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

Choose scalar quantities.

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

Find the vector equation of the following diagram.

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

Find the positive value of \(k\), correcting to two significant figures, if the length of \( \begin{pmatrix} k \\ 2 \end{pmatrix} \) is 5.

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

Find \(a\) and \(b\), if \(\dfrac{d}{{dx}}\dfrac{{{x^2}}}{{{{\left( {2x + 3} \right)}^2}}} = \dfrac{{ax}}{{{{\left( {2x + 3} \right)}^b}}}\).

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

CorrectIncorrect##### Hint

\(\dfrac{d}{{dx}}\dfrac{u}{v} = \dfrac{{u’v – uv’}}{{{v^2}}}\)

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

Find \(a\), if \(y = 2{x^3} + a{x^2} – 24x + 1\) has a maximum at \(x = – 4\).

\(a = \)

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

A particle \(P\) moves in a straight line with a velocity function of \(s\left( t \right) = {t^3} – 6{t^2} + 1\) metres, where \(t \ge 0\), \(t\) in seconds. Find the total distance travelled for the first 5 seconds.

metres

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

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

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

Find \(\int {\dfrac{{4{x^4} + 3{x^3}}}{x}dx} \).

CorrectIncorrect##### Hint

\(\int {{x^n}dx} = \dfrac{1}{{n + 1}}{x^{n + 1}} + C\)

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

If a curve has a stationary point \(\left( {-1,-3} \right)\) and a gradient of \(4x + 4\), find the value of \(y\) when \(x = 1\).

\(y = \)

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

Find the area between the \(x\)-axis and \(y = x – 2\) from \(x = 1\) to \(x = 3\).

Area =

CorrectIncorrect