WAEC Mathematics 2007 past questions and answers

Evaluate (111_two)² and leave your answer in base 2.

1. A.111001_two
2. B.110001_two
3. C.101001_two
4. D.10010_two

Find the LCM of 2³ × 3 × 5², 2 × 3² × 5 and 2² × 3³ × 5.

1. A.2² × 3³ × 5²
2. B.2³ × 3³ × 5
3. C.2² × 3² × 5²
4. D.2³ × 3³ × 5²

Simplify (0.3 × 10⁵) ÷ (0.4 × 10⁷), leaving your answer in the standard form.

1. A.7.5 × 10⁻⁴
2. B.7.5 × 10⁻³
3. C.7.5 × 10⁻²
4. D.7.5 × 10⁻¹

If p ∝ 1/q, which of the following is true?

1. A.q ∝ p²
2. B.q ∝ 1/p²
3. C.q ∝ √p
4. D.q ∝ 1/p

Simplify 3√45 − 12√5 + 16√20, leaving your answer in surd form.

1. A.29√5
2. B.14√15
3. C.12√15
4. D.11√5

Which of the following statements is true for the set P = {−3.2 ≤ x < 5} where x is an integer?

1. A.Least value of x is −3.2
2. B.Least value of x is −3
3. C.Greatest value of x is 4.9
4. D.Greatest value of x is 5

Simplify: 3x³/(3x)³

1. A.1
2. B.1/3
3. C.1/9
4. D.1/27

N140,000 is shared between Abu, Kayode and Uche. Abu has twice as much as Kayode, and Kayode has twice as much as Uche. What is Kayode's share?

1. A.N80,000
2. B.N40,000
3. C.N20,000
4. D.N10,000

I am x years old and my brother is 3 years older. How old was my brother last year?

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

If x = 3, y = 2 and z = 4, what is the value of 3x² − 2y + z?

1. A.17
2. B.27
3. C.35
4. D.71

Solve the simultaneous equations: x + y = 2 and 3x − 2y = 1.

1. A.x = 2 and y = 1
2. B.x = 1 and y = 1
3. C.x = 1 and y = 2
4. D.x = −1 and y = 1

If 8^x+1 = 1/4, find x.

1. A.−5/3
2. B.−1
3. C.−1/3
4. D.1/3

The area of a square field is 110.25 m². Find the cost of fencing it round at N75.00 per metre.

1. A.N1,575.00
2. B.N3,150.00
3. C.N4,734.30
4. D.N8,268.75

A chord of length 6 cm is drawn in a circle of radius 5 cm. Find the distance of the chord from the centre of the circle.

1. A.2.5 cm
2. B.3.0 cm
3. C.3.5 cm
4. D.4.0 cm

A sector of a circle of radius 14 cm containing an angle 60° is folded to form a cone. Calculate the radius of the base of the cone.

1. A.5½ cm
2. B.4⅔ cm
3. C.3½ cm
4. D.2⅓ cm

In the diagram, |LN| = 4 cm, LN̂M = 90° and tan y = 2/3. What is the area of the ΔLMN?

1. A.24 cm²
2. B.12 cm²
3. C.10 cm²
4. D.6 cm²

Find the volume of a solid cylinder with base radius 10 cm and height 14 cm. (Take π = 22/7)

1. A.220 cm³
2. B.880 cm³
3. C.1400 cm³
4. D.4400 cm³

From the diagram, find the value of x.

1. A.80°
2. B.70°
3. C.55°
4. D.35°

Find the value of x in the diagram.

1. A.281°
2. B.269°
3. C.201°
4. D.179°

Each interior angle of a regular polygon is 162°. How many sides has the polygon?

1. A.8
2. B.12
3. C.16
4. D.20

From the diagram, find the value of x.

1. A.40
2. B.30
3. C.25
4. D.20

In the diagram, |SP| = |SR| and ∠PRS = 50°. Calculate ∠PQR.

1. A.120°
2. B.110°
3. C.100°
4. D.80°

In the diagram, O is the centre of the circle and ∠PQR = 106°. Find the value of y.

1. A.16
2. B.37
3. C.74
4. D.127

In a ΔPQR, ∠PQR = ∠PRQ = 45°. Which of the following statements is/are correct?
I. ΔPQR is an equilateral triangle
II. ΔPQR is an isosceles triangle
III. ΔPQR is a right-angled triangle

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

The table gives the distribution of the marks of a number of students in a test.
Mark: 1, 2, 3, 4, 5, 6
Frequency: 5, 3, 6, 4, 2, 5
Find the mode of the distribution.

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

If the probability of an event occurring is x, what is the probability of the event not occurring?

