WAEC Mathematics 2009 past questions and answers

Simplify: (3½ + 4⅓) ÷ (5/6 − 2/3)

1. A.1¼
2. B.8½
3. C.35
4. D.47

In a particular year, the exchange rate of Naira (₦) varies directly with the Dollar ($). If ₦1122 is equivalent to $8, find the Naira equivalent of $36.

1. A.₦8976
2. B.₦5049
3. C.₦140.25
4. D.₦31.17

If log 2 = x, log 3 = y and log 7 = z, find, in terms of x, y and z, the value of log(28/3).

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

Arrange the following numbers in descending order of magnitude: 22_three, 34_five, 21_six.

1. A.21_six, 22_three, 34_five
2. B.21_six, 34_five, 22_three
3. C.22_three, 34_five, 21_six
4. D.34_five, 21_six, 22_three

Find the value to which N3000.00 will amount in 5 years at 6% per annum simple interest.

1. A.₦3,900.00
2. B.₦3,750.00
3. C.₦3,600.00
4. D.₦3,300.00

Express the square root of 0.000144 in the standard form.

1. A.1.2 × 10⁻⁴
2. B.1.2 × 10⁻³
3. C.1.2 × 10⁻²
4. D.1.2 × 10⁻¹

Two sets are disjoint if

1. A.they are both empty
2. B.their union is an empty set
3. C.their intersection is an empty set
4. D.one of them is a subset of the other.

Solve the following simultaneous equations: 2x + 3y = 7, x + 5y = 0.

1. A.x = 5, y = −1
2. B.x = 1/5, y = −1
3. C.x = −1/5, y = 1
4. D.x = −5, y = 1

If 3/2x − 2/3x = 4, solve for x.

1. A.4/5
2. B.4/13
3. C.5/24
4. D.13/24

The following is the graph of a quadratic function. Find the co-ordinates of point P.

1. A.(0, 4)
2. B.(4, 0)
3. C.(0, −4)
4. D.(−4, 0)

The following is the graph of a quadratic function. Find the values of x when y = 0.

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

Five bottles of Fanta and two packets of biscuits cost Gh¢6.00. Three bottles of Fanta and four packets of biscuits cost Gh¢5.00. Find the cost of a bottle of Fanta.

1. A.Gh¢0.50
2. B.Gh¢1.00
3. C.Gh¢1.50
4. D.Gh¢5.00

Factorize x² − 2x − 3xy + 6y completely.

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

Which of the following illustrates the solution of (3x + 4)/2 < x + 3?

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

The diameter of a bicycle wheel is 42 cm. If the wheel makes 16 complete revolutions, what will be the total distance covered by the wheel? [Take π = 22/7]

1. A.672 cm
2. B.1056 cm
3. C.2112 cm
4. D.4224 cm

PQRS is a trapezium. QR//PS, |PQ| = 5 cm, |QR| = 6 cm, |PS| = 10 cm and angle QPS = 42°. Calculate the perpendicular distance between the parallel sides.

1. A.3.35 cm
2. B.3.72 cm
3. C.4.50 cm
4. D.4.62 cm

PQRS is a trapezium. QR//PS, |PQ| = 5 cm, |QR| = 6 cm, |PS| = 10 cm and angle QPS = 42°. Calculate, correct to the nearest cm², the area of the trapezium.

1. A.27 cm²
2. B.30 cm²
3. C.36 cm²
4. D.37 cm²

In the diagram, |TP| = 12 cm and it is 6 cm from O, the centre of the circle. Calculate ∠TOP.

1. A.120°
2. B.90°
3. C.60°
4. D.45°

The interior angles of a pentagon are (2x + 5)°, (x + 20)°, x°, (3x − 20)° and (x + 15)°. Find the value of x.

1. A.80°
2. B.70°
3. C.65°
4. D.40°

In the diagram, IG is parallel to JE, JÊF = 120° and FĤG = 130°. Find the angle marked t.

1. A.40°
2. B.70°
3. C.80°
4. D.100°

If M and N are two fixed points in a plane, find the locus L = {P : PM = PN}.

1. A.A line equal to MN
2. B.A line parallel to MN
3. C.Perpendicular bisector of MN
4. D.A circle centre P, radius MN.

Find the value of x in the diagram.

1. A.50°
2. B.30°
3. C.22°
4. D.17°

In the diagram, |SQ| = 4 cm, |PT| = 7 cm, |TR| = 5 cm and ST//QR. If |SP| = x cm, find the value of x.

1. A.5.6
2. B.6.5
3. C.6.6
4. D.6.8

Given that sin 60° = √3/2 and cos 60° = 1/2, evaluate: (1 − sin 60°)/(1 + cos 60°)

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

Use the diagram to answer this question. Find the bearing of X from Y.

1. A.300°
2. B.240°
3. C.120°
4. D.60°

Use the diagram to answer this question. If |XY| = 50 m, how far east of X is Y?

