WAEC Mathematics 2016 past questions and answers

If 23_x + 101_x = 130_x, find the value of x.

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

Simplify: (¾ − ⅔) × 1⅕.

1. A.1/60
2. B.5/72
3. C.1/10
4. D.1⁷/₁₀

Simplify: (10√3/√5 − √15)²

1. A.75.00
2. B.15.00
3. C.8.66
4. D.3.87

The distance, d, through which a stone falls from rest varies directly as the square of the time, t, taken. If the stone falls 45 cm in 3 seconds, how far will it fall in 6 seconds?

1. A.90 cm
2. B.135 cm
3. C.180 cm
4. D.225 cm

Which of the following is a vaild conclusion from the premise: 'Nigerian footballers are good footballers'?

1. A.Joseph plays football in Nigeria therefore he is a good footballer.
2. B.Joseph is a good footballer therefore he is a Nigerian footballer.
3. C.Joseph is a Nigerian footballer therefore he is a good footballer.
4. D.Joseph plays good football therefore he is a Nigerian footballer.

On a map, 1 cm represents 5 km. Find the area on the map that respresents 100 km².

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

Simplify: (3ⁿ⁻¹ × 27ⁿ⁺¹)/81ⁿ

1. A.3²ⁿ
2. B.9
3. C.3ⁿ
4. D.3ⁿ⁺¹

What sum of money will amount to D10,400.00 in 5 years at 6% simple interest?

1. A.D8,000.00
2. B.D10,000.00
3. C.D12,000.00
4. D.D16,000.00

Which of the following number lines illustrates the solution of the inequality 4 ≤ ⅓(2x − 1) < 5?

1. A.Open circle at 6½ with arrow to the left, and open circle at 8 with arrow to the right
2. B.Closed circles at 6½ and 8
3. C.Open circles at 6½ and 8
4. D.Closed circle at 6½ and open circle at 8

The roots of a quadratic equation are 4/3 and −3/7. Find the equation.

1. A.21x² − 19x − 12 = 0
2. B.21x² + 37x − 12 = 0
3. C.21x² − x + 12 = 0
4. D.21x² + 7x − 4 = 0

Find the values of y for which the expression (y² − 9y + 18)/(y² + 4y − 21) is undefined

1. A.6, −7
2. B.3, −6
3. C.3, −7
4. D.−3, −7

Simplify: 2/(1 − x) − 1/x.

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

Make s the subject of the relation: p = s + sm²/nr

1. A.s = mrp/(nr + m²)
2. B.s = (nr + m²)/nrp
3. C.s = nrp/(mr + m²)
4. D.s = nrp/(nr + m²)

Factorize: (2x + 3y)² − (x − 4y)².

1. A.(3x − y)(x + 7y)
2. B.(3x + y)(2x − 7y)
3. C.(3x + y)(x − 7y)
4. D.(3x − y)(2x + 7y)

The curved surface area of a cylinder 5 cm high, is 110 cm². Find the radius of its base. [Take π = 22/7]

1. A.2.6 cm
2. B.3.5 cm
3. C.3.6 cm
4. D.7.0 cm

The volume of a pyramid with height 15 cm is 90 cm³. If its base is a rectangle with dimensions x cm by 6 cm, find the value of x.

1. A.3
2. B.5
3. C.6
4. D.8

In the diagram, YW is a tangent to the circle at X, |UV| = |VX| and ∠VXW = 50°. Find the value of ∠UXY

1. A.70°
2. B.80°
3. C.105°
4. D.110°

In the diagram, PF, QT, RG intersect at S and PQ/RG. If ∠SPQ = 113° and ∠RST = 22°, find ∠PSQ.

1. A.22°
2. B.45°
3. C.67°
4. D.89°

In the diagram, O, is the centre of circle, ∠XOZ = (10m)° and ∠XWZ = m°. Calculate the value of m.

1. A.30
2. B.36
3. C.40
4. D.72

Kweku walked 8 m up a slope and was 3 m above the ground. If he walks 12 m further up the slope, how far above the ground will he be?

1. A.4.5 m
2. B.6.0 m
3. C.7.5 m
4. D.9.0 m

In the diagram, TS is a tangent to the circle at S, |PR| = |RS| and ∠PQR = 117°. Calculate ∠PST.

1. A.54°
2. B.44°
3. C.34°
4. D.27°

In the diagram, PR/SV/WY, TX/QY, ∠PQT = 48° and ∠TXW = 60°. Find ∠TQU.

1. A.120°
2. B.108°
3. C.72°
4. D.60°

A straight line passes through the points P(1,2) and Q(5,8). Calculate the gradient of the line PQ

1. A.3/5
2. B.⅔
3. C.3/2
4. D.5/3

A straight line passes through the points P(1,2) and Q(5,8). Calculate the length PQ

1. A.4√11
2. B.4√10
3. C.2√17
4. D.2√13

In the diagram, TX is prependicular to UW, |UX| = 1 cm and |TX| = |WX| = √3 cm. Find ∠UTW.

