BECE 1995 Mathematics Past Questions and Answers

Paper 1: Objectives

1. P = {prime numbers less than 20} and Q = {odd numbers less than 10}. Find P ∩ Q.
   1. A. {2, 3}
   2. B. {1, 3, 5, 7, 11}
   3. C. {3, 5, 7, 9}
   4. D. {3, 5, 7}
   5. E. {3, 5, 7, 11}
   Answer: D

   The intersection (∩) are elements found in both sets. P = {2, 3, 5, 7, 11, 13, 17, 19}, Q = {1, 3, 5, 7, 9}. Thus, P ∩ Q = {3, 5, 7}.
2. Convert 104 to a binary numeral.
   1. A. 1101000
   2. B. 1010100
   3. C. 1101100
   4. D. 1011010
   5. E. 1110100
   Answer: A

   Binary conversion gives 104 = 1101000.
3. What is the H.C.F of 48, 30, and 18?
   1. A. 2
   2. B. 3
   3. C. 5
   4. D. 6
   5. E. 9
   Answer: D

   The H.C.F is 6, derived from the prime factors of 48, 30, and 18 in their lowest powers.
4. Express 34m 5cm 6mm in millimeters.
   1. A. 340506 mm
   2. B. 342506 mm
   3. C. 34056 mm
   4. D. 30456 mm
   5. E. 34565 mm
   Answer: C

   34m = 34000 mm, 5 cm = 50 mm, so total = 34000 + 50 + 6 = 34056 mm.
5. Write 356.07 in standard form.
   1. A. 35.607 × 10¹
   2. B. 35.607 × 10²
   3. C. 3.5607 × 10²
   4. D. 3.5607 × 10¹
   5. E. 0.35607 × 10²
   Answer: C

   Standard form is 3.5607 × 10², moving the decimal to the left twice.
6. Divide $(1\frac{1}{2}+\frac{1}{4})$ by $(1\frac{1}{2}-\frac{1}{4})$.
   1. A. $\frac{5}{7}$
   2. B. 1
   3. C. $1\frac{2}{5}$
   4. D. $1\frac{3}{4}$
   5. E. 3
   Answer: C

   $(\frac{3}{2}+\frac{1}{4})÷(\frac{3}{2}-\frac{1}{4})=\frac{7}{4}÷\frac{5}{4}=\frac{7}{5}=1\frac{2}{5}$
7. Which property is illustrated by the statement a × (b + c) = a × b + a × c?
   1. A. Inverse
   2. B. Identity
   3. C. Commutative
   4. D. Distributive
   5. E. Associative
   Answer: D

   The distributive property states that multiplying the sum by a number equals multiplying each term by that number.
8. How many edges does a cube have?
   1. A. 4
   2. B. 6
   3. C. 8
   4. D. 12
   5. E. 18
   Answer: D

   A cube has 12 edges.
9. What is the mode of the following numbers: 4, 5, 3, 3, 4, 2, 7, 6, 5, 4, 4, 1?
   1. A. 3
   2. B. 4
   3. C. 5
   4. D. 6
   5. E. 7
   Answer: B

   4 appears the most frequently, so it is the mode.
10. What is the rule for the mapping below: X = {1, 2, 3, 4, 5} and Y = {2, 4, 8, 16, 32}?
    1. A. y = 2x + 2
    2. B. y = 2ˣ
    3. C. y = x + 2
    4. D. y = x + 1
    5. E. y = 2x
    Answer: B

    The rule is y = 2ˣ, as each y-value is 2 raised to the power of x.

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11. Solve 4x - 6 < -2.
    1. A. x < 1
    2. B. x > 1
    3. C. x < -1
    4. D. x > -1
    5. E. x < 4
12. In a school, 80 pupils wrote an examination, and 64 of them passed. What is the percentage of pupils who passed?
    1. A. 8%
    2. B. 16%
    3. C. 20%
    4. D. 64%
    5. E. 80%
13. 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
    5. E. 8
14. Kofi throws a die. What is the probability that he throws the number 2?
    1. A. 1
    2. B. $\frac{2}{3}$
    3. C. $\frac{1}{2}$
    4. D. $\frac{1}{3}$
    5. E. $\frac{1}{6}$
15. What is the image of -4 under the mapping $x\to \frac{1}{2}x-2$?
    1. A. 4
    2. B. 2
    3. C. 0
    4. D. -2
    5. E. -4
16. 
    
