WAEC Mathematics 2008 past questions and answers

If x% of 240 equals 12, find x.

1. A.x = 1
2. B.x = 3
3. C.x = 5
4. D.x = 7

Evaluate ((3.2)² − (4.8)²)/(3.2 + 4.8)

1. A.−0.80
2. B.−1.60
3. C.−10.24
4. D.−12.80

Find the product of 0.0409 and 0.0021 leaving your answer in the standard form.

1. A.8.6 × 10⁻⁶
2. B.8.6 × 10⁻⁵
3. C.8.6 × 10⁴
4. D.8.6 × 10⁵

Simplify: √50 + 10/√2

1. A.10
2. B.10√2
3. C.20
4. D.20√2

P naira invested for 4 years at r % simple interest per annum yields 0.36 P naira interest. Find the value of r.

1. A.1 1/9
2. B.1 4/9
3. C.9
4. D.11

Convert 42₅ to a base three numeral.

1. A.201₃
2. B.210₃
3. C.211₃
4. D.222₃

A trader bought 100 tubers of yam at 5 for N350.00. She sold them in sets of 4 for N290.00. Find her gain per cent.

1. A.3.6%
2. B.3.5%
3. C.3.4%
4. D.2.5%

If p − 2g + 1 = g + 3p and p − 2 = 0, find g.

1. A.−2
2. B.−1
3. C.1
4. D.2

Simplify: ∛(27x³y⁹)

1. A.9xy³
2. B.3xy⁶
3. C.3xy³
4. D.9y³

Given that x = 2 and y = −1/4, evaluate (x²y − 2xy)/5

1. A.0
2. B.1/5
3. C.1
4. D.2

If 4y is 9 greater than the sum of y and 3x, by how much is y greater than x?

1. A.3
2. B.6
3. C.9
4. D.12

If p = (3/5)√(q/r), express q in terms of p and r.

1. A.9/(25pr²)
2. B.(9/25)p²r
3. C.(25/9)p²r
4. D.(25/9)pr²

Simplify: (2x² − 5x − 12)/(4x² − 9)

1. A.(x + 4)/(2x + 3)
2. B.(x + 4)/(2x − 3)
3. C.(x − 4)/(2x + 3)
4. D.(x − 4)/(2x − 3)

In the diagram, ∠QPR = 90°. If q² = 25 − r², find the value of p.

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

POR is a sector of a circle centre O, radius 4 cm. If PÔR = 30°, find, correct to 3 significant figures, the area of sector POR. [Take π = 22/7]

1. A.4.19 cm²
2. B.8.38 cm²
3. C.10.5 cm²
4. D.20.9 cm²

If the volume of a cube is 343 cm³, find the length of its side.

1. A.3 cm
2. B.6 cm
3. C.7 cm
4. D.8 cm

In the diagram, PQRS is a rhombus. |PR| = 10 cm and |QS| = 24 cm. Calculate the perimeter of the rhombus.

1. A.34 cm
2. B.52 cm
3. C.56 cm
4. D.96 cm

In the diagram, |PQ| = |QR| and |PR| = |RS| = |SP|. Calculate the size of ∠QRS.

1. A.150°
2. B.120°
3. C.90°
4. D.60°

In the figure shown, PQS is a straight line. What is the value of ∠PRQ?

1. A.128°
2. B.108°
3. C.98°
4. D.78°

In the diagram, PQ // RS, QU // PT and ∠PSR = 42°. Find angle x.

1. A.84°
2. B.48°
3. C.42°
4. D.32°

The angles of a quadrilateral are (x + 10)°, 2y°, 90° and (100 − y)°. Find y in terms of x.

1. A.y = 160 + x
2. B.y = 100 + x
3. C.y = 160 − x
4. D.y = x − 100

In the figure |PX| = |XQ|, PQ // YZ and XY // QR. What is the ratio of the area of XYZQ to the area of ΔYZR?

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

In the diagram, O is the centre of the circle and PQRS is a cyclic quadrilateral. Find the value of x.

1. A.25°
2. B.65°
3. C.115°
4. D.130°

If x° is obtuse, which of the following is true?

1. A.x > 90
2. B.180 < x < 270
3. C.x < 90
4. D.90 < x < 180

If tan x = 1, evaluate sin x + cos x, leaving your answer in the surd form.

1. A.2√2
2. B.½√2
3. C.√2
4. D.2

If cos (x + 25)° = sin 45°, find the value of x.

1. A.20
2. B.30
3. C.45
4. D.60

If 2ⁿ = 128, find the value of (2ⁿ⁻¹)(5ⁿ⁻²).

