BECE 2012 Mathematics Past Questions and Answers

Paper 1: Objectives

1. If P= {2,3,5,7} and Q= {2,4,6,8}, find P ∩ Q.
   1. A. {2}
   2. B. {3}
   3. C. {4}
   4. D. {5}
   Answer: A

   The intersection (∩) is the set of elements in both sets. Only 2 can be found in both sets P and Q.
2. Which of the following numbers is an integer?
   1. A. 5/4
   2. B. 2/3
   3. C. 0.5
   4. D. 1
   Answer: D

   An integer is a whole number (not fractional) that can be positive, negative, or zero.
3. Find the Lowest Common Multiple (LCM) of 2³ × 3 × 5 and 2 × 3² × 5².
   1. A. 2³ × 3 × 5
   2. B. 2³ × 3² × 5²
   3. C. 2² × 3 × 5
   4. D. 2³ × 3² × 5²
   Answer: D

   The LCM is the product of each prime factor in its highest power: 2³ × 3² × 5².
4. How many diagonals are in a rectangle?
   1. A. 1
   2. B. 2
   3. C. 3
   4. D. 4
   Answer: B

   
   
   A rectangle has two diagonals that connect opposite corners.
5. Simplify -4(3 - 5) + 10 - 3(7 + 4) + 30.
   1. A. -1
   2. B. 15
   3. C. 56
   4. D. 65
   Answer: B

   Simplify each bracket and perform the calculations: -4(-2) + 10 - 3(11) + 30 = 15.
6. An iron rod 15 m long is divided into 12 equal parts. How long is each part?
   1. A. 0.80 m
   2. B. 1.25 m
   3. C. 1.50 m
   4. D. 3.00 m
   Answer: B

   15 m divided by 12 gives 1.25 m per part.
7. Convert 42 to a base two numeral.
   1. A. 1001010
   2. B. 1010010
   3. C. 1010100
   4. D. 101010
   Answer: D

   42 in base 10 is 101010 in base 2.
8. Simplify 5⁷ / 5⁴.
   1. A. 5⁰
   2. B. 5⁸
   3. C. 5³
   4. D. 5¹³
   Answer: C

   Using the law of indices for division, a^m / a^n = a^(m-n); 5⁷ / 5⁴ = 5³.
9. A tank contains 400 litres of water. If 100 litres is used, what percentage is left?
   1. A. 25%
   2. B. 30%
   3. C. 40%
   4. D. 75%
   Answer: D

   75% of the water is left (300 / 400 × 100 = 75%).
10. 
    
    Triangle ABC is a right-angled triangle. If AB = 3 cm and BC = 4 cm, find the length of AC.
    1. A. 1 cm
    2. B. 5 cm
    3. C. 7 cm
    4. D. 12 cm
    Answer: B

    Using Pythagoras theorem, AC = √(3² + 4²) = 5 cm.

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11. Arrange the fractions 2/3, 5/7, 2/5, 1/2 in descending order of magnitude.
    1. A. 5/7, 2/5, 2/3, 1/2
    2. B. 5/7, 2/3, 1/2, 2/5
    3. C. 1/2, 2/5, 5/7, 2/3
    4. D. 1/2, 5/7, 2/3, 2/5
12. Find the image of 3 under the mapping x → 10 - 2x.
    1. A. 4
    2. B. 5
    3. C. 8
    4. D. 16
13. Simplify 1/3 + 1/9 + 1/27.
    1. A. 5/27
    2. B. 7/27
    3. C. 11/27
    4. D. 13/27
14. If 2x = 5(x - 2) + 7, find the value of x.
    1. A. -5 2/3
    2. B. -1
    3. C. 1
    4. D. 5 2/3
15. The average day temperature for a week was recorded as follows: {33, 29, 32, 34, 32, 30, 30}. Find the average.
    1. A. 24.4°C
    2. B. 30.2°C
    3. C. 31.4°C
    4. D. 32.2°C
16. The table below shows the day and night temperatures of a town during a week.
    