    Find the value of p in the triangle.
    1. A. 110
    2. B. 90
    3. C. 70
    4. D. 50
    5. E. 40
17. Make a the subject of the relation P = 2(a + b).
    1. A. a = (P - 2b) / 2
    2. B. a = (P + 2b) / 2
    3. C. a = -2b - P
    4. D. a = -P - b / 2
    5. E. a = P / 2 - b
18. What is the value of x in the relation 5ˣ = 125?
    1. A. 2
    2. B. 3
    3. C. 4
    4. D. 5
    5. E. 6
19. 
    
    Calculate the length of QR in triangle PQR.
    1. A. 11
    2. B. 14
    3. C. 16
    4. D. 17
    5. E. 25
20. Five cards are numbered one to five. A card is picked at random. What is the probability that it has an even number?
    1. A. 1
    2. B. $\frac{4}{5}$
    3. C. $\frac{3}{5}$
    4. D. $\frac{2}{5}$
    5. E. $\frac{1}{5}$
21. If $\mathbf{u}=\left(\begin{array}{c}2\\ 1\end{array}\right)$ and $\mathbf{v}=\left(\begin{array}{c}-1\\ 3\end{array}\right)$, find $3\mathbf{u}+2\mathbf{v}$.
    1. A. $\left(\begin{array}{c}8\\ 9\end{array}\right)$
    2. B. $\left(\begin{array}{c}4\\ -2\end{array}\right)$
    3. C. $\left(\begin{array}{c}4\\ 0\end{array}\right)$
    4. D. $\left(\begin{array}{c}4\\ 9\end{array}\right)$
    5. E. $\left(\begin{array}{c}-4\\ -9\end{array}\right)$
22. Arrange the following fractions in descending order: $\frac{3}{4},\frac{5}{8},\frac{4}{5},\frac{13}{20}$
    1. A. $\frac{4}{5},\frac{3}{4},\frac{13}{20},\frac{5}{8}$
    2. B. $\frac{4}{5},\frac{5}{8},\frac{3}{4},\frac{13}{20}$
    3. C. $\frac{5}{8},\frac{4}{5},\frac{3}{4},\frac{13}{20}$
    4. D. $\frac{4}{5},\frac{5}{8},\frac{13}{20},\frac{3}{4}$
    5. E. $\frac{13}{20},\frac{5}{8},\frac{4}{5},\frac{3}{4}$
23. How many lines of symmetry does a square have?
    1. A. 0
    2. B. 1
    3. C. 2
    4. D. 3
    5. E. 4
24. If $(x,y)\to (x,2y)$, find the image of $(2\frac{1}{2},-\frac{1}{4})$.
    1. A. $(2\frac{1}{2},-2)$
    2. B. $(2\frac{1}{2},-\frac{1}{2})$
    3. C. $(2,-2)$
    4. D. $(2,-\frac{1}{4})$
    5. E. $(2,2\frac{1}{2})$
25. The ages in years of eight boys are: 14, 14.5, 15, 12, 11.5, 13, 10.5, and 13.5. What is their average age?
    1. A. 14
    2. B. 13
    3. C. 12
    4. D. 11
    5. E. 10
26. Convert 133 in base five to a base ten numeral.
    1. A. 23
    2. B. 25
    3. C. 31
    4. D. 40
    5. E. 43
27. Find the simple interest on ₵15,000.00 at a rate of 20% per annum for 5 years.
    1. A. ₵10,000.00
    2. B. ₵15,000.00
    3. C. ₵30,000.00
    4. D. ₵50,000.00
    5. E. ₵90,000.00
28. List all members of the set {x: 2 < x < 8, x is an integer}.
    1. A. {3, 4, 5}
    2. B. {2, 3, 4, 5, 6, 7, 8}
    3. C. {2, 3, 4, 5, 6, 7}
    4. D. {3, 3, 3, 4, 5, 6, 7}
    5. E. {3, 4, 5, 6, 7}
29. Simplify 348.94 - 188.34.
    1. A. 60.60
    2. B. 60.68
    3. C. 160.60
    4. D. 200.60
    5. E. 206.60
30. Find the difference between the values of (2d)² and 2d³ when d = 3.
    1. A. 16
    2. B. 18
    3. C. 24
    4. D. 28
    5. E. 54
31. The heights of two boys are in the ratio 4:5. The shorter boy is 80 cm. What is the height of the taller boy?
    1. A. 100 cm
    2. B. 150 cm
    3. C. 164 cm
    4. D. 180 cm
    5. E. 200 cm
32. Factorize completely 5xy + 10ny.
    1. A. 5y(x + n)
    2. B. 5y(x + 2n)
    3. C. 5y(1 + 2n)
    4. D. 5(xy + 2ny)
    5. E. x(5x + 10n)
33. If 13x - 12 = 5x + 60, find x.
    1. A. -9
    2. B. -6
    3. C. 4
    4. D. 6
    5. E. 9
34. The length of a spring when a mass of n kg is hung on it is L = (74 + 15n) mm. What is the length of the spring when a mass of 1.20 kg is hung on it?
    1. A. 75.20 mm
    2. B. 89.00 mm
    3. C. 92.00 mm
    4. D. 97.00 mm
    5. E. 104.00 mm
35. 
    
