WAEC Mathematics 2000 past questions and answers

Express 7/19 as a percentage, correct to 1 decimal place.

1. A.2.7%
2. B.3.7%
3. C.27.1%
4. D.36.8%.

Express 398753 correct to three significant figures.

1. A.398000
2. B.398700
3. C.398800
4. D.399000

Simplify 10/√32

1. A.(5/4)√2
2. B.(4/5)√2
3. C.(5/16)√2
4. D.(16/5)√2

Find the missing number in the addition of the following numbers, in base seven.
4321 + 1234 + **** = 12341

1. A.3453
2. B.5556
3. C.6016
4. D.13453

What fraction must be subtracted from the sum of 2 1/6 and 2 7/12 to give 3 1/4?

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

Simplify (16/81)^−3/4 × √(100/81)

1. A.80/243
2. B.1/64
3. C.25/6
4. D.15/4

Which of the following numbers is a perfect cube?

1. A.350
2. B.504
3. C.950
4. D.1728.

If 104_x = 68, find the value of x

1. A.5
2. B.7
3. C.8
4. D.9.

The ages of three men are in the ratio 3 : 4 : 5. If the difference between the ages of the oldest and youngest is 18 years, find the sum of the ages of the three men.

1. A.45 years
2. B.72 years
3. C.108 years
4. D.216 years.

Given that log₄x = −3, find x.

1. A.1/81
2. B.1/64
3. C.64
4. D.81

Given that the logarithm of a number is 1̄.8732, find, correct to 2 significant figures, the square root of the number.

1. A.0.29
2. B.0.75
3. C.0.86
4. D.0.93

A car moves at an average speed of 30kmh⁻¹, how long does it take to cover 200 metres?

1. A.2.4 sec
2. B.24 sec
3. C.144 sec
4. D.240 sec.

A man bought a television set on hire purchase for N25,000, out of which he paid N10,000. If he is allowed to pay the balance in eight equal instalments, find the value of each instalment.

1. A.N1250
2. B.N1578
3. C.N1875
4. D.3125.

A tree is 8km due south of a building. Kofi is standing 8km west of the tree. How far is Kofi from the building?

1. A.4√2km
2. B.8 km
3. C.8√2km
4. D.16 km.

A tree is 8km due south of a building. Kofi is standing 8km west of the tree. Find the bearing of Kofi from the building.

1. A.315°
2. B.270°
3. C.225°
4. D.135°

Which of the following bearings is equivalent to S50°W?

1. A.040°
2. B.130°
3. C.220°
4. D.230°.

The bar chart shows the distribution of marks scored by a group of students in a test. How many students scored 4 marks and above?

1. A.15
2. B.11
3. C.10
4. D.7.

The bar chart shows the distribution of marks scored by a group of students in a test. How many students took the test?

1. A.38
2. B.22
3. C.15
4. D.11.

Calculate the standard deviation of the following marks: 2, 3, 6, 2, 5, 0, 4, 2.

1. A.1.5
2. B.1.7
3. C.1.8
4. D.1.9.

The probabilities that Kodjo and Adoga pass an examination are 3/4 and 3/5 respectively. Find the probability of both boys failing the examination.

1. A.1/10
2. B.3/10
3. C.9/20
4. D.2/3

Which of the following triangles is congruent?

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

Which of the following statements is/are not true about a rectangle? I. Each diagonal cuts the rectangle into two congruent triangles. II. A rectangle has four lines of symmetry. III. The diagonals intersect at right angles.

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

In the diagram, PQRS is a circle centre O. POR is a diameter and ∠PRQ = 40°. Calculate ∠QSR.

1. A.30°
2. B.40°
3. C.45°
4. D.50°

Each side of a regular convex polygon subtends an angle of 30° at its centre. Calculate each interior angle

1. A.75°
2. B.150°
3. C.160°
4. D.168°

If the interior angles of a hexagon are 107°, 2x°, 150°, 95°, (2x − 15)° and 123°, find x.

1. A.57½°
2. B.65°
3. C.106°
4. D.120°

In the diagram, POS and ROT are straight lines. OPQR is a parallelogram. |OS| = |OT| and ∠OST = 50°. Calculate ∠OPQ.

1. A.160°
2. B.140°
3. C.120°
4. D.100°

Given that x = 1/2 and y = 4, evaluate 3x²y + xy².

1. A.−5
2. B.−1
3. C.4
4. D.11.

Given that 27^{(1 + x)} = 9, find x.

