SSCE (WAEC and NECO) Practice Test - Further Mathematics - Online Learning and Assessment Portal for Nigerian and International Students

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In how many ways can 9 people be seated on a bench if only 3 places are available?

A. 1200 B. 504 C. 320 D. 204

A B C D

If $\frac{1}{5}=25\left ( 5^{4-2y} \right )$ , find the value of y

A. 4 B. 2 C. -4 D. -5

A B C D

A mass of 75kg is placed on a lift. Find the force exerted by the floor of the lift on the mass when the lift is moving up with a constant velocity. [Take g = 9.8 ms^-2]

A. 750 N B. 745 N C. 735 N D. 98 N

A B C D

If x = i - 3j and y = 6i - j, calculate the angle between x and y

A. 60^o B. 75^o C. 81^o D. 85^o

A B C D

Forces 90 N and 120 N act in directions 120^o and 240^o respectively. Find the resultant of these forces.

A. $45\sqrt{3i}-45j$ B. $-60\sqrt{3i}-60j$ C. $15\sqrt{3i}+105j$ D. $-15\sqrt{3i}-105j$

A B C D

Given that f: x → $\frac{2x-1}{x+2}$ , x ≠ -2, find f^-1, the inverse of f

A. f^-1: x → $\frac{1+2x}{2-x}$ , x ≠ 2

B. f^-1: x → $\frac{1-2x}{x+2}$ , x ≠ -2

C. f^-1: x → $\frac{1-2x}{x-2}$ , x ≠ 2

D. f^-1: x → $\frac{1+2x}{x+2}$ , x ≠ -2

A B C D

Given that y = 4 - 9x and Δx = 0.1, Calculate Δy

A. 9.0 B. 0.9 C. -0.3 D. -0.9

A B C D

A line passes through the origin and the point $\left ( 1\frac{1}{4},\: 2\frac{1}{2} \right )$ . What is the gradient of the line?

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

A B C D

Given that x ∗ y = $\frac{x+y}{2}$ , x º y = $\frac{x^{2}}{y}$ and (3 ∗ b) º 48 = $\frac{1}{3}$ , find b where b > 0

A. 8 B. 6 C. 5 D. 4

A B C D

If 8^x÷ $\left (\frac{1}{4} \right )^{y}$ = 1 and log₂(x - 2y) = 1, find the value of (x - y)

A. $\frac{5}{4}$ B. $\frac{3}{5}$ C. 1 D. $\frac{2}{3}$

A B C D

The first term of a linear sequence is 9 and the common difference is 7. If the nth term is 380, find the value of n.

A. 45 B. 54 C. 56 D. 65

A B C D

If Px² + (P + 1)x + P = 0, has equal roots, find the values of P

A. -1 and $-\frac{1}{3}$ B. -1 and $\frac{1}{3}$ C. 1 and $-\frac{1}{3}$ D. 1 and $\frac{1}{3}$

A B C D

If T = $\begin{pmatrix} -2 & -5\\ 3 & 8 \end{pmatrix}$ , find T¹, the inverse T

A. $\begin{pmatrix} -8 & -5\\ 3 & 2 \end{pmatrix}$ B. $\begin{pmatrix} -8 & -5\\ 3 & -2 \end{pmatrix}$ C. $\begin{pmatrix} -8 & -5\\ -3 & 2 \end{pmatrix}$ D. $\begin{pmatrix} -8 & -5\\ -3 & -2 \end{pmatrix}$

A B C D

Given that f: x → x² and g: x → x + 3 where x ∈ R, find fog(2)

A. 25 B. 9 C. 7 D. 5

A B C D

Force of magnitude 8 N and 5 N acts on a body as shown in the diagram below:

Calculate, correct to 2 decimal places, the resultant force acting at O

A. 14.06 N B. 13.00 N C. 9.83 N D. 8.26 N

A B C D

Solve: 2 cos x - 1 = 0 for 0 ≤ x ≤ 2π

A. $\left ( \frac{2\pi }{3}, \frac{4\pi }{3} \right )$ B. $\left ( \frac{\pi }{6}, \frac{5\pi }{6} \right )$ C. $\left ( \frac{\pi }{5}, \frac{2\pi }{5} \right )$ D. $\left ( \frac{\pi }{3}, \frac{5\pi }{3} \right )$

A B C D

If 36, p, $\frac{9}{4}$ and q are consecutive terms of an exponential sequence (G.P) , find the sum of p and q.

A. $\frac{9}{16}$ B. $\frac{81}{16}$ C. 9 D. $9\frac{9}{16}$

A B C D

If log₃x = log₉3, find the value of x.

A. 3² B. $3^{\frac{1}{2}}$ C. $3^{\frac{1}{3}}$ D. $2^{\frac{1}{3}}$

A B C D

Find $\int \frac{x^{3}+5x+1}{x^{3}}$

A. x² + 10x + C

B. $x+\frac{5}{3}x^{3} +x^{4}+C$

C. x - 5x² -2x³ + C

D. $x-\frac{5}{x} - \frac{1}{2x^{2}}+C$

A B C D

A function is defined by h : x → 2 - $\frac{1}{2x-3}$ , x ≠ $\frac{3}{2}$ , find h^-1 $\left (\frac{1}{2} \right )$

A. 6 B. $\frac{11}{6}$ C. $\frac{11}{4}$ D. $\frac{5}{3}$