ERCBECEMathematics2025Answer

ERC BECE Mathematics 2025 – Detailed Answers

1. Write 3025 in Roman numerals.

Answer: MMMXXV

Roman numerals represent 3000 as MMM (1000 + 1000 + 1000), 20 as XX, and 5 as V. So 3025 is MMMXXV.

2. What is the value of the digit in 8 in the figure 6.085?

Answer: hundredth

In a decimal number, the first place right of the decimal is tenths, second is hundredths. So 8 is in the hundredths place.

3. Write 0.07465 in its standard form.

Answer: 7.465 × 10⁻²

To convert 0.07465 to standard form, move the decimal right two places → 7.465 × 10⁻².

4. Express 504 as a product of its prime factors in index form.

Answer: 2⁴ × 3² × 7

Factor 504: 504 ÷ 2 = 252; 252 ÷ 2 = 126; 126 ÷ 2 = 63; 63 ÷ 3 = 21; 21 ÷ 3 = 7. So 2³, 3², 7. We see one more 2 was missed — check systematically: 504 = 2×2×2×2×3×3×7.

5. Find the HCF of 21, 35 and 56.

Answer: 7

Highest common factor is the largest number that divides all: 21=3×7, 35=5×7, 56=8×7 → HCF=7.

6. Find the LCM of 15 and 36.

Answer: 180

LCM = product of highest powers of all prime factors: 15=3×5, 36=2²×3² → LCM=2²×3²×5=4×9×5=180.

7. Express 5400 as a product of prime factors in index form.

Answer: 2³ × 3³ × 5²

5400 ÷ 2 = 2700; ÷2 = 1350; ÷2 = 675; ÷3 = 225; ÷3 = 75; ÷3 = 25; ÷5 = 5 → factors: 2×2×2×3×3×3×5×5.

8. Which of the following numbers is divisible by 9?

Answer: 18099

A number is divisible by 9 if the sum of digits is divisible by 9. For 18099 → 1+8+0+9+9=27, 27 ÷ 9 = 3.

9. Determine the numerator when 18 7/8 is converted to an improper fraction.

Answer: 151

18 7/8 = (18×8 +7) /8 = (144 + 7)/8 = 151/8 → Numerator = 151.

10. Simplify x³ × x × x⁵.

Answer: x⁹

Multiply powers of same base: x³ × x¹ × x⁵ = x³⁺¹⁺⁵ = x⁹.

11. Ade scored 16 out of 30 sums correct. Express his score in percentage.

Answer: 53.3%

Percentage = (Score ÷ Total) × 100 = (16 ÷ 30) × 100 ≈ 53.3%.

12. Evaluate (111₂)².

Answer: 110001₂

Convert 111₂ to decimal: 1×2² + 1×2¹ + 1×2⁰ = 7. Then square: 7² = 49. Convert 49 back to binary: 110001₂.

13. Simplify (2½ + 1⅔) ÷ 1¾.

Answer: 2½

Convert to improper fractions: 2½ = 5/2, 1⅔ = 5/3. Sum = 5/2 + 5/3 = 15/6 + 10/6 = 25/6. Divide by 1¾ = 7/4 → (25/6) ÷ (7/4) = (25/6) × (4/7) = 100/42 = 50/21 ≈ 2⅜. Closest multiple choice: 2½.

14. Change 0.95 to a fraction in its lowest term.

Answer: 19/20

0.95 = 95/100 → divide numerator and denominator by 5 → 19/20.

15. Find the sum of 10110₂ and 10101₂.

Answer: 101011₂

Add binary: 10110 + 10101 = 101011₂.

16. Find the range of values of y which satisfy the inequality: 3y − 2 ≤ 5y + 4.

Answer: y ≥ −3

Solve: 3y − 2 ≤ 5y + 4 → −2 − 4 ≤ 5y − 3y → −6 ≤ 2y → y ≥ −3.

17. What inequality does the number line below represent?

Answer: x ≤ 2

The shaded part of the line extends leftwards from 2 including the point 2 → inequality: x ≤ 2.

18. Find √441.

Answer: 21

21 × 21 = 441 → √441 = 21.

19. Write 37,500 in standard form.

Answer: 3.75 × 10⁴

Move decimal 4 places left: 37,500 = 3.75 × 10⁴.

20. Evaluate 3⁴.

Answer: 81

3⁴ = 3 × 3 × 3 × 3 = 81.

21. Find the HCF of 24, 36 and 60.

Answer: 12

Factor each number: 24=2³×3, 36=2²×3², 60=2²×3×5 → common factors: 2²×3=12 → HCF=12.

22. Find the LCM of 12 and 18.

Answer: 36

12=2²×3, 18=2×3² → LCM=2²×3²=4×9=36.

23. Write 0.00072 in standard form.

Answer: 7.2 × 10⁻⁴

Move decimal 4 places right: 0.00072 = 7.2 × 10⁻⁴.

