WAEC - Further Mathematics (2024)

• 1

  If \(\frac{5}{\sqrt{2}}\) - \(\frac{\sqrt{8}}{8}\) = m\(\sqrt{2}\), find the value of m

  回答

  (B)

  \(\frac{9}{4}\)
• 2

  Given that f: x → \(\sqrt{x}\) and g : x → 25 - x\(^2\), find the value of f o g(3)

  回答

  (A)

  4
• 3

  \(\sqrt{x}\) - \(\frac{6}{\sqrt{x}}\) = 1, find the value of x

  回答

  (C)

  9
• 4

  A binary operation * is defined on the set of real numbers, R by x * y = \(\frac{y^2 - x^2}{2xy}\), x, y ≠ 0, where x and y are real numbers. Evaluate -3 * 2

  回答

  (A)

  \(\frac{5}{12}\)
• 5

  If the n\(^{th}\) term of a linear sequence (A.P) is (5n - 2), find the sum of the first 12 terms of the sequence.

  回答

  (C)

  366
• 6

  If h(x) = x\(^2\) + px + 2 is divided by (x + 3), the remainder is 5, find p

  回答

  (C)

  2
• 7

  If 5x + 7 \(\equiv\) P(x + 3) + Q(x - 1), find the value of p

  回答

  (A)

  3
• 8

  If log\(_2^x\) = 2, evaluate log\(_x^{128}\). 

  回答

  (C)

  \(\frac{7}{2}\)
• 9

  Evaluate: \(\frac{cos^2 300º - 4sin^2 120º}{tan^2 135º}\)

  回答

  (A)

  -2\(\frac{3}{4}\)
• 10

  If f(x) = \(\frac{2 - x}{x}\), x ≠ 0, find the inverse of f.

  回答

  (B)

  \(\frac{2}{x+1}\), x ≠ -1
• 11

  Solve 2\(^{2x}\) -  5(2\(^x\)) + 4 = 0 

  回答

  (A)

  x = 0 and 2
• 12

  If p = \(\begin{pmatrix}2 \\ 4 \end{pmatrix}\) and q = \(\begin{pmatrix} 10 \\ -1 \end{pmatrix}\), find a vector, r such that 2p - 3r = q

  回答

  (A)

  \(\begin{pmatrix} -2 \\ 3 \end{pmatrix}\)
• 13

  Given that p = \(\begin{pmatrix} m + 1 & m - 1 \\ m + 4 & m - 8 \end{pmatrix}\) and |p| = - 34, find the value of m.

  回答

  (C)

  3
• 14

  If r = i + 2j and n = -i + 3j, find |2n - r|.

  回答

  (C)

  5.0
• 15

  The gradient of the curve y = mx\(^2\) + 3x - 1 at the point (-1, 1) is 9. Find the value of m

  回答

  (A)

  - 3
• 16

  If kx\(^2\) is a term in the binomial expansion of (1 - 2x)\(^4\), find the value of k. 

  回答

  (D)

  24
• 17

  A fair dice is thrown twice. Find the probability that the sum obtained will be a factor of 12.

  回答

  (A)

  \(\frac{1}{3}\)
• 18

  A body of mass 42 kg increases its speed from 15 ms\(^{-1}\) to 43 ms\(^{-1}\) in 12 seconds. Find the force acting on the body.

  回答

  (C)

  98N
• 19

  Given that M and N are two sets. Which of the following is the same as (M ∩ N)'? 

  回答

  (D)

  M' U N'
• 20

  A particle starts from rest accelerates at 4ms\(^{-2}\). Find the distance covered after 4 seconds.

  回答

  (D)

  32 m
• 21

  Find the range of values of x for which 9x - 1 > 14x\(^2\)

  回答

  (A)

  \(\frac{1}{7}\) < x < \(\frac{1}{2}\)
• 22

  A particle of mass 40 kg is kept on a smooth plane inclined at an angle of 30º to the horizontal by a force up the plane. find, correct to one decimal place, the magnitude of the normal reaction of the plane of the particle.[Take g = 10 ms\(^{-2}\)]

  回答

  (C)

  346.4N
• 23

  The point P(-3, 5) lies on a line which is perpendicular to 2x - 4y + 3 = 0. Find the equation of the line.

  回答

  (C)

  y + 2x + 1 = 0
• 24

  Find the coefficient of y\(^2\) in the binomial expansion of (y - 2x)\(^5\).

  回答

  (D)

  - 80x\(^3\)
• 25

  Given that f(x) = x\(^2\) + 3x + 1, find the value of x at the turning point.

  回答

  (C)

  -1\(\frac{1}{2}\)
• 26

  How many three-digit numbers can be formed from the digits 2, 3, 4, 5, 6, 7, and 8 if repetition is not allowed?

  回答

  (B)

  210
• 27

  If \(\begin{pmatrix} 6 & 4 \\ 7 & 5 \end{pmatrix}\) \(\begin{pmatrix} 2 \\ m \end{pmatrix}\) = 2\(\begin{pmatrix} 12 \\ 14.5 \end{pmatrix}\), find the value of m.

  回答

  (C)

  3
• 28

  A body of mass 80 kg moving with a velocity of 25 ) ms\(^{-1}\) collides with another moving in the opposite direction at 10 ms\(^{-1}\). After collision, both bodies moved with a common velocity of 12.8 ms\(^{-1}\). Calculate, correct to the nearest whole number, the mass of the second body.

  回答

  (C)

  43 kg
• 29

  In how many ways can 12 people be seated on a bench if only 5 spaces are available?

  回答

  (A)

  95040
• 30

  In triangle XYZ, |XY| = 10cm, |YZ| = 9 cm and |XZ| = 7 cm. If XZY = \(\alpha\), find the value of cos \(\alpha\).

  回答

  (C)

  \(\frac{5}{21}\)
• 31

  If y\(^2\) + 2xy - 8 = 0, find \(\frac{dy}{dx}\)

  回答

  (A)

   \(\frac{- y}{y + x}\)
• 32

  The mean of four numbers is 5 and the mean of another three numbers is 12. Find the mean of the seven numbers.

  回答

  (C)

  8
• 33

  Find, correct to the nearest degree, the acute angle between 3x - y - 5 = 0, and 7x - y - 3 = 0

  回答

  (A)

  10\(^0\)
• 34

  The gradient of a curve is given by 3x\(^2\) - 8x + 2. If the curve passes through P(0, 4), find the equation of the curve.

  回答

  (A)

  y = x\(^3\) - 4x\(^2\) + 2x + 4
• 35

  Given that y = 2x - 1 and Δx = 0.1, find Δ y

  回答

  (A)

  0.20