WAEC Mathematics 1995 past questions and answers

Find (101₂)², expressing the answer in base 2.

1. A.10101
2. B.11001
3. C.10010
4. D.11101
5. E.10110.

If 3 children share N10.50 among themselves in ratio 6:7:8, how much is the largest share?

1. A.N3.00
2. B.N3.50
3. C.N4.00
4. D.N4.50
5. E.N5.00

Express 0.000834 in standard form.

1. A.8.34 × 10^-4
2. B.8.34 × 10^-3
3. C.8.34 × 10³
4. D.8.34 × 10⁴
5. E.8.34 × 10⁶

Simplify: 0.027^-1/3

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

Given that log₂a = log₈4, find a.

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

By selling some crates of soft drinks for N600.00, a dealer makes a profit of 50%. How much did the dealer pay for the drinks?

1. A.N1,200.00
2. B.N900.00
3. C.N450.00
4. D.N400.00
5. E.N200.00

Find the nth term Un of the A.P., 11, 4, −3,........

1. A.Un = 19 + 7n
2. B.Un = 19 − 7n
3. C.Un = 18 − 7n
4. D.Un = 18 + 7n
5. E.Un = 17 − 7n.

If 16/9, x, 1, y are in Geometric Progression (G.P.), find the product of x and y.

1. A.9/16
2. B.3/4
3. C.1
4. D.4/3
5. E.16/6

If R = [2, 4, 6, 7] and S = [1, 2, 4, 8], then R∪S equal

1. A.[1,2,4,6,7,8]
2. B.[1,2,4,7,8]
3. C.[1,4,7,8]
4. D.[2,6,7]
5. E.[2,4].

In the diagram below, the shaded portion is

1. A.P'∩R
2. B.Q∩R
3. C.P'∩Q∩R
4. D.(P∪Q)'∩R.
5. E.(P∩Q) U (P'∩R).

Find the values of x for which the expression is underlined: (6x − 1)/(x² + 4x − 5)

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

Solve the inequality: 1/3(2x − 1) < 5.

1. A.x < −5
2. B.x < −6
3. C.x < 7
4. D.x < 8
5. E.x < 16

What is the smaller value of x for which x² − 3x + 2 = 0?

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

Factorize the expression x(a − c) + y(c − a)

1. A.(a − c)(y − x)
2. B.(a − c)(x − y)
3. C.(a + c)(x − y)
4. D.(a + c)(x + y)
5. E.(a − c)(x + y).

If y ∝ 1/x² and x = 3 when y = 4, find y when x = 2

1. A.1
2. B.3
3. C.9
4. D.18
5. E.21

Solve the equation 3x² + 25x − 18 = 0

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

Solve the equation (x + 2)(x − 7) = 0

1. A.x = 1 or 8
2. B.x = −2 or 7
3. C.x = −4 or 5
4. D.x = −3 or 6
5. E.x = −5 or −m2.

Solve the following simultaneous equations: x + y = 3/2; x − y = 5/2 and use your result to find the value of 2y + x

1. A.−2
2. B.−1
3. C.½
4. D.1
5. E.3½

Use the graph of y = 3x² + x − 7 to answer this question. What is the minimum value of y?

1. A.−10
2. B.−7
3. C.−4
4. D.−1
5. E.2.

Use the graph of y = 3x² + x − 7 to answer this question. Find the roots of the equation y = 3x² + x − 7

1. A.1.0 and −1.2
2. B.1.1 and −1.3
3. C.1.4 and −1.7
4. D.2.0 and −1.9
5. E.2.4 and −2.0.

In the diagram below. |AB| = 12cm, |AE| = 8cm, |DC| = 9cm and AB||DC. Calculate |EC|.

1. A.10cm
2. B.9cm
3. C.8cm
4. D.7.5
5. E.6cm.

The diagonals AC and BD of a rhombus ABCD are 16cm and 12cm long respectively. Calculate the area of the rhombus.

1. A.24cm²
2. B.36cm²
3. C.48cm²
4. D.60cm²
5. E.96cm²

A water tank of height ½m has a square base of side 1½m. If it is filled with water from a water tanker holding 1500 litres, how many litres of water are left in the water tanker? [1000 litres = 1m³]

1. A.37.5litres
2. B.375 litres
3. C.3750 litres
4. D.37500 litres
5. E.375000 litres.

Find the total surface area of solid circular cone with base radius 3cm and slant height 4cm. [Take π = 22/7]

1. A.37 5/7cm²
2. B.66cm²
3. C.75 3/7cm²
4. D.78 2/7cm²
5. E.88cm²

A hollow sphere has a volume of kcm³ and a surface area of kcm². Calculate the diameter of the sphere.