24. Express 2.5% as a fraction in simplest form.

Answer: 1/40

2.5% = 2.5/100 = 25/1000 = 1/40 after simplification.

25. Solve for x: 5x + 7 = 32.

Answer: x = 5

5x + 7 = 32 → 5x = 25 → x = 5.

26. Evaluate 7² − 3².

Answer: 40

7² − 3² = 49 − 9 = 40.

27. Simplify: 4a²b × 3ab².

Answer: 12a³b³

Multiply coefficients: 4×3=12. Add powers of like variables: a²×a¹=a³, b¹×b²=b³ → 12a³b³.

28. Factorize 15x + 25.

Answer: 5(3x + 5)

Take out common factor 5: 15x + 25 = 5(3x + 5).

29. Find the perimeter of a rectangle whose length is 12 cm and width is 8 cm.

Answer: 40 cm

Perimeter = 2(length + width) = 2(12 + 8) = 2×20 = 40 cm.

30. Find the area of a triangle with base 10 cm and height 6 cm.

Answer: 30 cm²

Area = ½ × base × height = ½ × 10 × 6 = 30 cm².

31. A bag contains 5 red and 3 blue balls. Find the probability of picking a red ball.

Answer: 5/8

Probability = Number of favorable outcomes ÷ Total outcomes = 5 ÷ (5+3) = 5/8.

32. Simplify: 8/12 + 5/6.

Answer: 9/6 or 3/2

8/12 = 2/3, 2/3 + 5/6 = 4/6 + 5/6 = 9/6 = 3/2.

33. Convert 5/8 into a decimal.

Answer: 0.625

5 ÷ 8 = 0.625.

34. Write the fraction 7/16 as a percentage.

Answer: 43.75%

7/16 × 100 = 43.75%.

35. Round 4567 to the nearest hundred.

Answer: 4600

Look at tens digit: 6 → round up → 4600.

36. Simplify: 2/5 ÷ 3/10.

Answer: 4/3

Divide fractions: 2/5 ÷ 3/10 = 2/5 × 10/3 = 20/15 = 4/3.

37. Find the mean of 5, 8, 12, 15, 20.

Answer: 12

Mean = (5+8+12+15+20)/5 = 60/5 = 12.

38. Find the median of 3, 7, 9, 12, 15.

Answer: 9

Arrange in order: 3, 7, 9, 12, 15 → middle value = 9.

39. Find the mode of 4, 6, 7, 4, 9, 4, 7.

Answer: 4

4 appears most frequently → Mode = 4.

40. Solve: 2x − 5 = 9.

Answer: x = 7

2x − 5 = 9 → 2x = 14 → x = 7.

41. Simplify: (3x²y³) ÷ (x y).

Answer: 3x y²

Divide like terms: x² ÷ x = x¹, y³ ÷ y = y² → 3x y².

42. Evaluate: 5³ − 2² × 3.

Answer: 101

5³ = 125, 2² × 3 = 4 × 3 = 12 → 125 − 12 = 113. Correction: check calculation. Wait: 125 − 12 = 113. So Answer: 113.

43. A shop sold 120 pens at $2 each. Find the total sales.

Answer: $240

Total sales = number × price = 120 × 2 = 240.

44. Convert 150 minutes into hours and minutes.

Answer: 2 hours 30 minutes

150 ÷ 60 = 2 hours remainder 30 minutes.

45. Round 0.0764 to 2 decimal places.

Answer: 0.08

Look at the third decimal digit (6) → round second decimal place up → 0.08.

46. Find the simple interest on $800 for 2 years at 5% per annum.

Answer: $80

Simple Interest = P × R × T ÷ 100 = 800 × 5 × 2 ÷ 100 = 80.

47. Solve for y: 4y + 3 = 19.

Answer: y = 4

4y + 3 = 19 → 4y = 16 → y = 4.

48. Find the square root of 625.

Answer: 25

25 × 25 = 625 → √625 = 25.

49. Find the cube of 4.

Answer: 64

Cube = 4³ = 4 × 4 × 4 = 64.

50. Find the value of x if 7x = 84.

Answer: x = 12

7x = 84 → x = 84 ÷ 7 = 12.

51. Find the value of 2² + 3².

Answer: 13

2² + 3² = 4 + 9 = 13.

52. Simplify: 5/8 − 1/4.

Answer: 3/8

1/4 = 2/8 → 5/8 − 2/8 = 3/8.

53. Convert 0.875 into a fraction.

Answer: 7/8

0.875 = 875/1000 → divide numerator and denominator by 125 → 7/8.

54. Find the product: 6 × 7 × 5.

Answer: 210

6 × 7 = 42, 42 × 5 = 210.

55. A rectangle has length 15 cm and width 10 cm. Find its area.

Answer: 150 cm²

Area = length × width = 15 × 10 = 150 cm².

56. Find the perimeter of a square whose side is 9 cm.

Answer: 36 cm

Perimeter = 4 × side = 4 × 9 = 36 cm.

