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.
2. Supply your name and name of school in the text box below.
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Express (14 N, 240o) as a column vector

A. $\binom{-7}{-7\sqrt{3}}$     B. $\binom{7\sqrt{3}}{7\sqrt{3}}$     C. $\binom{-7\sqrt{3}}{-7}$     D. $\binom{-7}{-7\sqrt{3}}$

If α and β are the roots of the equation x2 + x - 2 = 0, find the value of $\left&space;(&space;\frac{1}{\alpha&space;^{2}}+&space;\frac{1}{\beta&space;^{2}}&space;\right&space;)$

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

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

Find the variance of 1, 2, 0, -3, 5, -2, 4

A. $\frac{52}{7}$     B. $\frac{40}{7}$     C. $\frac{32}{7}$     D. $\frac{27}{7}$

In calculating the mean of 8 numbers, a boy mistakenly used 17 instead of 25 as one of the numbers. If he obtained 20 as the mean, find the correct mean.

A. 24     B. 23     C. 21     D. 19

If f(x) = 3x3 + 8x2 + 6x + k and f(2) = 1, find the value of k

A. -67    B. -61    C. 61    D. 67

Given that x2 + 4x + k ≡ (x + r)2 + 1, find the value of k and r.

A. k = 5, r = -1      B. k = 5, r = 2      C. k = 2, r = 5      D. k = -1, r = 5

The table below shows the distribution of marks scored by students in a test.

How many students scored above the median mark?

A. 3     B. 12    C. 22     D. 30

Four fair coins are tossed once. Calculate the probability of obtaining equal number of heads and tails.

A. $\frac{1}{4}$     B. $\frac{3}{8}$     C. $\frac{1}{2}$     D. $\frac{15}{16}$

If 2, (k + 1), 8, ........ form an exponential sequence (GP), find the value of k.

A. -3 and 5     B. 5 and -5     C. 3 and -3     D. -5 and 3

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

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

Given that  $\frac{2x}{(x+6)(x&space;+&space;3)}&space;\equiv&space;\frac{P}{x+6}+\frac{Q}{x+3}$  find P and Q

A. P = 4 and Q = 2     B. P = 2 and Q = 4     C. P = 4 and Q = -2     D. P = -2 and Q = 4

Using the binomial expansion (1 + x)6 = 1 + 6x + 15x2 + 20x3 + 15x4 + 6x5 + x6, find, correct to three decimal places, the value of (1.98)6

A. 68.245       B. 61.255       C. 60.255       D. 60.245

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 $\frac{1}{3}$

Which of the following is a factor of the polynomial 6x4 + 2x3 + 15x + 5?

A. 3x + 1      B. x + 1      C. 2x + 1      D. 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 function is defined by  h : x → 2 - $\frac{1}{2x-3}$,  x ≠ $\frac{3}{2}$, find h-1(x), the inverse of h.

A. h-1(x) = $\frac{3x-4}{2x-7}$, x ≠ $\frac{7}{2}$

B. h-1(x) = $\frac{3x-7}{2x-4}$, x  ≠ 2

C. h-1(x) = $\frac{2x-7}{4x-3}$, x ≠ $\frac{3}{4}$

D. h-1(x) = $\frac{4x-7}{2x-4}$, x ≠ 2

If a fair coin is tossed four times, what is the probability of obtaining at least one head?

A. $\frac{1}{2}$     B. $\frac{1}{4}$     C. $\frac{13}{16}$     D. $\frac{15}{16}$

Find the derivative of $\frac{1}{\sqrt[3]{\left&space;(&space;3x^{3}&space;+&space;1&space;\right&space;)}}$ with respect to x.

A. $\frac{3x}{\sqrt[3]{\left&space;(&space;3x&space;+&space;1&space;\right&space;)^{2}}}$      B. $\frac{3x^{2}}{\sqrt[3]{\left&space;(&space;3x^{3}&space;+&space;1&space;\right&space;)^{2}}}$      C. $\frac{3x}{\sqrt[3]{\left&space;(&space;3x^{3}&space;+&space;1&space;\right&space;)}}$      D. $\frac{3x^{2}}{\sqrt[3]{\left&space;(&space;3x^{3}&space;+&space;1&space;\right&space;)^{2}}}$

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