Mathematics: should I choose it?

What will I learn?

How will I be assessed?

Progression and companion subjects

No complete companion or exclusion review is attached to this profile. Check the official course-entry conditions, language eligibility and your school’s sequence before enrolling. Links between resource hubs show related learning; they do not establish a compulsory prerequisite.

Will I find it hard?

Difficulty depends on your experience, interests, teaching and assessment. These are our reflection prompts, not an official difficulty rating.

• How do you feel about explaining a method and working through unfamiliar multi-step problems?
• Try the sample without looking at a worked answer, then check the steps you need to practise.

Does it scale up or down?

Use SATAC subject evidence. An aggregate-to-ATAR table is not a subject scaling table.

Scaling is not a measure of difficulty or a guaranteed bonus. Prioritise content you can engage with and required subjects for courses you are considering.

Try a little of the subject

Functions and graphs

A straight line describes a constant change in one variable for each unit change in another. In y = mx + c, x is the independent variable, y is the dependent variable, m is the gradient and c is the vertical intercept. Calculate gradient as change in y divided by change in x: m = (y₂ − y₁)/(x₂ − x₁). Keep the order of the points consistent in both differences. A positive gradient means the graph rises from left to right; a negative gradient means it falls. Gradient has units of output per unit of input, so it is more informative than an unlabelled number. Worked example. A line passes through (1, 3) and (5, 11). Its gradient is (11 − 3)/(5 − 1) = 2. Substituting (1, 3) into y = 2x + c gives c = 1, so y = 2x + 1. Substitution of the second point gives 11 = 11 and verifies the equation. If a point and gradient are known, use y − y₁ = m(x − x₁), then rearrange if required. Distinct parallel nonvertical lines have equal gradients. Perpendicular nonvertical lines have gradients whose product is −1. Thus a line perpendicular to gradient 2 has gradient −1/2. Through (2, 4), its equation is y − 4 = −(x − 2)/2, or y = −x/2 + 5. Horizontal and vertical lines are perpendicular too, although a vertical line has undefined gradient and cannot be written as y = mx + c. For a delivery service charging $18 plus $3 per kilometre, C = 18 + 3d. The vertical intercept represents the fixed charge; the gradient is $3 per kilometre. At six kilometres the model predicts $36. A charge of $42 corresponds to eight kilometres. Although the algebraic line extends indefinitely, the context requires d ≥ 0, and the service may restrict the distances available. The horizontal intercept would be negative and has no practical meaning here. When constructing a model from data, plot the measurements, label

Original practice question: A line passes through (1, 3) and (5, 11). What is its equation?

This is ATARMAxxing’s original sample learning material. It is not an official assessment task or a prediction of your school’s workload.

Explore the resources

Open the Mathematics subject hub and free preview (opens in a new tab)

• Mathematical Methods — SACE Stage 2 (opens in a new tab)
• Specialist Mathematics — SACE Stage 2 (opens in a new tab)

Core subject information and planning are free. Full study resources are optional.