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BECE Mathematics 2024 Objective Past Questions

All 120 questions from the Basic Education Certificate Examination (Junior WAEC) (BECE) Mathematics 2024 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.

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Mathematics 2024 Objective — Question 1

Express 367900 in standard form.

  • A. 3.679 x 10^4
  • B. 3.679 x 10^5Correct
  • C. 3.679 x 10^6
  • D. 3.679 x 10^7
  • E. 3.679 x 10^8

Explanation

367900 = 3.679 x 100000 = 3.679 x 10^5.

Mathematics 2024 Objective — Question 2

Express 0.0007823 in standard form.

  • A. 7.823 x 10^-8
  • B. 7.823 x 10^-6
  • C. 7.823 x 10^-4Correct
  • D. 7.823 x 10^-3
  • E. 7.823 x 10^-2

Explanation

Move the decimal 4 places right: 7.823 x 10^-4.

Mathematics 2024 Objective — Question 3

Simplify (0.012 x 0.00009) / 0.06, correct to one significant figure.

  • A. 1.0 x 10^-5
  • B. 1.2 x 10^-5
  • C. 1.5 x 10^-5
  • D. 1.8 x 10^-5Correct
  • E. 2.0 x 10^-5

Explanation

0.012 x 0.00009 = 0.00000108; divided by 0.06 = 0.000018 = 1.8 x 10^-5.

Mathematics 2024 Objective — Question 10

Find the smallest number by which 60 must be multiplied to be a perfect square.

  • A. 2
  • B. 3
  • C. 5
  • D. 10
  • E. 15Correct

Explanation

60 = 2 x 2 x 3 x 5; multiply by 3 x 5 = 15 to pair all factors.

Mathematics 2024 Objective — Question 16

Find 7.5% of 4kg 300g, correct to 3 significant figures.

  • A. 225 g
  • B. 322 g
  • C. 323 gCorrect
  • D. 325 g
  • E. 332 g

Explanation

4 kg 300 g = 4300 g; 7.5% of 4300 = 322.5 = 323 g (3 s.f.).

Mathematics 2024 Objective — Question 20

If the simple interest on a certain amount for 2 years at 5% per annum is ₦2,400.00, find the principal.

  • A. ₦15,000.00
  • B. ₦24,000.00Correct
  • C. ₦29,000.00
  • D. ₦36,000.00
  • E. ₦48,000.00

Explanation

P = (100 x I)/(R x T) = 240000/10 = ₦24,000.

Mathematics 2024 Objective — Question 22

Find the simple interest on ₦15,000.00 deposited for 2 1/2 years at 5 1/2 % per annum.

  • A. ₦257.81
  • B. ₦515.63
  • C. ₦1031.25
  • D. ₦2062.50Correct
  • E. ₦4125.00

Explanation

15000 x 5.5 x 2.5 / 100 = ₦2062.50.

Mathematics 2024 Objective — Question 23

Felix bought a car at the rate of ₦3,088,144.00. He made the cash payment of 32% and paid the remaining through bank transfer. How much was paid through transfer?

  • A. ₦988,206.08
  • B. ₦2,099,937.92Correct
  • C. ₦2,099,938.87
  • D. ₦2,099,940.14
  • E. ₦2,099,941.93

Explanation

Transfer = 68% of 3,088,144 = ₦2,099,937.92.

Mathematics 2024 Objective — Question 24

Estimate the sum of the following amounts; ₦10.50, ₦5.85, ₦125.10, ₦16.20, ₦15.20.

  • A. ₦171.00
  • B. ₦172.85
  • C. ₦173.00Correct
  • D. ₦175.42
  • E. ₦176.00

Explanation

Round each to the nearest naira: 11 + 6 + 125 + 16 + 15 = ₦173.

Mathematics 2024 Objective — Question 25

What is the value of ∠QPR in the figure below?

