BECE 2002 (Paper A) Mathematics Past Questions and Answers

Paper 1: Objectives

1. If P = {multiples of 4 less than 16}, find P.
   1. A. {4, 8, 10}
   2. B. {4, 8, 12}
   3. C. {1, 4, 8, 12}
   4. D. {4, 8, 12, 16}
   Answer: B

   Multiples of 4 less than 16 are {4, 8, 12}.
2. The addition below was carried out in base x. Find x.
   
   243 + 221 = 1014_x
   1. A. Four
   2. B. Five
   3. C. Six
   4. D. Seven
   Answer: B

   In base 5: 3 + 1 = 4; 4 + 2 = 6 = 11_five (write 1, carry 1); 2 + 2 + 1 = 5 = 10_five. So 243 + 221 = 1014 in base five, x = 5.
3. A farmer left home at 4:35 am and arrived on his farm at 6:18 am. How long did he take to get to his farm?
   1. A. 1 hour 23 minutes
   2. B. 1 hour 43 minutes
   3. C. 2 hours 43 minutes
   4. D. 10 hours 53 minutes
   Answer: B

   The total time is 1 hour and 43 minutes (from 4:35 am to 6:18 am).
4. Express 2474.5 in standard form.
   1. A. 2.4745 x 10
   2. B. 2.4745 x 10³
   3. C. 2.4745 x 10²
   4. D. 2.4745 x 10⁴
   Answer: B

   2474.5 in standard form is 2.4745 x 10³.
5. Simplify 1/2 + 1/4 - 3/8.
   1. A. 1/8
   2. B. -3/8
   3. C. 3/16
   4. D. 5/16
   Answer: A

   Using a common denominator of 8, 1/2 = 4/8, 1/4 = 2/8, so 4/8 + 2/8 - 3/8 = 1/8.
6. Find the next two numbers in the sequence 2, 5, 9, 14, 20, _, _.
   1. A. 26, 34
   2. B. 26, 35
   3. C. 27, 34
   4. D. 27, 35
   Answer: D

   The rule is to add increasing increments, so the next terms are 27 and 35.
7. The sum of three numbers is 28,542. Two of the numbers are 10,250 and 9,750. Find the third number.
   1. A. 8,452
   2. B. 8,542
   3. C. 9,452
   4. D. 9,542
   Answer: B

   The third number is 28,542 - 20,000 = 8,542.
8. 135 pencils were to be packed into boxes. Each box could take 12 pencils. Find the number of boxes that were fully packed.
   1. A. 10 boxes
   2. B. 11 boxes
   3. C. 12 boxes
   4. D. 13 boxes
   Answer: B

   135 ÷ 12 = 11.25, so 11 boxes were fully packed.
9. Which of the fractions 13/20, 3/4, 3/5, 7/10 is the greatest?
   1. A. 3/5
   2. B. 3/4
   3. C. 7/10
   4. D. 13/20
   Answer: B

   The LCM of denominators is 20. Converting, we find 3/4 is the largest.
10. Out of ₵550,000.00 given to a school, an amount of ₵325,000.00 was used. What fraction of the total amount was used?
    1. A. 4/13
    2. B. 9/13
    3. C. 9/22
    4. D. 13/22
    Answer: D

    325,000/550,000 = 13/22.