1. A.1 − x
2. B.x − 1
3. C.0
4. D.1/x

The table shows the ages (in years) of twenty children chosen at random from a community.
Age (years): 1, 2, 3, 4, 5
Number of children: 2, 3, 5, 6, 4
What is the mean age?

1. A.4.46 years
2. B.3.35 years
3. C.3.30 years
4. D.3.00 years

The table shows the ages (in years) of twenty children chosen at random from a community.
Age (years): 1, 2, 3, 4, 5
Number of children: 2, 3, 5, 6, 4
What is the median of the distribution?

1. A.3.5 years
2. B.3.0 years
3. C.2.5 years
4. D.2.0 years

Divide the sum of 8, 6, 7, 2, 0, 4, 7, 2, 3 by their mean.

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

Q is 32 km away from P on a bearing 042° and R is 25 km from P on a bearing of 132°. Calculate the bearing of R from Q.

1. A.122°
2. B.184°
3. C.190°
4. D.226°

In the diagram, |PQ| = 4 cm, |QR| = 6 cm, |RS| = 12 cm and ∠QRS = 90°. Find the value of x.

1. A.27
2. B.26
3. C.18
4. D.13

The bearing of a point P from another point Q is 310°. If |PQ| = 200 m, how far west of Q is P?

1. A.128.6 m
2. B.153.2 m
3. C.167.8 m
4. D.187.9 m

Find the value of a if log₁₀a + log₁₀a² = 0.9030.

1. A.4.0
2. B.2.0
3. C.1.6
4. D.0.0

A messenger was paid N2.50 an hour during the normal working hours and N4.00 an hour during overtime. If he received N31.00 for 10 hours work, how many hours are for overtime?

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

At what rate per cent per annum will N520.00 yield a simple interest of N39.00 in three years?

1. A.4%
2. B.3½%
3. C.3%
4. D.2½%

If the ratio x : y = 3 : 5 and y : z = 4 : 7, find the ratio x : y : z.

1. A.15 : 28 : 84
2. B.12 : 20 : 35
3. C.3 : 5 : 4
4. D.5 : 4 : 7

The Venn diagram shows the choice of food of a number of visitors to a canteen. If there were 35 visitors in all, find the value of x.

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

The Venn diagram shows the choice of food of a number of visitors to a canteen. How many people took at least two kinds of food?

1. A.10
2. B.12
3. C.15
4. D.17

PQR is an equilateral triangle with side 2√3 cm. Calculate its height.

1. A.1.7 cm
2. B.3.0 cm
3. C.3.2 cm
4. D.3.9 cm

Which of the following is a factor of 2 − x − x²?

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

Make w the subject of the relation (a + bc)/(wd + f) = g

1. A.(a + bc − fg)/dg
2. B.(a − bc + fg)/fg
3. C.(a + bc − f)/dg
4. D.(a + bc − dg)/dg

Expand the expression (3a − xy)(3a + xy).

1. A.9a² − x²y²
2. B.9a² + x²y²
3. C.9a² − xy
4. D.9a² + x²y

For what range of values of x is 4x − 3(2x − 1) > 1?

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

Find the smallest value of k such that 2² × 3³ × 5 × k is a perfect square.

1. A.3
2. B.5
3. C.15
4. D.30

Two circles have radii 16 cm and 23 cm. What is the difference between their circumferences? (Take π = 22/7)

1. A.244.92 cm
2. B.149.92 cm
3. C.44.00 cm
4. D.43.96 cm

The volume of a cylinder is 1200 cm³ and the area of its base is 150 cm². Find the height of the cylinder.

1. A.80.00 cm
2. B.8.00 cm
3. C.0.80 cm
4. D.0.08 cm

In the diagram, |XR| = 4 cm, |RZ| = 12 cm, |SR| = n, |YZ| = m and SR || YZ. Find m in terms of n.

1. A.m = 2n
2. B.m = 3n
3. C.m = 4n
4. D.m = 5n

In the diagram, O is the centre of the circle and PQ is a diameter. Triangle RSO is an equilateral triangle of side 4 cm. Find the area of the shaded region.

1. A.43.36 cm²
2. B.32.07 cm²
3. C.18.21 cm²
4. D.6.93 cm²

(a) Evaluate, without using mathematical tables or calculator, (3.69 × 10⁵) ÷ (1.64 × 10⁻³), leaving your answer in the standard form.
(b) A man invested N20,000 in bank A and N25,000 in bank B at the beginning of a year. Bank A pays simple interest at a rate of y% per annum and B pays 1.5y% per annum. If his total interest at the end of the year from the two banks was N4,600, find the value of y.

(a) Simplify: (x² − 8x + 16)/(x² − 7x + 12)
(b) If 1/2, 1/x, 1/3 are successive terms of an arithmetic progression (A.P.), show that (2 − x)/(x − 3) = 2/3.