Diagram for question 25
  • A. 15°
  • B. 30°Correct
  • C. 45°
  • D. 60°
  • E. 90°

Explanation

The construction marks show a 60° angle that has been bisected, giving 30°.

Mathematics 2024 Objective — Question 26

The interior angle of a regular polygon is 165°. How many sides does the polygon have?

  • A. 10
  • B. 12
  • C. 14
  • D. 22
  • E. 24Correct

Explanation

Exterior angle = 180 - 165 = 15°; n = 360 ÷ 15 = 24.

Mathematics 2024 Objective — Question 27

If M varies inversely as the square of N, find the formula connecting M and N given that M = 2 and N = 1/2.

  • A. M = 2N²
  • B. M = 4N²
  • C. M = 1/(8N²)
  • D. M = 1/(4N²)
  • E. M = 1/(2N²)Correct

Explanation

M = k/N²; 2 = k/(1/4) so k = 1/2; M = 1/(2N²).

Mathematics 2024 Objective — Question 28

Which of the following angles cannot be constructed using a ruler and a pair of compasses only?

  • A. 30°
  • B. 60°
  • C. 90°
  • D. 120°
  • E. 140°Correct

Explanation

30°, 60°, 90° and 120° come from 60° and bisection; 140° cannot.

Mathematics 2024 Objective — Question 29

Find the sum of the interior angles of a polygon which has 10 sides.

  • A. 1,260°
  • B. 1,440°Correct
  • C. 1,620°
  • D. 1,800°
  • E. 1,980°

Explanation

(n - 2) x 180 = 8 x 180 = 1,440°.

Mathematics 2024 Objective — Question 31

Find the area of a circle with diameter 42 cm. (Take π = 22/7).

  • A. 50 cm²
  • B. 70 cm²
  • C. 108 cm²
  • D. 157 cm²
  • E. 1,386 cm²Correct

Explanation

r = 21; A = 22/7 x 21 x 21 = 1,386 cm².

Mathematics 2024 Objective — Question 32

Find the value of y in the diagram below, correct to one decimal place.

Diagram for question 32
  • A. 10.3 cm
  • B. 12.4 cm
  • C. 14.5 cm
  • D. 16.1 cmCorrect
  • E. 18.2 cm

Explanation

y is adjacent to 50°, hypotenuse 25: y = 25 cos 50° = 16.1 cm.

Mathematics 2024 Objective — Question 33

Calculate the radius of a circle whose circumference is 21 cm. Leave your answer in term of π.

  • A. √π cm
  • B. 4π cm
  • C. π/2 cm
  • D. 21/(2π) cmCorrect
  • E. 44/(3π) cm

Explanation

2πr = 21 so r = 21/(2π) cm.

Mathematics 2024 Objective — Question 34

Find the volume of a cylinder whose base radius is 3 1/2 cm and height 10 cm. (Take π = 22/7).

  • A. 110 cm³
  • B. 128 cm³
  • C. 193 cm³
  • D. 220 cm³
  • E. 385 cm³Correct

Explanation

V = 22/7 x 3.5 x 3.5 x 10 = 385 cm³.

Mathematics 2024 Objective — Question 36

The area of a circle is 154 cm². Find the perimeter of the circle. (Take π = 22/7).

  • A. 7 cm
  • B. 14 cm
  • C. 44 cmCorrect
  • D. 49 cm
  • E. 154 cm

Explanation

πr² = 154 gives r = 7; perimeter = 2 x 22/7 x 7 = 44 cm.

Mathematics 2024 Objective — Question 39

Find the area of the shape below:

Diagram for question 39
  • A. 28 cm²
  • B. 30 cm²
  • C. 38 cm²
  • D. 54 cm²
  • E. 60 cm²Correct

Explanation

ED = CF = 3 cm (3-4-5), so EF = 18 cm; area = (12 + 18)/2 x 4 = 60 cm².

