WAEC Mathematics 1998 past questions and answers

If S⊂R, then

1. A.S∩R = R
2. B.S∩R = S
3. C.S∪R = S
4. D.S∩R = S'
5. E.S∩R = R'

Convert 35 to a number in base two.

1. A.1011_two
2. B.10011_two
3. C.100011_two
4. D.110010_two
5. E.110001_two

The n^th term of a sequence is represented by 3 × 2⁽²⁻ⁿ⁾. Write down the first three terms of the sequence

1. A.3/2, 3, 6
2. B.6, 3, 3/2
3. C.3/2, 3, 1/3
4. D.2/3, 3, 8/3
5. E.3/2, 0, 6.

A piece of cloth was measured as 6.10m. If the actual length of the cloth is 6.35m, find the percentage error, correct to 2 decimal places.

1. A.3.05%
2. B.3.94%
3. C.15.00%
4. D.25.00%
5. E.39.30%.

Simplify: (8^2/3 × 27^−1/3)/64^1/3

1. A.−3
2. B.1/9
3. C.1/3
4. D.27/8
5. E.4.

Solve the equation 5x² − 4x − 1 = 0

1. A.−1, 1/5
2. B.−1, −1/5
3. C.1, 1/5
4. D.1, −1/5
5. E.−1, 5.

p and q are two positive numbers such that p > 2q. Which one of the following statements is not true?

1. A.−p < −2q
2. B.−p > −2q
3. C.−q < 2p
4. D.q < ½p
5. E.p² > 2q².

For what values of x is the expression (x − 5)/(x² − 2x − 3) not defined?

1. A.3, 1
2. B.−1, −3
3. C.−1, 3
4. D.3, −2
5. E.1, −3

Make S the subject of the formula: V = K/√(T − S)

1. A.S = T − K²/V²
2. B.S = (K² − T)/V²
3. C.S = T − V²/K²
4. D.S = T(V² − K²)/V²
5. E.S = (T + V²)/K²

Find (x − y) if 4x − 3y = 7 and 3x − 2y = 5.

1. A.4
2. B.3
3. C.2
4. D.−2
5. E.−3.

If h(m + n) = m(h + r) find h in terms of m, n and r

1. A.h = mr/(2m + n)
2. B.h = mr/(n + m)
3. C.h = (m + r)/n
4. D.h = (m + n)/m
5. E.h = mr/n

Given that (6x − y)/(x + 2y) = 2, find the value of x/y

1. A.3/8
2. B.5/8
3. C.4/5
4. D.5/4
5. E.8/5.

The radius of a geographical globe is 60cm. Find the length of the parallel of Latitude 60°N.

1. A.66πcm
2. B.60πcm
3. C.30πcm
4. D.15πcm
5. E.6πcm.

In the diagram below, O is the centre of the two concentric circles of radii 13cm and 10cm respectively. Find the area of the shaded portion in the sector with an angle of 120° at the centre.

1. A.1/3πcm²
2. B.πcm²
3. C.3πcm²
4. D.23πcm²
5. E.46πcm².

Express as a single fraction: x/(x − 2) − (x + 2)/(x + 3)

1. A.(2x² − 3x − 4)/((x − 2)(x + 3))
2. B.(2x² + 3x − 4)/((x − 2)(x + 3))
3. C.2/((x − 2)(x + 3))
4. D.(3x + 4)/((x − 2)(x + 3))
5. E.(3x − 4)/((x − 2)(x + 3))

The following numbers represent a set of scores for a class of 32 students, where the maximum score possible was 12, 6, 5, 9, 4, 4, 8, 7, 5, 6, 3, 2, 5, 4, 6, 9, 10, 4, 3, 2, 3, 4, 6, 8, 7, 4, 2, 1, 8, 7, 7, 6, 11. What percentage of the class, correct to the nearest whole number, scored above 6?

1. A.34%
2. B.35%
3. C.37%
4. D.38%
5. E.50%.

A die with faces numbered 1 to 6 is rolled once. What is the probability of obtaining 3 or 4?