1. A.−3
2. B.−1/3
3. C.5/3
4. D.2.

If x varies inversely as y and x = 2/3 when y = 9, find the value of y when x = 3/4

1. A.1/18
2. B.8/81
3. C.9/2
4. D.8

Given that (2x + 7) is a factor of 2x² + 3x − 14, find the other factor.

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

Simplify 1/(x − 3) − 3(x − 1)/(x² − 9)

1. A.(x − 1)/(x − 3)
2. B.−2/(x + 3)
3. C.(x − 1)/(x + 3)
4. D.4x/(x² − 9)

Which of the following number lines represents the inequality 2 ≤ x < 9?

1. A.Number line A
2. B.Number line B
3. C.Number line C
4. D.Number line D

For an inequality for a distance d metres which is more than 18m, but not more than 23m.

1. A.18 ≤ d ≤ 23
2. B.18 < d ≤ 23
3. C.18 ≤ d < 23
4. D.d < 18 or d > 23.

Find the equation whose roots are −8 and 5.

1. A.x² + 13x + 40 = 0
2. B.x² − 13x − 40 = 0
3. C.x² − 3x + 40 = 0
4. D.x² + 3x − 40 = 0.

Make t the subject of the formula k = m√((t − p)/r)

1. A.(rk² + p)/m²
2. B.(rk² + pm²)/m²
3. C.(rk² − p)/m²
4. D.(rk² − p²)/m²

Solve the equation 3y² = 27y.

1. A.y = 0 or 3
2. B.y = 0 or 9
3. C.y = −3 or 3
4. D.y = 3 or 9

Find the value of x such that the expression 1/x + 4/(3x) − 5/(6x) + 1 equals zero

1. A.1/6
2. B.1/4
3. C.−3/2
4. D.−7/2

Given that p varies directly as q while q varies inversely as r, which of the following statements is true?

1. A.r varies directly as p
2. B.p varies inversely as r
3. C.p varies directly as r
4. D.q varies inversely as p.

In the diagram, PQS is a circle with centre O. RST is a tangent at S and ∠SOP = 96°. Find ∠PST

1. A.42°
2. B.48°
3. C.60°
4. D.66°

A bicycle wheel of radius 42cm is rolled over a distance 66 metres. How many revolutions does it make? [Take π = 22/7]

1. A.2.5
2. B.5
3. C.25
4. D.50

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

1. A.8cm²
2. B.9.6cm²
3. C.16cm²
4. D.25cm²

A tap leaks at the rate of 2cm³ per second. How long will it take the tap to fill a container of 45 litres capacity? (1 litre = 1000cm³)

1. A.8 hours
2. B.6hr 15min.
3. C.4hr 25 min.
4. D.3hr.

The lengths of the parallel sides of a trapezium are 5cm and 7cm. If its area is 120cm², find the perpendicular distance between the parallel sides.

1. A.5.0cm
2. B.6.9cm
3. C.10.0cm
4. D.20.0cm.

The arc of a circle 50cm long, subtends an angle of 75° at the centre of the circle. Find, correct to 3 significant figures, the radius of the circle. [Take π = 22/7]

1. A.8.74cm
2. B.38.2 cm
3. C.61.2 cm
4. D.76.4cm.

In the diagram, |PQ| = |PS|. Which of the following statements is true?

1. A.∠QPS = ∠QRS
2. B.|PO| = |RO|
3. C.QR||PS
4. D.∠PQR = ∠PSR

The area of a circle is 38.5cm². Find its diameter. [Take π = 22/7]

1. A.22cm
2. B.14cm
3. C.7cm
4. D.6cm.

Solve the equation 3 + 5x − 2x² = 0

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

If the simple interest on N2,000 after 9 months is N60, at what rate per annum is the interest charged?

1. A.2¼%
2. B.4%
3. C.5%
4. D.6%.

(a) Evaluate and express your answer in standard form; (4.56 × 3.6)/0.12
(b) Without using mathematical tables or calculator, evaluate (73.8)² − (26.2)²
(c) Simplify √(1 19/81), expressing your answer in the form a/b where a and b are positive integers.

(a) Given that cos x = 0.7431, 0 < x < 90°, use tables to find the values of (i) 2 sin x; (ii) tan (x/2)
(b) The interior angles of a pentagon are in ratio 2 : 3 : 4 : 4 : 5. Find the value of the largest angle.