    Day	Day temperature (°C)	Night temperature (°C)
    Monday	33	24
    Tuesday	29	25
    Wednesday	32	23
    Thursday	34	26
    Friday	32	24
    Saturday	30	24
    Sunday	30	25

    
    On which day was the change in temperature the least?
    1. A. Monday
    2. B. Saturday
    3. C. Sunday
    4. D. Tuesday
17. A box contains 30 identical balls of which 16 are white and the rest yellow. What is the probability that a randomly chosen ball is yellow?
    1. A. 1/16
    2. B. 7/15
    3. C. 8/15
    4. D. 7/8
18. Find the truth set of (x + 3) < 2x - 1.
    1. A. {x : x < -3}
    2. B. {x : x < -1}
    3. C. {x : x > 1}
    4. D. {x : x > -3}
19. 
    
    The perimeter of the figure is 71 cm. Find the diameter of the semi-circumference portion.
    1. A. 1.0 cm
    2. B. 3.5 cm
    3. C. 7.0 cm
    4. D. 14.0 cm
20. Simplify 3x/4 - (x - y)/3.
    1. A. (5x - 4y) / 12
    2. B. (13x - 4y) / 12
    3. C. (5x + 4y) / 12
    4. D. (13x + 4y) / 12
21. Kojo is 20% heavier than Afua. If Kojo weighs 6 kg, what is Afua's weight?
    1. A. 4.8 kg
    2. B. 5.0 kg
    3. C. 6.0 kg
    4. D. 7.2 kg
22. Find the volume of a cylinder of height 3 cm and radius 2 cm.
    1. A. 6π cm³
    2. B. 12π cm³
    3. C. 18π cm³
    4. D. 24π cm³
23. Given the points S(5, -2) and T(3, 2), calculate the gradient of the line ST.
    1. A. -2
    2. B. -3/5
    3. C. -1/2
    4. D. 2
24. Kofi invested GHC 150,000 at 2.5% per annum simple interest. How long will it take this amount to yield an interest of GHC11,250?
    1. A. 2 years
    2. B. 3 years
    3. C. 4 years
    4. D. 5 years
25. Express 3.75 as a mixed fraction.
    1. A. 5/5
    2. B. 4
    3. C. 7/4
    4. D. 15/4
26. A map is drawn to the scale 1:100,000. What distance in kilometres is represented by 5 cm on the map?
    1. A. 0.5 km
    2. B. 5.0 km
    3. C. 50.0 km
    4. D. 500.0 km
27. Given that r = (-3, 4) and s = (1, -3) are column vectors, find r - 2s.
    1. A. (-5, 1)
    2. B. (-5, 10)
    3. C. (-2, 10)
    4. D. (-1, 10)
28. Esi bought 500 g of meat, 850 g of fish, and 900 g of eggs. What is the total weight in kilograms?
    1. A. 2.20 kg
    2. B. 2.25 kg
    3. C. 2.35 kg
    4. D. 22.50 kg
29. A watch gains 1.5 minutes per hour. What is the total time gained from 12 noon to 12 midnight in a day?
    1. A. 9 minutes
    2. B. 15 minutes
    3. C. 18 minutes
    4. D. 36 minutes
30. A printing machine prints 600 books in 3 hours. How many books will it print in 5 hours?
    1. A. 360 books
    2. B. 1000 books
    3. C. 1800 books
    4. D. 3000 books
31. 
    
    The bearing of Atoru from Busase is 275°. What is the bearing of Busase from Atoru?
    1. A. 180°
    2. B. 175°
    3. C. 095°
    4. D. 075°
32. 
    
    In a class of 24 pupils, 10 study French only and 8 study English only. If each pupil studies at least one of the two subjects, how many study English?
    1. A. 12
    2. B. 14
    3. C. 16
    4. D. 18
33. Convert 84 to a base five numeral.
    1. A. 413
    2. B. 301
    3. C. 314
    4. D. 114
34. 
    
    In the diagram, triangle ABC is an enlargement of triangle A'BC. Determine the scale factor.
    1. A. 0.50
    2. B. 0.75
    3. C. 2.00
    4. D. 4.00
35. Find the least number that must be added to 308 to make it divisible by 19.
    1. A. 4
    2. B. 7
    3. C. 15
    4. D. 18
36. In a school of 940 pupils, the number of girls exceeds the number of boys by 150. How many girls are there in the school?
    1. A. 620
    2. B. 545
    3. C. 470
    4. D. 395
37. Which of the following fractions is equivalent to 3/5?
    1. A. 21/30
    2. B. 12/20
    3. C. 15/45
    4. D. 6/15
38. 
    
