BECE 2023 Mathematics Past Questions and Answers

Paper 1: Objectives

1. Write 0.01723 in standard form.
   1. A. 0.01723 × 10⁵
   2. B. 0.01723 × 10⁶
   3. C. 1.723 × 10⁻²
   4. D. 1.723 × 10²
   Answer: C

   In standard form, the decimal point is moved after the first non-zero digit. 0.01723 = 1.723 × 10^-2.
2. What is the value of 3x² + 2x - 7 when x = -3?
   1. A. -40
   2. B. -33
   3. C. 14
   4. D. 26
   Answer: C

   3(-3)² + 2(-3) - 7 = 27 - 6 - 7 = 14.
3. Find the image of the point S(-2, 2) when it is reflected in the y-axis.
   1. A. (2, -2)
   2. B. (2, 2)
   3. C. (-2, -2)
   4. D. (-2, 2)
   Answer: B

   Reflecting in the y-axis changes the x-coordinate, resulting in (2, 2).
4. What is the actual bearing of S25°E?
   1. A. 035°
   2. B. 065°
   3. C. 115°
   4. D. 155°
   Answer: D

   
   
   The bearing of S25°E from the north is 90 + 65 = 155°.
5. Given that m = b/2 - t, make t the subject.
   1. A. (b - 2m) / 2
   2. B. (2m - b) / 2
   3. C. (2b - m) / 2
   4. D. (b + 2m) / 2
   Answer: A

   Multiply both sides by 2: 2m = b - 2t. Then 2t = b - 2m, so t = (b - 2m) / 2.
6. Expand (x - 2)(x + 4).
   1. A. x² + 2x - 8
   2. B. x² + 2x + 8
   3. C. x² - 4x - 8
   4. D. -x - 8
   Answer: A

   Expanding (x - 2)(x + 4) gives x² + 2x - 8.
7. If n(E) = 15, n(F) = 20, and n(E ∩ F) = 6, find n(E ∪ F).
   1. A. 21
   2. B. 26
   3. C. 29
   4. D. 35
   Answer: C

   
   
   n(E ∪ F) = n(E) + n(F) - n(E ∩ F) = 15 + 20 - 6 = 29.
8. Tony shared 2/3 of his plot of land equally among his three sons. What fraction of the plot did each get?
   1. A. 2/9
   2. B. 1/3
   3. C. 1/2
   4. D. 5/9
   Answer: A

   Each son receives (2/3) × (1/3) = 2/9 of the plot.
9. Araba and Ama share 20 oranges such that Ama receives 12 oranges. Find the ratio of Araba's share to Ama's.
   1. A. 2:5
   2. B. 3:5
   3. C. 3:2
   4. D. 2:3
   Answer: D

   Araba's share is 8, so the ratio is 8:12, which simplifies to 2:3.
10. Solve: 3(x - 2) - x/3 + 6 > 0.
    1. A. x < 0
    2. B. x > 0
    3. C. x > 3
    4. D. x > 1/8
    Answer: B

    Multiply every term by 3: 9(x - 2) - x + 18 > 0, so 9x - 18 - x + 18 > 0 and 8x > 0. Therefore x > 0.

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11. The stem and leaf plot shows the marks scored by students in a French test.
    

    Stem	Leaf
    2	0, 2, 5, 7, 8
    3	2, 7, 9
    4	3, 5, 5, 5
    5	4, 6, 6, 8
    6	3, 5, 7
    7	0, 6

    
    What is the modal mark?
    1. A. 35
    2. B. 45
    3. C. 56
    4. D. 76
12. The stem and leaf plot shows the marks scored by students in a French test.
    

    Stem	Leaf
    2	0, 2, 5, 7, 8
    3	2, 7, 9
    4	3, 5, 5, 5
    5	4, 6, 6, 8
    6	3, 5, 7
    7	0, 6

    
    How many students took the test?
    1. A. 20
    2. B. 21
    3. C. 22
    4. D. 27
13. The stem and leaf plot shows the marks scored by students in a French test.
    