1. A.1/36
2. B.1/6
3. C.1/3
4. D.1/2
5. E.2/3.

Use the graph to answer this question. The graph is that of the quadratic expression

1. A.y = x² + x − 2
2. B.y = x² − x + 2
3. C.y = x² − x − 2
4. D.y = x + 2x + 2
5. E.y = x² + 2x − 2

Use the graph to answer this question. The values of x when y = −1 are approximately

1. A.−1.0 and 2.0
2. B.−1.3 and 2.3
3. C.−0.6 and 2.6
4. D.−0.6 and 1.6
5. E.1.6 and 1.6.

In ΔPQR, ∠PQR is a right angle. |QR| = 2cm and ∠PRQ = 60°. Find |PR|.

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

In sin (X + 30)° = Cos 40°, find X.

1. A.10°
2. B.20°
3. C.50°
4. D.60°
5. E.90°.

A ladder 5cm long rests against a wall such that its foot makes an angle 30° with the horizontal. How far is the foot of the ladder from the wall?

1. A.5√2/3 m
2. B.2½m
3. C.5√3/2 m
4. D.10√3/3 m
5. E.10√3m

A chord of a circle of radius 26cm is 10cm from the centre of the circle. Calculate the length of the chord

1. A.16cm
2. B.27.86cm
3. C.32cm
4. D.48cm
5. E.55.72cm.

Two chords PQ and RS of a circle intersect at right angles at a point inside the circle. If ∠QPR = 35°, find ∠PQS

1. A.35°
2. B.45°
3. C.55°
4. D.70°
5. E.90°.

In the diagram, O is the centre of the circle and the reflex angle ROS is 264°. Find ∠RTS.

1. A.48°
2. B.53°
3. C.60°
4. D.132°
5. E.192°.

If the exterior angles of a quadrilateral are y°, (y + 5)°, (y + 10)° and (y + 25)°, find y.

1. A.10°
2. B.20°
3. C.40°
4. D.60°
5. E.80°.

In the diagram PQ is a diameter of circle PMQN centre O. If ∠PQM = 63°, find ∠MNQ.

1. A.58.5°
2. B.44°
3. C.35°
4. D.31.5°
5. E.27°.

In the diagram, O is the centre of circle PRQ. The radius is 3.5cm and ∠POQ = 50°. (Take π = 3.142) Calculate, correct to one decimal place, the length of arc PQ.

1. A.175.0 cm
2. B.157.1cm
3. C.37.7 cm
4. D.11.0cm
5. E.3.1cm.

In the diagram, O is the centre of circle PRQ. The radius is 3.5cm and ∠POQ = 50°. (Take π = 3.142) Calculate, correct to three significant figures, the area of sector OPQ.

1. A.3.403cm²
2. B.5.350cm²
3. C.10.99cm²
4. D.157.1cm²
5. E.175.0cm².

The pie chart below shows the distribution of how students travelled to a certain school on a particular day. What percentage, to the nearest whole number, of the students travelled to school on foot?

1. A.24%
2. B.23%
3. C.20%
4. D.15%
5. E.14%.

The diagram below is a rectangle. If the perimeter is 36m, find the area of the rectangle.

1. A.64m²
2. B.65m²
3. C.84m²
4. D.124m²
5. E.275m²

In Δ PQR, T is a point on QR such that ∠QPT = 39° and ∠PTR = 83°. Calculate ∠PQT.

1. A.34°
2. B.44°
3. C.45°
4. D.97°
5. E.107°.

Find the curved surface area of a cone of radius 3cm and slant height 7 cm. (Take π = 22/7)

1. A.22cm²
2. B.44cm²
3. C.66cm²
4. D.132cm²
5. E.198cm²

In the diagram below, |PQ| = |PR| = |RS| and ∠RSP = 35°. Find ∠QPR.

1. A.70°
2. B.50°
3. C.45°
4. D.40°
5. E.35°.

P varies inversely as Q. The table below shows the value of Q for some selected values of P.
P: 6, 8, 9, 12
Q: 24, 18, ?, 12
What is the missing value of Q in the table?

1. A.4
2. B.9
3. C.15
4. D.16
5. E.144.

Three of the angles of a hexagon are each x°. The others are each 3x°. Find x.

