WAEC Further Mathematics 2019 past questions and answers

Solve: 8^x−2 = 4^3x

1. A.−2
2. B.−1
3. C.1
4. D.2

Evaluate tan 75°, leaving the answer in surd form (radicals).

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

Solve: p/2 + k/3 = 5 and 2p − k = 6 simultaneously.

1. A.p = −6, k = −6
2. B.p = −6, k = 6
3. C.p = 6, k = 6
4. D.p = 6, k = −6

Rationalize: 1/(√2 + 1)

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

If ⁿC₂ = 15, find the value of n.

1. A.8
2. B.7
3. C.6
4. D.5

An operation (*) is defined on the set T = {−1, 0, …, 5} by x * y = x + y − xy. Which of the following operation(s) will give an image which is an element of T? I. 2(*)5 II. 3(*)2 III. 3(*)4

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

Given that g: x → 3x and f: x → cos x, find the value of g o f(20°).

1. A.0.50
2. B.0.94
3. C.2.60
4. D.2.82

A linear transformation is defined by T: (x, y) → (−x + y, −4y). Find the image, Q′, of Q(−3, 2) under T.

1. A.Q′(5, −8)
2. B.Q′(−8, 5)
3. C.Q′(5, −3)
4. D.Q′(−5, −8)

If g: r → 5 − 2r, r is a real number, find the image of −3.

1. A.13
2. B.11
3. C.−1
4. D.−9

Consider the following statements: p: Birds fly
q: The sky is blue
r: The grass is green
What is the symbolic representation of "If the grass is green and the sky is not blue, then the birds do not fly"?

1. A.(r ∧ p) ⇒ q
2. B.(r ∧ q) ⇒ ~p
3. C.(r ∧ ~q) ⇒ ~p
4. D.(r ∧ ~p) ⇒ ~q

Given that 1/(x² − 4) ≡ P/(x + 2) + Q/(x − 2), x ≠ ±2, find the value of (P + Q)

1. A.3/2
2. B.1
3. C.1/2
4. D.0

Find the sum of the first 20 terms of the sequence −7, −3, 1, ….

1. A.620
2. B.660
3. C.690
4. D.1240

Find the value of x for which 6√(4x² + 1) = 13x, where x > 0.

1. A.6/5
2. B.25/24
3. C.24/25
4. D.5/6

Calculate the distance between points (−2, −5) and (−1, 3).

1. A.√5 units
2. B.√17 units
3. C.√65 units
4. D.√73 units

If P = (2 3 / −4 1), Q = (6 / 8) and PQ = k(45 / −20), find the value of k. (Matrices written row by row; / separates the rows.)

1. A.−5/4
2. B.−4/5
3. C.4/5
4. D.5/4

The second and fourth terms of an exponential sequence (G.P.) are 2/9 and 8/81 respectively. Find the sixth term of the sequence

1. A.81/32
2. B.9/8
3. C.1/4
4. D.32/729

Points X and Y are on the same horizontal base as the foot of a building such that X is 96 m due east of the building and Y is due west. If the angle of elevation of the top of the building from X is 30° and that of Y is 60°, calculate the distance of Y from the base of the building.

1. A.30 m
2. B.32 m
3. C.42 m
4. D.50 m

Find the coordinates of the point on the curve y = 3x² − 2x − 5 where the tangent is parallel to the line y − 5 = 8x.

1. A.(−5/3, 0)
2. B.(0, −5/3)
3. C.(0, 5/3)
4. D.(5/3, 0)

A particle starts from rest and moves in a straight line such that its velocity, V ms⁻¹, at time t second is given by V = 3t² − 6t. Calculate the distance in 4 seconds.

1. A.12 m
2. B.16 m
3. C.64 m
4. D.96 m

Find the constant term in the binomial expansion of (2x² + 1/x²)⁴.

1. A.10
2. B.12
3. C.24
4. D.42

Which of these inequalities is represented by the shaded portion of the graph?

1. A.2y + x − 3 < 0
2. B.2y − x − 3 < 0
3. C.2y − x + 3 < 0
4. D.2y + x + 3 < 0

A 35 N force acts on a body of mass 5 kg for 2 seconds. Calculate the change in momentum of the body.

1. A.70 kg ms⁻¹
2. B.55 kg ms⁻¹
3. C.50 kg ms⁻¹
4. D.35 kg ms⁻¹

Solve, correct to three significant figures, (0.3)^x = (0.5)⁸.

1. A.4.61
2. B.4.606
3. C.0.461
4. D.0.0130

Given that P and Q are two non-empty subsets of the universal set, U. Find P ∩ (Q ∪ Q′)

1. A.P
2. B.P′
3. C.Q
4. D.Q′

Find the coefficient of the third term in the binomial expansion of (2x + 3y/4)³ in descending powers of x.

1. A.27y²/64
2. B.27y²/8
3. C.8y²
4. D.9y²

Find the coordinates of the centre of the circle 3x² + 3y² − 6x + 9y − 5 = 0.

1. A.(−3, 9/2)
2. B.(−1, 3/2)
3. C.(1, −3/2)
4. D.(3, −9/2)

Evaluate ∫₀⁹ √x dx.