The diagram shows the cross-section of a railway tunnel. If |AB| = 100 m and the radius of the arc is 56 m, calculate, correct to the nearest metre, the perimeter of the cross-section.

Y is 60 km away from X on a bearing of 135°. Z is 80 km away from X on a bearing of 225°. Find the: (a) distance of Z from Y; (b) bearing of Z from Y.

Out of the 24 apples in a box, 6 are bad. If three apples are taken from the box at random, with replacement, find the probability that: (a) the first two are good and the third is bad; (b) all the three are bad; (c) all the three are good.

(a) Simplify: (3 1/12 + 7/8)/(2 1/4 − 1/6)
(b) If p = m/2 − n²/5m, (i) make n the subject of the relation; (ii) find, correct to three significant figures, the value of n when p = 14 and m = −8.

(a) With the aid of four-figure logarithm tables, evaluate (0.004592)^1/3.
(b) If log₁₀y + 3log₁₀x = 2, express y in terms of x.
(c) Solve the equations: 3x − 2y = 21; 4x + 5y = 5.

(a) A cylinder with radius 3.5 cm has its two ends closed. If the total surface area is 209 cm², calculate the height of the cylinder. (Take π = 22/7)
(b) In the diagram, O is the centre of the circle and ABC is a tangent at B. If BD̂F = 66° and DB̂C = 57°, calculate, (i) EB̂F (ii) BĜF.

(a) Using a ruler and a pair of compasses only, construct: (i) a triangle PQR such that |PQ| = 10 cm, |QR| = 7 cm and PQ̂R = 90°; (ii) the locus l₁ of points equidistant from Q and R; (iii) the locus l₂ of points equidistant from P and Q.
(b) Locate the point O equidistant from P, Q and R.
(c) With O as centre, draw the circumcircle of the triangle PQR.
(d) Measure the radius of the circumcircle.

(a) Simplify (x² − y²)/(3x + 3y)
(b) In the diagram, PQRS is a rectangle. |PK| = 15 cm, |SK| = |KR| and PK̂S = 37°. Calculate, correct to three significant figures: (i) |PS|; (ii) |SK|; (iii) the area of the shaded portion.

(a) In the diagram, AOB is a straight line, ∠AOC = 3(x + y)°, ∠COB = 45°, ∠AOD = (5x + y)° and ∠DOB = y°. Find the values of x and y.
(b) From two points on opposite sides of a pole 33 m high, the angles of elevation of the top of the pole are 53° and 67°. If the two points and the base of the pole are on the same horizontal level, calculate, correct to three significant figures, the distance between the two points.

(a) The 3rd and 8th terms of an arithmetic progression (A.P.) are −9 and 26 respectively. Find the: (i) common difference; (ii) first term.
(b) In the diagram, PQ||YZ, |XP| = 2 cm, |PY| = 3 cm, |PQ| = 6 cm and the area of ΔXPQ = 24 cm². Calculate the area of the trapezium PQZY.

In a college, the number of absentees recorded over a period of 30 days was as shown in the frequency distribution table.
Number of absentees: 0–4, 5–9, 10–14, 15–19, 20–24
Number of days: 1, 5, 10, 9, 5
Calculate the: (a) mean; (b) standard deviation, correct to two decimal places.

(Questions 14 and 15 are for candidates in Ghana only.)
(a) Using a scale of 2 cm to 4 units on both axes, draw on a graph sheet, two perpendicular axes Ox and Oy for the intervals −16 ≤ x ≤ 16, −16 ≤ y ≤ 16.
(b) Draw the triangle ABC with the vertices A(2, 2), B(8, 2) and C(6, 6).
(c) Draw the image ΔA₁B₁C₁ of ΔABC through a rotation of 180° about the origin where A → A₁, B → B₁ and C → C₁.
(d) Draw the image ΔA₂B₂C₂ of ΔABC under the translation by the vector (−8, 8) where A → A₂, B → B₂ and C → C₂.
(e) Draw the image ΔA₃B₃C₃ of the ΔA₁B₁C₁ under the reflection in the line x − 2 = 0, where A₁ → A₃, B₁ → B₃ and C₁ → C₃.
(f) Describe the transformation that will map ΔABC onto ΔA₃B₃C₃.

(a) Given that f(x) = 2x − 1 and g(x) = x² + 1: (i) find f(1 + x); (ii) find the range of values of x for which f(x) < −3; (iii) simplify f(x) − g(x).
(b) Given that A(1, 3), B(−2, −1) and C(2, 3m) where m is a constant; find: (i) |BA|; (ii) the value of m if BC = (4, −5).