Further Mathematics Past QuestionsQuestion 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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