Further Mathematics Questions & Answers - Free Online Practice

361.

Simplify $(1 + 2\sqrt{3})^{2} - (1 - 2\sqrt{3})^{2}$

$8\sqrt{3}$

$2 - 4\sqrt{3}$

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Correct answer is B

$(1 + 2\sqrt{3})^{2} = 1 + 4\sqrt{3} + 12 = 13 + 4\sqrt{3}$

$(1 - 2\sqrt{3})^{2} = 1 - 4\sqrt{3} + 12 = 13 - 4\sqrt{3}$

$13 + 4\sqrt{3} - (13 - 4\sqrt{3}) = 13 + 4\sqrt{3} - 13 + 4\sqrt{3}$

= $8\sqrt{3}$

362.

Find the maximum value of $2 + \sin (\theta + 25)$ .

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Correct answer is C

$\sin \theta \leq 1$

i.e Maximum value of $\sin \theta \forall \theta = 1$ .

Therefore, $2 + \sin \theta \leq 2 + 1 = 3$

363.

The initial velocity of an object is $u = \begin{pmatrix} -5 \\ 3 \end{pmatrix} ms^{-1}$ . If the acceleration of the object is $a = \begin{pmatrix} 3 \\ -4 \end{pmatrix} ms^{-2}$ and it moved for 3 seconds, find the final velocity.

$\begin{pmatrix} -14 \\ 15 \end{pmatrix} ms^{-1}$

$\begin{pmatrix} -2 \\ 1 \end{pmatrix} ms^{-1}$

$\begin{pmatrix} 4 \\ -9 \end{pmatrix} ms^{-1}$

$\begin{pmatrix} 14 \\ -9 \end{pmatrix} ms^{-1}$

View answer & explanation

Correct answer is C

$u = \begin{pmatrix} -5 \\ 3 \end{pmatrix} ms^{-1}$

$a = \begin{pmatrix} 3 \\ -4 \end{pmatrix} ms^{-2}; t = 3 secs$

$v = u + at \implies v = \begin{pmatrix} -5 \\ 3 \end{pmatrix} + \begin{pmatrix} 3 \\ -4 \end{pmatrix} \times 3$

= $\begin{pmatrix} -5 \\ 3 \end{pmatrix} + \begin{pmatrix} 9 \\ -12 \end{pmatrix} = \begin{pmatrix} 4 \\ -9 \end{pmatrix} ms^{-1}$ \)

364.

A bicycle wheel of diameter 70 cm covered a distance of 350 cm in 2 seconds. How many radians per second did it turn?

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Correct answer is A

No explanation has been provided for this answer.

365.

A company took delivery of 12 vehicles made up of 7 buses and 5 saloon cars for two of its departments; Personnel and General Administration. If the Personnel department is to have at least 3 saloon cars, in how many ways can these vehicles be distributed equally between the departments?

350

455

462

571

View answer & explanation

Correct answer is C

No explanation has been provided for this answer.

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