WAEC Mathematics 1999 past questions and answers

Evaluate √20 × (√5)³

1. A.10
2. B.20
3. C.25
4. D.50

If P = {3, 7, 11, 13} and Q = {2, 4, 8, 16}, which of the following is correct?

1. A.(P∩Q)' = {2, 3, 4, 13}
2. B.n(P∪Q) = 4
3. C.P∪Q = ϕ
4. D.P∩Q = ϕ

It is observed that 1 + 3 = 2², 1 + 3 + 5 = 3², 1 + 3 + 5 + 7 = 4². If 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = p², find P.

1. A.6
2. B.7
3. C.8
4. D.9

Evaluate 3.0 × 10¹ − 2.8 × 10⁻¹ leaving the answer in standard form.

1. A.2 × 10⁻¹
2. B.2 × 10²
3. C.2.972 × 10¹
4. D.2.972 × 10²

A trader makes a loss of 15% when selling an article. Find the ratio, Selling Price: Cost Price.

1. A.3 : 20
2. B.3:17
3. C.17:20
4. D.20:23.

The side of a square is increased from 20cm to 21cm. Calculate the percentage increase in its area

1. A.2.5%
2. B.9.3%
3. C.10.0%
4. D.10.25%.

Arrange in ascending order of magnitude: 26₈, 36₇ and 25₉.

1. A.25₉, 26₈, 36₇
2. B.26₈, 25₉, 36₇
3. C.36₇, 26₈, 25₉
4. D.36₇, 25₉, 26₈.

The side of a rhombus is 10cm long, correct to the nearest whole number. Between what limits should the perimeter P lie?

1. A.39cm ≤ P ≤ 41cm
2. B.38cm ≤ P < 42cm
3. C.38.5 ≤ P < 41.5cm
4. D.38.5cm ≤ P ≤ 40cm.

Simplify log₇8 − log₇2 + log₇4

1. A.0
2. B.2 log₇2
3. C.3 log₇2
4. D.4 log₇2.

If K√28 + √63 − √7 = 0, find K.

1. A.−2
2. B.−1
3. C.1
4. D.2.

From the set A = {3, √2, 2√3, √9, √7}, a number is selected at random. Find the probability that it is a rational number.

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

The pie chart illustrates the amount of private time a student spends in a week studying various subjects. If he spends 2½ hours a week on Science, find the total number of hours he studies in a week.

1. A.3⅓ hours
2. B.5 hours
3. C.8 hours
4. D.12 hours.

A group of eleven people can speak either English or French or both. Seven can speak English and six can speak French. What is the probability that a person chosen at random can speak both English and French?

1. A.2/11
2. B.4/11
3. C.5/11
4. D.11/13

The interior angle of a regular polygon is twice the exterior angle. How many sides has the polygon?

1. A.5
2. B.6
3. C.8
4. D.9.

Which of the following figures have one line of symmetry only? I. Isosceles Triangle II. Rhombus III. Kite

1. A.I and II only
2. B.II and III only
3. C.I and III only
4. D.I, II and III.

In the diagram below, |XR| = |RY| = |YZ| and ∠XRY = ∠YRZ = 62°. Calculate ∠XYZ.

1. A.50°
2. B.62°
3. C.112°
4. D.115°

In the diagram, RST is a tangent to circle VSU centre O. ∠SVU = 50° and UV is a diameter. Calculate ∠RSV

1. A.90°
2. B.50°
3. C.45°
4. D.40°.

Calculate the value of y from the diagram

1. A.18°
2. B.42°
3. C.48°
4. D.132°.

In the diagram, PQR is a circle with centre O. ∠QPR = 50°, ∠PQO = 30° and ∠ORP = m. Find m.

1. A.20°
2. B.25°
3. C.30°
4. D.50°.

Given that m = −3 and n = 2, find the value of (3n² − 2m³)/m

1. A.−22
2. B.−14
3. C.14
4. D.22.

Simplify (2 − 18m²)/(1 + 3m)

1. A.2(1 + 3m)
2. B.2(1 + 3m²)
3. C.2(1 − 3m)
4. D.2(1 − 3m²).

If y = √(ax − b) express x in terms of y, a and b.

1. A.x = (y² − b)/a
2. B.x = (y + b)/a
3. C.x = (y − b)/a
4. D.x = (y² + b)/a

Simplify 4/(x + 1) − 3/(x − 1)

1. A.(x + 7)/(x² − 1)
2. B.(x − 7)/(x² + 1)
3. C.(x − 7)/(x² − 1)
4. D.(x − 11)/(x² − 1)

If y varies inversely as x², how does x vary with y?