1. A.5(10⁶)
2. B.2(10⁶)
3. C.5(10⁵)
4. D.2(10⁵)

If x ∝ (45 + ½y), which of the following is true?

1. A.x varies directly as y
2. B.x varies inversely as y
3. C.x is partly constant and partly varies as y
4. D.x varies jointly as 45 and directly as y

Simplify: log√8/(log 4 − log 2)

1. A.2/3
2. B.½ log 2
3. C.3/2
4. D.log 2

Every staff in an office owns either a Mercedes and/or a Toyota car. 20 own Mercedes, 15 own Toyota and 5 own both. How many staff are there in the office?

1. A.25
2. B.30
3. C.35
4. D.45

A train travels 60 km in M minutes. If its average speed is 400 km per hour, find the value of M.

1. A.15
2. B.12
3. C.10
4. D.9

An arc of a circle, radius 14 cm, is 18.33 cm long. Calculate, correct to the nearest degree, the angle which the arc subtends at the centre of the circle. [Take π = 22/7]

1. A.11°
2. B.20°
3. C.22°
4. D.75°

What is the length of an edge of a cube whose total surface area is X cm² and whose volume is X/2 cm³?

1. A.3
2. B.6
3. C.9
4. D.12

XY is a chord of circle centre O and radius 7 cm. The chord XY which is 8 cm long subtends an angle of 120° at the centre of the circle. Calculate the perimeter of the minor segment. [Take π = 22/7]

1. A.14.67 cm
2. B.22.67 cm
3. C.29.33 cm
4. D.37.33 cm

If the perimeter of ΔPQR in the diagram is 24 cm, what is the area of ΔPRS?

1. A.19.5 cm²
2. B.15.0 cm²
3. C.13.0 cm²
4. D.9.3 cm²

If p = ½ and 1/(p − 1) = 2/(p + x), find the value of x.

1. A.−2½
2. B.−1½
3. C.1½
4. D.2½

Find the quadratic equation whose roots are c and −c.

1. A.x² + c² = 0
2. B.x² − c² = 0
3. C.x² + 2cx + c² = 0
4. D.x² − 2cx + c² = 0

Which of the number lines below best represents the inequality −3 ≤ x < 4?

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

In the diagram, PX is a tangent to the circle and RST is an equilateral triangle. Calculate ∠PTS.

1. A.60°
2. B.90°
3. C.120°
4. D.150°

In the diagram, ∠QPR = 60°, ∠PQR = 50°, ∠QRS = 2x°, ∠SRP = 3x°, ∠UQP = y° and RS // TU. Calculate y.

1. A.102°
2. B.78°
3. C.70°
4. D.60°

In the diagram, find the size of the angle marked a°.

1. A.60°
2. B.80°
3. C.120°
4. D.160°

Given the sets A = {2, 4, 6, 8} and B = {2, 3, 5, 9}. If a number is selected at random from set B, what is the probability that the number is prime?

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

Given the sets A = {2, 4, 6, 8} and B = {2, 3, 5, 9}. If a number is picked at random from each of the two sets, what is the probability that their product is odd?

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

Given the sets A = {2, 4, 6, 8} and B = {2, 3, 5, 9}. If a number is picked at random from each of the two sets, what is the probability that their difference is 6 or 7?

1. A.1/256
2. B.1/16
3. C.1/8
4. D.1/2

Find the mean deviation of these numbers: 10, 12, 14, 15, 17, 19.

1. A.2.5
2. B.2.6
3. C.2.7
4. D.2.8

(a) Without using calculator or tables, find the value of log 3.6 given that log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990.
(b) If all numbers in the equation y/(y + 101) = 11/10010 are in base two, solve for y.

(a) Solve the inequality (2/5)(x − 2) − (1/6)(x + 5) ≤ 0
(b) Given that P = (x² − y²)/(x² + xy), (i) express P in its simplest form; (ii) find the value of P if x = −4 and y = −6.

The table below shows how a man spends his income in a month.
Food: ₦4500; House rent: ₦3000; Provisions: ₦2500; Electricity: ₦2000; Transportation: ₦5000; Others: ₦3000
(a) Represent the information on a pie chart.
(b) What percentage of his income is spent on transportation?

(a) A pentagon is such that one of its exterior angles is 60°. Two others are (90 − m)° each while the remaining angles are (30 + 2m)° each. Find the value of m.
(b) In the diagram, PQR is a straight line, QR = √3 cm and SQ = 2 cm. Calculate, correct to one decimal place, ∠PQS.

(a) A rectangular field is l metres long and b metres wide. Its perimeter is 280 metres. If the length is two and a half times its breadth, find the values of l and b.
(b) The base of a pyramid is a 4.5 m by 2.5 m rectangle. The height of the pyramid is 4 m. Calculate its volume.

