WAEC Mathematics 2025 past questions and answers

The bearing of F from G is 064°. What is the bearing of G from F?

1. A.128°
2. B.180°
3. C.244°
4. D.116°

Ajoke will be 31 years in x years time. If Ajoke is 6 years older than Chioma, find an expression for Chioma's present age.

1. A.25 − x
2. B.31 + x
3. C.25 + x
4. D.31 − x

Two ball bearings have volumes 1.6 cm³ and 5.4 cm³. Find the ratio of their surface areas.

1. A.4 : 9
2. B.2 : 3
3. C.3 : 8
4. D.5 : 12

Given that 21₅ = 14_x, find the value of x.

1. A.4
2. B.5
3. C.6
4. D.7

Given that x + y = 1 and x + 3y = 5, find the value of (x² + 4xy + 3y²).

1. A.1
2. B.5
3. C.10
4. D.25

Consider the following statements:
p: The weather is warm.
q: The sun is shining.
Which of the following correctly represents the statement. "The sun is shining if and only if the weather is warm"?

1. A.p ⇔ ~q
2. B.~p ⇔ ~q
3. C.~q ⇔ ~p
4. D.q ⇔ p

In a class of 42 students, 21 offer History and 28 offer Government. If each student offers at least one of the two subjects, find the probability that a student selected at random from the class offers Government only.

1. A.1/6
2. B.1/3
3. C.1/2
4. D.3/4

The sets M = {x: 2 ≤ x ≤ 6} and N = {x: 4 ≤ x ≤ 8} are subsets of μ = {x: 1 ≤ x ≤ 10, where x is an integer}. Find M′ ∩ N′

1. A.{1, 7, 8}
2. B.{1, 8, 9}
3. C.{1, 9, 10}
4. D.{1, 8, 10}

A variable P varies inversely as the square of Q. If P = 5 when Q = 6, find Q when P = 1.8.

1. A.5
2. B.10
3. C.15
4. D.20

A square has diagonal length of 10 cm. Find the perimeter of the square.

1. A.10√2 cm
2. B.15√2 cm
3. C.20√2 cm
4. D.25√2 cm

Make r the subject of the relation: 1/p = b/t + c/r

1. A.r = pct/(t − pb)
2. B.r = pct/(t + pb)
3. C.r = pc/(t − pb)
4. D.r = pc/(t + pb)

Write 0.0364891 in three significant figures and express the answer in standard form.

1. A.3.65 × 10²
2. B.3.64 × 10²
3. C.3.64 × 10⁻²
4. D.3.65 × 10⁻²

The radius and height of a circular base cylinder are 8 cm and 14 cm respectively. Find its curved surface area. [Take π = 22/7]

1. A.562 cm²
2. B.704 cm²
3. C.352 cm²
4. D.680 cm²

A cylinder and a cone have the same volume. If the height of the cone is 24 cm, find the height of the cylinder

1. A.4 cm
2. B.8 cm
3. C.12 cm
4. D.16 cm

Given that sin (x − 46)° = cos 62°, find the value of x.

1. A.46
2. B.62
3. C.74
4. D.90

The population of a town increases by 2% every year. After 2 years, the population is 83,232. Calculate, correct to the nearest thousand, the original population.

1. A.80,000
2. B.81,000
3. C.82,000
4. D.83,000

Simplify: (2⅓ + 5/2 − 1)/(12 − 11¾)

1. A.10⅔
2. B.15⅓
3. C.16¼
4. D.17½

Two consecutive odd integers are such that the sum of 5 times the smaller and 3 times the bigger integer is 222. Find the value of the smaller integer.

1. A.31
2. B.29
3. C.27
4. D.25

Simplify √200 − √72

1. A.8√2
2. B.4√2
3. C.2√2
4. D.10√2

Given that log₄16 = log_y36, find the value of y.

1. A.3
2. B.4
3. C.6
4. D.8

A fair dice is thrown once. Find the probability of obtaining an odd number or a prime number

1. A.1/2
2. B.1/3
3. C.2/3
4. D.3/4

The third and ninth terms of an Arithmetic Progression (AP) are 9 and −27 respectively. Find the fifth term.

1. A.18
2. B.3
3. C.−3
4. D.−6

A profit of 8% was made when an article was sold for $500.00. At what price should it be sold to make a profit of 16%?

1. A.$537.04
2. B.$540.00
3. C.$573.04
4. D.$580.00

John sold an article for ₦105,000.00 at a loss of 4%. Find the cost price of the article.