Mathematics 2024 Objective — Question 40

Calculate the value of x in the figure below, correct to two decimal places.

Diagram for question 40
  • A. 10.32 m
  • B. 12.59 mCorrect
  • C. 14.63 m
  • D. 16.25 m
  • E. 18.13 m

Explanation

x = 15 ÷ tan 50° = 12.59 m.

Mathematics 2024 Objective — Question 41

Calculate the area of a parallelogram whose base is 15 cm and height 2.5 cm.

  • A. 17.5 cm²
  • B. 22.5 cm²
  • C. 27.5 cm²
  • D. 31.5 cm²
  • E. 37.5 cm²Correct

Explanation

Area = base x height = 15 x 2.5 = 37.5 cm².

Mathematics 2024 Objective — Question 42

Find the volume of a cuboid 25cm long, 15cm wide and 10cm high.

  • A. 1,875 cm³
  • B. 2,250 cm³
  • C. 3,750 cm³Correct
  • D. 3,754 cm³
  • E. 4,750 cm³

Explanation

25 x 15 x 10 = 3,750 cm³.

Mathematics 2024 Objective — Question 43

Calculate the volume of a cone whose height is 14/3 cm and base radius 3/2 cm. (Take π = 22/7).

  • A. 10 cm³
  • B. 11 cm³Correct
  • C. 14 cm³
  • D. 22 cm³
  • E. 33 cm³

Explanation

V = 1/3 x 22/7 x 3/2 x 3/2 x 14/3 = 11 cm³.

Mathematics 2024 Objective — Question 44

In the figure below, find the height of the parallelogram ABCD if its area is 28 cm².

Diagram for question 44
  • A. 4 cmCorrect
  • B. 6 cm
  • C. 18 cm
  • D. 28 cm
  • E. 32 cm

Explanation

Height = area ÷ base = 28 ÷ 7 = 4 cm.

Mathematics 2024 Objective — Question 45

The bearing of X and Y is 145°. What is the bearing of Y from X?

  • A. 045°
  • B. 145°
  • C. 215°
  • D. 315°
  • E. 325°Correct

Explanation

Taking 145° as the bearing of X from Y, the back bearing is 145° + 180° = 325°.

Mathematics 2024 Objective — Question 47

State the three-figured bearing of X from Y in the figured below:

Diagram for question 47
  • A. 020°
  • B. 022°
  • C. 040°Correct
  • D. 220°
  • E. 320°

Explanation

Bearing of Y from X = 360° - 140° = 220°; back bearing of X from Y = 220° - 180° = 040°.

Mathematics 2024 Objective — Question 50

The linear scale factor of two similar shapes is 3:4. If the area of the smaller shape is 81cm², find the area of the bigger one.

  • A. 100 cm²
  • B. 121 cm²
  • C. 132 cm²
  • D. 140 cm²
  • E. 144 cm²Correct

Explanation

Area scale factor 9:16; 81 x 16/9 = 144 cm².

Mathematics 2024 Objective — Question 51

A man bought an article for ₦6,800.00 and received ₦420.00 as commission. Calculate the percentage of the commission, correct to one decimal place.

  • A. 3.5
  • B. 4.2
  • C. 5.9
  • D. 6.1
  • E. 6.2Correct

Explanation

420/6800 x 100 = 6.18 = 6.2%.

Mathematics 2024 Objective — Question 52

The area and a diagonal of a rhombus are 360cm² and 24 cm respectively. What is the length of the other diagonal?

  • A. 20 cm
  • B. 22 cm
  • C. 26 cm
  • D. 28 cm
  • E. 30 cmCorrect

Explanation

Area = (d1 x d2)/2; 360 = 24d/2; d = 30 cm.

Mathematics 2024 Objective — Question 53

The volume scale factor of two similar solids is 64: 125. Determine their area scale factor.

  • A. 4:5
  • B. 5:4
  • C. 4:25
  • D. 16:25Correct
  • E. 25:16

Explanation

Linear 4:5, so area 16:25.

