BECE 1991 Mathematics Past Questions and Answers

Paper 1: Objectives

1. P = {1, 2, 3, 8, 10}, Q = {8, 1, x, 3, 2}. If P = Q, what is the value of x?
   1. A. 1
   2. B. 2
   3. C. 3
   4. D. 8
   5. E. 10
   Answer: E

   Equal sets have the same elements. Since P = Q, the missing element x must be 10.
2. If Y = {house, tree} and V = {cat, house, tree}, which of the following is true of Y and V?
   1. A. Y = V
   2. B. Y ⊂ V
   3. C. V ⊂ Y
   4. D. V ∈ Y
   5. E. Y ∈ V
   Answer: B

   Y ⊂ V, as all elements of Y are found in V.
3. The following addition is in base ten. Find the missing addend.
   
   2345 + 1045 + **** = 5110
   1. A. 1300
   2. B. 1720
   3. C. 2765
   4. D. 4065
   5. E. 9500
   Answer: B

   2345 + 1045 + n = 5110. Thus, n = 5110 - 3390 = 1720.
4. Given that 2² × 3² × 7 = 252, find the least number that should be multiplied by 252 to make the product a perfect square.
   1. A. 2
   2. B. 3
   3. C. 6
   4. D. 7
   5. E. 252
   Answer: D

   Multiplying by 7 gives all primes even powers: 2² × 3² × 7².
5. Write 4687.02 in standard form.
   1. A. 46.8702 × 10³
   2. B. 46.8702 × 10⁴
   3. C. 4.68702 × 10⁵
   4. D. 4.68702 × 10³
   5. E. 0.468702 × 10⁴
   Answer: D

   4687.02 = 4.68702 × 10³ (move decimal 3 places left).
6. Convert 11001₂ to a decimal numeral.
   1. A. 6
   2. B. 7
   3. C. 14
   4. D. 25
   5. E. 50
   Answer: D

   11001₂ = 1×2⁴ + 1×2³ + 0×2² + 0×2¹ + 1×2⁰ = 25.
7. A boy spent ²/₇ of his pocket money on transport and ¹/₅ on sweets. What fraction of his pocket money does he spend on transport and sweets?
   1. A. 2/35
   2. B. 3/35
   3. C. 1/7
   4. D. 17/35
   5. E. 18/35
   Answer: D

   Add: ²/₇ + ¹/₅ = (5×2 + 7×1)/35 = 17/35.
8. The product of three numbers is 1197. Two of the numbers are 3 and 19. Find the third number.
   1. A. 21
   2. B. 54
   3. C. 210
   4. D. 544
   5. E. 1175
   Answer: A

   Let n = the third number. 3 × 19 × n = 1197. So, n = 21.
9. Find the GCF (HCF) of 2³ × 3² and 2³ × 3⁴.
   1. A. 8
   2. B. 9
   3. C. 72
   4. D. 81
   5. E. 648
   Answer: C

   GCF = 2³ × 3² = 8 × 9 = 72.
10. 
    
    Use the diagram to find the value of a°.
    1. A. 68°
    2. B. 75°
    3. C. 105°
    4. D. 112°
    5. E. 124°
    Answer: E

    a° + 56° = 180°; therefore, a° = 124°.

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11. 
    
    Use the diagram to find the value of b°.
    1. A. 68°
    2. B. 75°
    3. C. 105°
    4. D. 112°
    5. E. 124°
12. 
    