1. A.25.5 m
2. B.40.6 m
3. C.40.8 m
4. D.43.3 m

In an examination, Kofi scored x % in Physics, 50% in Chemistry and 70 % in Biology. If his mean score for the three subjects was 55 %, find x.

1. A.40
2. B.45
3. C.55
4. D.60

What is the median of the following scores: 22, 41, 35, 63, 82, 74?

1. A.82
2. B.52
3. C.49
4. D.22

Express 2.7864 × 10⁻³ to two significant figures.

1. A.0.28
2. B.0.27
3. C.0.0028
4. D.0.0027

If 9^2x = (1/3)(27^x), find x.

1. A.2
2. B.1
3. C.−1
4. D.−2

If 85% of x is ₦3230, what is the value of x?

1. A.₦2745.50
2. B.₦3714.50
3. C.₦3800.00
4. D.₦4845.00

The capacity of a water tank is 1,800 litres. If the tank is in the form of a cuboid with base 600 cm by 150 cm, find the height of the tank.

1. A.2 cm
2. B.20 cm
3. C.200 cm
4. D.2000 cm

An arc of a circle subtends an angle of 60° at the centre. If the radius of the circle is 3 cm, find, in terms of π, the length of the arc.

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

Solve: (2x + 1)/6 − (3x − 1)/4 = 0.

1. A.1
2. B.1/5
3. C.−1/5
4. D.−1

If x is a positive integer, list the values of x which satisfy the equations 3x − 4 < 6 and x − 1 > 0.

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

If c and k are the roots of 6 − x − x² = 0, find c + k.

1. A.2
2. B.1
3. C.−1
4. D.−3

In the diagram, angle 200° is subtended at the centre of the circle. Find the value of x.

1. A.30°
2. B.50°
3. C.80°
4. D.100°

Each of the interior angles of a regular polygon is 140°. Calculate the sum of all the interior angles of the polygon.

1. A.1080°
2. B.1260°
3. C.1800°
4. D.2160°

A bucket holds 10 litres of water. How many buckets of water will fill a reservoir of size 8 m × 7 m × 5 m. (1 litre = 1000 cm³).

1. A.28
2. B.280
3. C.2800
4. D.28000

A box contains black, white and red identical balls. The probability of picking a black ball at random from the box is 3/10 and the probability of picking a white ball at random is 2/5. If there are 30 balls in the box, how many of them are red?

1. A.3
2. B.7
3. C.9
4. D.12

The pie chart shows the distribution of 4320 students who graduated from four Departments in a University. How many students graduated from the Science Department?

1. A.840
2. B.864
3. C.920
4. D.960

The pie chart shows the distribution of 4320 students who graduated from four Departments in a University. If a student is picked at random from the four departments, what is the probability that he is not from the Education Department?

1. A.3/10
2. B.2/9
3. C.5/18
4. D.7/10

Simplify: ½√32 − √18 + √2.

1. A.0
2. B.√2
3. C.2√2
4. D.4√2

From the diagram, which of the following statements is/are correct?
I. XQ is a radius of a circle centre Q.
II. |XQ| = |QY|
III. |QX| = |XY|

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

Find the value of X in the diagram.

1. A.50°
2. B.60°
3. C.70°
4. D.80°

The angles of a triangle are (x + 10)°, (2x − 40)° and (3x − 90)°. Which of the following accurately describes the triangle?

1. A.It is a scalene triangle
2. B.It is a right angled isosceles triangle
3. C.It is an equilateral triangle
4. D.It is an isosceles triangle but not right angled.

Which shaded region in the following diagrams represents (P ∪ Q) ∩ R?

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

Simplify: (x − 3y)² − (x + 3y)².

1. A.2(x + 3y)
2. B.2(x − 3y)
3. C.−12xy
4. D.6xy

Find the quadratic equation whose roots are −1/2 and 3.

1. A.2x² − 2x + 3 = 0
2. B.2x² − 2x − 3 = 0
3. C.2x² − 5x + 3 = 0
4. D.2x² − 5x − 3 = 0

(a) Given that (√3 − 5√2)(√3 + √2) = a + b√6, find a and b.
(b) If (2^1−y × 2^y−1)/2^y+2 = 8^2−3y, find y.

(a) If 9 cos x° − 7 = 1 and 0° ≤ x ≤ 90°, find x.
(b) Given that x is an integer, find the three greatest values of x which satisfy the inequality 7x < 2x − 13.

The table shows the number of children per family in a community.
No. of children: 0, 1, 2, 3, 4, 5
No. of families: 3, 5, 7, 4, 3, 2
(a) Find the: (i) mode; (ii) third quartile; (iii) probability that a family has at least 2 children.
(b) If a pie chart were to be drawn for the data, what would be the sectorial angle representing families with one child?