1. A.3cm
2. B.6cm
3. C.9cm
4. D.12cm
5. E.More information is needed.

The diagram above shows a cone with the dimensions of its frustrum indicated. Calculate the height of the cone.

1. A.12cm
2. B.15cm
3. C.18cm
4. D.24cm
5. E.30cm.

The positions of two countries P and Q are (15°N, 12°E) and (65°N, 12°E) respectively. What is the difference in latitude?

1. A.104°
2. B.100°
3. C.80°
4. D.50°
5. E.24°

A 120° sector of a circle of radius 21cm is bent to form a cone. What is the base radius of the cone?

1. A.3½cm
2. B.7cm
3. C.10½cm
4. D.14cm
5. E.21cm

The angle of a sector of a circle is 108°. If the radius of the circle is 3½cm, find the perimeter of the sector

1. A.6 3/5cm
2. B.6 4/5cm
3. C.7 1/10cm
4. D.10 2/5cm
5. E.13 3/5cm.

In the diagram below; O is the centre of the circle and |BD| = |DC|. If ∠DCB = 35°, find ∠BAO.

1. A.20°
2. B.25°
3. C.30°
4. D.35°
5. E.40°

In the diagram above, AO is perpendicular to OB. Find x.

1. A.7.5°
2. B.15°
3. C.22.5°
4. D.30°
5. E.38.6°

In the diagram above, PQ is parallel to TU, ∠PQR = 50°, ∠QRS = 86° and ∠STU = 64°. Calculate the value of x.

1. A.136°
2. B.120°
3. C.108°
4. D.100°
5. E.96°

If log₁₀x = 2̄.3675 and log₁₀y = 2̄.9738, what is the value of x + y, correct to three significant figures?

1. A.0.117
2. B.0.118
3. C.0.903
4. D.0.944
5. E.0.946.

In the diagram below, AB//CD, the bisector of ∠BAC and ∠ACD meet at E. Find the value of ∠AEC.

1. A.30°
2. B.45°
3. C.60°
4. D.75°
5. E.90°

In the diagram above, AB//CD. What is the size of the angle marked x?

1. A.103°
2. B.93°
3. C.77°
4. D.62°
5. E.52°

The locus of a point which is equidistant from two given fixed points is the

1. A.perpendicular bisector of the straight line joining them
2. B.angle bisector of the straight lines joining the points to the origin
3. C.perpendicular to the straight line joining them
4. D.parallel line to the straight line joining them
5. E.a line making an acute angle with the line joining the two points.

Which of the following angles is an exterior angle of a regular polygon?

1. A.95°
2. B.85°
3. C.78°
4. D.75°
5. E.72°

In ΔABC above, BC is produced to D, |AB| = |AC| and ∠BAC = 50°: Find ∠ACD

1. A.50°
2. B.60°
3. C.65°
4. D.100°
5. E.115°

Without using tables, find the value of sin 20°/cos 70° + cos 25°/sin 65°

1. A.2
2. B.1
3. C.0
4. D.−1
5. E.−2

In the diagram below, ∠PRQ = 90°, ∠QPR = 30° and |PQ| = 12cm. Find y.

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

The bearing of two points Q and R from a point P are 030° and 120° respectively. If |PQ| = 12m and |PR| = 5m, find the distance QR.

1. A.13m
2. B.11m
3. C.9m
4. D.7m
5. E.5m.

What is the mode of the numbers 8, 10, 9, 9, 10, 8, 11, 8, 10, 9, 8 and 14?

1. A.8
2. B.9
3. C.10
4. D.11
5. E.14.

The mean of 20 observations in an experiment is 4. If the observed largest value is 23, find the mean of the remaining observations.

1. A.4
2. B.3
3. C.2.85
4. D.2.60
5. E.2.56.

Find the median of the following numbers: 2.64, 2.50, 2.72, 2.91 and 2.35.

1. A.2.91
2. B.2.72
3. C.2.64
4. D.2.50
5. E.2.35.

Two fair dice are tossed together once. Find the probability that the sum of the outcome is at least 10.

1. A.1/12
2. B.5/36
3. C.1/6
4. D.1/4
5. E.5/18

From a box containing 2 red, 6 white and 5 black balls, a ball is randomly selected. What is the probability that the selected ball is black?

