BECE 1996 Mathematics Past Questions and Answers

Paper 1: Objectives

1. U = {0, 1}. How many subsets does U have?
   1. A. 1
   2. B. 2
   3. C. 3
   4. D. 4
   5. E. 5
   Answer: D

   The number of subsets = 2ⁿ, where n is the number of elements in the set. U has 2 elements, so 2² = 4.
2. The following addition is done in base ten. What number represents abc?
   
   2 2 2
   
   +
   
   3 4 3
   
   +
   
   a b c
   
   =
   
   1 0 0 0
   1. A. 324
   2. B. 242
   3. C. 423
   4. D. 435
   5. E. 234
   Answer: D

   222 + 343 + abc = 1000. So, abc = 1000 - 565 = 435.
3. In the mapping 2³ → 8, 2² → 4, 2¹ → 2, 2⁰ → a, 2⁻¹ → b, what is the value of a?
   1. A. 0
   2. B. ½
   3. C. 1
   4. D. 16
   5. E. 32
   Answer: C

   The rule is dividing by 2. Thus, 2⁰ = 1.
4. In the mapping 2³ → 8, 2² → 4, 2¹ → 2, 2⁰ → a, 2⁻¹ → b, what is the value of b?
   1. A. −2
   2. B. ¼
   3. C. ½
   4. D. 1
   5. E. 2
   Answer: C

   The rule is dividing by 2. Thus, 2⁻¹ = ½.
5. Write two hundred thousand and fifty-seven in figures.
   1. A. 20,057
   2. B. 200,057
   3. C. 2,000,057
   4. D. 20,000,057
   5. E. 200,570
   Answer: B

   Two hundred thousand = 200000, fifty-seven = 57, so the number is 200,057.
6. 
   
   What time is the clock showing if the short hand points to 3 and the long hand points to the fourth division?
   1. A. 4:30
   2. B. 4:15
   3. C. 3:40
   4. D. 3:20
   5. E. 3:04
   Answer: D

   Each division represents 5 minutes. The long hand points to 20 minutes, making the time 3:20.
7. Kojo, Ebo, and Ama share ₵14,000. Kojo had twice as much as Ebo, and Ebo had twice as much as Ama. How much did Ebo get?
   1. A. ₵8,000
   2. B. ₵6,000
   3. C. ₵4,000
   4. D. ₵3,000
   5. E. ₵2,000
   Answer: C

   Ebo's share = x, Kojo's = 2x, Ama's = x/2. Solving for x, we find Ebo's share is ₵4000.
8. At what rate of simple interest will ₵5,000 amount to ₵7,500 in 5 years?
   1. A. 5%
   2. B. 6⅔%
   3. C. 7½%
   4. D. 10%
   5. E. 12½%
   Answer: D

   Interest = ₵7,500 - ₵5,000 = ₵2,500. Using the formula, rate = 10%.
9. Simplify ⅓ − ½ + ⅖.
   1. A. ¹⁷⁄₃₀
   2. B. ¹³⁄₃₀
   3. C. ⁷⁄₃₀
   4. D. −⁷⁄₃₀
   5. E. −¹⁷⁄₃₀
   Answer: C

   Using common denominators, the result is ⁷⁄₃₀.
10. If 2ˣ = 8, what is the value of x?
    1. A. 0
    2. B. 1
    3. C. 2
    4. D. 3
    5. E. 4
    Answer: D

    8 = 2³, so x = 3.

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11. The relation between Celsius (C) and Fahrenheit (F) is C = ⁵⁄₉(F - 32). If C is 40, find F.
    1. A. 104.0
    2. B. 78.4
    3. C. 72.0
    4. D. 65.6
    5. E. 40.0
12. The relation between Celsius (C) and Fahrenheit (F) is C = ⁵⁄₉(F - 32). If C is –40, find F.
    1. A. -104.0
    2. B. -78.4
    3. C. -72.0
    4. D. -65.6
    5. E. -40.0
13. The ages in years of 9 children at a party are 2, 3, 3, 3, 4, 5, 5, 5, 6. What is the mean age?
    1. A. 3.0
    2. B. 3.5
    3. C. 4.0
    4. D. 4.5
    5. E. 5.0
14. The ages in years of 9 children at a party are 2, 3, 3, 3, 4, 5, 5, 5, 6. What is the median age?
    1. A. 2.0
    2. B. 3.0
    3. C. 3.5
    4. D. 4.0
    5. E. 5.0
15. The ages in years of 9 children at a party are 2, 3, 3, 3, 4, 5, 5, 5, 6. If a child is picked at random, what is the probability they are 5 years old?
    1. A. ²⁄₉
    2. B. ¹⁄₃
    3. C. ⁴⁄₉
    4. D. ⁵⁄₉
    5. E. ²⁄₃
16. P(2, 5) and Q(-2, 3) are points on the Cartesian plane. Find the vector PQ.
    1. A. (4, 2)
    2. B. (-4, -2)
    3. C. (4, -2)
    4. D. (-4, 2)
    5. E. (0, -2)
17. Find k in the vector equation (3, 4) + k(3, 4) = (-3, -4).
    1. A. -3
    2. B. -2
    3. C. -1
    4. D. -¾
    5. E. 2
18. 
    
