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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 sum of all powers of 2 between 500 and 50000.

number of terms =

CorrectIncorrect##### Hint

\({S_n} = \dfrac{{{u_1}\left( {{r^n} – 1} \right)}}{{r – 1}}\)

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

Find \(x\) if \({\log _e}x = 7\), correct to 4 significant figures.

CorrectIncorrect##### Hint

\({e^x} = y \Leftrightarrow x = {\log _e}y\)

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

Find the constant term in the expansion of \({\left( {x + \dfrac{2}{{{x^2}}}} \right)^{15}}\).

Coefficient \( = \)

CorrectIncorrect##### Hint

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

n\\

k

\end{array}} \right){a^{n – k}}{b^k}\) - Question 4 of 10
##### 4. Question

State the domain and range of \(y = \sqrt {1 – x} + 2\).

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

The solutions of \(- 2{x^2} – 8x + 3 = 0\) are \( A \pm \sqrt {\dfrac{B}{C}} \). Find \(A\), \(B\) and \(C\).

\(A\) , \(B\) , \(C\)

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

The function \(y = f\left( x \right)\) is transformed to the function \(g\left( x \right) = 3 + 2f\left( {0.5x + 1} \right)\). Find the corresponding point of the point \(\left( { – 1, – 2} \right)\) on \(f\left( x \right)\).

( , )

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

Find \(x\) and \(y\), correcting to one decimal place.

\(x = \) , \(y = \)

CorrectIncorrect##### Hint

\(\dfrac{a}{{\sin A}} = \dfrac{b}{{\sin C}} = \dfrac{c}{{\sin C}}\)

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

Find \(A \), if the radius of a circle of the centre angle \(24^\circ \) and the arc length 12 cm is \(\dfrac{A}{\pi }\) cm.

\(A = \)

CorrectIncorrect##### Hint

\(l = r\theta \)

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

Solve \(\sin 4x = \sin 2x\) for \(0^\circ \le x \le 360^\circ \). Write answers in ascending order.

\(x = \) \(^\circ\), \(^\circ\), \(^\circ\), \(^\circ\), \(^\circ\), \(^\circ\), \(^\circ\), \(^\circ\), \(^\circ\)

CorrectIncorrect##### Hint

\(\sin 2x = 2\sin x\cos x\)

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

A biased coin has a 60% of probability of getting a Tail. This coin is tossed five times. Find the probability of obtaining at least two Tails.

CorrectIncorrect