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

Differentiate \(f\left( x \right) = \sqrt[3]{{{x^4}}}\) .

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

Find \(A\) and \(B\), if the equation of the normal to the curve \(f\left( x \right) = 2{x^2} – 8x\) at the point where where the gradient is \(4\) is \(x + Ay + B = 0\).

\(A = \) , \(B = \)

CorrectIncorrect##### Hint

\(\text{gradient of tangent } \times \text{gradient of normal } = – 1\)

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

Find \(\dfrac{d}{{dx}}{\log _e}{e^x}{\left( {{e^{2x}} – 1} \right)^3}\).

CorrectIncorrect##### Hint

\(\dfrac{d}{{dx}}{\log _e}f\left( x \right) = \dfrac{1}{{f\left( x \right)}} \times f’\left( x \right)\)

- Question 4 of 10
##### 4. Question

Find for the values of \(x\) for which \(f\left( x \right) = {x^3} – 9{x^2} + 9x + 10\) is concave upwards.

CorrectIncorrect##### Hint

\(\begin{align} \displaystyle

y” &> 0 \to {\rm{concave upwards}}\\

y” &< 0 \to {\rm{concave downwards}} \end{align}\) - Question 5 of 10
##### 5. Question

Find the maximum \(y\)-value given \(y = – 2{x^2} + 8x + 10\) for \(3 \le x \le 5\).

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

Find the maximum and minimum values of \(P = \cos 2t\).

maximum = , minimum =

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

Find \(p\) and \(q\), if \(\int {{{\left( {\dfrac{{ – 3x + 5}}{2}} \right)}^6}} dx = \dfrac{1}{p}{\left( { – 3x + 5} \right)^q} + C\).

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

CorrectIncorrect##### Hint

\(\int {{{\left( {ax + b} \right)}^n}} dx = \dfrac{{{{\left( {ax + b} \right)}^{n + 1}}}}{{a\left( {n + 1} \right)}} + C\)

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

Evaluate \(\int_{ – 1}^4 {\sqrt {3x + 4} } dx\).

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

A particle has velocity function \(v\left( t \right) = \cos 3t\) cm/s as it moves in a straight line. The particle is initially 0.5 cm to the right of the origin. Write a formula for the displacement function.

cm

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

Find \(\int {{{\cos }^4}x{{\sin }^5}xdx} \).

CorrectIncorrect##### Hint

\(\dfrac{d}{{dx}}\cos x = – \sin x\)