ERC BECE MATHEMATICS 2025

ERC MATHEMATICS 2025:

Instruction: Answer all the questions in this section.

1. Write 3025 in Roman numerals. A. MMMXXV B. MMMCCV  C. MMMXXV  D. CCXXV
2. What is the value of the digit in 8 in the figure 6.085? A. hundred  B. tens  C. hundredth  D. tenth
3. Write 0.07465 in its standard form. A. 7.45 x 10²   B. 7.465 x 10³  C. 7.465 x 10^-2  D. 7.465 x 10^-3
4. Express 504 as a product of its prime factors in index form.  A. 2² x 3³ x 7¹  B. 2⁴ x 3³ x 7¹  C. 2³ x 3² x 7¹   D. 2⁵ x 3⁴ x 7¹
5. Find the HCF of 21, 35 and 56?  A. 2  B. 5  C. 3  D. 7
6. Find the LCM of 15 and 36.   A. 160   B. 170  C. 180  D. 200
7. The number of students in a Secondary school in Bwari area Council is 5400. Express this figure as a product of its prime factor in the index form.  A. 2³ x 3³ x 5² B. 2² x 3³ x 5²    C. 2² x 3² x 5²  D. 2³ x 3³ x 5
8. Which of the following numbers is completely divisible by 9?  A. 18089  B. 18099  C. 18980  D. 19898
9. Determine the numerator, when 18 7/8 is converted to an improper fraction.  A. 127  B. 147  C. 151  D. 161
10. Simplify the expression x³ × x × x⁵.  A. x⁻⁸  B. x⁻¹  C. x⁻²  D. x⁸
11. Ade scored 16 out of 30 sums correct. Express his score in percentage.   A. 85.3%  B. 73.3%  C. 63.3%  D. 53.3%
12. Evaluate (111₂)².   A. 110001₂  B. 110010₂  C. 11001₂  D. 1010₂
13. Simplify \(\left(2\tfrac{1}{2} + 1\tfrac{2}{3}\right) \div 1\tfrac{3}{4}\) A. \(3\tfrac{1}{2}\) B. \(4\tfrac{1}{6}\) C. \(2\tfrac{1}{2}\) D. \(1\tfrac{2}{5}\)
14. Change 0.95 to a fraction in its lowest term.  A. \(\frac{95}{100}\) B. \(\frac{19}{20}\) C. \(\frac{15}{20}\) D. \(\frac{29}{50}\)
15. Find the sum of 10110₂ and 10101₂.
    A. 100101₂  B. 100111₂  C. 101010₂  D. 101011₂
16. Find the range of values of y which satisfy the inequality: 3y − 2 ≤ 5y + 4.   A. y ≥ 2  B. y ≥ 3  C. y ≤ 2  D. y ≤ 3
17. What inequality does the number line below represent?  A. x ≤ 2  B. x ≤ −2  C. x ≥ −2  D. x ≥ 2
    
    
    
18. Find √441.   A. 3  B. 9  C. 17  D. 21
19. Write 37,500 in standard form.  A. 3.75 × 10⁴  B. 3.75 × 10³  C. 3.75 × 10²  D. 3.75 × 10⁰
20. Evaluate 3⁴.  A. 81  B. 64  C. 12  D. 7
21. The population of a state is 3,652,473. Write this figure to the nearest hundreds.   A. 3,700,000  B. 3,650,000  C. 3,652,500  D. 3,600,000
22. Evaluate \(\frac{p^2 + 3q}{2r}\) given p = 4, q = 3 and r = −5.  A. −5  B. −5/2  C. 5/7  D. −11/5
23. Express 0.00853 to 1 significant figure.  A. 0.009  B. 0.0081  C. 0.0085  D. 0.008
24. Express\(\frac{7}{19}\) as a percentage, correct to 1 decimal place.   A. 2.7%  B. 3.7%  C. 27.1%  D. 36.8%
25. Simplify: 3(a − 2b + c) − 2(a + 3b − 2c).   A. a − 3  B. a − 12b + 7c  C. a − 12b + 3c  D. a − 12b − 3c
26. Find the next two terms in the sequence 4, 8, 12, 16, ___ ___    A. 20, 24  B. 28, 32  C. 36, 40  D. 20, 22
27. Find the simple interest of ₦500 for 3 years at 4%.  A. ₦45  B. ₦60  C. ₦70  D. ₦72
28. Mr. Obi sold a car for ₦84,000 at a loss of 4%. For how much did he buy the car?   A. ₦80,500  B. ₦80,640  C. ₦87,360  D. ₦87,500
29. In a boutique, two pairs of trousers and a packet shirt cost ₦17,000. The difference between three pairs of trousers and a packet shirt is ₦8,000. Find the cost of a pair of trousers and two packet shirts.  A. ₦19,000  B. ₦12,000  C. ₦9,000  D. ₦7,000
30. Adams runs a distance of 800 m in 2½ minutes. Calculate his speed.  A. 300 m/min  B. 320 m/min  C. 400 m/min  D. 600 m/min
31. It takes five girls eating the same ration six days to finish a supply of food. How long will the supply last three girls at the same ration?  A. 4 days  B. 5 days  C. 8 days  D. 10 days
32.   What number should be in the box to make 13 +  ロ  = 22  A. -9   B. 11   C. 13  D. 15 
33. Find the sum of angles in an octagon  A. 800°   B. 900°   C. 1080°  D. 1260°
34. The ratio of birds to livestock on Mr. oni’s on the farm, how many livestock are there?  A. 600  B. 500  C. 250  D. 100
35. Find the value of x in the figure below   A. 22°  B. 56°  C. 34°  D. 112°
    