    In the diagram, |RS| = |RT|. Find angle a.
    1. A. 146°
    2. B. 81°
    3. C. 73°
    4. D. 65°
    5. E. 34°
19. If a² – b² = (a + b)(a – b), evaluate 9.32² – 0.68².
    1. A. 87.32
    2. B. 86.4
    3. C. 74.65
    4. D. 10.0
    5. E. 8.64
20. Simplify 6² / (2² × 3).
    1. A. 1
    2. B. 2
    3. C. 3
    4. D. 6
    5. E. 9
21. The sum of the ages of Kwaku and Kojo is 30 years. Kwaku is 4 years older than Kojo. How old is Kojo?
    1. A. 19
    2. B. 17
    3. C. 13
    4. D. 11
    5. E. 9
22. 
    
    What type of triangle is ∆PQR?
    1. A. Equilateral
    2. B. Isosceles
    3. C. Scalene
    4. D. Right-angled
    5. E. Obtuse-angled
23. Use the equation y = (x + 2)(x - 2) to answer the question below. If x = -1, find y.
    1. A. -4
    2. B. -3
    3. C. 3
    4. D. 4
    5. E. 9
24. Use the equation y = (x + 2)(x - 2) to answer the question below. Find the set of values of x for which y is zero.
    1. A. {0}
    2. B. {0, 2}
    3. C. {0, -2}
    4. D. {-2, 2}
    5. E. {2}
25. 
    
    In the diagram above, the cylinder has diameter 4 cm and length 14 cm. [Take π = 22/7] Find the circumference of the base.
    1. A. 44 cm / 7
    2. B. 88 cm / 7
    3. C. 176 cm / 7
    4. D. 44 cm
    5. E. 176 cm
26. 
    
    In the diagram above, the cylinder has diameter 4 cm and length 14 cm. [Take π = 22/7] The area of the base is:
    1. A. 176 cm²
    2. B. 44 cm²
    3. C. 176 cm² / 7
    4. D. 88 cm² / 7
    5. E. 44 cm² / 7
27. 
    
    In the diagram above, the cylinder has diameter 4 cm and length 14 cm. [Take π = 22/7] What is the volume of the cylinder?
    1. A. 176 cm³
    2. B. 44 cm³
    3. C. 176 cm³ / 7
    4. D. 88 cm³ / 7
    5. E. 44 cm³ / 7
28. A woman bought 210 oranges for ₵650.00. She sold all of them at 3 for ₵20.00. How much profit did she make?
    1. A. ₵350.00
    2. B. ₵450.00
    3. C. ₵550.00
    4. D. ₵650.00
    5. E. ₵750.00
29. The ratio of boys to girls in a school is 9 : 11. If there are 400 pupils in the school, how many boys are there?
    1. A. 80
    2. B. 120
    3. C. 180
    4. D. 220
    5. E. 280
30. Express the product of 162.5 x 0.5 in standard form.
    1. A. 81.25 x 10⁻¹
    2. B. 81.25 x 10
    3. C. 8.125 x 10⁻¹
    4. D. 8.125 x 10
    5. E. 0.8125 x 10⁻²
31. What is 16% of ₵500,000.00?
    1. A. ₵80
    2. B. ₵8,000
    3. C. ₵80,000
    4. D. ₵420,000
    5. E. ₵492,000
32. Simplify 0.24 x 14.3 / 5.2.
    1. A. 66
    2. B. 6.60
    3. C. 0.70
    4. D. 0.66
    5. E. 0.60
33. The product of 2x and 3 is 138. Find x.
    1. A. 23
    2. B. 33
    3. C. 68
    4. D. 69
    5. E. 138
34. 
    