    Use the diagram to find the value of c°.
    1. A. 68°
    2. B. 75°
    3. C. 105°
    4. D. 112°
    5. E. 124°
13. Simplify 2ab² × 3a²b.
    1. A. 5a³b³
    2. B. 5a²b²
    3. C. 6a³b³
    4. D. 36ab
    5. E. 36a²b²
14. In the relation v = u + at, find v when u = 6, a = 10, and t = 2.
    1. A. 18
    2. B. 26
    3. C. 32
    4. D. 48
    5. E. 120
15. The marks obtained by 10 children in a mental drill are: 0, 1, 3, 3, 5, 7, 8, 9, 9, 9. What is the modal mark?
    1. A. 3
    2. B. 5
    3. C. 7
    4. D. 8
    5. E. 9
16. The marks obtained by 10 children in a mental drill are: 0, 1, 3, 3, 5, 7, 8, 9, 9, 9. Find the median mark.
    1. A. 3
    2. B. 5
    3. C. 6
    4. D. 7
    5. E. 8
17. Calculate the mean mark for: 0, 1, 3, 3, 5, 7, 8, 9, 9, 9.
    1. A. -54
    2. B. 5.4
    3. C. 10
    4. D. 54
    5. E. 540
18. What is the probability that a child chosen at random scored 3 marks?
    1. A. 2/54
    2. B. 3/54
    3. C. 2/10
    4. D. 3/10
    5. E. 1/3
19. A trader received a commission of 12 1/2% on his sales. His commission was ₵35,000. Find total sales.
    1. A. ₵36,250.00
    2. B. ₵59,750.00
    3. C. ₵245,000.00
    4. D. ₵280,000.00
    5. E. ₵315,000.00
20. A map is drawn to the scale of 1 : 100,000. What is the distance represented by a line segment 4 cm?
    1. A. 0.04 km
    2. B. 0.4 km
    3. C. 4 km
    4. D. 40 km
    5. E. 400 km
21. Adjoa and Ama share ₵600.00 between them in the ratio 3:2. Find Adjoa's share.
    1. A. ₵200.00
    2. B. ₵240.00
    3. C. ₵300.00
    4. D. ₵360.00
    5. E. ₵400.00
22. 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. $a-b$
23. If a⁶ ÷ a⁴ = 64, find a.
    1. A. 8
    2. B. 10
    3. C. 16
    4. D. 20
    5. E. 24
24. Find one-hundredth of 1.0756
    1. A. 107.56
    2. B. 10.756
    3. C. 0.01756
    4. D. 0.010756
    5. E. 0.001756
25. What is the rule for the mapping where x: 1, 2, 3, 4, 5 maps to y: 1, 3, 5, 7, 9?
    1. A. x → 3x - 2
    2. B. x → 2(x - 1)
    3. C. x → 2x + 1
    4. D. x → 2(x + 1)
    5. E. x → 2x - 1
26. The circumference of a circular track is 440 m. Find the diameter. [Take π = 22/7]
    1. A. 70 m
    2. B. 140 m
    3. C. 280 m
    4. D. 690 m
    5. E. 1400 m
27. If $\mathbf{r}=\left(\begin{array}{c}3\\ 1\end{array}\right)$ and $\mathbf{s}=\left(\begin{array}{c}-2\\ 1\end{array}\right)$, calculate $6(\mathbf{r}+2\mathbf{s})$.
    1. A. $\left(\begin{array}{c}-1\\ 3\end{array}\right)$
    2. B. $\left(\begin{array}{c}1\\ 3\end{array}\right)$
    3. C. $\left(\begin{array}{c}7\\ 3\end{array}\right)$
    4. D. $\left(\begin{array}{c}-6\\ 18\end{array}\right)$
    5. E. $\left(\begin{array}{c}6\\ 18\end{array}\right)$
28. Which of the following would you use to measure an angle?
    1. A. Ruler
    2. B. A pair of compasses
    3. C. A set square
    4. D. A protractor
29. Express the ratio of 64 cm to 48 cm in its simplest form.
    1. A. 3 : 4
    2. B. 4 : 3
    3. C. 16 : 12
    4. D. 12 : 16
    5. E. 64 : 48
30. 
    
    What is the scale factor of the enlargement if P→P₁, Q→Q₁, R→R₁?
    1. A. -2
    2. B. 1/3
    3. C. 1/2
    4. D. 3
    5. E. 2
31. 
    