    In the diagram, line PQ is parallel to RS. Find angle a.
    1. A. 35°
    2. B. 55°
    3. C. 135°
    4. D. 145°
39. 
    
    In the diagram, line PQ is parallel to RS. Angle b and angle c are:
    1. A. Alternate angles
    2. B. Vertically opposite angles
    3. C. Corresponding angles
    4. D. Interior opposite angles
40. Expand -x(3 - 2x).
    1. A. -2x² - 3x
    2. B. 2x² - 3x
    3. C. -2 + 3
    4. D. 2 + 3x

Paper 2: Theory

1. (a) Evaluate 0.035 × 1.02 ÷ 0.00015 and leave the answer in standard form.
   
   (b) An amount of GHC4,200.00 was shared between Aba and Kwame. If Aba had 5/7 of the amount,
   
   (i) how much did Kwame receive?
   
   (ii) What percentage of Aba's share did Kwame receive?
   
   (c) Find the value of x in the diagram below:
   
   
2. (a) A car consumes a gallon of petrol for every 30 km drive. The driver of the car set out on a journey of 420 km with 10 gallons of petrol in the fuel tank.
   
   (i) How many more gallons of petrol will he need to complete the journey?
   
   (ii) Find the cost of the petrol used for the journey of 420 km if a gallon of petrol costs GHC5.50.
   
   (b) The average number of spectators at a football competition for the first five days was 3,144. The attendance on the sixth day was 3,990. Find:
   
   (i) The total attendance on the first five days.
   
   (ii) The average attendance for the 6 days.
   
   (c) The area enclosed by a square garden is 121 m². What is the distance around the garden?
3. (a) The table shows the number of students who scored more than 80% in the listed subjects:
   
   Subject: Biology (26), Physics (30), Chemistry (32), French (38), Geography (24), History (30).
   
   (i) Draw a pie chart for the distribution.
   
   (ii) What is the probability that a student chosen at random from the distribution offers Chemistry?
   
   (b) A woman bought 210 oranges for GHC7.50. She sold all of them at 3 for 15 Gp. Find:
   
   (i) The total selling price of the oranges.
   
   (ii) The percentage profit.
4. (a) Construct a frequency distribution table for the following scores:
   
   Scores: {3, 3, 5, 6, 3, 4, 7, 8, 3, 4, 5, 4, 7, 4, 3, 7, 4, 6, 4, 8, 4, 5, 6, 3, 8, 4, 5, 6, 4, 5}
   
   (b) Using the table, find:
   
   (i) The mode;
   
   (ii) The mean, correct to one decimal place;
   
   (iii) The median.
5. (a) (i) Find the Least Common Multiple (LCM) of 9, 18, and 16.
   
   (ii) Arrange 8/9, 7/18, and 10/16 in ascending order of magnitude.
   
   (b) Using a ruler and a pair of compasses only:
   
   (i) Construct a triangle PQR with PQ = 10 cm, ∠QPR = 45°, and ∠PQR = 60°.
   
   (ii) Construct the perpendicular bisectors of PR and RQ to meet at T.
   
   (iii) Measure the length of TP.
6. (i) Using a scale of 2 cm to 1 unit on both axes, draw two perpendicular axes Ox and Oy on a graph sheet.
   
   (ii) Mark on the same graph sheet, the x-axis from -5 to 5 and the y-axis from -6 to 6.
   
   (iii) Plot the points P(4, 2), Q(2, 5), and R(2, 2). Join the points P, Q, R to form a triangle PQR.
   
   (iv) Using the x-axis as a mirror line, draw the image P₁Q₁R₁ of the triangle PQR such that P → P₁, Q → Q₁, R → R₁.
   
   (v) Write down the coordinates of P₁, Q₁, and R₁.
   
   (vi) Translate triangle PQR by the vector (-3, 1) such that P → P₂, Q → Q₂, R → R₂.
   
   (vii) Label the vertices of triangle P₂Q₂R₂.

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