    In the figure above, triangle ABC is an enlargement of triangle ADE. If [AE] = 20 cm and [EC] = 10 cm, what is the scale factor of the enlargement?
    1. A. -1/2
    2. B. -3/2
    3. C. 2
    4. D. 3
    5. E. 5/2
36. Which number line below represents the inequality 2 < x ≤ 6?
    1. A.
    2. B.
    3. C.
    4. D.
    5. E.
37. A cylinder has a radius of 6 cm and height of 7 cm. Find its volume. [Take π = 22/7]
    1. A. 132 cm³
    2. B. 264 cm³
    3. C. 294 cm³
    4. D. 792 cm³
    5. E. 924 cm³
38. 
    
    The angles a and b in the figure above are:
    1. A. Interior opposite
    2. B. Corresponding
    3. C. Vertically opposite
    4. D. Acute
    5. E. Alternate
39. A man traveled a distance of 1.2 km in 30 minutes. What distance can he cover in 55 minutes at the same speed?
    1. A. 1.375 km
    2. B. 2.02 km
    3. C. 2.2 km
    4. D. 12.02 km
    5. E. 13.25 km
40. 
    
    In the diagram, triangle ABC is an isosceles triangle, with ∠ABD = 108°. Find the value of y.
    1. A. 72
    2. B. 60
    3. C. 48
    4. D. 36
    5. E. 24

Paper 2: Theory

1. (a) There are 20 students in a hostel. 16 of them are fluent in French and 10 of them are fluent in English. Each student is fluent in at least one of the two languages.
   
   (i) Illustrate this information on a Venn diagram.
   
   (ii) How many students are fluent in both English and French?
   
   (b) The sum of the ages of two brothers, Kofi and Kweku, is 35. Kofi's age is two-thirds of Kweku's age. Find their ages.
2. (a) Using a ruler and a pair of compasses only:
   
   (i) Construct triangle ABC such that |AB| = 9 cm, ∠BAC = 60°, and ∠ABC = 45°.
   
   (ii) Construct a line from the point C perpendicular to line AB and let it meet AB at P. Measure |CP| and |AP|.
   
   (b) What is the value of angle ACP?
3. (a) Mansah earns a salary of ₵10,000.00 per month as a salesgirl. In addition to the salary, she is given a commission of 1.5% of whatever sales she makes in a month. In January, she made sales of ₵7,500,000.00. What was the total amount Mansah earned at the end of January?
   
   (b) The diagram below shows a circle with center O and radius 14 cm. The shaded region AOB is a sector with angle AOB = 72°.
   
   (i) Find the length of the minor arc AB.
   
   (ii) Find the area of the shaded sector AOB [Take π = 22/7].
4. (a) Using a scale of 2 cm to 1 unit on both axes, draw two perpendicular axes, OX and OY, on a graph sheet.
   
   (b) On the graph sheet, mark the x-axis from -5 to 5 and the y-axis from -6 to 6.
   
   (c) (i) Plot on the same graph sheet the points $A(1,1\frac{1}{2})$, $B(4,1\frac{1}{2})$ and C(1, 4).
   
   (ii) Join the points to form a triangle. What type of triangle have you drawn?
   
   (d) Draw the image triangle A1B1C1 of triangle ABC under a reflection in the y-axis, where A → A1, B → B1 and C → C1. Label the vertices and the coordinates clearly.
   
   (e) Draw the image triangle A2B2C2 of triangle ABC under an enlargement with scale factor -1 with the centre of enlargement as the origin (0, 0), where A → A2, B → B2 and C → C2. Show all lines of enlargement. Label the vertices and coordinates clearly.
   
   (f) What single transformation maps A1B1C1 onto A2B2C2, where A1 → A2, B1 → B2 and C1 → C2?
5. (a) The data below shows the distribution of the ages of workers in a factory.
   
   Ages (in years): 19, 24, 29, 34, 39, 44
   
   No. of workers: 3, 7, 8, 4, 5, 3
   
   (i) How many workers are there in the factory?
   
   (ii) What is the modal age of the distribution?
   
   (iii) Calculate the mean age of the workers, correct to one decimal place.
   
   (b) (i) Make T the subject of the relation I = (P × R × T) ÷ 100.
   
   (ii) If I = ₵40,000.00, P = ₵64,000.00, and R = 25%, find the value of T in years.

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