WAEC Further Mathematics 2017 past questions and answers

If log_y (1/8) = 3, find the value of y.

1. A.−2
2. B.−½
3. C.½
4. D.2

If x² − kx + 9 = 0 has equal roots, find the values of k.

1. A.3, 4
2. B.±3
3. C.±5
4. D.±6

Find the coordinates of the centre of the circle 3x² + 3y² − 4x + 8y − 2 = 0.

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

The function f: x → √(4 − 2x) is defined on the set of real numbers R. Find the domain of f.

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

Given that f(x) = (x + 1)/2, find f⁻¹(−2).

1. A.−5
2. B.−3
3. C.3
4. D.5

Given that (6x + m)/(2x² + 7x − 15) = 4/(x + 5) − 2/(2x − 3), find the value of m.

1. A.20
2. B.12
3. C.−10
4. D.−22

Find the coefficent of x⁴ in the expansion of (1 − 2x)⁶.

1. A.−320
2. B.−240
3. C.240
4. D.320

Find the 21^st term of the Arithmetic Progression (AP): −4, −1.5, 1, 3.5, …

1. A.43.5
2. B.46
3. C.48.5
4. D.51

How many ways can six students be seated around a circular table?

1. A.36
2. B.48
3. C.72
4. D.120

If (2 1 / 4 3)(5 / 4) = k(17.5 / 40.0), find the value of k. (Matrices written row by row; / separates the rows.)

1. A.0.20
2. B.0.40
3. C.0.80
4. D.1.25

Express Cos 150° in surd form.

1. A.−√3
2. B.−√3/2
3. C.−½
4. D.√2/2

A straight line parallel to 2x + 3y = 6, passes through the point (−1, 2). Find the equation of the line.

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

α and β are the roots of the equation 2x² − 3x + 4 = 0. Find (α + β).

1. A.−2
2. B.−3/2
3. C.3/2
4. D.2

α and β are the roots of the equation 2x² − 3x + 4 = 0. Find (α/β + β/α).

1. A.−9/8
2. B.−7/8
3. C.7/8
4. D.9/8

If B = (2 5 / 1 3), find B⁻¹. (Matrices written row by row; / separates the rows.)

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

Given that sin x = 5/13 and sin y = 8/17, where x and y are acute, find the value of cos (x + y).

1. A.130/221
2. B.140/221
3. C.140/204
4. D.220/23

Given that f(x) = 5x² − 4x + 3, find the coordinates of the point where the gradient is 6.

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

If y = (1 + x)/(1 − x), find dy/dx.

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

Evaluate ∫₋₁⁰ (x + 1)(x − 2) dx

1. A.7/6
2. B.5/6
3. C.−5/6
4. D.−7/6

Simplify: √128/(√32 − 2√2).

1. A.4√2
2. B.3√2
3. C.3
4. D.4

There are 7 boys in a class of 20. Find the number of ways of selecting 3 girls and 2 boys.

1. A.1638
2. B.2730
3. C.6006
4. D.7520

The 3^rd and 7^th terms of a Geometric Progression (G.P) are 81 and 16 respectively. Find the 5^th term.

1. A.4/729
2. B.16/81
3. C.27
4. D.36

Differentiate (5x³ + x²)/x, x ≠ 0 with respect to x

1. A.10x + 1
2. B.10x + 2
3. C.x(15x + 1)
4. D.x(15x + 2)

A curve is given by y = 5 − x − 2x². Find the equation of its line of symmetry.

1. A.x = −41/8
2. B.x = −1/4
3. C.x = 1/4
4. D.x = 41/8

In a class of 10 boys and 15 girls, the average score in a Biology test is 90. If the average score for the girls is x, find the average score for the boys in terms of x.

1. A.200 − (2/3)x
2. B.225 − (3/2)x
3. C.250 − 2x
4. D.250 − 3x

A fair die is tossed twice. What is the sample size?

1. A.6
2. B.12
3. C.36
4. D.48

Given that a = (2, 3) and b = (−1, 4) (column vectors), evaluate (2a − ¼b).

1. A.(17/4, 7)
2. B.(17/4, 5)
3. C.(17/4, 3)
4. D.(17/4, 2)

The table shows the results of tossing a fair die 150 times.
Face: 1, 2, 3, 4, 5, 6
Frequency: 12, 18, y, 30, 2y, 45
Find the probability of obtaining a 5.

1. A.1/10
2. B.1/6
3. C.1/5
4. D.3/10

The table shows the results of tossing a fair die 150 times.
Face: 1, 2, 3, 4, 5, 6
Frequency: 12, 18, y, 30, 2y, 45
Find the mode.

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

Given that a = 5i + 4j and b = 3i + 7j, evaluate (3a − 8b).

1. A.9i + 44j
2. B.−9i + 44j
3. C.−9i − 44j
4. D.9i − 44j

A force (10i + 4j)N acts on a body of mass 2 kg which is at rest. Find the velocity after 3 seconds.

1. A.(5/3 i + 2/3 j) ms⁻¹
2. B.(10/3 i + 4/3 j) ms⁻¹
3. C.(5i + 2j) ms⁻¹
4. D.(15i + 6j) ms⁻¹

Find the magnitude and direction of the vector p = (5i − 12j).