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11. Kofi bought four pencils at ₵200.00 each and five pens at ₵350.00 each. How much did he pay altogether?
    1. A. ₵2,400.00
    2. B. ₵2,450.00
    3. C. ₵2,550.00
    4. D. ₵2,650.00
12. John's uncle sent him ₵120,000.00 through a bank which charges 5% commission. How much commission was paid?
    1. A. ₵5,000.00
    2. B. ₵6,000.00
    3. C. ₵7,000.00
    4. D. ₵7,200.00
13. 8 girls can weed a plot of land in 10 days. How many days will 5 girls take to weed the same plot of land, working at the same rate?
    1. A. 6 days
    2. B. 8 days
    3. C. 12 days
    4. D. 16 days
14. A mapping is defined by x → x² - 1. What is the image of 3 under the mapping?
    1. A. 5
    2. B. 6
    3. C. 7
    4. D. 8
15. A typist charges ₵2,000.00 for the first 5 sheets typed and ₵600.00 for any additional sheet. How much will Barbara pay if she presents 20 sheets for typing?
    1. A. ₵8,000.00
    2. B. ₵11,000.00
    3. C. ₵12,000.00
    4. D. ₵19,000.00
16. Ama covered a distance of 100 m in 12 seconds. Express her speed in kilometers per hour.
    1. A. 5 km/h
    2. B. 10 km/h
    3. C. 20 km/h
    4. D. 30 km/h
17. Yakubu, Seidu, and Amina shared an amount of money in the ratio 3 : 4 : 5. Find how much was shared, if Amina received ₵40,000.00.
    1. A. ₵72,000.00
    2. B. ₵80,000.00
    3. C. ₵96,000.00
    4. D. ₵120,000.00
18. Abban paid ₵630,000.00 for a bicycle at a discount of 10%. Find the actual selling price of the bicycle.
    1. A. ₵567,000.00
    2. B. ₵573,000.00
    3. C. ₵693,000.00
    4. D. ₵700,000.00
19. The population of a town in 1990 was 88,000. The population increased by 20% in 1998. Find the population in 1998.
    1. A. 70,400
    2. B. 94,600
    3. C. 96,800
    4. D. 105,600
20. If a × b = 2a - b, find 3 × 2.
    1. A. 1
    2. B. 4
    3. C. 5
    4. D. 6
21. If r = (2m + 1) / (m - 2), express m in terms of r.
    1. A. m = (2r + 1) / (r - 1)
    2. B. m = 2r + 1
    3. C. m = - (2r + 1) / (r + 1)
    4. D. m = - (2r - 1) / (r - 1)
22. 
    
    Forty percent of students in a class speak Ga and seventy-five percent speak Twi. Each student speaks at least one of the two languages. What percentage of the class speaks both Ga and Twi?
    1. A. 5%
    2. B. 10%
    3. C. 15%
    4. D. 30%
23. If there are 40 students in the class, how many of them speak Twi?
    1. A. 10
    2. B. 16
    3. C. 24
    4. D. 30
24. A point (2, 1) is reflected in the y-axis. Find its image.
    1. A. (-1, 2)
    2. B. (1, -2)
    3. C. (-2, 1)
    4. D. (2, -1)
25. Expand (2a + b)(a - b).
    1. A. 2a² - 3ab - b²
    2. B. 2a² - ab - b²
    3. C. 2a² + ab + b²
    4. D. 2a² + 3ab + b²
26. If $\mathbf{s}=\left(\begin{array}{c}-1\\ 4\end{array}\right)$ and $\mathbf{r}=\left(\begin{array}{c}3\\ 2\end{array}\right)$, find $3\mathbf{s}+\mathbf{r}$.
    1. A. $\left(\begin{array}{c}0\\ 14\end{array}\right)$
    2. B. $\left(\begin{array}{c}0\\ 6\end{array}\right)$
    3. C. $\left(\begin{array}{c}6\\ 6\end{array}\right)$
    4. D. $\left(\begin{array}{c}6\\ 14\end{array}\right)$
27. Solve for y in the equation $\frac{1}{3}y+\frac{1}{5}y=8$
    1. A. 15
    2. B. 30
    3. C. 45
    4. D. 60
28. 
    
    Which of the following statements best describes the construction above?
    1. A. Constructing 30°
    2. B. Constructing 60°
    3. C. Constructing 120°
    4. D. Constructing 135°
29. 
    
    In the diagram, ΔSTR is the enlargement of ΔPQR. If |TQ| = 8 cm, |QR| = 4 cm and |PQ| = 2.4 cm, find |ST|.
    1. A. 4.8 cm
    2. B. 7.2 cm
    3. C. 8.4 cm
    4. D. 9.6 cm
30. 
    
    The pie chart shows how a man spends his monthly salary. Find the value of angle 'a' for a sector.
    1. A. 75°
    2. B. 78°
    3. C. 117°
    4. D. 120°
31. 
    
    If the man earns ₵720,000.00 monthly, find how much he spends on food represented by 105°.
    1. A. ₵120,000.00
    2. B. ₵180,000.00
    3. C. ₵210,000.00
    4. D. ₵240,000.00
32. 
    
