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BECE Mathematics 2025 Objective Past Questions

All 120 questions from the Basic Education Certificate Examination (Junior WAEC) (BECE) Mathematics 2025 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.

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Mathematics 2025 Objective — Question 6

Find the L.C.M of 36, 24 and 8 ! (last number printed blurred; read as 81)

  • A. 141
  • B. 216
  • C. 324
  • D. 648Correct

Explanation

If the last number is 81: 36=2²·3², 24=2³·3, 81=3⁴ → LCM = 2³·3⁴ = 648, which is option D. (With 8 the LCM would be 72, not offered.) (figure/print partly unclear).

Mathematics 2025 Objective — Question 8

Express 0.00402 in standard form.

  • A. 4.02 × 10⁻³Correct
  • B. 4.02 × 10⁻²
  • C. 4.02 × 10⁻¹
  • D. 4.02 × 10²

Explanation

0.00402 = 4.02 × 10⁻³ (exponent signs blurred in scan). (figure/print partly unclear).

Mathematics 2025 Objective — Question 12

The L.C.M and H.C.F of two numbers are 90 and 3 respectively. If one of the numbers is 15, find the other number.

  • A. 16
  • B. 18Correct
  • C. 30
  • D. 36

Explanation

Product = 270; 270/15 = 18.

Mathematics 2025 Objective — Question 14

A telephone company charges 40 kobo per second for the first minute of a call and 20 kobo per second for subsequent minutes. How much will a caller spend on a two minutes call?

  • A. ₦24.00
  • B. ₦30.00
  • C. ₦36.00Correct
  • D. ₦40.00

Explanation

60×40 = 2400 k = ₦24; 60×20 = 1200 k = ₦12; total ₦36.

Mathematics 2025 Objective — Question 15

An estate agent gets a commission of 5% for selling a house. How much does he get on a house worth 3 million naira?

  • A. ₦120,000.00
  • B. ₦150,000.00Correct
  • C. ₦300,000.00
  • D. ₦600,000.00

Explanation

5% of 3,000,000 = ₦150,000.

Mathematics 2025 Objective — Question 16

If the weight of a car is 950kg and the weight of a load in the car is 55kg, estimate the total weight in kg.

  • A. 955
  • B. 960
  • C. 1000Correct
  • D. 1050

Explanation

950+55 = 1005 ≈ 1000 (estimate).

Mathematics 2025 Objective — Question 17

Mr. Gambo's salary per annum is ₦720,000.00. If he pays 2% monthly as income tax, how much does he take home at the end of the month?

  • A. ₦14,400.00
  • B. ₦45,600.00
  • C. ₦58,800.00Correct
  • D. ₦60,000.00

Explanation

Monthly 60,000; tax 2% = 1,200; take-home 58,800.

Mathematics 2025 Objective — Question 23

12 men can plough a farmland in 5 hours. How many hours will it take 15 men to do the same work if they are working at the same rate?

  • A. 3
  • B. 4Correct
  • C. 5
  • D. 6

Explanation

12×5/15 = 4.

Mathematics 2025 Objective — Question 25

Fig. 1.1 is drawn with a scale of 1cm to 5m. Find the volume of the scale drawing.

Diagram for question 25
  • A. 50cm³
  • B. 45cm³
  • C. 30cm³Correct
  • D. 15cm³

Explanation

Actual 15m×10m×25m → 3cm×2cm×5cm = 30 cm³.

Mathematics 2025 Objective — Question 34

Find the value of x in Fig. 1.4.

Diagram for question 34
  • A. 30
  • B. 45
  • C. 50Correct
  • D. 60

Explanation

Reading the figure: parallel lines give base angle 60° (corresponding) and the other base angle is 70°, so x = 180−60−70 = 50. (figure/print partly unclear).

Mathematics 2025 Objective — Question 35

The angle of elevation of the top of a tower from a point 30 m away from its base is 60°. Find the height of the tower, correct to two decimal places.

  • A. 15.00m
  • B. 17.32m
  • C. 25.98m
  • D. 34.64m

Explanation

30 tan 60° = 51.96 m.

