 and the y-axis from -6 to 6.
   
   (i) Plot points A(2, 3) and B(-3, 4) and join them with a long straight line.
   
   (ii) Plot points C(4, 2) and D(-2, -3) and join them with a long straight line to meet the line through AB.
   
   (iii) Measure the angle between the lines through AB and CD.
   
   (iv) Find the coordinates of the point at which the lines through AB and CD meet.
6. The following table shows the frequency distribution of the number of letters in the surnames of some students:
   
   Number of letters: 4, 5, 6, 7, 8, 9, 10.
   
   Number of students: 7, 3, 2, 8, 5, 3, 1.
   
   (a) From the distribution, determine:
   
   (i) the mode;
   
   (ii) the mean.
   
   (b) If a student is selected at random, find the probability that his/her name will contain more than 7 letters.
   
   (c) Draw a bar chart for the distribution.

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