    Stem	Leaf
    2	0, 2, 5, 7, 8
    3	2, 7, 9
    4	3, 5, 5, 5
    5	4, 6, 6, 8
    6	3, 5, 7
    7	0, 6

    
    Find the median mark from the given stem and leaf plot.
    1. A. 45
    2. B. 47
    3. C. 54
    4. D. 76
14. Which of the following is an even prime number?
    1. A. 2
    2. B. 1
    3. C. 4
    4. D. 8
15. If 2n - 5 = (1/2)n, find the value of n.
    1. A. 1/3
    2. B. 1/2
    3. C. 2 1/2
    4. D. 3 1/3
16. Find the simple interest on GHC 350.00 for 4 years at 5% per annum.
    1. A. GHC 20.00
    2. B. GHC 35.00
    3. C. GHC 70.00
    4. D. GHC 140.00
17. A straight line passes through points P(-5, -3) and Q(-4, -7). Find the gradient of line PQ.
    1. A. -4
    2. B. 1/4
    3. C. -1/4
    4. D. 4
18. Given that 1 kilometre = 5/8 mile, what is 240 miles in kilometres?
    1. A. 150 km
    2. B. 190 km
    3. C. 384 km
    4. D. 390 km
19. John walks for 22 1/2 minutes and runs 7 1/2 minutes to school. What percentage of the total time does he spend walking?
    1. A. 25%
    2. B. 30%
    3. C. 33%
    4. D. 75%
20. Kobby is 5 years older than his brother. If Kobby is 13 years old, how old is his brother?
    1. A. 7 years
    2. B. 8 years
    3. C. 10 years
    4. D. 18 years
21. Find the rule for the mapping:
    x: 1, 2, 3, 4, 5
    y: 4, 2, 0, -2, -4
    1. A. y = 2x + 2
    2. B. y = -2x + 2
    3. C. y = 4x
    4. D. y = -2x + 6
22. Arrange the following numbers in ascending order: 9/5, 1.88, 15/8.
    1. A. 9/5, 15/8, 1.88
    2. B. 15/8, 1.88, 9/5
    3. C. 1.88, 9/5, 15/8
    4. D. 9/5, 1.88, 15/8
23. Simplify: (x - 1)² - 1.
    1. A. x² - 2x
    2. B. x² + 2x
    3. C. x² - 2x - 1
    4. D. x² - 2x + 1
24. A bag contains 20 oranges, of which 6 are bad. Find the probability of picking a good orange.
    1. A. 1/20
    2. B. 3/10
    3. C. 1/6
    4. D. 7/10
25. 
    
    In the diagram, AB is parallel to CD, Angle AGE is 80°, angle CFG = 5k, and angle CFE = r. What is the value of r?
    1. A. 16°
    2. B. 20°
    3. C. 80°
    4. D. 160°
26. 
    
    In the diagram, AB is parallel to CD, Angle AGE is 80°, angle CFG = 5k, and angle CFE = r. Find the value of k.
    1. A. 16°
    2. B. 20°
    3. C. 80°
    4. D. 160°
27. Simplify: (1 1/2 - 5/6) × 9/10.
    1. A. 1/10
    2. B. 3/20
    3. C. 1/5
    4. D. 3/5
28. Factorize: 2pq + 6p - 6q - 18.
    1. A. 2(p - 3)(q - 3)
    2. B. 2(p + 3)(q + 3)
    3. C. 2(p - 3)(q + 3)
    4. D. 2(p + 3)(-3)
29. 
    
    Find the area of the shaded portion of a square with side 2 cm, with an inscribed circle.
    1. A. 0.86 cm²
    2. B. 3.00 cm²
    3. C. 6.28 cm²
    4. D. 12.56 cm²
30. 
    
