WAEC Mathematics 2018 past questions and answers

Simplify: √108 + √125 − √75

1. A.√3 + 5√5
2. B.6√3 − 5√5
3. C.6√3 + √2
4. D.6√3 − √2

Evaluate: (64^½ + 125^⅓)²

1. A.121
2. B.144
3. C.169
4. D.196

Given that y varies inversely as the square of x. If x = 3 when y = 100, find the equation connecting x and y.

1. A.yx² = 300
2. B.yx² = 900
3. C.y = 100x/9
4. D.y = 900²

Find the value of x for which 32_four = 22_x.

1. A.three
2. B.five
3. C.six
4. D.seven

Simplify: 2¼ × 3½ ÷ 4⅜.

1. A.5/9
2. B.1⅕
3. C.1¼
4. D.1⅘

There are 250 boys and 150 girls in a school. If 60% of the boys and 40% of the girls play football, what percentage of the school play football?

1. A.40.0%
2. B.42.2%
3. C.50.0%
4. D.52.5%

If log₁₀(6x − 4) − log₁₀2 = 1, solve for x.

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

If F = 9/5 C + 32, find C when F = 98.6

1. A.30
2. B.37
3. C.39
4. D.41

If x : y : z = 2 : 3 : 4, evaluate (9x + 3y)/(6z − 2y).

1. A.1½
2. B.2
3. C.2½
4. D.3

A curve is such that when y = 0, x = −2 or x = 3. Find the equation of the curve.

1. A.y = x² − 5x − 6
2. B.y = x² + 5x − 6
3. C.y = x² + x − 6
4. D.y = x² − x − 6

The volume of a cylindrical tank, 10m high is 385m³. Find the diameter of the tank. [Take π = 22/7]

1. A.14m
2. B.10m
3. C.7m
4. D.5m

The surface area of a sphere is 792/7 cm². Find, correct to the nearest whole number, its volume [Take π = 22/7]

1. A.113 cm³
2. B.131 cm³
3. C.311 cm³
4. D.414 cm³

A piece of thread of length 21.4 cm is used to form a sector of a circle of radius 4.2 cm on a piece of cloth. Calculate, correct to the nearest degree, the angle of the sector. [Take π = 22/7]

1. A.170°
2. B.177°
3. C.182°
4. D.192°

In the diargram, which of the following ratios is equal to |PN|/|PQ|?

1. A.|PN|/|PR|
2. B.|PM|/|PQ|
3. C.|PM|/|PR|
4. D.|PR|/|PQ|

In the diagram, PS and RS are targents to the circle centre O. ∠PSR = 70°, ∠POR = m and ∠PQR = n. Find (m + n).

1. A.110°
2. B.135°
3. C.165°
4. D.225°

Find the value of t in the diagram.

1. A.63°
2. B.117°
3. C.126°
4. D.234°

In the diagram, PR is a targents to the circle at Q, QT//RS, ∠SQR = 35° and ∠RSQ = 50°. Find the value of ∠QST.

1. A.40°
2. B.65°
3. C.85°
4. D.95°

If M and N are the points (−3, 8) and (5, −7) respectively, fnd MN.

1. A.8 units
2. B.11 units
3. C.15 units
4. D.17 units

The equation of the line through the points (4, 2) and (−8, −2) is 3y = px + q, where p and q are constants. Find the value of p.

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

The angle of elevation of the top of a tree from a point 27 m away and on the same horizontal ground as the foot of the tree is 30°. Find the height of the tree.

1. A.27 m
2. B.13.5√3 m
3. C.13.5√2 m
4. D.9√3 m

If tan x = 4/3, 0° < x < 90°, find the value of sin x − cos x.

1. A.1/10
2. B.⅕
3. C.5/12
4. D.1⅖

Given that Y is 20 m on a bearing of 300° from X, how far south of Y is X?

1. A.10 m
2. B.15 m
3. C.25 m
4. D.30 m

The mean of 1, 3, 5, 7 and x is 4. Find the value of x.

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

The table shows the distribution of goals scored by 25 teams in a football competition.
Number of goals: 1, 2, 3, 4, 5, 6, 7
Number of teams: 3, 1, 6, 6, 4, 2, 3
Calculate the probability that a team selected at random scored at most 3 goals.

1. A.3/25
2. B.⅕
3. C.6/25
4. D.⅖

The table shows the distribution of goals scored by 25 teams in a football competition.
Number of goals: 1, 2, 3, 4, 5, 6, 7
Number of teams: 3, 1, 6, 6, 4, 2, 3
Find the probability that a team selected random scored either 4 or 7 goals.

