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Further Maths Past Questions and Answers

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Further Maths Questions

Question 126:

Simplify: \(^{n}C_{r} à· ^{n}C_{r-1}\)

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A \(\frac{n(n-r)}{r}\)
B \(\frac{n}{r(n-r)}\)
C \(\frac{1}{r(n-r)}\)
D \(\frac{n+1-r}{r}\)

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Question 127:

If \(2\sin^{2} \theta = 1 + \cos \theta, \leq \theta \leq find the value of \(\theta\).

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A 90Â°
B 60°
C 45Â°
D 30Â°

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Question 128:

If \(\begin{vmatrix} 1+2x & -1 \\ 6 & 3-x \end{vmatrix} = -3 \), find the values of x.

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A \(x = 3, -2\)
B \(x = 4, \frac{-2}{3}\)
C \(x = -4, \frac{3}{2}\)
D \(x = 4, \frac{-3}{2}\)

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Question 129:

Find \(\int \frac{x^{3} + 5x + 1}{x^{3}} \mathrm {d} x\)

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A \(x^{2} + 10x + c\)
B \(x + \frac{5}{3}x^{3} + x^{4} + c\)
C \(x - 5x^{2} - 2x^{3} + c\)
D \(x - \frac{5}{x} - \frac{1}{2x^{2}} + c\)

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Question 130:

Find the coordinates of the point which divides the line joining P(-2, 3) and Q(4, 6) internally in the ratio 2 : 3.

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A \((5\frac{2}{5}, \frac{2}{5})\)
B \((\frac{2}{5}, 5\frac{2}{5})\)
C \((\frac{-2}{5}, 5\frac{2}{5})\)
D \((\frac{2}{5}, 4\frac{1}{5})\)

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