Further Mathematics Past Questions

Question 11

waec 2025

The area of a sector of a circle is 3cm\(^2\). If the sector subtends an angle of 1.5 radians at the centre. Calculate the radius of the circle

A2 cm

B\(\sqrt{2}\)cm

C4 cm

D1 cm

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Question 12

waec 2025

Which of the following matrices is a singular matrix?

A\(\begin{bmatrix}
2 & 1 \\ 3 &2
\end{bmatrix}\)

B\(\begin{bmatrix}
1 & 0 \\ 0 &1
\end{bmatrix}\)

C\(\begin{bmatrix}
0 & 1 \\ 1 & 0
\end{bmatrix}\)

D\(\begin{bmatrix}
3 & 8 \\ 6 & 16
\end{bmatrix}\)

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Question 13

waec 2025

Simplify \(\frac{^n P_4}{ ^n C_4}\)

A6

B12

C18

D24

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Question 14

waec 2025

A committee of 4 is to be selected from a group of 5 men and 3 women. In how many ways can this be done if the chairman of the committee must be a man?

A15

B175

C40

D70

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Question 15

waec 2025

The mean age of n men in a club is 50 years. Two men aged 55 and 63 left the club, and the mean age reduced by 1 year. Find the value of n

A30

B14

C18

D20

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Question 16

waec 2025

Evaluate lim\(_{x→1}\) \(\frac{1-x}{x^2 - 3x + 2}\)

A0

B1

C-1

D\(\frac{1}{2}\)

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Question 17

waec 2025

Evaluate log\(_{0.25}\) 8

A-\(\frac{3}{2}\)

B\(\frac{2}{3}\)

C\(\frac{3}{2}\)

D-\(\frac{2}{3}\)

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Question 18

waec 2025

Find the sum of the exponential series 96 + 24 + 6 +......

A128

B72

C144

D64

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Question 19

waec 2025

The roots of the equation 2x\(^2\) + kx + 5 = 0 are α and β, where k is a constant. If α\(^2\) + β\(^2\) = -1, find the values of k

A±2

B±4

C±16

D±8

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Question 20

waec 2025

Find the equation of the line passing through (0, -1) and parallel to the y-axis

Ay = -1

Bx=-1

Cy=0

Dx=0

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Question 21

waec 2025

Find the coefficient of x\(^4\) in the binomial expansion (1 - 2x)\(^6\)

A240

B-240

C-320

D320

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Question 22

waec 2025

If f(x) = \(\frac{1}{2 - x}\), x \(\neq\) 2. Find f\(^{-1}\)(\(\frac{-1}{2}\))

A-5

B4

C-7

D-4

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Question 23

waec 2025

Given that (\(\sqrt{3}\) - 5\(\sqrt{2}\))(\(\sqrt{3}\) + \(\sqrt{2}\)) = p + q\(\sqrt{6}\). Find q

A-4

B-7

C-5

D4

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Question 24

waec 2025

Given that \(\frac{1}{8^{2-3y}}\)  = 2\(^{y + 2}\), find y.

A1

B\(\frac{1}{5}\)

C\(\frac{7}{8}\)

D\(\frac{1 1}{5}\)

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Question 25

waec 2025

Two functions f and g are defined by f:x → 3x - 1, g: x → 2x\(^3\), find fg(- 2).

A-9

B-47

C-49

D-10

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Question 26

waec 2025

A binary operation * is defined on the set R of real numbers by a*b = \(\frac{\text{ab}}{4}\), find the value of \(\sqrt{2}\) * \(\sqrt{6}\)

A3\(\frac{\sqrt{2}}{4}\)

B\(\frac{\sqrt{2}}{2}\)

C\(\frac{\sqrt{3}}{2}\)

D\(\sqrt{3}\)

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Question 27

waec 2025

If (x - 3)is a factor of 2x\(^3\) + 3x\(^2\) - 17x - 30, find the remaining factors.

A(2x-5)(x-2)

B(2x+5)(x-2)

C(2x-5)(x+2)

D(2x+5)(x+2)

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Question 28

waec 2025

simplfy \(\sqrt{(\frac{1}{64}}\))\(^{\frac{-2}{3}}\).

A\(\frac{1}{8}\)

B-4

C\(\frac{1}{4}\)

D4

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Question 29

waec 2025

Solve the inequality 2x\(^2\) + 5x - 3 ≥ 0.

A-\(\frac{1}{2}\) x ≤ x ≤3

B-3 ≤ x ≤ \(\frac{1}{2}\)

Cx ≤ -3 or x ≥ \(\frac{1}{2}\)

Dx ≤ -\(\frac{1}{2}\) or x ≥3

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Question 30

waec 2025

If P = {x:1 ≤ x ≤ 6} and Q = {x: 2

A{x:1 ≤ x < 6}

B{x:2 < x < 6}

C{x:2 ≤ x ≤ 6}

D{x:2 < x ≤ 6}

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