    What percentage of his salary does he save if saving is represented by 60°?
    1. A. 16.7%
    2. B. 21.7%
    3. C. 25.0%
    4. D. 29.2%
33. 
    
    In the diagram, XYZ is a triangle, and angle XYZ = 52° and angle XZW = 125°. Find angle YXZ.
    1. A. 35°
    2. B. 55°
    3. C. 73°
    4. D. 107°
34. There are 18 girls and 22 boys in a class. A prefect is to be chosen at random from the class. What is the probability that the prefect will be a girl?
    1. A. $\frac{1}{18}$
    2. B. $\frac{9}{20}$
    3. C. $\frac{11}{20}$
    4. D. $\frac{9}{11}$
35. The length of a rectangle is three times its width. If its perimeter is 24 cm, find its width.
    1. A. 3 cm
    2. B. 4 cm
    3. C. 6 cm
    4. D. 8 cm
36. The interior angle of a regular polygon is 135°. How many sides does the polygon have?
    1. A. 6
    2. B. 8
    3. C. 9
    4. D. 12
37. A square of side 4 cm is enlarged by a scale factor of 3. Calculate the area of the enlarged square.
    1. A. 36 cm²
    2. B. 72 cm²
    3. C. 96 cm²
    4. D. 144 cm²
38. A rectangular tank has length 3 m, width 2 m, and height 1.5 m. If the tank is filled to ⅔ of its capacity, calculate the volume of water.
    1. A. 4.5 m³
    2. B. 6.0 m³
    3. C. 7.5 m³
    4. D. 13.5 m³
39. The Alpha Water Company charges ₵40,000.00 per m³ of water. How much will it cost to fill a 3 m × 2 m × 1.5 m tank completely?
    1. A. ₵180,000.00
    2. B. ₵240,000.00
    3. C. ₵300,000.00
    4. D. ₵360,000.00
40. Express 34 m 5 cm 6 mm in millimetres.
    1. A. 3,456 mm
    2. B. 34,056 mm
    3. C. 34,506 mm
    4. D. 340,506 mm

Paper 2: Theory

1. a) Simplify 2 - (3/4 - 1/8).
   
   b) A ribbon of length 3 m is to be cut into strips of length 14 cm.
   
   (i) How many strips of length 14 cm were cut?
   
   (ii) What length of ribbon remained?
   
   c) One-fourth of a number is added to one-fifth of the same number. If the result is 18, find the number.
2. A trader took a loan of ₵1,800,000.00 at an interest of 12 ½ percent per annum. It was agreed that the loan and the interest must be paid in one year in equal monthly instalments.
   
   (a) Calculate:
   
   (i) the interest on the loan
   
   (ii) the amount to be paid at the end of the year
   
   (iii) the monthly instalment
   
   (b) Another trader took a loan at the same rate of interest and conditions. If she had to pay ₵200,000.00 monthly instalments, find to the nearest cedi how much loan she took.
3. A teacher conducted a class test, and the result is displayed in a frequency table below.
   
   

   Marks	Frequency
   1	2
   2	4
   3	2
   4	2
   5	10
   6	5
   7	6
   8	7
   9	2

   
   
   a) From the table, find:
   
   (i) the modal mark for the class
   
   (ii) the number of candidates who wrote the test
   
   (iii) the mean mark for the test
   
   b) If the teacher decides that the pass mark is 4, what is the probability that a student chosen at random from the class failed the test?
   
   c) Draw a bar chart for the distribution.
4. a) Three numbers are in the ratio 2:3:4, and their average is 36.
   
   (i) Calculate the sum of the three numbers.
   
   (ii) Find the greatest number.
   
   b) It costs ₵875,000 to tile a rectangular floor measuring 7 m by 5 m. How much does it cost to tile a floor measuring 8 m by 4 m using the same tiles?
   
   c) It is estimated that the population of a village increases by 10 percent every five years. If the population is 150,000 this year, what will the population be ten years from now?
5. The diagram shows a plane figure made up of a rectangle (50 cm by 28 cm) and an equilateral triangle of height 24.25 cm. A circle is cut out of the rectangle. If the circle touches three sides of the triangle:
   
   a) Calculate the perimeter of the figure.
   
   b) Calculate the area of the remaining portion of the figure (take π = 22/7).

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