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

The first three terms in an arithmetic sequence are 55, 51, 47, and the \(k\)

^{th}term is . Find \(k\).\(k = \)

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

Find the interest rate per annum, correcting to 2 decimal places, that would enable an investment of \($5000\) to grow to \($7000\) over 3 years if interest is compounded quarterly.

CorrectIncorrect##### Hint

\(A = P{\left( {1 + r} \right)^n}\)

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

Solve \({\log _3}27 + {\log _3}\frac{1}{3} = {\log _3}x\).

\(x = \)

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

Given \(f\left( x \right) = 2x – 3\), \(g\left( x \right) = – x + k\) and \(\left( {g \circ f} \right)\left( x \right) = \left( {f \circ g} \right)\left( x \right)\), find \(k\).

CorrectIncorrect##### Hint

\(\left( {f \circ g} \right)\left( x \right) = f\left( {g\left( x \right)} \right)\)

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

Find the total surface of the prism, leaving in \({{\rm{m}}^2}\).

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

Given \(\vec b = \left( {\begin{array}{*{20}{c}}

– 2\\

3

\end{array}} \right)\) and \(\vec c = \left( {\begin{array}{*{20}{c}}

{ 1}\\

– 4

\end{array}} \right)\), find \(\left| {\vec 2c – \vec b} \right|\), correcting to two significant figures.CorrectIncorrect - Question 7 of 10
##### 7. Question

Find the interquartile range of the data represented in box-and-whisker plot.

\( \begin{array}{c|cccccc}

1 & 4 & 8 &&&& \\

2 & 2 & 6 & 9 &&& \\

3 & 0 & 3 & 4 & 7 & 8 & \\

4 & 1 & 2 & 4 &&& \\

\end{array} \)List the scores in ascending order.

The upper quartile is .

The lower quartile is .

The interquartile range is .

CorrectIncorrect##### Hint

Interquartile Range = Upper Quartile – Lower Quartile

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

A box contains balls numbered \( 1 \) to \( 50 \). One ball is taken randomly out of the box. Find the probability that it is a multiple of \( 12 \), given that it is a multiple of \( 3 \). Answer to two decimal places.

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

For normally distributed data \(X \sim N\left( {38.7,{8.2^2}} \right)\), find the value of \(k\) for \(\Pr \left( {X < k} \right) = 0.9\), correcting to three decimal places.

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

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

CorrectIncorrect