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

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

If the gradient of \(\left( {8,a} \right)\) and \(\left( {-1,3} \right)\) is \(2 \), find the value of \(a \).

\(a = \)

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

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

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

If the domain of \(y = \dfrac{x}{2} + 1\) is \(1 < x \le 2\), state the range of \({y^{ - 1}}\).

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

Solve for \(r \), \(2000 \times {\left( {1 + r} \right)^{10}} = 3000\), correcting to two decimal places.

\( r = \)

CorrectIncorrect##### Hint

\({a^t} = B \Rightarrow a = \sqrt[t]{B}\)

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

The mass of bacteria \(t\) hours after establishment is \({A_t} = 500 \times {1.6^{1.1t}}\) grams. Find the time for the mass to reach 600 grams. Answer correct to the nearest minute.

minute(s)

CorrectIncorrect##### Hint

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

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

When estimating a value within the range of collected data, this is called interpolation and the estimate is quite reliable.

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

Find the first two values of \(t\) when \(h = 3\) given \(y = 3 + 5\sin \dfrac{\pi }{3}\left( {2t – 4} \right)\).

,

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

If \(f\left( x \right) = \dfrac{1}{x}\), find \(2f\left( {x – 1} \right) + 3\) in simplest form.

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

For the function \(f\left( x \right) = \dfrac{{ – 4x – 10}}{{x + 3}}\), find the horizontal and vertical asymptotes.

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

CorrectIncorrect