BECE 1990 Mathematics Past Questions and Answers

Paper 1: Objectives

1. If $P=\{7,9,13\}$, $Q=\{1,7,13\}$. Find $P\cap Q$.
   1. A. $\{1,7,13\}$
   2. B. $\{1,9,13\}$
   3. C. $\{7,13\}$
   4. D. $\{7,9,13\}$
   5. E. $\{13\}$
   Answer: C

   Intersection $(\cap )$ of two sets is the set of elements common to both. $P\cap Q=\{7,13\}$.
2. 
   
   In the diagram, $Q$ is the set of numbers inside the circle, and $T$ is the set of numbers inside the triangle. Find $Q\cup T$.
   1. A. {5}
   2. B. {6, 7}
   3. C. {3, 4, 5}
   4. D. {5, 6, 7}
   5. E. {3, 4, 5, 6, 7}
   Answer: E

   Union $(\cup )$ of two sets lists each unique element. $Q\cup T=\{3,4,5,6,7\}$.
3. Given $(23\times 82)\times 79=148,994$, find the exact value of $(2.3\times 82)\times 7.9$.
   1. A. 14.8994
   2. B. 148.994
   3. C. 1489.94
   4. D. 14899.4
   5. E. 148994.0
   Answer: C

   Divide both sides by 100: $(2.3\times 82)\times 7.9=1489.94$.
4. Convert 25 (base 10) to base 2.
   1. A. 1000
   2. B. 100111
   3. C. 10101
   4. D. 11001
   5. E. 11100
   Answer: D

   Divide by 2 repeatedly and list remainders bottom to top: $25_{10}=11001_2$.
5. If $(3.14\times 18)\times 17.5=3.14\times (3a\times 17.5)$, find $a$.
   1. A. 3.0
   2. B. 5.8
   3. C. 6.0
   4. D. 9.0
   5. E. 18.0
   Answer: C

   Cancel common terms: $18=3a\Rightarrow a=6$.
6. If 26039 oranges are shared equally among 13 women, how many oranges does each woman receive?
   1. A. 23
   2. B. 1203
   3. C. 230
   4. D. 2003
   5. E. 2300
   Answer: D

   $26039÷13=2003$ oranges per woman.
7. Mr. Mensah withdrew some money from the bank. He gave $\frac{1}{2}$ of it to his sons and $\frac{1}{3}$ to his daughter. If he had ₵500 left, how much did he withdraw?
   1. A. ₵600.00
   2. B. ₵750.00
   3. C. ₵1500.00
   4. D. ₵2000.00
   5. E. ₵3000.00
   Answer: E

   Remaining fraction $=1-\frac{5}{6}=\frac{1}{6}$. So, total withdrawn = ₵500 × 6 = ₵3000.
8. Simplify $\frac{1}{2}(1\frac{1}{2}+\frac{3}{4}÷\frac{1}{4})$.
   1. A. $1\frac{1}{2}$
   2. B. $2\frac{1}{4}$
   3. C. $2\frac{3}{4}$
   4. D. $4\frac{1}{2}$
   5. E. $6$
   Answer: B

   Convert mixed fraction, use BODMAS, then simplify.
9. If $21:2x=7:10$, find $x$.
   1. A. 3
   2. B. \frac{21}{4}
   3. C. 15
   4. D. 35
   5. E. 50
   Answer: C

   Cross-multiply and solve: $x=15$.
10. X is a point on line segment AB such that $|AB|=10\text{ cm}$ and $|AX|=4\text{ cm}$. Find the ratio $|AX|:|XB|$.
    1. A. 5 : 3
    2. B. 3 : 2
    3. C. 5 : 4
    4. D. 1 : 1
    5. E. 2 : 3
    Answer: E

    Find $|XB|=6\text{ cm}$; $|AX|:|XB|=4:6=2:3$.

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11. In an examination, 60% of candidates passed. If 240 candidates passed, how many failed?
    1. A. 140
    2. B. 160
    3. C. 360
    4. D. 400
    5. E. 600
12. A table costing ₵2400 was sold for ₵3000. Find the profit percent.
    1. A. 80%
    2. B. 25%
    3. C. 24%
    4. D. 20%
    5. E. 11.1%
13. If a = 2² × 2³ ÷ 2⁴, find the value of a.
    1. A. 29
    2. B. 25
    3. C. 22
    4. D. 2
    5. E. 20
14. Express 12875 km in standard form.
    1. A. 1.2875 × 10³ km
    2. B. 1.2875 × 10⁴ km
    3. C. 12.875 × 10³ km
    4. D. 128.75 × 10² km
    5. E. 12.875 × 10⁴ km
15. 
    