    
    
36. The adjacent sides of a right angle triangle are 5cm and 12cm respectively. What is the length of the hypotenuse  A. 13cm   B. 17cm  C. 45cm   D. 60cm
37. Find the size of the missing angle x° in the quadrilateral, in the figure below  A. 104°  B. 360°   C. 256°   D. 420°
    
    
    
38. Calculate the area of a parallelogram of base 12cm and 7cm high  A. 19cm²  B. 38 cm²   C. 42cm²  D. 84 cm²
39. What is the perimeter of the figure below? A. 54cm  B. 44cm  C. 49  D. 32cm 
    
    
    
40. Suppose that θ is an acute angle for which tan θ = \(\frac{3}{4}\), find sinθ  A. 3/5    B. 4/5  C. 5/4  D. 4/3
41. In the figure below, two equal angles are shown. These angles are A. alternate angles  B. corresponding angles   C. acute angles  D. vertically opposites angles
    
    
    
42. What is the value of x in the figure below?  A. 180°  B. 85°  C. 90°  D. 60°
    
    
    
43. What is the diameter of a circle whose area is 616cm²? A. 30cm  B. 25cm    C. 28cm  D. 14cm
44. The radius of a cone is 6cm. given that the height of the cone is 14cm and \(\pi = \frac{22}{7}\). Calculate the volume of the cone.  A, 250 cm²   B. 350 cm²  C. 500 cm²  D. 528cm²
45. The adjacent sides of a triangle are 12cm and 15cm respectively, calculate its perimeter.  A. 60cm  B. 30cm  C. 17cm  D. 13cm
46. Find the value of x in the figure below  A. 180°  B. 21°   C. 138°  D. 42°
    
    
    
47. Find the sum of interior angles of a regular pentagon.  A. 180°   B. 720°   C. 540°  D. 900°
48. Given that, v = u + at, make t the subject  A. \(t = \frac{v - u}{a}\) B. \(t = \frac{v + u}{a}\) C. \(t = \frac{u - v}{a}\) D. \(t = u - av\)
49. Solve the simultaneous equation 3x – y = 4 and x + 2y = 6  A. x = 2, y = 2  B. x = 2, y = 3   C. x = 3, y = 2   D. x = 1, y = 2
50. The bearing of a school farm from the library is 075°. Obtain the bearing of the library from the farm.  A. 015°  B. 075°  C. 105°  D. 255°
51. If the probability of scoring in a match is 0.8. What is the probability that they will not score in that particular match?  A. 1   B. 0.4    C. 0.2  D. 0
52. The sum of two numbers is 12. Their difference is 2, find the numbers. A. 7, 5  B. 7, 8  C. 9, 3  D. 9, 4
53. If 6 students bought a pen and a novel for ₦50 and ₦300 respectively. Find the total cost of the items  A. ₦ 1200  B. ₦1100  C. ₦1000   D. ₦ 900
54. If 4 is the mean of the following set of numbers 1, 2, x, 7, 6. What is the value of x? A. 7  B. 8  C. 4  D. -4 
55. What is the range of the following set of numbers -2, -1, -5, 0, 2?   A. 7  B. 4  C. -4  D. 6
56. If b 2 directly proportional to a and  b = 10 when a = 2, find a if b = 35.   A.

The pie chart below shows the record of animals in a ranch, use the chart to answer questions 57 to 60.

57. If there are 36 animals in the ranch, how many rabbit are there?  A. 120  B. 36  C. 24  D. 12
58. What is the size of angle represented by sheep?  A. 140°   B. 100°  C. 80°  D. 60°
59. If an animal is picked at random from the ranch, what is the probability that it is a cow?  A. \(\frac{1}{2}\) B. \(\frac{1}{3}\) C. \(\frac{2}{5}\) D. \(\frac{1}{4}\)
60. How many goats are in the ranch?  A. 6  B. 7  C. 8  D. 10

Section B: ESSAY

Instruction: Answer all questions. Each question carries 10 marks

NOTE: Calculator is NOT allowed.

1. The scores obtained by some students in a mathematics test are given below; 4,5,6,9,7,5,8,6,5,7,6,7,5,6,10,5,6,7,6,8,4,6,10,9,8,7,9,8,6,7

a. prepare a frequency distribution table

b. Find:  i. Range of the scores    ii. Modal of the scores    iii. Mean of the scores  iv. Probability of selecting a student who scored 7

2. a. if the sum of two numbers is 60 and the positive difference between the numbers is 20. Determine the numbers.

b. Make f the subject of the formula \(\frac{1}{u} = \frac{1}{f} - \frac{1}{v}\)

3. a. A ladder 5m long leans against an electric pole. If the distance between the foot of the ladder and that of the electric pole is 4m, how far up the electric pole does the ladder reach?

b. calculate the simple interest on ₦450.00 for 1½ years at 8% per annum.

c. convert 110111_two to base ten.

4. a. How many liters can be held by a cylindrical can 7cm in diameter and 30cm high? If \(\pi = \frac{22}{7}\)

b. Calculate the number of sides in a regular polygon whose one interior angle is 160°

 

 

 

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