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Further Mathematics Past Questions


Question 51:


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

A. 6
B. 12
C. 36
D. 48


Question 52:


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

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. \(\begin{pmatrix} \frac{17}{4} \\ 2 \end{pmatrix}\)


Question 53:


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

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


Question 54:


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

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


Question 55:


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

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






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