1. A.x varies inversely as y²
2. B.x varies inversely as √y
3. C.x varies directly as y²
4. D.x varies directly as √y

If tan x = 1/√3, find cos x − sin x such that 0° ≤ x ≤ 90°

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

From the top of a cliff 20m high, a boat can be sighted at sea 75m from the foot of the cliff. Calculate the angle of depression of the boat from the top of the cliff.

1. A.14.9°
2. B.15.5°
3. C.74.5°
4. D.75.1°.

From the diagram below. ABC is a triangle inscribed in a circle centre O. ∠ACB = 40° and |AB| = x cm. Calculate the radius of the circle.

1. A.x/sin 40°
2. B.x/cos 40°
3. C.x/(2 sin 40°)
4. D.x/(2 cos 40°)

The diagram shows the position of three ships A, B and C at sea. B is due north of C such that |AB| = |BC| and the bearing of B from A = 040°. What is the bearing of A from C?

1. A.040°
2. B.070°
3. C.110°
4. D.290°

In the diagram, PQST and QRST are parallelograms. Calculate the area of the trapezium PRST.

1. A.60cm²
2. B.50cm²
3. C.40cm²
4. D.30cm²

The height of a pyramid on a square base is 15cm. If the volume is 80cm³, find the length of the side of the base

1. A.3.3cm
2. B.5.3cm
3. C.4.0cm
4. D.8.0cm.

Simplify 3.72 × 0.025 and express your answer in the standard form.

1. A.9.3 × 10³
2. B.9.3 × 10²
3. C.9.3 × 10⁻²
4. D.9.3 × 10⁻³

Two numbers 24 and 31 are equal in value when converted to base ten. Find the equation connecting x and y.

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

A car travels at x km per hour for 1 hour and at y km per hour for 2 hours. Find its average speed.

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

The height and base of a triangle are in ratio 1 : 3 respectively. If the area of the triangle is 216cm², find the length of the base.

1. A.24cm
2. B.36cm
3. C.72cm
4. D.144cm.

Water flows from a tap into a cylindrical container at the rate of 5π cm³ per second. If the radius of the container is 3cm, calculate the level of water in the container at the end of 9 seconds.

1. A.2cm
2. B.5cm
3. C.8cm
4. D.15cm.

Amina had m mangoes. She ate 3 and shared the remainder equally with her brother Uche. Each had at least 10. Which of the following inequalities represents the statements above.

1. A.m/2 − 3 ≤ 10
2. B.m/2 − 3 ≥ 10
3. C.(m − 3)/2 ≥ 10
4. D.(m − 3)/2 ≤ 10.

Which of the following pairs of inequalities is represented on the number line?

1. A.x < −2 and x ≥ 1
2. B.x ≤ −2 and x > 1
3. C.x ≤ −2 and x ≥ 1
4. D.x < −2 and x > 1.

If x² + 15x + 50 = ax² + bx + c = 0, which of the following statements is not true?

1. A.x = −5
2. B.x = 10
3. C.x + 10 = 0
4. D.bc = 750.

The roots of a quadratic equation in x, are −m and 2n. Find the equation.

1. A.x² + x(m − 2n) − 2mn = 0
2. B.x² − x(m − 2n) − 2mn = 0
3. C.x² − x(2n − m) + 2mn = 0
4. D.x² + x(m − 2n) + 2mn = 0.

A survey shows that 28% of all the men in a village wear size 9 shoes. What is the probability that a man selected at random in the village wears size 9 shoes?

1. A.7/25
2. B.41/50
3. C.1/2
4. D.1.

Solve the inequality 2x + 3 < 5x.

1. A.x > 1
2. B.x < 3/7
3. C.x > 3/7
4. D.x > −1.

In the diagram, DE||BC, |AD| = x cm and |DB| = |AE| = y cm. Find |CE| in terms of x and y.

1. A.x
2. B.x²/y
3. C.y/x²
4. D.y²/x

Describe the locus L shown in the diagram below.

1. A.Locus of points equidistant from X and Y.
2. B.Locus of points equidistant from X and Z
3. C.Locus of points equidistant from ZX and ZY
4. D.Locus of points equidistant from XY and ZY

Which of the following statements is true from the diagram below?

1. A.m + n = 90°
2. B.m = n
3. C.n > 45°
4. D.m < 45°.

In the diagram, O is the centre of the circle. ∠PQR = 75°, ∠OPS = y° and OR is parallel to PS. Find y.