    In an enlargement, if |PR| = 3.6 m, what is |P₁R₁|?
    1. A. -7.2 m
    2. B. -1.8 m
    3. C. 1.2 m
    4. D. 1.8 m
    5. E. 7.2 m
32. 
    
    Find the tangent of the angle marked y in the diagram.
    1. A. 3/5
    2. B. 3/4
    3. C. 4/5
    4. D. 4/3
    5. E. 5/3
33. Kojo paid ₵270,000 for a TV after a 10% discount. Find the marked price.
    1. A. ₵300,000
    2. B. ₵297,000
    3. C. ₵280,000
    4. D. ₵260,000
    5. E. ₵243,000
34. In a class, 23 pupils study Economics, 6 study both Government and Economics, and 48 study Government or Economics. Find the number of pupils who study Government.
    1. A. 17
    2. B. 23
    3. C. 24
    4. D. 25
    5. E. 31
35. In the same class, how many pupils study only Government?
    1. A. 17
    2. B. 23
    3. C. 24
    4. D. 25
    5. E. 31
36. How many pupils study only Economics?
    1. A. 17
    2. B. 23
    3. C. 24
    4. D. 25
    5. E. 31
37. When a number is subtracted from 10 and the result is multiplied by 2, the final result is 4. Find the number.
    1. A. 8
    2. B. 12
    3. C. 16
    4. D. 24
    5. E. 32
38. 
    
    Calculate the bearing of point X from Y.
    1. A. 035°
    2. B. 045°
    3. C. 135°
    4. D. 145°
    5. E. 225°
39. If 22% of a rope's length is 55 cm, find the full length.
    1. A. 12.1 cm
    2. B. 25 cm
    3. C. 121 cm
    4. D. 250 cm
    5. E. 2500 cm
40. 
    
    Which of these best describes the given construction?
    1. A. Bisecting a line
    2. B. Constructing the bisector of a line segment
    3. C. Constructing the perpendicular to a line
    4. D. Constructing a perpendicular to a given line from a point outside the line
    5. E. Constructing a perpendicular to a given line through a point on the line

Paper 2: Theory

1. a) If X = {Prime numbers less than 13} and Y = {odd numbers less than 13}
   
   (i) List the members of X and Y
   
   (ii) List the members of X ∩ Y and X ∪ Y
   
   b) Three school children share some oranges as follows: Akwasi gets 1/3 of the total, and the remainder is shared between Abena and Jantuah in the ratio 3:2. If Jantuah gets 24 oranges, how many does Akwasi get?
2. Using a ruler and a pair of compasses only,
   
   a) Construct the triangle XYZ, in which |YZ| = 6 cm, angle XYZ = 60°, and |XZ| = 9 cm. Measure |XY|.
   
   b) (i) Construct the mediator of YZ.
   
   (ii) Draw a circle, centre X and radius 5 cm. Measure |YA|, where A is the point of intersection of the mediator and the circle in the triangular region XYZ.
3. a) Solve the equation: (2x/3) - 1 - (x/4) - 2 = 1
   
   b) Factorize completely: 2ap + aq - bq - 2bp
   
   c) Given that m = -2 and n = 3/4, find the value of:
   
   (i) m²(n - 1)
   
   (ii) n² - (3/m)
4. a) The following table shows the distribution of votes in an election for class prefect:
   
   Name | Number of votes:
   
   Acquaye: 6
   
   Borquaye: 12
   
   Commey: 18
   
   (i) Draw a pie chart to illustrate the distribution.
   
   (ii) What fraction of the votes was cast for Borquaye?
   
   b) The heights in cm of 10 school children are as follows: 165, 165, 155, 159, 174, 154, 169, 155, 155, 150.
   
   (i) Make a frequency table for this data.
   
   (ii) Use your table to find the mode and median of the distribution.

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