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- Question 1 of 10
##### 1. Question

Find \(\overrightarrow {BO} \) in terms of \(\vec a\) , \(\vec b\) or \(\vec c\).

CorrectIncorrect - Question 2 of 10
##### 2. Question

Find \(A\), if \(\dfrac{{\sin \theta }}{{1 – \cos \theta }} – \dfrac{{\sin \theta }}{{\sin \theta + 1}} = \dfrac{A}{{\tan \theta }}\).

\(A = \)

CorrectIncorrect##### Hint

- Question 3 of 10
##### 3. Question

If \({\cos ^4}\theta – {\sin ^4}\theta = a\cos \left( {b\theta } \right)\), find \(a\) and \(b\).

\(a = \) , \(b = \)

CorrectIncorrect##### Hint

\(\begin{align} \displaystyle

\cos 2\theta &= {\cos ^2}\theta – {\sin ^2}\theta \\

&= 2{\cos ^2}\theta – 1\\

&= 1 – 2{\sin ^2}\theta

\end{align}\) - Question 4 of 10
##### 4. Question

Find \(p\) and \(q\), if \(\int {\dfrac{{3x}}{{\sqrt {{x^2} + 8} }}} dx = p\sqrt {{{\left( {{x^2} + 8} \right)}^q}} + C\).

\(p = \) , \(q = \)

CorrectIncorrect##### Hint

- Question 5 of 10
##### 5. Question

Find the area of the region bounded by \(y = {x^3}\) and \(y = {x^2} + 2x\), correcting to two decimal place.

CorrectIncorrect - Question 6 of 10
##### 6. Question

Find \(a\) and \(b\), if the volume of the solid formed when \(y = {x^2} \) for \(2 \le x \le 4\) is revolved through \(2\pi \) or \(360^\circ \) about the \(y\)-axis is \(a\pi \) where \(a\) and \(b\) have no common factors.

\(a = \)

CorrectIncorrect - Question 7 of 10
##### 7. Question

A binomial random variable has a mean of 8 and a variance of 6.4. Find \(\Pr \left( {X = 10} \right)\), correcting to four significant figures.

CorrectIncorrect - Question 8 of 10
##### 8. Question

A fair coin is tossed five times. Find the probability of obtaining two Heads and three Tails.

CorrectIncorrect - Question 9 of 10
##### 9. Question

Find the positive value of \(k\), correcting to three significant figures, if the length of \( \begin{pmatrix} k \\ – 3 \end{pmatrix} \) is 7.2.

CorrectIncorrect - Question 10 of 10
##### 10. Question

Find the first two values of \(t\) when \(h = 5\) given \(y = 3 + 4\cos \dfrac{\pi }{3}\left( {t – 4} \right)\).

,

CorrectIncorrect