1. A.9/25
2. B.11/25
3. C.⅗
4. D.18/25

In the diagram, WXYZ is a rectangle with dimension 8 cm by 6 cm. P, Q, R and S are the midpoints of the sides of the rectangle as shown. What type of quadrilateral is the shaded region?

1. A.Trapezium
2. B.Prism
3. C.Rectangle
4. D.Rhombus

In the diagram, WXYZ is a rectangle with dimension 8 cm by 6 cm. P, Q, R and S are the midpoints of the sides of the rectangle as shown. Calculate the area of the part of the rectangle that is not shaded.

1. A.25 cm²
2. B.24 cm²
3. C.16 cm²
4. D.12 cm²

The total surface area of a hemisphere is 75π cm². Find is radius.

1. A.5.0 cm
2. B.7.0 cm
3. C.8.5 cm
4. D.12.0 cm

Find the values of x for which (x − 5)/(x(x − 1)) is undefined.

1. A.0 or 5
2. B.−5 or 5
3. C.−1 or 5
4. D.0 or 1

Solve the equation 2x² − x − 6 = 0.

1. A.x = −3/2 or 2
2. B.x = −2 or 3/2
3. C.x = −3 or 2
4. D.x = 3 or 2

Find the n^th term of the sequence 2 × 3, 4 × 6, 8 × 9, 16 × 12...

1. A.2ⁿ × 3(n − 1)
2. B.2ⁿ × 3n
3. C.2ⁿ × 3ⁿ
4. D.2ⁿ × 3ⁿ⁻¹

If 3x ≡ 4 (mod 5) find the least value of x.

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

The solution of x − 2 ≥ 2x − 1 illustrated on the number line as

1. A.Number line −3 to 2: dot at 1, arrow to the left
2. B.Number line −3 to 2: dot at 1, arrow to the right
3. C.Number line −3 to 2: dot at −1, arrow to the left
4. D.Number line −3 to 2: dot at −1, arrow to the right

If p and q are two statements, under what condition would p ⇒ q be false?

1. A.If p is true and q is true
2. B.If p is true and q is false
3. C.If p is false and q is false
4. D.If p is false and q is true

The diagram shows a trapezion inscribed in a semi-circle. If O is the mid-point of WZ and |WX| = |XY| = |YZ|, calculate the value of m.

1. A.90°
2. B.60°
3. C.45°
4. D.30°

Find the inter-quartile range of 1, 3, 4, 5, 8, 9, 10, 11, 12, 14, 16.

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

Donations during the launching of a church project were sent in sealed envelopes. The table shows the distribution of the amount of money in the envelope.
No. of envelopes: 4, 7, 20, 9, 4, 5, 3, 1, 2
Amount (N): 5000, 2000, 1000, 700, 500, 100, 50, 2, 10
How much was the total donation?

1. A.N26,792.00
2. B.N26,972.00
3. C.N62,792.00
4. D.N62,972.00

In the diagram, PQ is a straight line. (m + n) = 110°, (n + r) = 130° and (m + r) = 120°. Find the ratio of m : n : r.

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

If x : y = ¼ : ⅜ and y : z = ⅓ : 4/9, find x : z.

1. A.2 : 3
2. B.3 : 4
3. C.3 : 8
4. D.1 : 2

Find the mean deviation of 20, 30, 25, 40, 35, 50, 45, 40, 20 and 45.

1. A.8
2. B.9
3. C.10
4. D.12

M and N are two subsets of the universal set (U). If n(U) = 48, n(M) = 20, n(N) = 30 and n(M ∪ N) = 40, find n(M ∩ N)′.

1. A.18
2. B.20
3. C.30
4. D.38

Express 0.612 in the form x/y, where x and y are integers and y ≠ 0.

1. A.153/250
2. B.68/111
3. C.61/100
4. D.21/33

In the diagram. PQ//RS. Find x in terms of y and z.

1. A.x = 240° − y − z
2. B.x = 180° − y − z
3. C.x = 360° + y − z
4. D.x = 360° − y − z

The diagonals of a rhombus WXYZ intersect at M. If |MW| = 5 cm and |MX| = 12 cm, caluclate its perimeter.

1. A.42 cm
2. B.48 cm
3. C.52 cm
4. D.60 cm

The graphs of y = x² and y = x intersect at which of these points?

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

A used car was purchased at N900,000.00. Its value depreciated by 30% in the first year. In each subsequent year, the depreciation was 22% of its value at the beginning of that year. If the car was bought on 1st March, 2011, calculate, correct to the nearest hundred naira, the value of the car on 28th February, 2015.

