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- A mixture of short answer and multiple-choice questions
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- Question 1 of 10
##### 1. Question

State whether $y=x-1$ is a function or not.

CorrectIncorrect##### Hint

The relation is a function if each vertical line cuts the graph no more than once.

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

Given \(f\left( x \right) = ax + b\), \(f\left( -2 \right) = 7\) and \(f\left( 3 \right) = 3\), find \(a \) and \(b\).

\(a = \)

\(b = \)

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

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

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

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

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

Find all values of \(k\) for which \({x^2} + 4x + k = 0\) has two distinct real roots.

CorrectIncorrect##### Hint

\(\begin{align} \displaystyle

{b^2} – 4ac &\gt 0 \text{ two real solutions }\\

{b^2} – 4ac &= 0 \text{ one real solution }\\

{b^2} – 4ac &\lt 0 \text{ no real solutions }

\end{align}\) - Question 6 of 10
##### 6. Question

Solve \({\log _{10}}x = – 1\) .

$x=$

CorrectIncorrect##### Hint

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

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

Find \(x\) , given \({\log _{10}}500 = x – {\log _{10}}2\) .

CorrectIncorrect##### Hint

\({\log _b}xy = {\log _b}x + {\log _b}y\)

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

Find \(k\) if \({\log _e}\dfrac{1}{{\sqrt {27} }} = k{\log _e}3\). Answer in decimal form.

\( k = \)

CorrectIncorrect##### Hint

\({\log _e}{x^n} = n{\log _e}x\)

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

Find \(a \), if the vertex of \(y = {2ax^2} – 8x + a\) is \(\left( {4, 1} \right)\).

\(a = \)

CorrectIncorrect##### Hint

\(x = – \dfrac{b}{{2a}}\)

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

Find the value of \(k \) that the straight lines \(y = 2kx + 6\) and \(y = \dfrac{x}{4} – 5\) are perpendicular.

\(k = \)

CorrectIncorrect