Specialist Mathematics: should I choose it?

What will I learn?

How will I be assessed?

Progression and companion subjects

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?

Specialist Mathematics, 2025. Table 6 of QTAC’s 2025 report publishes separate raw and scaled subject medians for General subjects with at least 50 students. Historical cohort data cannot predict your result or a future scaling direction.

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

Combinatorics

Combinatorics is the mathematics of counting without listing. Listing every outcome works for tiny problems, but once there are hundreds or millions of possibilities we need principles that let us count in a structured way. Three principles underpin the whole topic: the multiplication principle, the addition principle and the inclusion–exclusion principle. Multiplication principle. If a task is completed in stages, where the first stage can be done in m ways and, for each of those, the second stage can be done in n ways, then the whole task can be done in m × n ways. This extends to any number of stages. The key word is and : you choose an entrée and a main and a dessert. A tree diagram shows why the principle works: each branch at one stage splits into the same number of branches at the next stage. Addition principle. If a task can be done in one of several mutually exclusive ways (they cannot happen together), the total number of ways is the sum of the numbers for each way. The key word is or : you travel by bus or by train. The cases must not overlap; if they do, simple addition double counts. Inclusion–exclusion principle. When sets overlap, we correct for double counting. For two sets, |A ∪ B| = |A| + |B| − |A ∩ B|. Elements in both sets were counted twice, so we subtract them once. For three sets, |A ∪ B ∪ C| = |A| + |B| + |C| − |A ∩ B| − |A ∩ C| − |B ∩ C| + |A ∩ B ∩ C|. After subtracting the pairwise overlaps, the elements in all three sets have been added three times and subtracted three times, so they must be added back once. A Venn diagram is the best way to check this reasoning, and the number of elements in none of the sets is the total minus the union. Worked example 1. A café offers 4 entrées, 6 mains and 3 desserts. A three-course meal is one of each: 4 ×

Original practice question: What is the value of 5!?

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

• Specialist Mathematics — QCE Units 3 & 4 (opens in a new tab)

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