Mathematics 2025 Objective — Question 38

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

  • A. 105°
  • B. 120°
  • C. 135°
  • D. 145°Correct

Explanation

The others are multiples of 15°; 145° is not.

Mathematics 2025 Objective — Question 41

Which of the following is not a property of a parallelogram?

  • A. It has one line of symmetry.Correct
  • B. Opposite angles are equal.
  • C. Opposite sides are equal.
  • D. Opposite sides are parallel.

Explanation

A general parallelogram has no line of symmetry.

Mathematics 2025 Objective — Question 42

Ade walks from town A on a bearing of N43°W to town B. What is the bearing of A from B?

  • A. 043°
  • B. 047°
  • C. 137°Correct
  • D. 227°

Explanation

Bearing of B from A = 317°; back bearing = 137°.

Mathematics 2025 Objective — Question 43

Find the value of y in Fig. 1.5.

Diagram for question 43
  • A. 35°
  • B. 71°
  • C. 74°
  • D. 99°

Explanation

y is vertically opposite 35°+74° = 109°. Option E is cut off at the page edge (reads '10…'), taken as 109°. (figure/print partly unclear).

Mathematics 2025 Objective — Question 44

Which of the following is/are appropriate for the construction of angle 45°? I Bisection of angle 75°; II Bisection of angle 90°; III Bisection of angle 135°

  • A. I only
  • B. II onlyCorrect
  • C. III only
  • D. I and II only

Explanation

Bisecting 90° gives 45°; 75° → 37.5°, 135° → 67.5°.

Mathematics 2025 Objective — Question 47

A kite has the following properties except

  • A. it has a diagonal which bisects a pair of opposite angles.
  • B. it has two lines of symmetry.Correct
  • C. it has two pairs of equal and adjacent sides.
  • D. its diagonals are perpendicular to each other.

Explanation

A kite has only one line of symmetry.

Mathematics 2025 Objective — Question 51

If one side of a rectangle is 12cm and the diagonal is 20cm, determine the area of the rectangle.

  • A. 144cm²
  • B. 192cm²Correct
  • C. 240cm²
  • D. 256cm²

Explanation

Other side = 16; 12×16 = 192.

Mathematics 2025 Objective — Question 56

A trapezium has two parallel sides of lengths 6cm and 12cm. If the area is 36cm², find the distance between the parallel sides.

  • A. 3cm
  • B. 4cmCorrect
  • C. 5cm
  • D. 6cm

Explanation

½×18×h = 36 → h = 4.

Mathematics 2025 Objective — Question 57

A scale drawing of a football field whose actual length is 96m, has a length of 16cm. What is the scale of the drawing?

  • A. 1cm represents 3m
  • B. 1cm represents 6mCorrect
  • C. 3cm represents 4m
  • D. 4cm represents 6m

Explanation

96/16 = 6 m per cm.

Mathematics 2025 Objective — Question 59

Use the sample to find the missing value in the last triangle (2/5 top-left, 4/5 top-right, 3/5 bottom).

Diagram for question 59
  • A. 2/5
  • B. 3/5Correct
  • C. 4/5
  • D. 1 1/5

Explanation

In the samples, inside value = (top-left + top-right) − bottom (e.g. 1/2+1/2−1/2 = 1/2; 1/2+1/4−1/2 = 1/4; 2/3+1/3−1/4 = 3/4). So 2/5+4/5−3/5 = 3/5. (figure/print partly unclear).

Mathematics 2025 Objective — Question 60

Using the same sample, find the missing top-right value (top-left 3/4, inside 1/2, bottom 1/2).

Diagram for question 60
  • A. 1/4Correct
  • B. 1/2
  • C. 2/3
  • D. 3/4

Explanation

Inside = (top-left + top-right) − bottom → 1/2 = 3/4 + ? − 1/2 → ? = 1/4. (figure/print partly unclear).

Mathematics 2025 Objective — Question 63

What is the inequality illustrated by the number line in Fig. 2.1?

