WAEC 2025 THEORY QUESTIONS.

Perimeter of Circle from Equation

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Mathematics Examination Paper 2

Answer all the questions in this section.
All questions carry equal marks.

Given that $ \mu = \{ x : 1 < x < 20,\; x \in \mathbb{Z} \} $,
$ P = \{ x : x \text{ is a multiple of } 3 \} $,
$ Q = \{ x : x \text{ is a prime number} \} $,
where $ P $ and $ Q $ are subsets of $ \mu $. Find:
1. $ P' \cap Q' $
2. $ P' \cup Q $
3. $ (P \cup Q)' $
The product of the ages of Adu and Tanko is 9 less than Akorfu's age. If Tanko is 4 years older than Adu and Akorfu's age is six times Tanko's age, find Akorfu's age.
A company installs solar panels and the monthly savings on electricity (\$) is modelled by:
\[ S = 200 + 50x - 2x^2 \] where $ x $ is the number of months after installation.
1. At what time will the savings stop increasing?
2. Find the maximum savings.
(Diagram: right-angled triangle with observer at O and tower TR)
|OR| = 84 m; angle of elevation of T from O is 37°.
1. Calculate, correct to three significant figures, the height of the tower.
2. The observer at O moved away from the tower until the angle of elevation of T became 49°. Find, correct to two decimal places, how far the observer moved backwards.
The scores obtained by 9 applicants in ascending order:
\[ (3x + 2),\; 22,\; (4x - 2),\; 23,\; 25,\; (5x - 4),\; 29,\; 29,\; (x^2 - 7) \]
1. Given that the range is 9, find:
  1. Value of $ x $
  2. Mean mark of the applicants
2. If the four highest scores were selected, determine the pass mark.

Answer five questions only from this section.
All questions carry equal marks.

Electricity charges: first 30 units at \$1/unit; next 30 units at \$7/unit; each additional unit at \$5.
1. If Amaka used 420 units in January, calculate the amount paid.
2. If Amaka paid \$2,740 in February, find the number of units consumed.
3. Find, correct to two decimal places, the percentage change in units consumed between January and February.
Yaro drove from Gaja to Banga. After 2 hours, he had covered 80 km. At that speed he’d be 15 min late. By increasing speed by 10 km/h, he would arrive 36 min early. Find the distance from Gaja to Banga.
1. Using ruler and compasses only, construct:
  1. Quadrilateral $ PQRS $: |PQ| = 8.5 cm, |QR| = 7.5 cm, ∠QPS = 60°, ∠PQR = 105°, S on locus $ L_1 $ (equidistant from PQ and QR)
  2. Locus $ L_2 $: points equidistant from P and Q
  3. Point K: intersection of $ L_1 $ and $ L_2 $
2. Measure |KS|
1. Mrs. Otoo spends $\frac13$ of salary on rent, $\frac14$ on food, $\frac15$ on clothes, with \$195 left. Find monthly salary.
2. Sector of circle, radius = 6 cm, angle = 105°.
  1. Perimeter
  2. Area
  [Take $\pi = \frac{22}{7}$]
The cost $ C $ of feeding students: partly constant and partly varies as number of students $ n $.
For $ n=8 $, $ C=\$70 $; for $ n=10 $, $ C=\$90 $.
1. Find expression for $ C $ in terms of $ n $
2. Cost of feeding 12 students

(Diagram: cyclic quadrilateral ABCD with AC and BD intersecting at X, ∠BDC=40°)

1. Given: \[ P = \begin{pmatrix} 2 & -9 \\ 4 & 1 \end{pmatrix}, \quad Q = \begin{pmatrix} 1 & -1 \\ 3 & -2 \end{pmatrix} \] Find $ PQ + 2Q $
2. Bag contains 8 red balls and some white balls. If probability of drawing white ball = half of red ball, find number of white balls.
1. The 8th term of an A.P. is 46; sum of first 8 terms is 200.
  1. First term
  2. Sum of first 12 terms
2. Points $ X(70^\circ S, 60^\circ E) $ and $ Y(7^\circ S, 60^\circ E) $.
  1. Illustrate in diagram
  2. Distance between X and Y along meridian. [Take $\pi=\frac{22}{7}$; $R=6400\, \text{km}$]
Marks of 20 students:
15, 11, 17, 25, 13, 15, 16, 22, 24, 27, 20, 22, 15, 16, 15, 19, 22, 24, 22, 11
1. Prepare frequency table (class intervals: 10–12, 13–15, 16–18, ...)
2. Calculate variance
3. If pass mark is 16, find probability that a student failed