Mathematics 2024 Objective — Question 54

The linear scale factor of two similar shapes is 3:7. Determine their volume scale factor.

  • A. 9:27
  • B. 27:9
  • C. 27:49
  • D. 27:343Correct
  • E. 343:27

Explanation

3³ : 7³ = 27 : 343.

Mathematics 2024 Objective — Question 56

The area scale factor of two solid shapes are 4:9. If the volume of the bigger shape is 270cm³, what is the volume of the smaller one?

  • A. 70 cm³
  • B. 80 cm³Correct
  • C. 90 cm³
  • D. 100 cm³
  • E. 120 cm³

Explanation

Linear 2:3, volume 8:27; 270 x 8/27 = 80 cm³.

Mathematics 2024 Objective — Question 57

PQRS is a parallelogram such that /PQ/ = 15cm, /QR/ = 18 cm and ∠PQR = 30°. Determine the area of the parallelogram.

  • A. 105 cm²
  • B. 135 cm²Correct
  • C. 180 cm²
  • D. 210 cm²
  • E. 270 cm²

Explanation

Area = 15 x 18 x sin 30° = 135 cm².

Mathematics 2024 Objective — Question 60

Calculate the area of the shaded portion in the figure below: (Take π = 22/7).

Diagram for question 60
  • A. 88 cm²
  • B. 108 cm²
  • C. 154 cm²
  • D. 212 cm²Correct
  • E. 308 cm²

Explanation

Rectangle = 20 x 15 = 300 cm²; semicircle (diameter 15) = 1/2 x 22/7 x 7.5² = 88.4 cm²; shaded = 300 - 88.4 = 211.6, about 212 cm².

Mathematics 2024 Objective — Question 63

Mr. Abraka thought of a number and added 3 times the number. If the result is 2 times the number plus 4, what is the number?

  • A. 2Correct
  • B. 3
  • C. 5
  • D. 7
  • E. 8

Explanation

n + 3n = 2n + 4; 2n = 4; n = 2.

Mathematics 2024 Objective — Question 65

Factorise 2m² - 8n².

  • A. 2(m + 2n)(m + 2n)
  • B. (m + 4n)(m + 4n)
  • C. (m - 4n)(m + 4n)
  • D. 2(m + 8n)(m + 4n)
  • E. 2(m - 2n)(m + 2n)Correct

Explanation

2(m² - 4n²) = 2(m - 2n)(m + 2n).

Mathematics 2024 Objective — Question 66

Factorise 25x² - y².

  • A. 5(x + y)(2x + y)
  • B. 2(5x + y)(x - y)
  • C. (3x + y)(5x - y)
  • D. (5x - y)(5x + y)Correct
  • E. (x + y)(x - y)

Explanation

Difference of two squares: (5x)² - y² = (5x - y)(5x + y).

Mathematics 2024 Objective — Question 71

If 2((4x - 1)/2) = 9((x + 1)/4), find the value of x.

  • A. 2 4/7
  • B. 2 3/7
  • C. 2 2/7
  • D. 2 1/7
  • E. 1 6/7Correct

Explanation

4x - 1 = 9(x + 1)/4; 16x - 4 = 9x + 9; 7x = 13; x = 1 6/7.

Mathematics 2024 Objective — Question 74

Factorise 3x² - y² - 3xy + xy.

  • A. (x + y)(3x + y)
  • B. (x - y)(y + 3x)
  • C. (x - y)(3x - y)
  • D. (x + y)(3x - y)
  • E. (x - y)(3x + y)Correct

Explanation

3x² - 3xy + xy - y² = 3x(x - y) + y(x - y) = (x - y)(3x + y).

Mathematics 2024 Objective — Question 75

Expand and simplify (5x - 3y)(2x + 4y).

