BECE 2009 Mathematics Past Questions and Answers

Paper 1: Objectives

1. Given that 𝐀 = {𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔} and 𝐁 = {𝟑, 𝟔, 𝟗, 𝟏𝟐}, find 𝐀 ∪ 𝐁.
   1. A. {𝟑, 𝟔}
   2. B. {𝟔, 𝟏𝟐}
   3. C. {𝟐, 𝟑, 𝟒, 𝟓, 𝟗, 𝟏𝟐}
   4. D. {𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔, 𝟗, 𝟏𝟐}
   Answer: D

   Union (∪) includes all unique elements in both sets: {𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔, 𝟗, 𝟏𝟐}.
2. Write 𝟐𝟑𝟒𝟎𝟎𝟎𝟎 in standard form.
   1. A. 𝟐.𝟑𝟒 × 𝟏𝟎⁵
   2. B. 𝟐.𝟑𝟒 × 𝟏𝟎⁴
   3. C. 𝟐.𝟑𝟒 × 𝟏𝟎⁶
   4. D. 𝟐.𝟑𝟒 × 𝟏𝟎⁷
   Answer: C

   Moving the decimal left 6 places yields 𝟐.𝟑𝟒 × 𝟏𝟎⁶.
3. How many faces does a cuboid have?
   1. A. 𝟏𝟐
   2. B. 𝟖
   3. C. 𝟔
   4. D. 𝟒
   Answer: C

   A cuboid has 6 faces.
4. Subtract 𝟏𝟐𝟓.𝟒𝟕 from 𝟐𝟎𝟑.𝟗𝟎.
   1. A. 𝟕𝟖.𝟓𝟕
   2. B. 𝟕𝟖.𝟒𝟑
   3. C. -𝟏𝟐𝟏.𝟓𝟕
   4. D. -𝟏𝟐𝟐.𝟑𝟖
   Answer: B

   𝟐𝟎𝟑.𝟗𝟎 - 𝟏𝟐𝟓.𝟒𝟕 = 𝟕𝟖.𝟒𝟑.
5. Simplify (𝟓𝑚 + 𝟑𝑛) - (𝟐𝑚 - 𝑛).
   1. A. 𝟓𝑚 - 𝟒𝑛
   2. B. 𝟑𝑚 + 𝟒𝑛
   3. C. 𝟑𝑚 - 𝟐𝑛
   4. D. 𝟕𝑚 + 𝟒𝑛
   Answer: B

   (𝟓𝑚 + 𝟑𝑛) - (𝟐𝑚 - 𝑛) = 𝟑𝑚 + 𝟒𝑛.
6. Which of the following sets is equal to {𝟏, 𝟐, 𝟑, 𝟒}?
   1. A. {𝟐, 𝟒, 𝟏, 𝟓}
   2. B. {𝟐, 𝟏, 𝟒, 𝟑}
   3. C. {𝟏, 𝟐, 𝟑, 𝟒, ... }
   4. D. {𝟐, 𝟑, 𝟒, 𝟓, ... }
   Answer: B

   Two sets are equal when they contain the same elements: {𝟐, 𝟏, 𝟒, 𝟑}.
7. In a town of 𝟒𝟐,𝟖𝟎𝟎 inhabitants, 𝟒𝟖% are male. How many more females are there than males?
   1. A. 𝟐𝟐,𝟐𝟓𝟔
   2. B. 𝟐𝟎,𝟓𝟒𝟒
   3. C. 𝟏,𝟕𝟏𝟐
   4. D. 𝟏,𝟔𝟏𝟐
   Answer: C

   Percentage difference is 4% of 𝟒𝟐,𝟖𝟎𝟎, which is 𝟏,𝟕𝟏𝟐.
8. 
   
   What set does the following graph represent: (-∞, 𝟐]?
   1. A. {𝐱:𝐱 < 𝟐}
   2. B. {𝐱:𝐱 ≤ 𝟐}
   3. C. {𝐱:𝐱 > 𝟐}
   4. D. {𝐱:𝐱 ≥ 𝟐}
   Answer: B

   The shaded circle indicates inclusion (≤).
9. 
   
   In a pie chart showing Kate’s exam scores, what is the angle for French?
   1. A. 𝟏𝟐𝟎°
   2. B. 𝟏𝟎𝟎°
   3. C. 𝟕𝟎°
   4. D. 𝟑𝟓°
   Answer: C

   360° - (120° + 90° + 55° + 25°) = 70°.
10. 
    
    If Kate scored 60% in Social Studies, what was her score in Economics?
    1. A. 45%
    2. B. 54%
    3. C. 72%
    4. D. 90%
    Answer: A

    Using the angle ratio: 90° = 45%.