    The pie chart shows the monthly expenditure of Mr. Awuah whose monthly income is ₵18,000.00. What fraction of Mr. Awuah's income is spent on food?
    1. A. 1/6
    2. B. 1/4
    3. C. 1/3
    4. D. 1/5
    5. E. 1/2
16. 
    
    How much does Mr. Awuah spend on rent if his monthly income is ₵18,000.00?
    1. A. ₵90.00
    2. B. ₵450.00
    3. C. ₵4,500.00
    4. D. ₵9,000.00
    5. E. ₵16,200.00
17. 
    
    What is the size of the angle that represents savings in Mr. Awuah's expenditure?
    1. A. 40°
    2. B. 60°
    3. C. 130°
    4. D. 230°
    5. E. 320°
18. Find the missing addend in: 2045 + ? + 1918 = 4430.
    1. A. 8339
    2. B. 1969
    3. C. 2512
    4. D. 2385
    5. E. 467
19. Remove the brackets: a – 2(b – 3c).
    1. A. a – 2b – 3c
    2. B. a – 2b - 6c
    3. C. a – 2b + 6c
    4. D. a + 2b + 6c
    5. E. a – 2b + 3c
20. Simplify: $\frac{2a}{3}-\frac{a-b}{2}$.
    1. A. $a-3$
    2. B. $\frac{a-3b}{6}$
    3. C. $\frac{a+3b}{6}$
    4. D. $a+3b$
    5. E. $a-b$
21. If q = ut + ½ ft, find q when u = 20, t = 10, and f = 15.
    1. A. 350
    2. B. 275
    3. C. 237.5
    4. D. 55
    5. E. 42.5
22. If ³⁄₁₅ is equivalent to ⁴⁵⁄ₐ, find a.
    1. A. 225
    2. B. 150
    3. C. 135
    4. D. 30
    5. E. 9
23. Find the least common multiple of 7, 14, and 18.
    1. A. 71418
    2. B. 1764
    3. C. 252
    4. D. 126
    5. E. 98
24. In △XYZ, |XZ| = 13 cm, |XY| = 12 cm, ∠XYZ = 90°. Find |YZ| if area = 30 cm².
    1. A. 25 cm
    2. B. 14 cm
    3. C. 12.5 cm
    4. D. 5 cm
    5. E. 1 cm
25. Write 1204₅ as a number in base ten.
    1. A. 9996
    2. B. 179
    3. C. 39
    4. D. 35
    5. E. 19
26. Multiply (2x + y) by (2x – y).
    1. A. 4x² - 4xy - y²
    2. B. 4x² + xy - y²
    3. C. 4x² - xy - y²
    4. D. 4x² + y²
    5. E. 4x² - y²
27. A watchman was paid ₵250.00 daily. Calculate his wage for February 1988 if he worked every day.
    1. A. ₵6250.00
    2. B. ₵7200.00
    3. C. ₵7250.00
    4. D. ₵7750.00
    5. E. ₵8750.00
28. A tank contains 250 litres of water. If 96 litres are used, what percentage of the original quantity is left?
    1. A. 61.6%
    2. B. 60.5%
    3. C. 59.0%
    4. D. 54.2%
    5. E. 38.4%
29. Evaluate 10 ÷ (3½ + 1⅕)
    1. A. ²⁄₄₇
    2. B. ⁴⁄₃₅
    3. C. 4
    4. D. ²¹⁄₆
    5. E. ⁴⁄₁₀
30. A bag contains 24 marbles, 10 are blue and the rest green. What is the probability of picking a green marble?
    1. A. ¹⁄₁₄
    2. B. ⁷⁄₁₇
    3. C. ⁵⁄₁₂
    4. D. ⁷⁄₁₂
    5. E. ⁷⁄₁₀
31. 
    
