WAEC Mathematics 1997 past questions and answers

Express (0.0425 ÷ 2.5) as a fraction

1. A.17/10,000
2. B.17/1,000
3. C.17/250
4. D.17/100
5. E.17/10

What is log₁₀ (6.95 × 10⁻³)?

1. A.0.8420
2. B.3.8420
3. C.3̄.8420
4. D.3.9777
5. E.3̄.9777

If P = {3, 5, 6} and Q = {4, 5, 6} then P∩Q equals

1. A.{3, 4}
2. B.{4, 5}
3. C.{4, 6}
4. D.{5, 6}
5. E.{3, 6}

A and B are two sets. The number of elements in A∪B is 49, the number in A is 22 and number in B is 34. How many elements are in A∩B?

1. A.105
2. B.27
3. C.15
4. D.12
5. E.7

A student found the approximate value of 0.02548 correct to two places of decimal instead of two significant figures. Find the percentage error.

1. A.0%
2. B.13 1/3%
3. C.15 5/13%
4. D.16 2/3%
5. E.20%

Simplify log₃9 + log₃15 − log₃5

1. A.log₃19
2. B.log₃…
3. C.3
4. D.1
5. E.0

Solve the equation: 2/3 (x + 5) = 1/4(5x − 3)

1. A.1 1/7
2. B.1 8/23
3. C.3
4. D.4 3/7
5. E.7

Solve the equations: 4x − y = 11, 5x + 2y = 4

1. A.x = 6, y = 13
2. B.x = −2, y = −3
3. C.x = −2, y = 3
4. D.x = 2, y = −3
5. E.x = 2, y = 3

Make q the subject of the relation t = √(pq/r − r²q)

1. A.q = rt²/(p − r³)
2. B.q = t²/(p − r²)
3. C.q = rt/(p − r³)
4. D.q = (p − r³)/rt²
5. E.q = rt²(p − r³)

One of the roots of the equation 6x² = 5 − 7x is

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

P varies inversely as the square of W. When W = 4, P = 9. Find the value of P when W = 9

1. A.729/16
2. B.6
3. C.4
4. D.16/9
5. E.4/3

In the triangle XYZ, XM is the altitude from X to YZ. XY = 13cm, XZ = 15cm and YM = 5cm. Find the length of YZ

1. A.9cm
2. B.12cm
3. C.14cm
4. D.19.85cm
5. E.23cm

Two points P and Q are on longitude 67°W. Their latitudes differ by 90°. Calculate their distance apart in terms of π. (Take radius of the earth = 6400km).

1. A.6400πkm
2. B.6400km/π
3. C.3200πkm
4. D.3200km
5. E.3200km/π

The length of the two parallel sides of trapezium are 6cm and 10cm and the perpendicular distance between them is 5cm. Find the area of the trapezium.

1. A.21cm²
2. B.40cm²
3. C.80cm²
4. D.150cm²
5. E.300cm²

Calculate the total surface area of a solid cone of slant height 15cm and base radius 8cm in terms of π.

1. A.64πcm²
2. B.120πcm²
3. C.184πcm²
4. D.200πcm²
5. E.320πcm²

The cross-section of a prism is a right-angled triangle 3cm by 4cm by 5cm. The height of the prism is 8cm. Calculate its volume

1. A.48cm³
2. B.60cm³
3. C.96cm³
4. D.120cm³
5. E.240cm³

Find the radius of a circle in which an arc of length 44cm subtends angle 200° at the centre of the circle. {Take π = 22/7}

1. A.3.9cm
2. B.12.6cm
3. C.25.2cm
4. D.38.4cm
5. E.124.5cm

The diagram below is a triangle XYZ whose area is 23.5cm². XY = 10cm and YZ = 8cm, calculate θ, correct to the nearest degree.

1. A.34°
2. B.35°
3. C.36°
4. D.37°
5. E.40°

Which of the following is not necessarily sufficient for the construction of a triangle?

1. A.Three sides
2. B.Two sides and an included angle
3. C.Two sides and a right angle
4. D.Two sides and an angle
5. E.Two angles and a side.

In the diagram, EF//QR, PE = 2cm, EQ = 4cm and FR = 6cm. Find x.

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

Which of the following statements is/are true when two straight lines intersect?
I. Adjacent angles are equal
II. Vertically opposite angles are equal
III. Adjacent angles are supplementary

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

PQRS and GHRS are parallelograms on the same base SR and between the same parallel straight line PH and SR. Which of the following is true?