Diagram for question 63
  • A. x > 1
  • B. x < 1
  • C. x > −1
  • D. x < −1Correct

Explanation

Open circle at −1 with arrow pointing left: x < −1.

Mathematics 2025 Objective — Question 64

₦x is shared equally among 5 boys. If one of the boys spent ₦200, how much does he have left in naira?

  • A. (x+1000)/5
  • B. (x−200)/5
  • C. (x−1000)/5Correct
  • D. (x−5)/200

Explanation

Each share = x/5; left = x/5 − 200 = (x−1000)/5.

Mathematics 2025 Objective — Question 65

Mary treks 3x km to school, then 4x km to her uncle's house and 2x km back home. Find the total distance covered.

  • A. 24x km
  • B. 12x km
  • C. 9x kmCorrect
  • D. 8x km

Explanation

3x+4x+2x = 9x km.

Mathematics 2025 Objective — Question 66

Factorise 63x²y⁴ − 99x³y².

  • A. 3x²y(7y³ + 11x²)
  • B. 3xy²(7x² − 11y²)
  • C. 9x²y²(7x + 11y²)
  • D. 9x²y²(7y² − 11x)Correct

Explanation

HCF = 9x²y²; 63x²y⁴ ÷ 9x²y² = 7y², 99x³y² ÷ 9x²y² = 11x. Option text partly small/blurred in the scan; D is the only option consistent with the HCF.

Mathematics 2025 Objective — Question 69

Tony's monthly pocket money is ₦2,500.00. If he spends 4/5 of it monthly, how much does he save in 6 months?

  • A. ₦500.00
  • B. ₦2,000.00
  • C. ₦2,500.00
  • D. ₦3,000.00Correct

Explanation

Saves 1/5 × 2,500 = ₦500 per month; ×6 = ₦3,000. (The fraction is printed small and reads as 4/5.)

Mathematics 2025 Objective — Question 71

Find the co-ordinates of the points Q and R respectively in Fig. 2.2.

Diagram for question 71
  • A. (1,4) and (5,2)
  • B. (2,1) and (1,5)
  • C. (2,4) and (5,1)
  • D. (2,5) and (4,1)Correct

Explanation

Reading the grid: Q is at x=2, y=5; R is at x=4, y=1.

Mathematics 2025 Objective — Question 72

What are the factors of 15 − 2a − a²?

  • A. (15 − 3a)(5a − a)
  • B. (15 + a)(3 + a)
  • C. (5 + a)(3 − a)Correct
  • D. (5 − a)(3 + a)

Explanation

15−2a−a² = −(a²+2a−15) = −(a+5)(a−3) = (5+a)(3−a).

Mathematics 2025 Objective — Question 73

If today is 2nd January, what will be the date in p days' time? Assuming that the month is still January.

  • A. p + 31
  • B. 15 + p
  • C. 2 + pCorrect
  • D. 1 + p

Explanation

Date = 2 + p.

Mathematics 2025 Objective — Question 76

A bicycle that costs ₦x was sold for ₦y. Express the percentage loss in terms of x and y.

  • A. (x+y)/x × 100
  • B. (x+y)/y × 100
  • C. (x−y)/x × 100Correct
  • D. (x−y)/y × 100

Explanation

Loss = x − y; percentage loss = loss/cost × 100 = (x−y)/x × 100.

Mathematics 2025 Objective — Question 78

Solve the equations a + 10b = 6 and 5a − 10b = 18 simultaneously.

  • A. a = −4, b = −1/5
  • B. a = −4, b = 1/5
  • C. a = −1/5, b = 4
  • D. a = 1/5, b = 4

Explanation

Add: 6a = 24 → a = 4; then 10b = 2 → b = 1/5.

Mathematics 2025 Objective — Question 80

An apple and 2 oranges cost ₦110.00 while 3 apples and 10 oranges cost ₦410.00. How much does each of the fruit cost?

