WAEC 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Factorize 3-2 x-x^{2}.
A. (x-3)(x+1)
B. (x+3)(x+1)
C. (x-3)(1-x)
D. (x +3)(1-x)
Question 2
Make r the subject of the relation: \frac{1}{p}=\frac{b}{t}+\frac{c}{r}.
A. r=\frac{p c t}{t-p b}
B. r=\frac{p c t}{t+p b}
C. r=\frac{p c}{t-p b}
D. r=\frac{p c}{1+p b}
Question 3
x 2 \log \left(\frac{1-\sqrt{x}}{\sqrt{x}}\right)=0, find the value of x.
A. \frac{1}{2}
B. \frac{1}{4}
C. 1
D. 0
Question 4
NOT DRAWN TO SCALE In the diagram \( \overline{\mathrm{SR}} \| \overline{U W}, \angle W V T=x \), \( \angle V U T=y, \angle R S T=45^{\circ} \) and \( \angle V T U=20 \). Find the angle marked \( x \).
A. 20^{\circ}
C. 45^{\circ}
D. 135^{\circ}
Question 5
Two towns \( \mathbf{X} \) and \( \mathbf{Y} \) are located at points ( \( -2,-5 \) ) and ( 3,7 ) respectively. Calculate the distance between the two towns.
A. 114 units
B. 25 units
C. 13 units
D. 12 units
Question 6
A variable P varies inversely as the square of Q. If P=5 where Q=6, find (1) when P=1.8.
A. 5
B. 10
C. 15
D. 20
Question 7
The Ven diagram illustrates the information about the sets, \( \mathbf{P}=\{ \text{Pharmacists} \}, \mathbf{C}=\{ \text{Smart People} \} \) and \( \mathbf{F}= \{\text{My Friends}\} \). Which of the following is a valid conclusion from the diagram?
A. All pharmacists are my friends
B. Some of my friends are smart.
C. All smart people are my friends.
D. None of my friends is smart.
Question 8
The sets M={x: 2 \leq x \leq 6} and N={x: 4 \leq x \leq 8} are subsets of \mu={x: 1 \leq x \leq 10, where x is an integer}. Find M^{\prime} \cap N^{\prime}.
A. \{1,7,8\}
B. \{1,8,9\}
C. \{1,9,10\}
D. \{1, 8, 10\}
Question 9
NOT DRAWN TO SCALE In the diagram, \( P, Q, R \) and \( S \) are points on the circle with centre \( O . \angle Q R S= (5 x)^{\circ} \) and \( \angle Q O S=(6 x+24)^{\circ} \). Find \( \angle Q P S \).
A. 75^{\circ}
B. 87^{\circ}
C. 105^{\circ}
D. 150^{\circ}
Question 10
NOT DRAWN TO SCALE In the diagram, \( Q, R, S \) and \( T \) are points on the circle with centre \( Q . \angle S T R= 37^{\circ} \) and \( \angle Q R T=59^{\circ} \). Find \( \angle S P R \).
A. 121^{\circ}
B. 96^{\circ}
C. 84^{\circ}
D. 59^{\circ}
Question 11
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.
A. 25-x
B. 31+x
C. 25+x
D. 31-x
Question 12
Find \angle MPN. In the diagram, \angle PMQ=34^{\circ} and \angle NQM=28^{\circ}.
A. 62^{\circ}
B. 56^{\circ}
C. 34^{\circ}
Question 13
The interior angles of a hexagon are 107^{\circ},(2 x)^{\circ}, 150^{\circ}, 95^{\circ},(2 x-15)^{\circ} and 123^{\circ}. Find the value of x.
A. 57
B. 65
C. 106
D. 120
Question 14
A fair dice is thrown once. Find the probability of obtaining an odd number or a prime number.
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}
Question 15
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.
A. \frac{1}{6}
B. \frac{1}{3}
C. \frac{1}{2}
D. \frac{3}{4}

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