    Find the area of the circle inscribed in a square with side 2 cm.
    1. A. 3.14 cm²
    2. B. 6.28 cm²
    3. C. 4.00 cm²
    4. D. 12.56 cm²
31. A man can complete a task in 12 hours. How long will it take 6 men working at the same rate?
    1. A. 6 hours
    2. B. 3 hours
    3. C. 2 hours
    4. D. 72 hours
32. Convert 12.03 metres to centimetres.
    1. A. 0.1203 cm
    2. B. 120.3 cm
    3. C. 1203 cm
    4. D. 12030 cm
33. A quadrilateral with one pair of opposite sides parallel is called?
    1. A. Kite
    2. B. Rectangle
    3. C. Square
    4. D. Trapezium
34. A book was sold for GHC 48.00 at a profit of 20%. Find the cost price.
    1. A. GHC 38.40
    2. B. GHC 40.00
    3. C. GHC 60.00
    4. D. GHC 57.00
35. Find the vector that translates the point (2,6) to (5,4).
    1. A. [3, -2]
    2. B. [2, 4]
    3. C. [1, -3]
    4. D. [0, 2]
36. Cement and sand were mixed in the ratio 2:5. How many kilograms of cement is in 35 kg of mixture?
    1. A. 7 kg
    2. B. 10 kg
    3. C. 14 kg
    4. D. 88 kg
37. Which of the following is not an integer?
    1. A. 0
    2. B. 1
    3. C. 0.5
    4. D. -5
38. Simplify: (5⁷ × 5⁻⁴) / 5³.
    1. A. 0
    2. B. 1
    3. C. 5
    4. D. 25
39. The height of a cylinder is 5 cm and the radius is 7 cm. Find the volume of the cylinder.
    1. A. 770 cm³
    2. B. 700 cm³
    3. C. 154 cm³
    4. D. 110 cm³
40. If q = (-2, 3) and r = (3, -2), find q - r.
    1. A. (-5, 5)
    2. B. (5, 5)
    3. C. (-1, 1)
    4. D. (1, 1)

Paper 2: Theory

1. a) Given the sets A = {multiples of 3 less than 12}, B = {integers between 4 and 8}, and C = {4, 5, 7}, find:
   
   i) A ∩ B
   
   ii) (A ∪ B) ∩ C
   
   iii) (A ∩ B) ∪ C.
   
   b) Simplify: 13/4 - 25/6 - 19/10 + 47/8.
2. a) Simplify: 15(4 - 6) × 49 ÷ 7.
   
   b) Expand and simplify: b(12a - 3) - (a - b)(3 + b).
   
   c) Akosua walked for 3 hours at the rate of 1 km/h from her village to Paamu. The bus traveling at 155 km/h takes 2 hours from Paamu to Quamu.
   
   i) What is the distance from Akosua's village to Quamu?
   
   ii) How long would it take a man riding a bicycle at 5 km/h to travel from Akosua's village to Quamu?
3. a) i) Express 8 × 32 × 4 × 2 in the form 2ᵐ.
   
   ii) State the value of m.
   
   b) i) Factorize: n²k - n²q.
   
   ii) Find the value of the expression when n = 2, k = 19, q = 20.
   
   c) Gifty and Justina shared GHC 418. If Gifty had 20% more than Justina, how much did Justina receive?
4. a) If 4m - 2(3 + 2m) + m(2m + 4) = 0, find the values of m.
   
   b) At a political rally, there were 240 women, 200 men, 160 boys, and 120 girls.
   
   i) Draw a pie chart to illustrate the information.
   
   ii) What percentage of the people at the rally were females?
5. Madam Esi used 1/4 and 2/3 of her x acres of land to cultivate mangoes and oranges, respectively.
   
   a) Express, in terms of x, the number of acres of land used for:
   
   i) Mangoes
   
   ii) Oranges
   
   b) If Madam Esi used 20 more acres of land to cultivate oranges than mangoes, find the value of x.
   
   c) How many acres of land were used to cultivate mangoes?
   
   d) Calculate the percentage of the land not used, correct to the nearest whole number.
6. a) Using a scale of 2 cm to 2 units on both axes, draw two perpendicular axes Ox and Oy for -10 < x < 10 and -10 < y < 10.
   
   b) On the same graph sheet, draw:
   
   i) A quadrilateral ABCD with vertices A(2,4), B(2,8), C(8,8), and D(8,4).
   
   ii) The image A₁B₁C₁D₁ of ABCD under a translation by vector (-5, -2).
   
   iii) The image A₅B₅C₅D₅ of ABCD under a reflection in the y-axis.
   
   c) i) What type of quadrilateral is ABCD?
   
   ii) Find the gradient of A₅B.

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