  • A. ₦100.00, ₦50.00
  • B. ₦50.00, ₦30.00
  • C. ₦70.00, ₦20.00Correct
  • D. ₦90.00, ₦20.00

Explanation

a+2o=110 and 3a+10o=410. 3a+6o=330 → 4o=80 → o=20; a=70. (apple ₦70, orange ₦20)

Mathematics 2025 Objective — Question 82

(Fig. 2.4) Find the value of x.

Diagram for question 82
  • A. −4
  • B. −2
  • C. 2
  • D. 4Correct

Explanation

Opposite sides of a rectangle are equal: x+3y = 2x+y → x = 2y; 8−y = x+y → x = 8−2y. So 2y = 8−2y → y = 2, x = 4.

Mathematics 2025 Objective — Question 86

Solve m + 2n = 5 and 5m − 2n = 7 simultaneously.

  • A. m = −2, n = −1½
  • B. m = 2, n = −1½
  • C. m = 1½, n = 2
  • D. m = 1½, n = −2

Explanation

Add: 6m = 12 → m = 2; then 2n = 3 → n = 1½.

Mathematics 2025 Objective — Question 87

Simplify 5ab / (10ab² − 5a²).

  • A. 1/(b²−a)
  • B. 1/(2b−a)
  • C. b/(2b²−a)Correct
  • D. b/(b²−a)

Explanation

Denominator = 5a(2b²−a); cancel 5a: b/(2b²−a). Option letters/powers are slightly blurred in the scan.

Mathematics 2025 Objective — Question 88

Factorise x² + x − 2.

  • A. (x−2)(x−3)
  • B. (x−1)(x−2)
  • C. (x−1)(x+2)Correct
  • D. (x+1)(x+2)

Explanation

Numbers with product −2 and sum +1: +2 and −1 → (x−1)(x+2).

Mathematics 2025 Objective — Question 90

Ada's pocket money is ₦350.00 and Peter's pocket money is ₦x less than Ada's. How much is Peter's pocket money in naira?

  • A. 350x
  • B. 350 + x
  • C. 350 − xCorrect
  • D. 350/x

Explanation

350 − x.

Mathematics 2025 Objective — Question 93

There are two numbers. If the first number is x and the second number is twice the first, find the sum of their reciprocals.

  • A. 3x/2
  • B. 3/2xCorrect
  • C. 2x/3
  • D. 2/3x

Explanation

Numbers x and 2x; 1/x + 1/(2x) = 3/(2x).

Mathematics 2025 Objective — Question 96

Given the equation of a straight line 2x + 2y = 5, find the missing values of x and y respectively in Table 2.2.

Diagram for question 96
  • A. 0 and 0.5Correct
  • B. 0.5 and 0
  • C. 1 and 0
  • D. 1.5 and 2

Explanation

If y = 2.5 then 2x = 5 − 5 = 0, so x = 0. If x = 2 then 2y = 5 − 4 = 1, so y = 0.5. (Check: x=1, y=1.5 gives 2+3 = 5 ✓.)

Mathematics 2025 Objective — Question 97

Solve the following pair of equations simultaneously: x = 5 − 2y, 5x + 2y = 1.

  • A. x = −1, y = −3
  • B. x = −1, y = 3Correct
  • C. x = −1, y = 0
  • D. x = 1, y = −3

Explanation

Substitute: 5(5−2y) + 2y = 1 → 25 − 8y = 1 → y = 3; x = 5 − 6 = −1.

Mathematics 2025 Objective — Question 99

Solve for x if (4x − 3)/9 − x/3 = 5(x − 1)/6.

  • A. 12
  • B. 3
  • C. 9/13Correct
  • D. 1/2

Explanation

Multiply through by 18: 2(4x−3) − 6x = 15(x−1) → 2x − 6 = 15x − 15 → 9 = 13x → x = 9/13.

Mathematics 2025 Objective — Question 100

A man is twice his son's age. If the man is 50 years, how old will the son be in 5 years' time?

  • A. 20 years
  • B. 25 years
  • C. 30 yearsCorrect
  • D. 50 years

Explanation

Son is 25 now; in 5 years he will be 30.