1. A.15
2. B.30
3. C.45
4. D.75.

The sides of a right-angle triangle, in ascending order of magnitude are 8cm, (x − 2) cm and x cm. Find x.

1. A.16
2. B.17
3. C.34
4. D.90.

In the diagram, CDE is a triangle, ABEF is cyclic quadrilateral, AB || CD, ∠BAF = 65° and ∠AFE = 85°. Calculate ∠CDE

1. A.20°
2. B.30°
3. C.50°
4. D.65°

(b) Evaluate log₅(3/5) + 3log₅(15/2) − log₅(81/8)

(a) If a is the set {1, 2, 3, ……, 19, 20} and A, B and C are subsets of a such that A = {multiples of five}, B = {multiples of four}, C = {multiples of three}, list the elements of (i) A (ii) B (iii) C
(b) Find; (i) A∩B (ii) A∩C (iii) B∪C
(c) Using your results in (b) show that (A∩B) ∪ (A∩C) = A∩(B∪C).

ABC is a triangle right-angled at C. P is the mid-point of AC, ∠PBC = 37° and |BC| = 5cm. Calculate: (a) |AC| correct to 3 significant figures (b) ∠PBA.

In the diagram, ABCD is a trapezium in which AD//BC and ∠ABC is a right angle. If |AD| = 15cm, |BD| = 17cm and |BC| = 9cm, calculate (a) |AB|. (b) the area of the triangle BCD. (c) |CD|. (d) the perimeter of the trapezium.

(a) Solve the simultaneous equations 3y − 2x = 21; 4y + 5x = 5.
(b) Six identical cards numbered 1–6 are placed face down. A card is to be picked at random. A person wins $60.00 if he picks the card numbered 6. If he picks any of the other cards, he loses $10.00 times the number on the card. Calculate the probability that he: (i) loses (ii) loses $20.00.

The table gives the frequency distribution of marks obtained by a group of students in a test.
Marks: 3, 4, 5, 6, 7, 8
Frequency: 5, x−1, x, 9, 4, 1
If the mean mark is 5, (a) Calculate the value of x. (b) find the: (i) mode: (ii) median of the distribution (c) If one of the students is selected at random, find the probability that he scored at least 7 marks

(a) A cylindrical pipe is 28 metres long. Its internal radius is 3.5cm and external radius 5cm, calculate: (i) the volume, in cm³, of metal used in making the pipe; (ii) the volume of water in litres that the pipe can hold when full, correct to 1 decimal place. [Take π = 22/7].
(b) In the diagram, MP is a tangent to the circle LMN at M. If the chord LN is parallel to MP, show that the triangle LMN is isosceles.

(a) Given that sin (A + B) = sin A cos B + cos A sin B, without using mathematical tables or calculator, evaluate sin 105°, leaving your answer in the surd form. (You may use 105° = 60° + 45°).
(b) The houses on the side of a particular street are assigned odd numbers, starting from 11. If the sum of the numbers is 551, how many houses are there?
(c) The 1st and 3rd term of a Geometric Progression (G.P.) are 2 and 2/9 respectively. Find: (i) the common difference, (ii) the 5th term

In the diagram, a ladder TF, 10m long is placed against a wall at an angle of 70° to the horizontal. (a) How high up the wall, correct to the nearest metre, does the ladder reach? (b) If the foot (F) of the ladder is pulled from the wall to F¹ by 1 metre. (i) how far, correct to 2 significant figures, does the top T, slide down the wall to T¹ (ii) Calculate, correct to the nearest degree, ∠QF¹T¹.

The cost of maintaining a school is partly constant and partly varies as the number of pupils. With 50 pupils, the cost is $15,705.00 and with 40 pupils, it is $13,305.00. (a) Find the cost when there are 44 pupils. (b) If the fee per pupil is $360.00, what is the least number of pupils for which the school can be run without loss?

On a graph sheet, using a scale of 2cm to 2 units on both axes. (a) draw the straight line joining points P (−5,3) and Q (2,3); (b) construct the locus L of points equidistant from P and Q; (c) by construction, locate points R and S on L, such that PRQS form a rhombus of sides 5cm; (d) find; (i) coordinates of R and S; (ii) area of the rhombus in cm².

(a) A shop-owner marked a shirt at a price to enable him make a gain of 20%. During a special sales period, the shirt was sold at 10% reduction to a customer for N864.00. What was the original cost to the shop-owner?
(b) A rectangular lawn of length (x + 5) metres is (x − 2) metres wide. If the diagonal is (x + 6) metres, find; (i) the value of x (ii) the area of the lawn.