1. A.ΔPGS = ΔQHR
2. B.Parallelogram PQRS = ΔQHR
3. C.Trapezium PQXS = ΔGHR
4. D.ΔPGS = Parallelogram GHRS
5. E.Parallelogram PQRS = Parallelogram GHRS.

From the diagram below, which of the following is true?

1. A.a + b + x = 180
2. B.a = b + x
3. C.a − b = 180 − x
4. D.a + b = x + 180
5. E.a − b = x − 180.

The interior angles of a pentagon are 126°, 114°, y, 92° and 83°. Find the value of y.

1. A.85°
2. B.95°
3. C.105°
4. D.115°
5. E.125°.

Solve the inequality 3x − 8 ≥ 5x

1. A.x ≤ 4
2. B.x ≥ 1
3. C.x ≤ −4
4. D.x ≤ −1
5. E.x < 2.

Divide 3̄.6721 by 4

1. A.0.9180
2. B.1̄.4180
3. C.1.1680
4. D.1̄.1680
5. E.1.9180.

The eleventh term of an A.P. is 25 and its first term is −3. Find its common difference.

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

Find the common ratio in the G.P: log 3, log 9, log 81……….

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

Find the value of t for which 64/27 = (3/4)^t−1

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

O is the centre of the circle PQRS. PR and QS intersect at T. POR is a diameter, ∠PQT = 42° and ∠QTR = 64°. Find ∠QRT

1. A.68°
2. B.64°
3. C.42°
4. D.32°
5. E.22°.

TR is the tangent to the circle PQR with centre O. Find the size of ∠PRT

1. A.44°
2. B.46°
3. C.60°
4. D.74°
5. E.118°.

Two angles of a triangle are 41° and 49°. Which of the following is true? It is

1. A.an equilateral triangle
2. B.an isosceles triangle
3. C.a triangle with an obtuse angle
4. D.a right-angled triangle
5. E.a right-angled isosceles triangle.

Given that 1/2 log₁₀ P = 1, find the value of P

1. A.10⁴
2. B.10³
3. C.10²
4. D.10¹
5. E.10⁻¹

If two triangles are similar, which of the following is true? Their

1. A.corresponding sides are equal
2. B.corresponding angles are equal
3. C.corresponding altitudes are equal
4. D.areas are equal
5. E.perimeters are equal.

Which of the following is not necessarily true of a rectangle?

1. A.The diagonals are equal
2. B.The diagonals bisect each other
3. C.The diagonals are perpendicular
4. D.Each diagonal divides the area of the rectangle equally
5. E.Each diagonal divides the rectangle into two congruent triangles.

A chord is 5cm from the centre of a circle of diameter 26cm. Find the length of the chord

1. A.16cm
2. B.18cm
3. C.24cm
4. D.25.51cm
5. E.51.1cm.

The angle of elevation of a point T on a tower from a point U on the horizontal ground is 30°. If TU = 54m, how high is T above the horizontal ground?

1. A.108m
2. B.72m
3. C.46.3m
4. D.31.2m
5. E.27m.

Express the true bearing of 250° as a compass bearing

1. A.N20°E
2. B.S20°E
3. C.N20°W
4. D.S70°W
5. E.S70°E.

Cos 65° has the same value as

1. A.Sin 65°
2. B.Cos 25°
3. C.Cos 115°
4. D.Cos 205°
5. E.Cos 295°

Two sides of a triangle are perpendicular. If the two sides are 8cm and 6cm, calculate correct to the nearest degree, the smallest angle of the triangle.

1. A.35°
2. B.36°
3. C.37°
4. D.38°
5. E.53°.

The graph is the cumulative frequency curve for the weight distribution of 100 workers in a factory. Which of the points P, Q, R, S and T indicates the median weight?

1. A.T
2. B.S
3. C.R
4. D.Q
5. E.P.

Calculate the standard deviation of the numbers 2, 5, 6, 4 and 8

1. A.2
2. B.4
3. C.6
4. D.7
5. E.20.

What is the probability of having an odd number in a single throw of a fair die with the faces numbered 1,2,3,4,5 and 6?

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

A bag contains red, black and green identical balls. A ball is picked and replaced. The table shows the result of 100 trials. Find the experimental probability of picking a green ball.
Colour of ball: Red, Black, Green
No. of occurrences: 54, 30, 16

1. A.16
2. B.21/25
3. C.1/3
4. D.4/21
5. E.4/25.

A bag contains 3 white, 6 red 5 blue identical balls. A ball is picked at random from the bag. What is the probability that it is either white or blue?

