## Are you ready to take your first step toward achieving your goal?

- 10 diagnosis quiz questions
- 10 minutes in duration
- Required to attempt all questions
- A mixture of short answer and multiple-choice questions
- Instant feedback straight after the test

## OK, let’s get started now!

## Are you ready to take your first step toward achieving your goal?

- Ten diagnosis quiz questions
- Ten minutes in duration
- Required to attempt all questions
- A mixture of short-answer and multiple-choice questions
- Instant feedback straight after the quiz

## OK, let’s get started now!

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

If \({u_{10}} = 100\) and \({u_{15}} = 175\), find \({u_{100}}\) of the arithmetic sequence.

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

Solve \({\log _{10}}x = – 5\), correcting to one significant figures.

$x=$

CorrectIncorrect##### Hint

\(a = {b^x} \Leftrightarrow x = {\log _b}a\)

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

The amount in an investment account is initially \($4500 \) at the beginning of January 2019 and decrease by 5% per annum due to deflation. At which year and month the amount becomes half.

CorrectIncorrect##### Hint

\(A = P \times {\left( {1 – r} \right)^t}\)

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

Find \(\theta \), correcting to the nearest degree, if the area of the triangle is 12 cm

^{2}. Ensure \(\theta \) is an obtuse angle.\(\theta = \) degree(s)

CorrectIncorrect##### Hint

\(Area = \dfrac{1}{2}ab\sin C\)

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

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

degree(s)

CorrectIncorrect##### Hint

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

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

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

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

1 & 0 & 1 &&&& \\

2 & 1 & 2 & 6 &&& \\

3 & 2 & 4 & 7 & 7 && \\

4 & 3 &&&&& \\

\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 7 of 10
##### 7. Question

Find the probability that a randomly chosen student plays rugby given that he plays soccer.

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

Daniel is a marathon runner. On the Olympic course in the northern hemisphere, the meantime is 2 hours 16 minutes with a standard deviation of 5 minutes. On the southern hemisphere, the meantime is 2 hours 20 minutes with a standard deviation of 4 minutes. In the northern hemisphere, Daniel’s time was 2 hours 18 minutes and in the southern hemisphere, his time was 2 hours 21 minutes. By writing these \(z\)-scores, determine the better performance.

\(z\)-score on northern hemisphere:

\(z\)-score on northern hemisphere:Which is the better result? (northern or southern)

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

For what values of \(x\) is \(y = \dfrac{{{x^2}}}{{2{x^2} + x + 1}}\) decreasing?

CorrectIncorrect##### Hint

increasing: \(f’\left( x \right) > 0\), decreasing: \(f’\left( x \right) < 0\)

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

Find the value of \(k\) if \(\int_{ – 1}^2 {\left( {3{x^2} + 4x + k} \right)dx} = 30\).

CorrectIncorrect