(a) Out of 30 candidates applying for a post, 17 have degrees, 15 diplomas and 4 neither degree nor diploma. How many of them have both?
(b) In triangle PQR, M and N are points on the sides PQ and PR respectively such that MN is parallel to QR. If ∠PRQ = 75°, PN = QN and ∠PNQ = 125°, determine (i) ∠NQR; (ii) ∠NPM.

In the diagram, ABCDEF is a triangular prism. ∠ABC = ∠DEF = 90°, |AB| = 24 cm, |BC| = 7 cm and |CD| = 40 cm. Calculate: (a) |AC|; (b) the total surface area of the prism.

(a) If log 5 = 0.6990, log 7 = 0.8451 and log 8 = 0.9031, calculate: log ((35 × 49)/(40 ÷ 56))
(b) For a musical show, x children were present. There were 60 more adults than children. An adult paid D5 and a child D2. If a total of D1280 was collected, calculate the (i) value of x; (ii) ratio of the number of children to the number of adults; (iii) average amount paid per person; (iv) percentage profit if the organisers spent D720 on the show.

(a) A woman looking out from the window of a building at a height of 30 m, observed that the angle of depression of the top of a flag pole was 44°. If the foot of the pole is 25 m from the foot of the building and on the same horizontal ground, find, correct to the nearest whole number, the (i) angle of depression of the foot of the pole from the woman; (ii) height of the flag pole.
(b) In the diagram, O is the centre of the circle, ∠OQR = 32° and ∠TPQ = 15°. Calculate: (i) ∠QPR; (ii) ∠TQO.

The marks scored by 50 students in a Geography examination are as follows:
60 54 40 67 53 73 37 55 62 43
44 69 39 32 45 58 48 67 39 51
46 59 40 52 61 48 23 60 59 47
65 58 74 47 40 59 68 51 50 50
71 51 26 36 38 70 46 40 51 42
(a) Using class intervals 21 − 30, 31 − 40, …, prepare a frequency distribution table.
(b) Calculate the mean mark of the distribution.
(c) What percentage of the students scored more than 60%?

(a) Simplify (x + 2)/(x − 2) − (x + 3)/(x − 1)
(b) The graph of the equation y = Ax² + Bx + C passes through the points (0, 0), (1, 4) and (2, 10). Find the: (i) value of C; (ii) values of A and B; (iii) co-ordinates of the other point where the graph cuts the x-axis.

(a) Using ruler and a pair of compasses only, construct: (i) quadrilateral PQRS such that |PQ| = 10 cm, |QR| = 8 cm, |PS| = 6 cm, ∠PQR = 60° and ∠QPS = 75°; (ii) the locus l₁ of points equidistant from QR and RS; (iii) locus l₂ of points equidistant from R and S.
(b) Measure |RS|.

(a) A circle is inscribed in a square. If the sum of the perimeter of the square and the circumference of the circle is 100 cm, calculate the radius of the circle. [Take π = 22/7]
(b) A rope 60 cm long is made to form a rectangle. If the length is 4 times its breadth, calculate, correct to one decimal place, the (i) length; (ii) diagonal of the rectangle.

(a) Copy and complete the table of values for y = sin x + 2 cos x, correct to one decimal place.
x: 0°, 30°, 60°, 90°, 120°, 150°, 180°, 210°, 240°
y: __, 2.2, __, __, __, −1.2, −2.0, __, −1.9
(b) Using a scale of 2 cm to 30° on the x-axis and 2 cm to 0.5 units on the y-axis, draw the graph of y = sin x + 2 cos x for 0° ≤ x ≤ 240°.
(c) Use your graph to solve the equation: (i) sin x + 2 cos x = 0; (ii) sin x = 2.1 − 2 cos x.
(d) From the graph, find y when x = 171°.

(a) How many numbers between 75 and 500 are divisible by 7?
(b) The 8th term of an Arithmetic Progression (A.P) is 5 times the third term while the 7th term is 9 greater than the 4th term. Write the first five terms of the A.P.

(Questions 14 and 15 are for candidates in Ghana, Sierra Leone and The Gambia only.)
(a) Copy and complete the multiplication table modulo 5 on the set {1, 2, 3, 4}.
(b) From your table; (i) solve the expression 2n * 4 ≡ 3; (ii) find the value of n for which 2 * (3 * n) ≡ 2.
(c) The functions f and g are defined as f : x → x − 2 and g : x → 2x² − 1. Solve: (i) f(x) = g(−1/2); (ii) f(x) + g(x) = 0.

(a) P(7, 4) is a vertex of triangle PQR. If QP = (3, 5) and PR = (−3, 4), find: (i) the co-ordinates of Q; (ii) PN where N is the midpoint of QR.
(b) A straight line passes through the points (1, 4) and (3, 0). Find the (i) gradient; (ii) equation of the line.