    Which of the following inequalities is represented on the number line, where $n$ is a real number?
    1. A. n ≥ -3
    2. B. n < -3
    3. C. n ≤ -3
    4. D. n > -3
    5. E. n = 3
32. What is the line segment joining two points on the circumference of a circle?
    1. A. arc
    2. B. chord
    3. C. radius
    4. D. sector
    5. E. segment
33. Use the mapping: (1) → (1) → (3.14), (1) → (2) → (6.28), (2) → (4) → (12.56), (3) → (6) → (x). Find x.
    1. A. 9.42
    2. B. 12
    3. C. 18
    4. D. 18.84
    5. E. 25.12
34. Use the mapping: (1) → (1) → (3.14), (1) → (2) → (6.28), (2) → (4) → (12.56), (y) → (10) → (31.4). Find y.
    1. A. 2
    2. B. 5
    3. C. 7
    4. D. 9
    5. E. 10
35. The area of a square is 49 cm². Find the perimeter.
    1. A. 7 cm
    2. B. 14 cm
    3. C. 28 cm
    4. D. 49 cm
    5. E. 196 cm
36. The least number is 24 and the greatest is 30. Interpret the statement.
    1. A. 24 ≤ x ≤ 30
    2. B. 24 < x < 29
    3. C. 23 < x < 29
    4. D. 24 < x < 30
    5. E. 23 ≤ x ≤ 29
37. 
    
    Find the area of the trapezium MNOP.
    1. A. 120 cm²
    2. B. 72 cm²
    3. C. 60 cm²
    4. D. 48 cm²
    5. E. 38 cm²
38. The length of a 1.2 km field is represented by a 40 mm line on a map. Find the map's scale.
    1. A. 1:100
    2. B. 1:300
    3. C. 1:1000
    4. D. 1:3000
    5. E. 1:30000
39. 
    
    The diagram above shows the construction for:
    1. A. Copying a given angle
    2. B. Bisecting a line segment
    3. C. Drawing a perpendicular to a given line
    4. D. Bisecting a given angle
    5. E. Drawing an angle of 30°
40. Simplify $\left(\begin{array}{c}2\\ -3\end{array}\right)-\left(\begin{array}{c}-1\\ 5\end{array}\right)$
    1. A. $\left(\begin{array}{c}-3\\ 8\end{array}\right)$
    2. B. $\left(\begin{array}{c}3\\ -8\end{array}\right)$
    3. C. $\left(\begin{array}{c}-3\\ -8\end{array}\right)$
    4. D. $\left(\begin{array}{c}3\\ 8\end{array}\right)$
    5. E. $\left(\begin{array}{c}-3\\ 2\end{array}\right)$

Paper 2: Theory

1. a) List the members of each of the sets B = {Whole numbers from 20 to 30} and D = {factors of 63}.
   
   i) List the members of B ∩ D.
   
   ii) List the members of B U D.
   
   b) In a class of 60 students, 46 passed Mathematics and 42 passed English language. Everybody passed at least one of the two subjects.
   
   i) Illustrate this information on a Venn diagram.
   
   ii) How many students passed in both subjects?
2. a) Factorize completely 3a² + 2ab - 12ac - 8bc.
   
   b) Solve (x ÷ 4) + (3 ÷ 5) = (3x ÷ 2) - 2.
   
   c) Find the solution set of x + 3 > 19 - 3x, where x is a real number. Illustrate your answer on the number line.
3. a) Using a ruler and a pair of compasses only,
   
   i) Construct triangle PQR such that |PQ| = 6 cm, |QR| = 4 cm, and ∠PQR = 90°.
   
   ii) Construct the perpendicular bisectors of PQ and QR. Name the intersection O.
   
   iii) Draw a circle O as the center and OQ as the radius.
   
   b) Measure
   
   i) |PR|.
   
   ii) ∠QPR.
4. The following is the result of a survey conducted in a class of a junior secondary school to find the favourite soft drink of each pupil in the class.
   
   

   Soft Drink	Number of pupils preferring soft drink
   Coca-cola	6
   Pepsi-cola	5
   Pee-cola	8
   Fanta	3
   Muscatella	5
   Mirinda	4
   Club-cola	6
   Sprite	3

   
   
   a) Draw a bar chart showing this information, using a scale of 2 cm to 1 unit on the vertical axis.
   
   b) How many pupils are in the class?
   
   c) What is the percentage of pupils who prefer Club-cola?

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