1. A.9/14
2. B.4/7
3. C.3/7
4. D.5/14
5. E.3/14.

(a) Copy and complete the binary multiplication table
× | 10 | 11 | 100 | 101
10 | 100 | – | 1000 | –
11 | 110 | – | 1100 | –
100 | – | – | 10000 | 10100
(b) Convert 11.011_two to a number in base ten
(c) Simplify (9.6 × 10¹⁸)/(0.24 × 10⁵) and express your answer in the form P × 10^m where 1 < P < 10 and m is an integer.

(a) The 6th term of an A.P. is 35 and the 13th term is 77. Find the 20th term.
(b) The Venn diagram represents three subsets P, Q and R of the universal set U. Copy the Venn diagram. Shade and indicate the regions represented by: (i) P∩Q'∩R (ii) P'∩Q∩R'.

(a) Given that sin x = 5/13, 0° ≤ x ≤ 90°, find (cos x − 2 sin x)/(2 tan x)
(b) The diagram represents the vertical cross-section of a mountain with height NQ standing on a horizontal ground PRN. If the angles of elevation of the top Q of the mountain from P and R are 30° and 70° respectively and PR = 500m, calculate, correct to 3 significant figures: (i) |QP|; (ii) the height of the mountain.

The table below shows how a company's sales manager spent his 1995 annual salary.
Food – 30%
Rent – 18%
Car maintenance – 25%
Savings – 12%
Taxes – 5%
Others – 10%
(a) Represent this information on a pie chart
(b) Find his savings at the end of the year if his annual salary was N60,000.00

(a) Given that (5y − x)/(8y + 3x) = 1/5, find the value of x/y to two decimal places.
(b) If 3 is a root of the quadratic equation x² + bx − 15 = 0, determine the value of b. Find the other root.

(a) Use logarithm tables to evaluate (15.05 × √0.00695)/(6.95 × 10²), correct to 3 significant figures.
(b) The first 5 students to arrive in a school on a Monday morning were 2 boys and 3 girls. Of these, two were chosen at random for an assignment. Find the probability that: (i) both were boys; (ii) the two were of different sexes.

(a) Using a ruler and a pair of compasses only, construct ΔABC in which |AB| = 7cm, |BC| = 5cm and ∠ABC = 75°. Measure AC.
(b) In (a) above, locate by construction, a point D such that CD is parallel to AB and D is equidistant from points A and C. Measure ∠BAD.

(a) Solve the simultaneous equations:
log₁₀x + log₁₀y = 4
log₁₀x + 2 log₁₀y = 3
(b) The time t taken to buy fuel at a petrol station varies directly as the number of vehicles V on queue and jointly varies inversely as the number of pumps P available in the station. In a station with 5 pumps, it took 10 minutes to fuel 20 vehicles. Find (i) the relationship between t, P and V; (ii) the time it will take to fuel 50 vehicles in the station with 2 pumps; (iii) the number of pumps required to fuel 40 vehicles in 20 minutes.

The solid above is a cylinder surmounted by a hemispherical bowl. Calculate its: (a) total surface area; (b) Volume. (Take π = 22/7).

Above is the graph of the quadratic function y = ax² + bx + c where a, b and c are constants. Using the graph, find: (a)(i) The scales on both axis; (ii) The equation of the line of symmetry of the curve; (iii) The roots of the quadratic equation ax² + bx + c = 0. (b) Use the coordinates of points D, E and G to find the values of the constants a, b, and c and hence write down the quadratic function illustrated in the graph. (c) Find the greatest value of y within the range −3 ≤ x ≤ 5.

(a) PQRST is a circle with centre C. PCS is a straight line, RS//QT, |QR| = |RS| and ∠QTS = 56°. Find (i) ∠SQT (ii) ∠PQT
(b) In the diagram, points B and C are on a horizontal plane and |BC| = 30cm. A and D are points vertically above B and C respectively. |DC| = 40cm and |AB| = 26cm. Calculate the angles of depression of: (i) B from D; (ii) A from D: correct to the nearest degree.

The table below shows the mark distribution of candidates in an aptitude test for selection into the public service.
Mark (in %): 44–46, 47–49, 50–52, 53–55, 56–58, 59–61, 62–64, 65–67, 68–70, 71–73
Frequency: 2, 5, 11, 20, 26, 42, 46, 36, 9, 3
(a) Make a cumulative frequency for the distribution.
(b) Draw the cumulative frequency curve.
(c) From your graph estimate the median mark.
(d) The cut-off mark was 63%. What percentage of the candidates was selected?