(a) Given the expression y = ax² − bx − 12, find the values of x when a = 1, b = 2 and y = 3
(b) If √(x² + 1) = 5/4 find the positive value of x.

Using ruler and a pair of compasses only, (a) construct ΔPQR such that |PQ| = 7cm, |PR| = 6cm and ∠PQR = 60° (b) Locate point M, the mid-point of PQ. (c) Measure ∠RMQ.

The pie chart shows the distribution of marks scored by 200 pupils in a test. (a) How many pupils scored (i) between 41 and 50 marks? (ii) above 60 marks? (b) What fraction of the pupils scored at most 50 marks? (c) What is the modal class?

(a) The table shows the number of limes and apples of the same size in a bag.
Good: Limes 10, Apples 8
Bad: Limes 6, Apples 6
If two of the fruits are picked at random, one at a time, without replacement, find the probability that: (i) both are good limes; (ii) both are bad fruits; (iii) one is a good apple and the other a bad lime
(b) Solve the equation log₃(4x + 1) − log₃(3x − 5) = 2

(a) A man earns N150,000 per annum. He is allowed a tax free pay of N40,000. If he pays 25 kobo in the naira as tax on his taxable income, how much has he left?
(b) A bookshop had 650 copies of a book for sale. The books were marked at N75 per copy in order to make a profit of 30%. A bookseller bought 300 copies at 5% discount. If the remaining copies are sold at N75 each, calculate the percentage profit the bookshop would make on the whole?

(a) Copy and complete the following table of values for the relation y = x² − 2x − 5.
x: −3, −2, −1, 0, 1, 2, 3, 4, 5
y: , , −2, , −6, , −2, 3, 10
(b) Draw the graph of the relation y = x² − 2x − 5, using a scale of 2cm to 1 unit on the x-axis, and 2cm to 2 units on the y-axis.
(c) Using the same axes, draw the graph of y = 2x − 3.
(d) Obtain in the form ax² + bx + c = 0 where a, b and c are integers, the equation which is satisfied by the x-coordinate of the points of intersection of the two graphs.
(e) From your graphs, determine the roots of the equation obtained in (d) above.

(a) The mean of 1, 2, x, 11, y, 14 is 8 and the median is 9. Find the values of x and y.
(b) In the diagram, MN||PQ, |LM| = 3cm and |LP| = 4cm. If the area of ΔLMN is 18cm², find the area of quadrilateral MPQN.

(a) A surveyor walks 100m up a hill which slopes at an angle of 24° to the horizontal. Calculate, correct to the nearest metre, the height through which he rises
(b) In the diagram, ABC is an isosceles triangle. |AB| = |AC| = 5cm and |BC| = 8cm. Calculate, correct to the nearest degree, ∠BAC.
(c) Two boats, 70 metres apart and on opposite sides of a light house, are in a straight line with the light-house. The angles of elevation of the top of the light-house from the two boats are 71.6° and 45°. Find the height of the light-house. [Take tan 71.6° = 3]

(a) A cylindrical well of radius 1 metre is dug out to a depth of 8 metres. (i) Calculate, in m³, the volume of soil dug out (ii) If the soil is used to raise the level of the rectangular floor of a room 4m by 12m, calculate, correct to the nearest cm, the thickness of the new layer of soil. [Take π = 22/7]
(b) The diagram shows a quadrilateral ABCD in which ∠DAB is a right angle. |AB| = 3.3cm, |BC| = 3.9cm, |CD| = 5.2cm and |DA| = 5.6cm (i) find the length of BD (ii) show that ∠BCD = 90°

(a) The first term of an Arithmetic progression (A.P) is −8. The ratio of the 7th term to the 9th term is 5:8. Calculate the common difference of the progression.
(b) A sphere of radius 2cm is of mass 11.2g. Find: (i) the volume of the sphere, (ii) the density of the sphere, (iii) the mass of a sphere of the same material but with radius 3cm, [Take π = 22/7]

(a) Two places X and Y on the equator are on longitude 67°E and 123°E respectively. (i) What is the distance between them along the equator? (ii) How far is X from the North pole? [Take π = 22/7] and radius of the Earth as 6400 km).
(b) In the diagram, PQR is a circle centre O. N is the midpoint of chord PQ. |PQ| = 8 cm, |ON| = 3cm and ∠ONR = 20°. Calculate the size of ∠ORN to the nearest degree.