1. A.(13, 113.38°)
2. B.(13, 067.38°)
3. C.(13, 025.38°)
4. D.(13, 157.38°)

Solve: 3^2x − 3^x+2 = 3^x+1 − 27.

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

The velocity, V, of a particle, in ms⁻¹, after t seconds, is V = 3t² + 2t − 1. Find the acceleration of the particle after 2 seconds.

1. A.10 ms⁻²
2. B.13 ms⁻²
3. C.14 ms⁻²
4. D.17 ms⁻²

Given that f(x) = 2x² − 3 and g(x) = x + 1, where x ∈ R, find g o f(x).

1. A.2(x² − 1)
2. B.2x² + 4x − 1
3. C.2x² + 6x − 1
4. D.3(x² − 1)

If (2x² − x − 3) is a factor of f(x) = 2x³ − 5x² − x + 6, find the other factor.

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

If P = {n² + 1 : n = 0, 2, 3} and Q = {n + 1 : n = 2, 3, 5}, find P ∩ Q.

1. A.{5, 10}
2. B.{4, 6}
3. C.{1, 3}
4. D.{ }

(a) If f(x) = (4 − 5x)/2 and g(x) = x + 6, x ∈ R, find f o g⁻¹
(b) P(x, y) divides the line joining (7, −5) and (−2, 7) internally in the ratio 5:4. Find the coordinates of P.

Evaluate ∫₁³ (x − 1)/(x + 1)² dx.

(a) Given that log₁₀ p = a, log₁₀ q = b and log₁₀ s = c, express log₁₀(p^1/3q⁴/s²) in terms of a, b and c.
(b) The radius of a circle is 6 cm. If the area of the circle is increasing at the rate of 20 cm²s⁻¹, find, leaving the answer in terms of π, the rate at which the radius is increasing.

If (x + 1) and (x − 2) are factors of the polynomial g(x) = x⁴ + ax³ + bx² − 16x − 12, find the values of a and b.

Bottles of the same sizes produced in a factory are packed in boxes. Each box contains 10 bottles. If 8% of the bottles produced are defective, find correct to two decimal places, the probability that a box chosen at random contains at least three defective bottles.

The table shows the heights in cm of some seedlings in a certain garden:
Height (cm): 36 − 40, 41 − 45, 46 − 50, 51 − 55, 56 − 60
Frequency: 3, 9, 21, 12, 5
(a) Draw a cumulative frequency curve for the distribution (b) Using the curve in 6(a), find the semi-interquartile range.

A parallelogram MNQR has vertices M(4, −6), N(10, 2), Q(8, 16) and R(x, y). Find the coordinates of R.

Forces F₁ (18 N, 330°), F₂ (10 N, 090°) and F₃ (25 N, 180°) act on a body at rest. Find, correct to one decimal place, the magnitude and direction of the resultant force.

(a) Simplify: 1/(1 − cos θ) + 1/(1 + cos θ) and leave the answer in terms of sin θ.
(b) Find the equation of the line joining the stationary points of y = x²(x − 3) and the distance between them.

(a) If f(x) = (2x − 3)/((x² − 1)(x − 2)), (i) find the values of x for which f(x) is undefined. (ii) express f(x) in partial fractions.
(b) A circle with centre (−3, 1) passes through the point (3, 1). Find its equation.

(a) If f(x) = ∫(4x − x²) dx and f(3) = 21, find f(x).
(b) The second, fourth and eight terms of an Arithmetic Progression (A.P.) form the first three consecutive terms of a Geometric Progression (G.P.). The sum of the third and fifth terms of the A.P. is 20. Find the: (i) first four terms of the A.P., (ii) sum of the first ten terms of the A.P.

(a) In a school, the ratio of those who passed to those who failed in a History test is 4 : 1. If 7 students are selected at random from the school, find, correct to two decimal places, the probability that: (i) at least 3 students passed the test: (ii) between 3 and 6 students failed the test. (b) A fair die is thrown five times, find the probability of obtaining a six three times.

The table shows the frequency distribution of the ages of patients in a clinic.
Age (years): 17 − 19, 20 − 22, 23 − 28, 29 − 34, 35 − 43
No of patients: 6, 9, 12, 18, 18
(a) Draw a histogram for the distribution. (b) Find, correct to two decimal places, the mean age of the patients.

(a) A body P of mass q kg is suspended by two light inextensible strings AB and DB attached to a horizontal table. The strings are inclined at 30° and 60° respectively to the horizontal and the tension in AB is 48 N. If the system is in equilibrium: (i) sketch a diagram to represent the information; (ii) calculate the tension in DB, (iii) find the value of q. [Take g = 10 ms⁻²]
(b) A ball is thrown vertically upwards with a velocity of 20 ms⁻¹. Find, correct to two decimal places the: (i) maximum height reached by the ball; (ii) time taken to reach the maximum height. [Take g = 10 ms⁻²]

(a) Given that m = (6i + 8j) and n = (−8i + (7/3)j), find the: (i) magnitudes and directions of m and n, (ii) angle between m and n.
(b) The position vectors of points P, Q, R, S are (−2, 3), (10, 4), (3, 12) and (4, 0) (column vectors) respectively. Show that PQ is pependicular to RS