1. A.30°
2. B.40°
3. C.60°
4. D.80°
5. E.120°.

A, B and C are subsets of the universal set U such that:
U = {0, 1, 2, 3, ……, 12}
A = {x: 0 ≤ x ≤ 7}
B = {4, 6, 8, 10, 12}
C = {1 < y < 8}, where y is a prime number
(a) Draw a Venn diagram to illustrate the information given above.
(b) Find: (i) (B∪C)' (ii) A'∩B∩C

(a) Given that log₁₀2 = 0.3010, log₁₀7 = 0.8451 and log₁₀5 = 0.6990, evaluate without using logarithm tables. (i) log₁₀35; (ii) log₁₀2.8
(b) Given that N^0.8942 = 2.8, use your result in (a)(ii) to find the value of N.

(a) The value of the expression 2Ax − Kx² is 7 when x = 1 and 4 when x = 2. Find the values of the constants A and K.
(b) Solve the equation x² − 3x − 1 = 0, giving your answers correct to 1 decimal place.

The area of a rectangular floor is 13.5m². One side is 1.5m longer than the other.
(a) Calculate the dimensions of the floor
(b) If it costs N250.00 per square metre to carpet the floor and only N2,200.00 is available, what area of the floor can be covered with carpet?

(a) A number is selected at random from each of the sets {2,3,4} and {1,3,5}. What is the probability that the sum of the two numbers will be less than 7 but greater than 3?
(b) In the diagram above, ABCD is a circle. DAE, CBE, ABF and DCF are straight lines. If y + m = 90°, find the value of x.

The third term of a Geometric Progression (G.P) is 360 and the sixth term is 1215. Find the first four terms.

(a) A radio which a dealer bought for N6,000.00 and marked to give a profit of 30% was reduced in a sale by 10%. Find (i) the final sale price (ii) the percentage profit.
(b) Solve the equation 2^(2x+1) − 9(2^x) + 4 = 0

(a) Copy and complete the table of values for the relation y = 5 − 7x − 6x² for −3 ≤ x ≤ 2.
x: −3, −2, −1, −0.5, 0, 1, 2
y: −28, , 6, , 5, ,
(b) Using a scale of 2cm to 1 unit on the x-axis and 2cm to 5 units on the y-axis, draw the: (i) graph of y = 5 − 7x − 6x² (ii) line y = 3 on the same axes.
(c) Use your graph to find the; (i) Roots of the equation 2 − 7x − 6x² = 0 (ii) Maximum value of y = 5 − 7x − 6x²

Using a ruler and a pair of compasses only, construct (a) triangle QRT with |QR| = 8cm, |RT| = 5cm and |QT| = 4.5cm (b) a quadrilateral QRSP which has a common base QR with ΔQRT such that QTP is a straight line, PQ||SR, |QP| = 9cm and |RS| = 4.5cm (i) Measure |PS| (ii) Find the perpendicular distance between RS and PQ. (iii) What is QRSP?

A surveyor standing at a point X sights a pole Y due east of him and a tower Z of a building on a bearing of 046°. After walking to a point, W, a distance of 180m in the south-east direction, he observes the bearing of Z and Y to be 337° and 050° respectively. (a) Calculate, correct to the nearest metre (i) |XY| (ii) |ZW|. (b) If N is on XY such that XZ = ZN, find the bearing of Z from N.

In the diagram, ASRTB represents a piece of string passing over a pulley of radius 10cm in a vertical plane. O is the centre of the pulley and AMB is a horizontal straight line touching the pulley at M. Angle SAB = 90° and angle TBA = 60°.
(a) Calculate (i) the obtuse angle SOT, (ii) arc SRT (iii) |BT|.
(b) Find, correct to the nearest cm, the length of the string. [Take π = 22/7].

The table below shows the number of eggs laid by chicken in a man's farm in a year.
No. of Eggs Per Year: 45–49, 50–54, 55–59, 60–64, 65–69, 70–74
No. of Chicken: 10, 36, 64, 52, 28, 10
(a) Draw a cumulative frequency curve of the distribution. (b) Use your graph to find the interquartile range. (c) If a woman buys a chicken from the farm, what is the probability that the chicken lays at least 60 eggs in a year?