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

Find the vector equation of the following diagram.

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

Find \(\overrightarrow {BM} \).

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

Differentiate \(y = \dfrac{1}{{\sqrt {5x – 1} }}\).

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

At an open-cut coal mine, a machine removes \( V\) cubic metres of coal in t hours, where \(V = 10t – \dfrac{{{t^2}}}{{10}}\). At what time is the machine removing coal at the rate of 9 m

^{3}per hour?CorrectIncorrect - Question 6 of 10
##### 6. Question

Find the maximum and minimum values of \(P = 400 + 100\sin \dfrac{{\pi t}}{3}\).

maximum = , minimum =

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

Find \(p\) and \(q\), if \(\int {\left( {x + 2} \right)\sqrt {2{x^2} + 8x} } dx = \dfrac{1}{p}\sqrt {{{\left( {2{x^2} + 8x} \right)}^q}} + C\).

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

CorrectIncorrect##### Hint

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

Find \(a\), if \(\int_0^3 {x\sqrt {x + 1} } dx = \dfrac{a}{{15}}\).

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

Find \(a\) and \(b\), if \(\int_3^6 {\dfrac{{4{x^3} – 3x + 2}}{x}} dx = a + {\log _e}b\).

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

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

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

CorrectIncorrect