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11. A teacher is to be chosen from 6 male and 2 female teachers. What is the probability of choosing a female?
    1. A. 𝟑/𝟒
    2. B. 𝟐/𝟑
    3. C. 𝟏/𝟑
    4. D. 𝟏/𝟒
12. Solve the equation: 2𝑥 - 3(𝑥 - 1) = 6.
    1. A. 3
    2. B. -3
    3. C. -7
    4. D. -9
13. If 𝑚 = 3 and 𝑛 = -3, evaluate 𝟏/𝟐 (3𝑚 - 𝑛).
    1. A. 6
    2. B. 3
    3. C. 0
    4. D. -6
14. Which set of angles form a right-angled triangle?
    1. A. {20°, 50°, 90°}
    2. B. {80°, 60°, 90°}
    3. C. {45°, 45°, 90°}
    4. D. {65°, 90°, 35°}
15. What is the rule for the mapping given by the table?
    

    𝑥	0	1	2	3	4
    𝑦	0	1/4	1/2	3/4	1

    1. A. 𝑥 → 𝑥/4
    2. B. 𝑥 → 𝑥/2
    3. C. 𝑥 → 3𝑥/4
    4. D. 𝑥 → 1/(2𝑥)
16. A rectangle has an area of 36 cm² and a width of 3 cm. Find its perimeter.
    1. A. 12 cm
    2. B. 18 cm
    3. C. 24 cm
    4. D. 30 cm
17. Find the value of 4 + 𝑥⁰.
    1. A. 3
    2. B. 4
    3. C. 5
    4. D. 6
18. A van travels 154 km in 1¾ hours. Find its speed in km/h.
    1. A. 77 km/h
    2. B. 88 km/h
    3. C. 100 km/h
    4. D. 269.5 km/h
19. 
    
    In the figure, PQ and RS are straight lines. Find angle 𝑤.
    1. A. 27°
    2. B. 53°
    3. C. 63°
    4. D. 127°
20. If 𝑥 + 5 = -7, find 𝑥/6.
    1. A. -5
    2. B. -2
    3. C. 1
    4. D. 2
21. 
    
    In the following diagram, rectangle OABC is enlarged into rectangle O'A'B'C' from center O. OC = 5 cm, OA = 2 cm, and A'A = 1 cm. Find the scale factor of the enlargement.
    1. A. 1
    2. B. 1.5
    3. C. 2
    4. D. 2.5
22. 
    
    Using the same diagram, calculate OC'.
    1. A. 7.5 cm
    2. B. 8 cm
    3. C. 9 cm
    4. D. 12 cm
23. The height of a flag pole in a scale drawing is 5 cm. If the scale is 1 cm to 3 m, what is the actual height of the pole?
    1. A. 10 m
    2. B. 15 m
    3. C. 8 m
    4. D. 5 m
24. Factorize ax + 3x + a + 3.
    1. A. x(a + x)
    2. B. (x - a)(x + 3)
    3. C. x(a - x)
    4. D. (a + 3)(x + 1)
25. If y = (x + 8) / (x - 4), find the value of y when x = 2.
    1. A. 5
    2. B. -5
    3. C. 4
    4. D. -4
26. Find the Greatest Common Factor (GCF) of 90, 126, and 72.
    1. A. 6
    2. B. 9
    3. C. 18
    4. D. 24
27. Given that 1 : 3 = x : 21, find the value of x.
    1. A. 4
    2. B. 5
    3. C. 7
    4. D. 63
28. Find the difference between 432₅ and 143₅.
    1. A. 234₅
    2. B. 334₅
    3. C. 1130₅
    4. D. 1310₅
29. Simplify: 14 1/3 - 2 3/8 + 5 7/12.
    1. A. 6 3/8
    2. B. 7 5/12
    3. C. 17 5/12
    4. D. 17 13/24
30. Nine bottles of equal capacity hold 4 liters of water. How much do x bottles hold?
    1. A. (4x) / 9 liters
    2. B. 2x liters
    3. C. 20 liters
    4. D. 2 liters
31. A sales girl receives a 5% commission on all she sells. How much must she sell to receive GHC 15.00?
    1. A. GHC 750.00
    2. B. GHC 300.00
    3. C. GHC 75.00
    4. D. GHC 30.00
32. Arrange the following fractions in ascending order: 7/12, 3/5, 7/15, 3/4.
    1. A. 3/5, 7/15, 7/12, 3/4
    2. B. 7/12, 7/15, 3/5, 3/4
    3. C. 7/15, 7/12, 3/5, 3/4
    4. D. 3/5, 3/4, 7/12, 7/15
33. Add 2.5 to the product of 4.2 and 0.2.
    1. A. 13.4
    2. B. 10.9
    3. C. 3.34
    4. D. 1.34
34. What is the value of four in the number 7073.48?
    1. A. four tenths
    2. B. four
    3. C. forty
    4. D. four hundred
35. What is the modal age of children at a birthday party with ages [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] and frequencies [3, 4, 2, 5, 4, 4, 6, 4, 2, 1]?
    1. A. 10
    2. B. 7
    3. C. 5
    4. D. 4
36. A child is selected at random; what is the probability that he or she is 4 years old?
    1. A. 4/35
    2. B. 1/7
    3. C. 2/5
    4. D. 4/5
37. How many children are 7 or more years old?
    1. A. 28
    2. B. 22
    3. C. 13
    4. D. 6
38. Write the vector (-6, -4) using Cartesian components.
    1. A. (-6, -4)
    2. B. (6, 4)
    3. C. (4, 6)
    4. D. (0, 0)
39. Simplify: 5 - 7 + 2(3 - 8).
    1. A. -12
    2. B. -8
    3. C. -5
    4. D. -4
40. If r = (-10, -3) and n = (8, -6), find n + r.
    1. A. (-2, -9)
    2. B. (2, -9)
    3. C. (18, 9)
    4. D. (-2, -3)

