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- A mixture of short answer and multiple-choice questions
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- Question 1 of 10
##### 1. Question

Find the vertical asymptote(s) of \(f\left( x \right) = \dfrac{1}{{{x^2} + 4x + 3}}\).

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

Solve \( 3x^2 – 10x + 4 \lt 2x^2 – 5x – 2 \).

\( \lt x \lt \)

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

Find \(a\) and \(b\), if \(\dfrac{{\sin 2\theta + \sin \theta }}{{1 + \cos 2\theta + \cos \theta }} = a\tan \left( {b\theta } \right)\).

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

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

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 in the time from \(t = 1\) and \(t = 6\).

metres

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

The mass of radioactive \(t \) hours after establishment is \({R_t} = 200 \times {1.4^{ – t}}\) grams. Find the time for the mass to reach 150 grams. Answer correct to the nearest minute.

hour(s) minute(s)

CorrectIncorrect##### Hint

\({a^x} = y \Rightarrow x = {\log _a}y\)

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

Simplify \(\dfrac{{n! + \left( {n – 1} \right)!}}{{\left( {n – 1} \right)!}}\).

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

Find the coefficient of \({x^{9}}\) in the expansion of \({\left( {{x^2} + \frac{2}{x}} \right)^{15}}\).

Coefficient \( = \)

CorrectIncorrect##### Hint

\({T_{k + 1}} = \left( {\begin{array}{*{20}{c}}

n\\

k

\end{array}} \right){a^{n – k}}{b^k}\) - Question 8 of 10
##### 8. Question

Find the Cartesian equation of \( \displaystyle x = t+1, y = t + \frac{1}{t} \).

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

Factorise \( f(x) = x^4 – 2x^2 – 16x – 15 \) over real number field.

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

State the domain and range of \( y = \cos^{-1} (x+2) – \displaystyle \frac{\pi}{2} \).

CorrectIncorrect