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- 10 minutes in duration
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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 $y=1$ 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

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

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

Given \(f\left( x \right) = 2x – 1\), \(g\left( x \right) = x + 1\), \(\left( {f \circ f} \right)\left( 2 \right) = a\), \(\left( {g \circ f} \right)\left( 1 \right) = b\), \(\left( {f \circ g} \right)\left( c \right) = 3\) and \(\left( {g \circ g} \right)\left( d \right) = 1\) find the domain and range of \(a + b + c + d\).

\(a + b + c + d = \)

CorrectIncorrect##### Hint

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

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

Find all values of \(k\) for which \({x^2} – 2x + k = 0\) has a repeated root.

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 5 of 10
##### 5. Question

Find the maximum or minimum value of \(y = {x^2} – 4\), and the corresponding value of \(x\).

CorrectIncorrect##### Hint

\(y = a{x^2} + bx + c\)

\(a > 0\) concave up, thus minimum

\(a < 0\) concave down, thus maximum - Question 6 of 10
##### 6. Question

Solve \({\log _{10}}x = 0\) .

$x=$

CorrectIncorrect##### Hint

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

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

Solve \({\log _{10}}x + {\log _{10}}\left( {x + 1} \right) = {\log _{10}}30\).

\(x = \)

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

Solve \({e^{2x}} – 5{e^x} + 6 = 0\).

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

Find the inverse of the graph below.

CorrectIncorrect##### Hint

\(x \) values become \(y \) values, and vice versa.

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

The equation of a straight line perpendicular to \(y = – \dfrac{x}{2} + 4\) and passing through \(\left( {3,1} \right)\) is \(y = Ax + B\).

\(A = \) , \(B = \)

CorrectIncorrect