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Further Maths Past Questions and Answers

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Further Maths Questions

Question 51:

A fair die is tossed twice. What is its smple size?

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A 6
B 12
C 36
D 48

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Question 52:

Given that \( a = \begin{pmatrix} 2 \\ 3 \end{pmatrix}\) and \(b = \begin{pmatrix} -1 \\ 4 \end{pmatrix}\), evaluate \((2a - \frac{1}{4}b)\).

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A \(\begin{pmatrix} \frac{17}{4} \\ 7 \end{pmatrix}\)
B \(\begin{pmatrix} \frac{17}{4} \\ 5 \end{pmatrix}\)
C \(\begin{pmatrix} \frac{17}{4} \\ 3 \end{pmatrix}\)
D \(\begin{pmatrix} \frac{17}{4} \\ 2 \end{pmatrix}\)

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Question 53:

If \(y = \frac{1+x}{1-x}\), find \(\frac{dy}{dx}\).

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A \(\frac{2}{(1-x)^{2}}\)
B \(\frac{-2}{(1-x)^{2}}\)
C \(\frac{-1}{\sqrt{1-x}}\)
D \(\frac{1}{\sqrt{1-x}}\)

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Question 54:

Evaluate \(\int_{-1}^{0} (x+1)(x-2) \mathrm{d}x\)

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A \(\frac{7}{6}\)
B \(\frac{5}{6}\)
C \(\frac{-5}{6}\)
D \(\frac{-7}{6}\)

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Question 55:

Simplify \(\frac{\sqrt{128}}{\sqrt{32} - 2\sqrt{2}}\)

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A \(2\sqrt{2}\)
B \(3\sqrt{2}\)
C 3
D 4

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