1. A.135°
2. B.105°
3. C.75°
4. D.60°

If cos θ = x and sin 60° = x + 0.5, 0° < θ < 90°, find, correct to the nearest degree, the value of θ.

1. A.66°
2. B.67°
3. C.68°
4. D.69°

The table shows the ages of students in a club.
Age (Years): 13, 14, 15, 16, 17
Frequency: 10, 24, 8, 5, 3
How many student are in the club?

1. A.50
2. B.55
3. C.60
4. D.65

The table shows the ages of students in a club.
Age (Years): 13, 14, 15, 16, 17
Frequency: 10, 24, 8, 5, 3
Find the median age:

1. A.13
2. B.14
3. C.15
4. D.16

The figure is a pie chart which represents the expenditure of a family in a year. If the total income of the family was Le 10,800,000.00, how much was spent on food?

1. A.Le 2,250,000.00
2. B.Le 2,700,000.00
3. C.Le 3,600,000.00
4. D.Le 4,500,000.00

A fair die is thrown two times. What is the probability that the sum of the score is at least 10?

1. A.5/36
2. B.1/6
3. C.5/18
4. D.⅔

The marks of eight students in a test are: 10, 4, 5, 3, 14, 16 and 7. Find the range.

1. A.16
2. B.14
3. C.13
4. D.11

If log₂(3x − 1) = 5, find x.

1. A.2.00
2. B.3.67
3. C.8.67
4. D.11.00

A sphere of radius r cm has the same volume as a cylinder of radius 3 cm and height 4 cm. Find the value of r.

1. A.⅔
2. B.2
3. C.3
4. D.6

Express 1975 correct to 2 significant figures.

1. A.20
2. B.1,900
3. C.1,980
4. D.2,000

In the diagram, MOPQ is a trapezium with QP//MO, MQ//NP, NQ//OP, |QP| = 9 cm and the height of ΔQNP = 6 cm, calculate the area of the trapezium.

1. A.96 cm²
2. B.90 cm²
3. C.81 cm²
4. D.27 cm²

The perimeter of a sector of a circle of radius 21 cm is 64 cm. Find the angle of the sector. [Take π = 22/7]

1. A.70°
2. B.60°
3. C.55°
4. D.42°

Determine M′ ∩ N from the Venn diagram.

1. A.{f, g}
2. B.{e}
3. C.{c, f, g}
4. D.{e, f, g}

If 20 (mod 9) is equivalent to y (mod 6), find y.

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

Simplify: ((p − r)² − r²)/(2p² − 4pr)

1. A.½
2. B.p − 2r
3. C.1/(p − 2r)
4. D.2p/(p − 2r)

In the diagram, O is the centre of the circle, ∠QPS = 100°, ∠PSQ = 60° and ∠QSR = 80°. Calculate ∠SQR.

1. A.20°
2. B.40°
3. C.60°
4. D.80°

A bag contains 5 red and 4 blue identical balls. If two balls are selected at random from the bag, one after the other, with replacement, find the probability that the first is red and the second blue.

1. A.2/9
2. B.5/18
3. C.20/81
4. D.5/9

Find the next three terms of the sequence: 0, 1, 1, 2, 3, 5, 8,…

1. A.13, 19, 23
2. B.9, 11, 13
3. C.11, 15, 19
4. D.13, 21, 34

Find the lower quartile of the distribution illustrated by the cumulative frequency curve.

1. A.17.5
2. B.19.0
3. C.27.5
4. D.28.0

The ratio of the exterior angle to the interior angle of a regular polygon is 1:11. How many sides has the polygon?

1. A.30
2. B.24
3. C.18
4. D.12

Halima is n years old. Her brother's age is 5 years more than half of her age. How old is her brother?

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

In the diagram, MN is a chord of a circle KMN centre O and radius 10 cm. If ∠MON = 140°, find correct to the nearest cm, the length of the chord MN.

1. A.19 cm
2. B.18cm
3. C.17 cm
4. D.12 cm

From the diagram, which of the following is true?

1. A.m + n + p = 180°
2. B.m + n = 180°
3. C.m − p + n
4. D.n = m + p

(a) Without using Mathematical tables or calculators, evaluate: (0.09 × 1.21)/(3.3 × 0.00025), leaving the answer in standard form (Scientific Notation)
(b) A principal of GH¢5,600 was deposited for 3 years at compound interest. If the interest earned was GH¢1,200.00, find, correct to 3 significant figures, the interest rate per annum.