1. A.3
2. B.9
3. C.18
4. D.27

The function f: x → x² + px + q has turning point when x = −3 and remainder of −6 when divided by (x + 2). Find the vale of q.

1. A.6
2. B.2
3. C.−2
4. D.−8

If y = (5 − x)⁻³, find dy/dx.

1. A.−15/(5 − x)⁴
2. B.−3/(5 − x)⁴
3. C.3/(5 − x)⁴
4. D.15/(5 − x)⁴

Find correct to the nearest degree, the angle between p = 12i − 5j and q = 4i + 3j.

1. A.59°
2. B.60°
3. C.75°
4. D.76°

Find, the area between line y = x + 1 and the x − axis from x = −2 to x = 0.

1. A.5 square units
2. B.4 square units
3. C.2 square units
4. D.1 square unit

How many numbers greater than 200 can be formed from the digits 1, 2, 3, 4, 5 if no digit is to be repeated in any particular number?

1. A.50
2. B.60
3. C.288
4. D.300

The probabilities that John and Jane will pass an examination are 0.9 and 0.7 respectively. Find the probability that at least one of them will pass the examination.

1. A.0.28
2. B.0.67
3. C.0.72
4. D.0.97

Given that X and Y are independent events such that P(X) = 0.5, P(Y) = m and P(X ∪ Y) = 0.75, find the value of m.

1. A.0.6
2. B.0.5
3. C.0.4
4. D.0.3

A uniform beam, PQ, is 100 cm long and weighs 35 N. It is placed on a support at a point 40 cm from P. If weights of 54 N and F N are attached at P and Q respectively in order to keep it in a horizontal position, calculate, correct to the nearest whole number, the value of F.

1. A.69
2. B.60
3. C.35
4. D.30

Simplify: (625^{(3x/4 − 1)} + 125^(x−1))/5^(3x−2).

(a) Find the coordinates of the point which divides the line joining (7, −5) and (−2, 7) externally in the ratio 3 : 2.
(b) Without using calculators or mathematical tables, evaluate 2/(1 − √2) − 2/(2 + √2), leaving the answer in the form p + q√n, where p, q and n are integers.

How many terms of the series −3 − 1 + 1 + … add up to 165?

If sin X = (p − q)/(p + q), where 0° ≤ X ≤ 90°, find 1 − tan²X.

Three forces 10 N, 14 N and 16 N acting on a particle keep it in equilibrium. Find the angle between the forces 10 N and 16 N.

A uniform beam, WX, of length 90 cm and weight 50 N is suspended on a pivot, 35 cm from W. It is kept in equilibrium by means of forces T and 20 N applied at Y and Z respectively. |WY| = 10 cm and |XZ| = 10 cm. Find the value of T.

The table shows the age distribution in years of a group of people.
Age (in years): 1 − 5, 6 − 10, 11 − 15, 16 − 20, 21 − 25, 26 − 30
Number of People: 18, 12, 25, 15, 20, 10
Using an assumed mean of 13 years, find the mean age of the people.

Two fair dice are thrown together two times. Find the probability of obtaining a sum of seven in the first throw and a sum of four in the second throw.

The curve y = 7 − 6/x and the line y + 2x − 3 = 0 intersect at two points. Find the: (a) coordinates of the two points; (b) equation of the perpendicular bisector of the line joining the two points.

(a) Find the range of values of p for which 4x² − px + 1 = 0 has real roots. (b)(i) Expand (1 + 3xy)⁶ in assending powers of x. (ii) Using the expansion in 10(b)(i), find, correct to four significant figures, the value of (1.03)⁶.

Given that M: (x, y) → (7y, 3x − y) and N: (x, y) → (2x − y, 5x + 3y), (a) write down matrices M and N of the linear transformations; (b) find the image of P(2, −3) under the linear transformation N followed by M; (c) find the coordinates of the point Q whose image is Q′(2, 4) under the linear transformation N.

In an examination, 60% of the candidates passed. If 10 candidates are selected at random, find the probability that: (a) at least two of them failed; (b) exactly half of them passed; (c) at most two of them failed.

In a research to determine the relationship between performance of students in an entrance examination and subsequent school performance, the results of ten randomly selected students were obtained as follows:
Students: A, B, C, D, E, F, G, H, I, J
Performance in Entrance Examination: 11, 12, 8, 13, 6, 15, 10, 14, 17, 16
School Performance: 5, 10, 9, 7, 4, 8, 6, 14, 11, 12
(a) Calculate the Spearman's rank correlation coefficient. (b) What would be the researcher's conclusion from the result in 13(a)?

A body, moving at 20 ms⁻¹ accelerates uniformly at 2½ ms⁻² for 4 seconds. It continues the journey at this speed for 8 seconds, before coming to rest t seconds after with uniform retardation. If the ratio of the acceleration to retardation is 3 : 4, (a) sketch the velocity − time graph of the journey; (b) find t; (c) find the total distance of the journey.

(a) Given that m = i − j, n = 2i + 3j and 2m + n − r = 0, find |r|. (b) The distance, S metres of a moving particle at any time t seconds is given by S = 3t − t³/3 + 9. Find the: (i) time; (ii) distance travelled; when the particle is momentarily at rest.