(a) If 2^x+y = 16 and 4^x−y = 1/32, find the values of x and y.
(b) P, Q and R are related in such a way that P ∝ Q²/R. When P = 36, Q = 3 and R = 4. Calculate Q when P = 200 and R = 2.

(a) Solve, correct to two decimal places, the equation 4x² = 11x + 21.
(b) A man invests £1500 for two years at compound interest. After one year, his money amounts to £1560. Find the: (i) rate of interest; (ii) interest for the second year.
(c) A car costs ₦300,000.00. It depreciates by 25% in the first year and 20% in the second year. Find its value after 2 years.

The ages, in years, of 50 teachers in a school are given below:
21 37 49 27 49 42 26 33 46 40
50 29 23 24 29 31 36 22 27 38
30 28 42 39 34 23 21 32 41 46
46 31 33 29 28 43 47 40 34 44
26 38 34 49 45 27 25 33 39 40
(a) Form a frequency distribution of the data using the intervals: 21 − 25, 26 − 30, 31 − 35, etc.
(b) Draw the histogram of the distribution.
(c) Use your histogram to estimate the mode.
(d) Calculate the mean age.

(a) The triangle ABC has sides AB = 17 m, BC = 12 m and AC = 10 m. Calculate the: (i) largest angle of the triangle; (ii) area of the triangle.
(b) From a point T on a horizontal ground, the angle of elevation of the top R of a tower RS, 38 m high, is 63°. Calculate, correct to the nearest metre, the distance between T and S.

(a) Using ruler and a pair of compasses only, construct: (i) a quadrilateral PQRS such that |PQ| = 7 cm, ∠QPS = 60°, |PS| = 6.5 cm, ∠PQR = 135° and |QS| = |QR|; (ii) locus l₁ of points equidistant from P and Q; (iii) locus l₂ of points equidistant from P and S.
(b)(i) Label the point T where l₁ and l₂ intersect. (ii) With centre T and radius |TP|, construct a circle l₃.

(a) In the diagram, AB//CD and BC//FE. CD̂E = 75° and DÊF = 26°. Find the angles marked x and y.
(b) The diagram shows a circle ABCD with centre O and radius 7 cm. The reflex angle AOC = 190° and angle DAO = 35°. Find: (i) ∠ABC; (ii) ∠ADC.
(c) Using the diagram in 11(b) above, calculate, correct to 3 significant figures, the length of: (i) arc ABC; (ii) the chord AD. [Take π = 3.142]

(a) Copy and complete the table of values for y = 3 sin x + 2 cos x for 0° ≤ x ≤ 360°.
x: 0°, 60°, 120°, 180°, 240°, 300°, 360°
y: 2.00, –, –, –, –, –, 2.00
(b) Using a scale of 2 cm to 60° on x-axis and 2 cm to 1 unit on y-axis, draw the graph of y = 3 sin x + 2 cos x for 0° ≤ x ≤ 360°.
(c) Use your graph to solve the equation: 3 sin x + 2 cos x = 1.5.
(d) Find the range of values of x for which 3 sin x + 2 cos x < −1.

(a) If 3, x, y, 18 are in Arithmetic Progression (A.P), find the values of x and y.
(b)(i) The sum of the second and third terms of a geometric progression is six times the fourth term. Find the two possible values of the common ratio. (ii) If the second term is 8 and the common ratio is positive, find the first six terms.

(Questions 14 and 15 are for candidates in Ghana, Sierra Leone and The Gambia only.)
(a) The function f is defined as f: x → 3x² − 5x. (i) Evaluate f(−2). (ii) Find the values of x for which f(x) = −7/4.
(b) A rhombus ABCD has A at (0, 2) and B at (5, 3). If the diagonals intersect at (0, 3), find the coordinates of C and D.

(a) Using a scale of 2 cm to 2 units on both axes, draw two perpendicular axes OX and OY for the interval −8 ≤ x ≤ 8 and −10 ≤ y ≤ 10.
(b) Draw, clearly labelling all the vertices and coordinates, (i) triangle PQR with P(−3, 6), Q(−1, 1) and R(4, 2); (ii) ΔP₁Q₁R₁, with P₁(5, 6), Q₁(3, 1) and R₁(−2, 2); (iii) ΔP₂Q₂R₂, the image of ΔPQR under a rotation through 180° about the origin where P → P₂, Q → Q₂ and R → R₂; (iv) the point Q₃, the image of Q under a translation by the vector (−4, 3).
(c) What single transformation maps ΔPQR onto ΔP₁Q₁R₁?