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

Find \(k \) value to make \(f\left( x \right)\) continuous.

\(f\left( x \right) = \left\{ {\begin{array}{*{20}{l}}

{k{x^2} – 3,}&{{\rm{for }} \ x \le 3}\\

{2x,}&{{\rm{for }} \ x > 3}

\end{array}} \right.\)\(k = \)

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

Evaluate \(\mathop {\lim }\limits_{x \to \infty } \dfrac{{\left( {2x – 1} \right)\left( {x – 2} \right)}}{{\left( {x – 1} \right)\left( {x + 2} \right)}}\).

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

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

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

CorrectIncorrect##### Hint

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

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

Find \(A\) and \(B\), if the equation of the normal to the curve \(y = \dfrac{1}{2}{x^2} + 3x – 7\) at the point where it crosses the \(y\)-axis is \(x + Ay + B = 0\).

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

CorrectIncorrect##### Hint

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

- Question 5 of 10
##### 5. 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 6 of 10
##### 6. Question

The displacement of a particle \(x\left( t \right)\) metres in a straight line from a fixed point \(O \), the origin, at any time \(t \) seconds is given by \(x\left( t \right) = 2{t^2} – 4t + 7\). Find the total distance traveled in the first \(4 \) seconds.

distance =

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

Over a period of 12 hours, the temperature of a classroom is described by the function \(T\left( h \right) = {h^2} + 5h + 12\) where \(T \) is the temperature in degrees after \(h \) hours. Find the average rate of change between \(h = 2 \) and \(h = 6 \).

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

Evaluate \(\mathop {\lim }\limits_{x \to 3} \dfrac{{2{x^2} – 18}}{{x – 3}}\).

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

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

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

The curve \(y = a{x^2} – 7x + 6\) has a gradient of 1 when \(x = 2 \). Find the value of \(a\).

\(a = \)

CorrectIncorrect