(a) The graph of y = 2px² − p²x − 14 passes through the point (3, 10). Find the values of p.
(b) Two lines, 3y − 2x = 21 and 4y + 5x = 5, intersect at the point Q. Find the coordinates of Q.

(a) The diagonals of a rhombus are 10.2 cm and 9.3 cm long. Calculate, correct to one decimal place, the perimeter of the rhombus.
(b) Given that sin x = ⅗, 0° < x < 90°, find the value of 5 cos x − 4 tan x.

(a) In the diagram, QOS is a diameter, ∠RQS = x° and ∠QST = (3x + 15)°. Find: (i) the value of x. (ii) ∠RSQ.
(b) If 2N4_seven = 15N_nine, find the value of N.

(a) If the mean of m, n, s, p and q is 12, calculate the mean of (m − 4), (n − 3), (s + 6), (p − 2) and (q − 8).
(b) In a community of 500 people, the 75^th percentile age is 65 years while the 25^th percentile age is 15 years. How many of the people are between 15 and 65 years?

In a road worthiness test on 240 cars, 60% passed. The number that failed had faults in Clutch, Brakes and Steering as follows: Clutch only − 28: Clutch and Steering − 14; Clutch, Steering and Brakes − 8: Clutch and Brakes − 20: Brakes and Steering only − 6. The number of cars with faults in Steering only is twice the number of cars with faults in Brakes only. (a) Draw a Venn diagram to illustrate this information. (b) How many cars had: (i) faulty Brakes? (ii) only one fault?

(a) Find the equation of the line passing through the points (2,5) and (−4, −7).
(b) Three ships P, Q and R are at sea. The bearing of Q from P is 030° and the bearing of P from R is 300°. If |PQ| = 5 km and |PR| = 8 km, (i) illustrate the information in a diagram. (ii) calculate, correct to three significant figures, the: (I) distance between Q and R; (II) bearing of R from Q.

(a) Lamin bought a book for N300.00 and sold it to Bola at a profit of x%. Bola then sold the same book to James at a profit of x%. If James paid N(6x + ¾) more for the book than what Lamin paid, find the value of x.
(b) Find the range of values of x which satisfies the inequality 3x − 2 < 10 + x < 2 + 5x.

In the diagram, |PT| = 4 cm, |TS| = 6 cm |PQ| = 6 cm and ∠SPR = 30°. Calculate, correct to the nearest whole number: (a) |SR|; (b) area of TQRS.

(a) In ΔPQS, PQ = 12 cm, PS = 5 cm, ∠SPQ = ∠PRQ = 90°. Find, correct to three significant figures, PR.
(b) The lengths of two ladders, L and M are 10 m and 12 m respectively. They are placed against a wall such that each ladder makes the same angle with the horizontal ground. If the foot of L is 8 m from the foot of the wall, (i) draw a diagram to illustrate this information; (ii) calculate the height at which M touches the wall.

(a) Copy and complete the table of values for y = 2x² + x − 10 for −5 ≤ x ≤ 4.
x: −5, −4, −3, −2, −1, 0, 1, 2, 3, 4
y: __, __, 5, __, −9, −10, __, 0, __, __
(b) Using scales of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of y = 2x² + x − 10 for −5 ≤ x ≤ 4.
(c) Use the graph to find the solution of: (i) 2x² + x = 10; (ii) 2x² + x − 10 = 2x.

(a) If x = (2 / 3), y = (5 / −2) and z = (−4 / 13), find scalars p and q such that px + qy = z.
(b)(i) Using a scale of 2 cm to 2 units on both axes, draw on a graph paper two perpendicular axes Ox and Oy for −5 ≤ x ≤ 5, −5 ≤ y ≤ 5 respectively. (ii) Draw, on the graph paper, indicating clearly the vertices and their coordinates, (I) the quadrilateral WXYZ with W(2, 3), X(4, −1), Y(−3, −4) and Z(−3, 2); (II) the image W₁X₁Y₁Z₁ of the quadrilateral WXYZ under an anticlockwise rotation of 90° about the origin where W→W₁, X→X₁, Y→Y₁ and Z→Z₁.

Marks: 10, 20, 30, 40, 50, 60, 70, 80, 90
Frequency: 1, 1, x, 5, y, 1, 4, 3, 1
The frequency table shows the marks distribution of a class of 30 students in an examination. The mean mark of the distribution is 52. (a) Find the values of x and y. (b) Construct a group frequency distribution table starting with a lower class limit of 1 and a class interval of 10. (c) Draw a histogram for the distribution. (d) Use the histogram to estimate the mode.