1. A.₦100,800.00
2. B.₦105,400.00
3. C.₦109,200.00
4. D.₦109,375.00

In ΔPQR, |QR| = 2 cm, ∠PRQ = 60° and ∠PQR = 90°. Find |PR|

1. A.4√3 cm
2. B.4 cm
3. C.2√4 cm
4. D.4√3/3 cm

The volume of a cone of height 18 cm is 8,316 cm³. Find the base radius of the cone. [Take π = 22/7]

1. A.21 cm
2. B.14 cm
3. C.28 cm
4. D.42 cm

Two towns X and Y are located at points (−2, −5) and (3, 7) respectively. Calculate the distance between the two towns.

1. A.114 units
2. B.25 units
3. C.13 units
4. D.12 units

The interior angles of a triangle are in the ratio 2 : 5 : 8. Find the difference between the smallest and largest angles

1. A.12°
2. B.24°
3. C.48°
4. D.72°

Given that (x⁻ⁿ)⁴ = 1/x⁶, find the value of n.

1. A.−2/3
2. B.−3/2
3. C.3/2
4. D.2/3

The angle of elevation of the top P of a ladder PQ from its base Q, 12 m away from a wall is 36°. Find, correct to the nearest metre, the length of the ladder.

1. A.9 m
2. B.12 m
3. C.15 m
4. D.17 m

In the diagram, ∠PMQ = 34° and ∠NQM = 28°. Find ∠QTN.

1. A.152°
2. B.146°
3. C.124°
4. D.118°

In the diagram, ∠PMQ = 34° and ∠NQM = 28°. Find ∠MPN.

1. A.62°
2. B.56°
3. C.34°
4. D.28°

The height of 4 orange seedlings: are 2 cm, 5 cm, 7 cm and 10 cm. Calculate the variance

1. A.7.2
2. B.6.0
3. C.8.5
4. D.9.1

In the diagram, P, Q, R and S are points on the circle with centre O. ∠QRS = (5x)° and ∠QOS = (6x + 24)°. Find ∠QPS.

1. A.75°
2. B.87°
3. C.105°
4. D.150°

In the diagram, Q, R, S and T are points on the circle with centre O. ∠STR = 37° and ∠QRT = 59°. Find ∠SPR.

1. A.121°
2. B.96°
3. C.84°
4. D.59°

What is the gradient of the line 7x − 5y + 3 = 0?

1. A.7/5
2. B.5/7
3. C.−5/7
4. D.−7/5

In the diagram SR ∥ UW, ∠WVT = x, ∠VUT = y, ∠RST = 45° and ∠VTU = 20°. Find the angle marked x.

1. A.20°
2. B.65°
3. C.45°
4. D.135°

In the diagram SR ∥ UW, ∠WVT = x, ∠VUT = y, ∠RST = 45° and ∠VTU = 20°. Find the angle marked y.

1. A.20°
2. B.25°
3. C.45°
4. D.135°

Kwakye, Sabina and Owusu shared an amount of $12,000.00. Kwakye had 20% of the amount and the remaining amount was shared between Sabina and Owusu in the ratio 5 : 3 respectively. How much did Sabina receive?

1. A.$2,400.00
2. B.$3,600.00
3. C.$6,000.00
4. D.$9,600.00

The Venn diagram illustrates the information about the sets, P = {Pharmacists}, C = {Smart People} and F = {My Friends}. Which of the following is a valid conclusion from the diagram?

1. A.All pharmacists are my friends.
2. B.Some of my friends are smart.
3. C.All smart people are my friends.
4. D.None of my friends is smart.

The table shows the ages of students in a class.
Age (Years): 13, 14, 15, 16, 17
Number of Students: 3, 14, 13, 8, 3
Find, correct to the nearest whole number, the average age of the students.

1. A.13
2. B.14
3. C.15
4. D.16

The table shows the ages of students in a class.
Age (Years): 13, 14, 15, 16, 17
Number of Students: 3, 14, 13, 8, 3
What is the median age?

1. A.14
2. B.15
3. C.16
4. D.17

Solve: d² − 4d − 96 = 0.

1. A.d = 8, 12
2. B.d = −8, −12
3. C.d = −8, 12
4. D.d = 8, −12

Given that μ = {x: 1 < x < 20, where x is an integer}, P = {x: x is a multiple of 3} and Q = {x: x is a prime number} where P and Q are subsets of μ, find: (a) P ∩ Q′; (b) P′ ∪ Q; (c) (P ∪ Q)′.

