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

Two apples and three peaches cost \($1.35\), while four apples and nine peaches cost \($3.75\). Find the cost of each.

apple = cents, peach = cents

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

Find \(c \), if the vertex of \(y = {x^2} – 6x + c\) is \(\left( {3, – 11} \right)\).

\(c = \)

CorrectIncorrect##### Hint

\(x = – \dfrac{b}{{2a}}\)

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

Find the largest angle in the triangle, correcting to the nearest degree.

degree(s)

CorrectIncorrect##### Hint

\(\cos A = \dfrac{{{b^2} + {c^2} – {a^2}}}{{2bc}}\)

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

Ben drove from Town A to Town B, a distance of \( 60 \) km, at an average speed of \( 80 \) km/h. He cycled back at an average speed of \( 20 \) km/h. Find his average speed for the whole journey.

*Note that it is not \( \textit{50} \) km/h.*Answer: km/h

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

For a “55 days interest-free” credit card, calculate the interest charged on a purchase of \$4900 made on 12 December and repaid on 25 February next year with a purchase interest rate of 17% per annum.

$ , correcting to the nearest cent

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

Given the principal is \$4800, the interest rate is 9% per annum and the monthly repayment is \$400, find the principal reduced during the first 2 months.

Balance at the end of the 1

^{st}month: $

Balance at the end of the 2^{nd}month: $

Principal reduced during the first 2 months: $

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

Cooper takes out a \$76000 home loan. The terms of the loan are 5.1% per annum compounded monthly over 22 years, with monthly repayments.

Find the following, correct to the nearest cent.Monthly repayment: $

Total amount paid: $

Total interest paid: $

CorrectIncorrect##### Hint

\( \displaystyle M = PV \times \frac{r \times (1+r)^n}{(1+r)^n-1} \)

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

The table shows the mean and standard deviation of times in the 100-m by the same group of athletes on four different days. It also shows Kate’s time on each of these days. On what day did Kate give her best performance?

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

day & mean & standard \ deviation & Kate’s \ time \\ \hline

1^{\text {st}} \ day & 10.22 & 0.16 & 10.15 \\ \hline

2^{\text {nd}} \ day & 10.45 & 0.18 & 10.31 \\ \hline

3^{\text {rd}} \ day & 10.17 & 0.11 & 10.08 \\ \hline

4^{\text {th}} \ day & 10.21 & 0.13 & 10.12 \\ \hline

\end{array} \)\(z\)-score on the 1

^{st}day:

\(z\)-score on the 2^{nd}day:

\(z\)-score on the 3^{rd}day:

\(z\)-score on the 4^{th}day:

Which is the best result? (first/second/third/fourth)

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

For normally distributed data \(X \sim N\left( {25,{3^2}} \right)\), find the value of \(k\) for \(\Pr \left( {X < k} \right) = 0.348\), correcting to two decimal places.

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

Calculate the compounded value of investment:

$6000 for 15 months at 4.5% per annum with interest compounded monthly.$ , correcting to the nearest cent

CorrectIncorrect