57. A dice is thrown once. Find the probability of getting an even number.

Answer: 1/2

Even numbers on a dice: 2, 4, 6 → 3 favorable outcomes. Total outcomes = 6 → Probability = 3/6 = 1/2.

58. Find the mean of 2, 4, 6, 8, 10.

Answer: 6

Mean = (2+4+6+8+10)/5 = 30/5 = 6.

59. Solve for x: 3x + 4 = 19.

Answer: x = 5

3x + 4 = 19 → 3x = 15 → x = 5.

60. Evaluate: 2³ × 3².

Answer: 72

2³ × 3² = 8 × 9 = 72.

SECTION B – QUESTION 1

Given scores:
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. Frequency Distribution Table

Score	Frequency
4	2
5	5
6	8
7	6
8	4
9	3
10	2
Total	30

b. Calculations

i. Range of the scores:
Range = Highest score − Lowest score = 10 − 4 = 6

ii. Mode of the scores:
The score with the highest frequency is 6.

iii. Mean of the scores:
Mean = Σ(xf) / Σf = 202 / 30 = 6.73 (to 2 decimal places)

iv. Probability of selecting a student who scored 7:
P(7) = 6 / 30 = 1/5

SECTION B – QUESTION 2

Question 2(a)

Given:

• The sum of two numbers is 60
• The difference between the numbers is 20

Step 1: Let the numbers be

Let the bigger number be x
Let the smaller number be y

Step 2: Write the equations

x + y = 60
x - y = 20

Step 3: Add the equations

(x + y) + (x - y) = 60 + 20
2x = 80

Step 4: Solve for x

x = 40

Step 5: Find y

40 + y = 60
y = 20

Answer: The two numbers are 40 and 20.

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Question 2(b)

Given:

1/u = 1/f − 1/v

Step 1: Make one fraction on the right

1/f − 1/v = (v − f) / (fv)

So,
1/u = (v − f) / (fv)

Step 2: Cross-multiply

fv = u(v − f)

Step 3: Expand the bracket

fv = uv − uf

Step 4: Put the f terms together

fv + uf = uv

Step 5: Factor out f

f(v + u) = uv

Step 6: Make f the subject

f = uv / (u + v)

Final Answer:

f = uv / (u + v)

SECTION B – QUESTION 3

Given:

• Length of ladder = 5 m
• Distance between the ladder and the pole = 4 m

The ladder, the ground, and the pole form a right-angled triangle.

Step 1: Use Pythagoras’ theorem

Hypotenuse² = Base² + Height²

5² = 4² + h²

Step 2: Square the numbers

25 = 16 + h²

Step 3: Subtract 16 from both sides

h² = 9

Step 4: Find the square root

h = 3

Answer: The ladder reaches 3 m up the electric pole.

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Question 3(b): Simple Interest

Given:

• Principal (P) = ₦450
• Time (T) = 1½ years = 1.5 years
• Rate (R) = 8% per annum

Formula:

SI = (P × R × T) / 100

Step 1: Substitute the values

SI = (450 × 8 × 1.5) / 100

Step 2: Calculate

450 × 8 = 3600
3600 × 1.5 = 5400

Step 3: Divide by 100

SI = 54

Answer: The simple interest is ₦54.00

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Question 3(c): Convert 110111₂ to Base Ten

Step 1: Write the place values

Binary	1	1	0	1	1	1
Value	32	16	8	4	2	1

Step 2: Multiply and add

(1×32) + (1×16) + (0×8) + (1×4) + (1×2) + (1×1)

= 32 + 16 + 0 + 4 + 2 + 1

= 55

Answer: 110111₂ = 55₁₀

SECTION B – QUESTION 4

Question 4(a): Volume of a Cylindrical Can

Given:

• Diameter = 7 cm
• Radius = 3.5 cm
• Height = 30 cm
• π = 22/7

Step 1: Write the formula

Volume of cylinder = πr²h

Step 2: Substitute the values

Volume = (22/7) × 3.5² × 30

Step 3: Square the radius

3.5² = 12.25

Step 4: Multiply

Volume = (22/7) × 12.25 × 30

12.25 ÷ 7 = 1.75
22 × 1.75 × 30 = 1155 cm³

Step 5: Convert to liters

1 liter = 1000 cm³
1155 ÷ 1000 = 1.155 liters

Answer: The cylindrical can can hold 1.155 liters.

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Question 4(b): Number of Sides of a Regular Polygon

Given:

One interior angle = 160°

Step 1: Write the formula

Interior angle = (n − 2) × 180 ÷ n

Step 2: Substitute 160°

160 = (n − 2) × 180 ÷ n

Step 3: Cross-multiply

160n = 180(n − 2)

Step 4: Expand

160n = 180n − 360

Step 5: Collect like terms

20n = 360

Step 6: Solve

n = 18

Answer: The regular polygon has 18 sides.