The product of the ages of Adu and Tanko is 9 less than Akorfa's age. If Tanko is 4 years older than Adu and Akorfa's age is six times Tanko's age, find Akorfa's age.

A company installs solar panels in its premises to reduce its electricity cost. The monthly savings on electricity in $, is modelled by S = 200 + 50x − 2x², where x is the number of months after installation (a) At what time will the savings on electricity stop increasing? (b) Find the maximum savings.

The diagram shows a tower TR and an observer at O. |OR| = 84 m and the angle of elevation of the top of the tower T from O is 57°.
(a) Calculate, correct to three significant figures, the height of the tower.
(b) The observer at O, moved away from the tower in the same straight line until the angle of elevation of T is 49°. Find, correct to two decimal places, how far the observer moved backwards.

The data represent the scores obtained by 9 applicants in an interview arranged in ascending order: (3x + 2), 22, (4x − 2), 23, 25, (5x − 4), 29, 29 and (x² − 7). (a) Given that the range is 9, find the: (i) value of x; (ii) mean mark of the applicants. (b) If four of the applicants who obtained the highest score were selected, determine the pass mark.

In a certain year, the consumption pattern of electricity charges in a town was as follows: the cost of the first 30 units was $1.00 per unit; the cost of the next 30 units was $7.00 per unit, the cost of each additional unit was $5.00. (a) If Amaka used 420 units of electricity in January that year, calculate the amount paid. (b) If Amaka paid $2,740.00 in the month of February, calculate the number of units of electricity consumed. (c) Find, correct to two decimal places, the percentage change in units of electricity consumed by Amaka in January and February.

Yaro drove from a town Gaja to Banga. After 2 hours in the journey, he observed that he had covered 80 km and realized that if he continued driving at same average speed, he would end up being late for 15 minutes. If he decided to increase the average speed by 10 km/h, he would arrive at Banga 36 minutes earlier. Find the distance between Gaja and Banga.

(a) Using a ruler and a pair of compasses only, construct: (i) a quadrilateral PQRS such that |PQ| = 8.5 cm, |QR| = 7.5 cm, ∠QPS = 60°, ∠PQR = 105° and S is a point on the locus, L₁, which is equidistant from PQ and QR. (ii) locus L₂, of points equidistant from P and Q. (iii) locate the point K, which is the point of intersection of L₁ and L₂. (b) Measure |KS|

(a) Mrs Otoo spends 1/9 of her monthly salary on rent, 1/2 on food, 1/4 on clothes and still had $195.00 left. How much does she earn in a month? (b) A sector of a circle of radius 6 cm subtends an angle of 105° at the centre. Calculate the: (i) perimeter; (ii) area, of the sector [Take π = 22/7]

(a) The cost, C, of feeding some students in a class is partly constant and partly varies as the number of students, n, in the class. For 8 students, the cost is $70.00 and for 10 students the cost is $90.00. Find: (i) an expression for C in terms of n; (ii) the cost of feeding 12 students.
(b) In the diagram. A, B, C and D are points on a circle. AB ∥ DC, AC and BD intersect at X and ∠BDC = 40°. Find: (i) ∠ACD; (ii) ∠AXD

(a) Given that P = (2 4 / −9 1) and Q = (1 −1 / 3 −2), find PQ + 2Q
(b) A bag contains 8 red balls and some white balls, all of the same size. If the probability of drawing at random a white ball from the bag is half the probability of drawing a red ball, find the number of white balls in the bag.

(a) The eighth term of an Arithmetic Progression (A.P) is 46 and the sum of the first eight terms is 200. Find the: (i) first term; (ii) sum of the first 12 terms.
(b) The points X(70°S, 60°E) and Y(7°S, 60°E) lie on the surface of the earth. (i) Illustrate the information in a diagram. (ii) Find the distance between X and Y along the meridian. [Take π = 22/7 and R = 6,400 km]

The following are the marks scored by 20 students in a test:
15, 11, 17, 25, 13, 15, 16, 22, 24, 27,
20, 22, 15, 16, 15, 19, 22, 24, 22, 11
(a) Prepare a frequency table for the distribution using class intervals 10 − 12, 13 − 15, 16 − 18 … .
(b) Calculate the variance of the distribution.
(c) If the pass mark for the test was 16, find the probability, that a student selected at random from the class failed.