- Answer all 15 questions in the spaces provided.
- Show all your working — marks are given for the method, not just the final answer.
- Section A — Recall: short answers and one or two steps.
- Section B — Application: full worked solutions.
- Section C — Challenge: multi-part questions. Answer each part (a), (b), (c) separately.
- Give exact answers in surd form where asked — do not round.
State the difference between an expression and an equation.
Solve $2x + 7 = 15$.
Write an expression for the product of two consecutive even numbers.
Write down the standard form of a quadratic equation.
Make $x$ the subject of the formula $y = 2x + 1$.
Solve $4(x – 1) = 2x + 6$.
Solve the fractional equation $\dfrac{x}{3x – 2} = 2$.
Solve the simultaneous equations:
$3x + y = 11$
$2x – y = 4$
Solve $x^2 + 7x + 12 = 0$ by factorisation.
Make $x$ the subject of the formula $y = \sqrt{x – 2}$.
• 3 adult tickets and 2 child tickets cost \$23.
• 1 adult ticket and 2 child tickets cost \$13.
(a) Write two equations to represent this information.
(b) Solve your equations to find the price of an adult ticket and a child ticket.
Solve $\dfrac{3}{x + 1} + \dfrac{2}{x – 1} = 1$.
(a) Write $x^2 + 8x + 10$ in completed square form.
(b) Hence solve $x^2 + 8x + 10 = 0$, giving your answers in surd form.
(c) Solve $2x^2 – 4x – 3 = 0$ using the quadratic formula, giving your answers in surd form.
Consider the simultaneous equations $y = x + 1$ and $y = x^2 – 1$.
(a) Solve the equations to find all pairs of values of $x$ and $y$.
(b) Explain why this pair of equations has two solution pairs.
(a) Make $x$ the subject of $y = \dfrac{x + 4}{x – 2}$.
(b) Make $r$ the subject of $V = \pi r^2 h$.