  • A. 5x² + xy - 12y²
  • B. 5x² - xy - 12y²
  • C. 10x² + 14xy + 12y²
  • D. 10x² + 14xy - 12y²Correct
  • E. 10x² - 14xy + 12y²

Explanation

10x² + 20xy - 6xy - 12y² = 10x² + 14xy - 12y².

Mathematics 2024 Objective — Question 76

Olu thought of a number and subtracted 2 from it. He divided 32 by the result. If his answer is 4, find the number.

  • A. 2
  • B. 4
  • C. 6
  • D. 8
  • E. 10Correct

Explanation

32/(n - 2) = 4; n - 2 = 8; n = 10.

Mathematics 2024 Objective — Question 80

Which of the following line graphs represents the solution of 2x > 6x + 8?

Diagram for question 80
  • A. Open circle at -2, arrow pointing leftCorrect
  • B. Open circle at 2, arrow pointing left
  • C. Closed circle at -2, arrow pointing left
  • D. Closed circle at -2, arrow pointing right
  • E. Open circle at -2, arrow pointing right

Explanation

2x - 6x > 8; -4x > 8; x < -2 (divide by -4 reverses the sign): open circle at -2 with arrow to the left.

Mathematics 2024 Objective — Question 82

Which of the following is/are not method(s) of solving simultaneous linear equations? I. Elimination II. Completing the square III. Graphical IV. Substitution V. Use of formula

  • A. I only
  • B. II only
  • C. III only
  • D. II and V onlyCorrect
  • E. I, III and IV only

Explanation

Completing the square and use of formula are for quadratic equations.

Mathematics 2024 Objective — Question 87

If 7 is added to a number x and the result is greater than 15, find the range of the number.

  • A. x < 8
  • B. x > 8Correct
  • C. x ≤ 8
  • D. x > 12
  • E. x < 22

Explanation

x + 7 > 15; x > 8.

Mathematics 2024 Objective — Question 88

The inequality represented on the line graph below is ____.

Diagram for question 88
  • A. x > -8
  • B. x < -8
  • C. x ≥ -8Correct
  • D. x ≤ -8
  • E. x ≥ 8

Explanation

Closed circle at -8 with the arrow to the right: x ≥ -8.

Mathematics 2024 Objective — Question 91

Solve the following equations simultaneously; 2x + 3y = 4, 6x - y = 2.

  • A. x = 2, y = 3
  • B. x = 1, y = 2
  • C. x = 1/2, y = 1Correct
  • D. x = 1/4, y = 0
  • E. x = 1, y = 1/2

Explanation

y = 6x - 2; 2x + 18x - 6 = 4; x = 1/2, y = 1.

Mathematics 2024 Objective — Question 94

Simplify m/(3t) - 2n/(4p).

  • A. (pm - 6nt)/(12tp)
  • B. (4pm - 6n)/(tp)
  • C. (4pm - nt)/(12tp)
  • D. (2pm - 3nt)/(6tp)Correct
  • E. (3pm - 2nt)/(6tp)

Explanation

LCD 12tp: (4pm - 6nt)/(12tp) = (2pm - 3nt)/(6tp).

Mathematics 2024 Objective — Question 95

When twice a certain number is subtracted from 13, the result is less than or equal to 5. Find the range of values of the number.

  • A. x ≤ -4
  • B. x ≥ -4
  • C. x ≤ 4
  • D. x ≥ 4Correct
  • E. x < 4

Explanation

13 - 2x ≤ 5; -2x ≤ -8; x ≥ 4.

Mathematics 2024 Objective — Question 96

Given that x varies inversely as the square of y and varies directly as z. If x = 4, y = 1, z = 1. Find x if y = 3, z = 2.

  • A. 1
  • B. 1/3
  • C. 1/2
  • D. 8/9Correct
  • E. 8/3

Explanation

x = kz/y²; 4 = k(1)/1 so k = 4; x = 4 x 2/9 = 8/9.