1. A.2/13
2. B.5/13
3. C.5/11
4. D.5/6
5. E.11/13

(a) Factorize: px − 2qx − 4qy + 2py.
(b) Given that the universal set U = [1,2,3,4,5,6,7,8,9,10], P = [1,2,4,6,10] and Q = [2,3,6,9], show that [P∪Q]' = P'∩Q'.

The quantity y is partly constant and partly varies inversely as the square of x. (a) Write down the relationship between x and y. (b) When x = 1, y = 11 and when x = 2, y = 5, find the value of y when x = 4.

(a) In the diagram below, PQSR and SRYZ are parallelograms and PQYZ is a straight line. If |QY| = 2cm and RS = 3cm, find |PZ|.
(b) P and Q are two towns on the earth's surface on latitude 56°N. Their longitudes are 25°E and 95°E respectively. Find the distance PQ along their parallel of latitude, correct to the nearest km. [Take radius of the earth as 6400km and π = 22/7].

(a) A pack of 52 playing cards in shuffled and a card is drawn at random. Calculate the probability that it is either a five or a red nine. [Hint: There are 4 fives and 2 red nines in a pack of 52 cards].
(b) P, Q and R are points in the same horizontal plane. The bearing of Q from P is 150° and the bearing of R from Q is 060°. If |PQ| = 5cm and |QR| = 3m, find the bearing of R from P, correct to the nearest degree.

(a) The frequency table shows the marks scored by 32 students in a test.
Marks scored: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
No. of Students: 2, 3, 4, 4, 4, 4, 5, 3, 2, 1
Find the: (a) (i) Mean (ii) Median (iii) Mode
(b)(i) Find the number of students that scored at least 8 marks. (b) Caculate the percentage that scored at least 8 marks.

(a) Using mathematical tables, find; (i) 2 sin 63.35° (ii) log cos 44.74°
(b) Find the value of K given that log K − log (K − 2) = log 5.
(c) Use logarithm tables to evaluate (3.68)² × 6.705/√0.3581

(a) Given that p = x + ym³, find m in terms of p, x and y.
(b) Using the method of completing the square, find the roots of the equations x² − 6x + 7 = 0, correct to 1 decimal place.
(c) The product of two consecutive positive odd numbers is 195. By constructing a quadratic equation and solving it, find the two numbers.

(a) Copy and complete the table for the relation y = 2 cos 2x − 1
x: 0°, 30°, 60°, 90°, 120°, 150°, 180°
y = 2cos 2x − 1: 10, 0, __, __, __, __, 1.0
(b) Using a scale of 2 cm = 30° on the x-axis and 2cm = 1 unit on the y-axis, draw the graph of y = 2 cos 2x − 1 for 0° ≤ x ≤ 180°
(c) On the same axis draw the graph of y = 1/180 (x − 360).
(d) Use your graphs to find the: (i) values of x for which 2 cos 2x + ½ = 0; (ii) roots of the equation 2 cos 2x − x/180 + 1 = 0.

(a) Using a ruler and a pair of compasses only construct triangle ABC with |AB| = 7.5cm, |BC| = 8.1cm and ∠ABC = 105°.
(b) Locate a point D on BC such that |BD| : |DC| is 3:2
(c) Through D, construct a line l perpendicular to BC.
(d) If the line l meets AC at P, measure |BP|

(a) A man travels from a village X on a bearing of 060° to a village Y which is 20km away. From Y, he travels to a village Z, on a bearing of 195°. If Z is directly east of X, calculate, correct to three significant figures, the distance of: (i) Y from Z (ii) Z from X.
(b) An aircraft flies due south from an airfield on latitude 36°N longitude 138°E to an airfield on latitude 36°S longitude 138°E. (i) Calculate the distance travelled, correct to three significant figures (ii) if the speed of the aircraft is 800km per hour, calculate the time taken, correct to the nearest hour. [Take π = 22/7 R = 6400km].

The table below shows the scores of 2000 candidates in an entrance examination into a private secondary school.
% Marks: 11-20, 21-30, 31-40, 41-50, 51-60, 61-70, 71-80, 81-90
No. of Pupils: 68, 184, 294, 402, 480, 310, 164, 98
(a) Prepare a cumulative frequency table and draw the cumulative frequency curve for the distribution.
(b) Use your curve to estimate the: (i) cut-off mark, if 300 candidates are to be offered admission. (ii) probability that a candidate picked at random scored at least 45%.

A box contains 5 blue balls, 3 black balls and 2 red balls of the same size. A ball is selected at random from the box and then replaced. A second ball is then selected. Find the probability of obtaining; (a) two red balls: (b) two blue balls or two black balls; (c) one black ball and one red ball in any order.