    What was the average speed for the return journey from town Y to town X?
    1. A. 100 km/h
    2. B. 50 km/h
    3. C. 33.33 km/h
    4. D. 25 km/h
    5. E. 20 km/h
35. 
    
    State the period within which he traveled to town Y after his first rest.
    1. A. 1:00 – 2:00 pm
    2. B. 1:00 – 4:00 pm
    3. C. 1:15 – 1:30 pm
    4. D. 1:30 – 2:00 pm
    5. E. 2:00 – 4:00 pm
36. 
    
    How many minutes did the cyclist spend at town Y?
    1. A. 15 minutes
    2. B. 20 minutes
    3. C. 30 minutes
    4. D. 45 minutes
    5. E. 60 minutes
37. 200 bottles of equal capacity hold 350 litres of water. How much water does each bottle hold?
    1. A. 1750 litres
    2. B. 175 litres
    3. C. 17.5 litres
    4. D. 1.75 litres
    5. E. 0.17 litres
38. Find the solution set of 2x + 4 > -6.
    1. A. {x = -5}
    2. B. {x < 5}
    3. C. {x > 5}
    4. D. {x < -5}
    5. E. {x > -5}
39. A rectangular field 50 metres wide and x metres long requires 260 metres of fencing. Which of the following statements is true?
    1. A. x + 100 = 260
    2. B. 2x + 50 = 260
    3. C. 4x + 200 = 260
    4. D. 2x + 100 = 260
    5. E. 4x + 100 = 260
40. 
    
    In the diagram above, PQSR is a trapezium. PQ is parallel to RS. ∠PQR = ∠QRS. What type of triangle is triangle RQS?
    1. A. Isosceles
    2. B. Scalene
    3. C. Equilateral
    4. D. Right-angled
    5. E. Obtuse-angled

Paper 2: Theory

1. a) Kofi is n years old now:
   
   (i) How old was he 5 years ago?
   
   (ii) How old will he be 10 years from now?
   
   (iii) If his age in 10 years time will be four times his age 5 years ago, how old is he now?
   
   b) Convert 2342₅ to a base ten numeral.
   
   c) Given that f = (vu) ÷ (v + u), find v, if f = 20 and u = 5.
2. a) A man deposited ₵350,000.00 in his account in a bank. A simple interest of 4% per annum was paid on his deposit. Calculate the total amount at the end of 4 years.
   
   b) The cost of sending a telegram is ₵500 for the first 12 words and ₵25.00 for every extra word. Find the cost of sending a telegram containing 20 words.
3. The table below shows the distribution of pupils in a JSS form one class who speak some of the Ghanaian languages:
   
   

   Ghanaian Language	No. of Students
   Nzema	5
   Ga	20
   Twi	30
   Ewe	25
   Fante	10

   
   
   a) Draw a pie chart for the distribution.
   
   b) What is the modal Ghanaian language?
   
   c) If a pupil is selected at random, what is the probability that they speak Ga?
4. Using a ruler and a pair of compasses only:
   
   a) Construct triangle ABC such that |AB| = 6 cm, |AC| = 10 cm, and |BC| = 8 cm. Measure angle ABC.
   
   b) Construct the perpendicular bisectors (mediators) of |AB| and |BC|. Let the bisectors meet at O.
   
   c) Construct a circle with centre O and radius OA. Measure the radius of the circle.
5. a) Using a scale of 2 cm to 2 units on both axes, draw two perpendicular axes OX and OY on a graph sheet.
   
   b) Mark the x-axis from −10 to 10 and the y-axis from −12 to 12.
   
   c) Plot the points A(2, 1), B(3, 4), and C(4, 2). Join them to form triangle ABC.
   
   d) Draw an enlargement A1B1C1 of triangle ABC with scale factor 2 from the origin O(0, 0), such that A → A1, B → B1, and C → C1. Indicate the coordinates of triangle A1B1C1. Show all lines of transformation.
   
   e) Using the x-axis as the mirror line, draw the image A2B2C2 of triangle ABC, where A → A2, B → B2, and C → C2. Indicate the coordinates of triangle A2B2C2.

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