Mathematics 2024 Objective — Question 98

Which of the options below describes a direct variation?

  • A. y = 0.7xCorrect
  • B. y = 21/x
  • C. y - x = 4
  • D. y = 3x + 2
  • E. y - 1 + x = 0

Explanation

A direct variation has the form y = kx.

Mathematics 2024 Objective — Question 100

Use the relationship below to answer the next three questions. Find the missing number (?) in the relationship.

Diagram for question 100
  • A. 3
  • B. 6
  • C. 9
  • D. 12Correct
  • E. 15

Explanation

In each figure the top number is the product of the square roots of the two bottom numbers (e.g. √81 x √9 = 9 x 3 = 27). So ? = √9 x √16 = 3 x 4 = 12.

Mathematics 2024 Objective — Question 105

If a coin is tossed twice, what is the probability of getting a head and a tail?

  • A. 1/3
  • B. 1/2Correct
  • C. 2/3
  • D. 3/4
  • E. 4/5

Explanation

Outcomes HH, HT, TH, TT; HT or TH = 2/4 = 1/2.

Mathematics 2024 Objective — Question 106

Find the sum of the median and the range of the following set of numbers; 1, 4, 2, 5, 3.

  • A. 1
  • B. 2
  • C. 3
  • D. 5
  • E. 7Correct

Explanation

Ordered 1, 2, 3, 4, 5: median = 3, range = 4; sum = 7.

Mathematics 2024 Objective — Question 107

Find the mode of the following set of numbers; 7, 7, 15, 12, 9, 5, 1, 7, 5, 12.

  • A. 5.0
  • B. 7.0Correct
  • C. 7.5
  • D. 8.0
  • E. 8.5

Explanation

7 appears three times, more than any other number.

Mathematics 2024 Objective — Question 108

The graphical representation of statistical data in block form joined together is ____.

  • A. bar chart
  • B. data
  • C. histogramCorrect
  • D. pictogram
  • E. pie chart

Explanation

A histogram has adjacent blocks joined together.

Mathematics 2024 Objective — Question 110

Find the mean of the following set of numbers; 16, 13, 15, 18, 27, 30, correct to two decimal places.

  • A. 14.83
  • B. 14.88
  • C. 19.83Correct
  • D. 19.88
  • E. 59.50

Explanation

Sum = 119; 119 ÷ 6 = 19.83.

Mathematics 2024 Objective — Question 112

In a set of 18 scores arranged in ascending order, the 9th score is 4 more than the 10th score. If the 10th score is 12, find the median score.

  • A. 12
  • B. 13
  • C. 14Correct
  • D. 15
  • E. 16

Explanation

9th score = 12 + 4 = 16; median = (9th + 10th)/2 = (16 + 12)/2 = 14.

Mathematics 2024 Objective — Question 113

Use the information below to answer the next two questions. Everton and Chelsea played 20 matches each and their average goals scored are 8.5 and 10.5 respectively. What is the total goal scored by both clubs?

  • A. 40
  • B. 90
  • C. 170
  • D. 210
  • E. 380Correct

Explanation

Everton: 20 x 8.5 = 170; Chelsea: 20 x 10.5 = 210; total = 380.

Mathematics 2024 Objective — Question 115

The pie chart below shows the weekly sales of a motor dealer. Use the chart to answer the next three questions. What fraction of the cars were Honda?

Diagram for question 115
  • A. 1/5
  • B. 1/4Correct
  • C. 1/3
  • D. 3/4
  • E. 4/5

Explanation

Honda = 90° (from the figure); 90/360 = 1/4.

Mathematics 2024 Objective — Question 118

A box contains six red balls and four blue balls. If a ball is selected at random, what is the probability of selecting a blue ball?

  • A. 1/5
  • B. 2/5Correct
  • C. 3/5
  • D. 3/4
  • E. 4/5

Explanation

4/10 = 2/5.

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