Mathematics 2025 Objective — Question 101

In a poultry, the average number of eggs laid daily by a layer is 1. If 20 crates of eggs are gathered in a day, how many layers are in the poultry?

  • A. 300
  • B. 350
  • C. 400
  • D. 500

Explanation

20 crates × 30 eggs per crate = 600 eggs; at 1 egg per layer per day that is 600 layers. (The number of eggs in a crate is not stated in the visible text; the standard crate of 30 was assumed.)

Mathematics 2025 Objective — Question 102

If x varies directly as p² and x = 2 when p = 4, find the formula connecting x and p.

  • A. x = 8/p
  • B. x = 8/p²
  • C. x = p²/8Correct
  • D. x = p/8

Explanation

x = kp²; 2 = 16k → k = 1/8; so x = p²/8.

Mathematics 2025 Objective — Question 103

Find the product of the median and the mode of the following data: 6, 6, 7, 9, 11, 13, 15, 17.

  • A. 105
  • B. 100
  • C. 69
  • D. 60Correct

Explanation

Median = (9+11)/2 = 10; mode = 6; product = 60.

Mathematics 2025 Objective — Question 105

(Fig. 2.5) Find the sectorial angle representing the first son's money.

Diagram for question 105
  • A. 20°
  • B. 60°
  • C. 162°Correct
  • D. 180°

Explanation

Total = 162,000 + 100,000 + 98,000 = ₦360,000, so every ₦1,000 = 1°. First son = 162°.

Mathematics 2025 Objective — Question 107

(Fig. 2.5) Find the percentage representing the second son's money, correct to one decimal place.

Diagram for question 107
  • A. 50
  • B. 27.8Correct
  • C. 25
  • D. 20.5

Explanation

100,000/360,000 × 100 = 27.78 ≈ 27.8%.

Mathematics 2025 Objective — Question 110

In a tally system, 29 is written as ____.

Diagram for question 110
  • A. (five groups of crossed five-strokes followed by four single strokes)Correct
  • B. (option B as printed – strokes not grouped into crossed fives)
  • C. (option C as printed)
  • D. (option D as printed)

Explanation

29 = 5 × 5 + 4 → five crossed bundles of five followed by four single strokes, which matches option A. Tally marks cannot be typed exactly; options B–E are mis-grouped tallies in the scan. — please confirm against the picture.

Mathematics 2025 Objective — Question 111

Find the median of the following set of numbers: 25, 30, 22, 24, 29, 31, 26, 25, 30.

  • A. 22
  • B. 24
  • C. 25
  • D. 26Correct

Explanation

Ordered: 22, 24, 25, 25, 26, 29, 30, 30, 31. The 5th of 9 values is 26.

Mathematics 2025 Objective — Question 112

Which of the following cannot be used to represent data?

  • A. Bar chart
  • B. Frequency table
  • C. MeanCorrect
  • D. Pictogram

Explanation

The mean is a measure of average, not a way of displaying data.

Mathematics 2025 Objective — Question 113

The average of the numbers 12, 40, x, 60 and 20 is 36. Find the value of x.

  • A. 28
  • B. 33
  • C. 36
  • D. 48Correct

Explanation

Sum = 36 × 5 = 180; 12+40+60+20 = 132; x = 180 − 132 = 48.

Mathematics 2025 Objective — Question 115

Find the product of the median and the range of the following set of numbers: 3, 7, 5, 4, 3, 2, 6, 2.

  • A. 5.5
  • B. 9.7
  • C. 15.6
  • D. 17.5Correct

Explanation

Ordered: 2,2,3,3,4,5,6,7. Median = (3+4)/2 = 3.5; range = 7 − 2 = 5; product = 17.5.

Mathematics 2025 Objective — Question 118

A ball is picked from a bag that contains 6 green, 8 yellow and 4 brown balls. What is the probability that the ball is green?

  • A. 0
  • B. 1/3Correct
  • C. 1/2
  • D. 3/4

Explanation

6 green out of 18 balls = 1/3.

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