Hello and Welcome to SSCE (WAEC and NECO) Practice Test - Further Mathematics

1. You are to attempt 20 Random Objectives Questions ONLY for 15 minutes.
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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

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

A. 4      B. 2      C. -4      D. -5

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

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

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

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

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

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

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

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

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

A. 1     B. 2     C. 3     D. 4

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

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

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

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

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 $\frac{1}{3}$

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

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

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

A. 25      B. 9      C. 7      D. 5

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

Solve: 2 cos x - 1 = 0 for 0 ≤ x ≤ 2π

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

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. $9\frac{9}{16}$

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

A. x2 + 10x + C

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

C. x - 5x2 -2x3 + C

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

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

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

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