Paper 2: Theory

1. (a) Simplify 1200 × 1260 ÷ 800 and write your answer in standard form.
   
   (b) A plot of land measures 25 m by 12 m. A portion of this plot measuring 8 m by 8 m is used for the cultivation of vegetables. Find the area of the plot not cultivated.
   
   (c) The table below shows the performance of Aisha in her final examination:
   
   Subject: English Language (54%), Mathematics (36%), Ga (68%), Science (50%), Social Studies (32%).
   
   Draw a pie chart to represent this information.
2. (a) The table below shows the scores of some students in an examination:
   
   Scores: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
   
   Frequency: {3, 5, 3, 2, 7, 6, 5, 4, 2, 2, 1}
   
   Find:
   
   (i) How many students wrote the examination;
   
   (ii) The modal score;
   
   (iii) The number of students that scored 7 or more;
   
   (iv) The mean score correct to one decimal place.
3. (a) (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 the x-axis from -5 to 5 and y-axis from -6 to 6.
   
   (iii) Plot the points A(2, 5), B(2, 2), and C(4, 2). Join the points to form triangle ABC.
   
   (iv) Using the y-axis as a mirror line, draw the image triangle A₁B₁C₁ of triangle ABC and write the coordinates of A₁, B₁, and C₁.
   
   (v) Draw the image triangle A₂B₂C₂ of triangle ABC under an anticlockwise rotation of 180° about the origin and write the coordinates of A₂, B₂, and C₂.
   
   (b) Simplify 2a - 3c + b - 4 where a = 2, b = -7, c = -5.
4. (a) The ratio of sheep to goats on a farm is 4:7. If there are 1,428 sheep, find how many goats are on the farm.
   
   (b) Using a ruler and a pair of compasses only, construct a triangle ABC with AB = 6 cm, AC = 8 cm, and ∠BAC = 30°. Construct the bisector of ∠ACB to meet line AB at D.
   
   (i) Measure [AD] and [BD].
   
   (ii) Write down the ratio [AD]:[BD].
5. (a) The diagram shows triangle ABC with side AC produced to D.
   
   
   
   Find:
   
   (i) The value of x;
   
   (ii) ∠ACB.
   
   (b) The simple interest formula, I = PRT/100, gives the interest, I, on a principal, P, invested at a rate, R, per annum for time, T, years.
   
   (i) Find the simple interest on GHC 3,600.00 at 15% per annum for 2 years.
   
   (ii) Make R the subject of the formula.
   
   (iii) At what rate per annum will GHC 6,000.00 earn GHC 2,400.00 simple interest in 2 years?
6. (a) Given that C10,000 = GHC 1.00, complete the table relating cedis (x) to Ghana cedis (y):
   
   Cedis: {10,000, 50,000, 150,000, 250,000, 350,000, 450,000}
   
   Ghana Cedis: {1, 5, 15, 25, 35, 45}
   
   (b) (i) On a graph sheet, draw two perpendicular axes OX and OY.
   
   (ii) Using a scale of 2 cm to C50,000.00 on the OX axis and 2 cm to GHC 5.00 on the OY axis, plot the points and join them with a straight line.
   
   (c) From the graph, find:
   
   (i) GHC 8.00 in cedis;
   
   (ii) GHC 35.00 in cedis;
   
   (iii) C260,000.00 in Ghana cedis.

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