(a) Solve: 7(x + 4) − ⅔(x − 6) ≤ 2[x − 3(x + 5)].
(b) A transport company has a total 20 vehicles made up of tricycles and taxicabs. Each tricycle carries 2 passengers while each taxicab carries 4 passengers. If the 20 vehicles carry a total of 66 passengers at a time, how many tricycles does the company have?

(a) In the diagram, ∠RTS = 28°, ∠VRM = 46°, MQ is a tangent to the circle VRSTU at the point R. Find ∠VUS.
(b) A cylindrical tin, 7 cm high, is closed at one end. If its total surface area is 462 cm², calculate its radius. [Take π = 22/7]

The table shows the outcome when a die is thrown a number of times.
Scores: 1, 2, 3, 4, 5, 6
Frequency: 25, 30, x, 28, 40, 32
If the probability of obtaining a 3 is 0.225: (a) how many times was the die thrown? (b) calculate the probability that a trial chosen at random gives a score of an even number or a prime number.

(a) In the diagram, PQST is a parallelogram, PQR is a straight line, |TS| = 8 cm, |SM| = 6 cm and area of triangle PSR = 36 cm². Find the value of |QR|
(b) A tree and a flagpole are on the same horizontal ground. A bird on top of the tree observes the top and bottom of the flagpole below it at angles of 45° and 60° respectively. If the tree is 10.65 m high, calculate, correct to 3 significant figures, the height of the flagpole.

(a) Find the sum of the Arithmetic Progression (AP) 1, 3, 5, … 101.
(b) Out of the 95 travellers interviewed, 7 travelled by bus and train only, 3 by train and car only and 8 travelled by all three means of transport. The number, x, of travellers who travelled by bus only was equal to the number who travelled by bus and car only. If 47 people travelled by bus and 30 by train: (i) represent this information in a Venn diagram; (ii) calculate the I. value of x; II. number who travelled by at least two means.

(a) Using completing the squares method, solve, correct to 2 decimal places, (x − 2)/4 = (x + 2)/2x.
(b) In the diagram, PQRST is a circle with centre O. If PS is a diameter, RS//QT, |QR| = |RS| and ∠QTS = 52°, find: (i) ∠SQT; (ii) ∠PQT.

(a) In the diagram, ∠KLM = x, ∠LMK = y, ∠KJH = r and ∠KGF = 110°. If 2x = r = y, find the value of x.
(b) Ten boys and twelve girls collected donations for a project. The total amount colected by the boys was N600.00 greater than that collected by the girls. If the average collection of the boys was N100.00 greater than the average collection of the girls, how much was collected by the two groups?

The weight (in kg) of 50 contestants at a competition is as follows:
65 66 67 66 64 66 65 63 65 68
64 62 66 64 67 65 64 66 65 67
65 67 66 64 65 64 66 65 64 65
66 65 64 65 63 63 67 65 63 64
66 64 68 65 63 65 64 67 66 64
(a) Construct a frequency table for the discrete data.
(b) Calculate, correct to 2 decimal places, the: (i) mean; (ii) standard deviation of the data.

Using ruler and a pair of compasses only. (a) construct: (i) ΔXYZ such that |XY| = 10 cm, ∠XYZ = 30° and ∠YXZ = 45°; (ii) locus, l₁, of points equidistant from Y and Z; (iii) locus, l₂, of points parallel to XY through Z. (b) Locate point M, the point of intersection of l₁ and l₂. (c) Measure ∠ZMY.

(a) If (3p + 4q)/(3p − 4q) = 2, find p : q
(b) The diagram shows the cross section of a bridge with a semi circular hollow in the middle. If the perimeter of the cross section is 34 m, calculate the: (i) length PQ; (ii) area of the cross section [Take π = 22/7]

x: 0°, 30°, 60°, 90°, 120°, 150°, 180°, 210°, 240°, 270°, 300°, 330°, 360°
y: 2.0, __, __, 3.0, 1.6, __, −2.0, __, −3.6, −3.0, __, __, 2.0
(a) Copy and complete the table of values, correct to one decimal place, for the relation y = 3sin x + 2cos x for 0° ≤ x ≤ 360°.
(b) Using scales of 2 cm to 30° on the x-axis and 2 cm to 1 unit on the y-axis, draw the graph of the relation y = 3sin x + 2cos x for 0° ≤ x ≤ 360°.
(c) Use the graph to solve: (i) 3sin x + 2cos x = 0; (ii) 2 + 2cos x + 3sin x = 0.

(a) Find the equation of a straight line which passes through the point (2, −3) and is parallel to the line 2x + y = 6.
(b) The operation Δ is defined on the set T = {2, 3, 5, 7} by x Δ y = (x + y + xy) mod 8. (i) Construct modulo 8 table for the operation Δ on the set T. (ii) Use the table to find: I. 2 Δ (5 Δ 7); II. 2 Δ n = 5 Δ 7.