A short orientation first. Year 12 functions covers polynomial, exponential, logarithmic and circular functions, transformations, composite and inverse functions, and solving equations involving them exactly and numerically.

Our tutors wrote and checked these questions against the VCE study design, which is why the wording and the difficulty match what a Year 12 student meets at school.

The usual functions errors at Year 12

If your child gets a question wrong here, it is worth checking whether one of these is behind it. They are the functions misconceptions RHZ tutors correct most often with Year 12 students:

Each of these is fixable in a session or two once it has been named, which is why the results panel below shows the correct answer and an explanation rather than just a score.

How to practise functions at home

Practice works when it is short, regular and specific. For functions, our tutors suggest:

For VCE maths, fluency in the foundations frees up working memory for the extended questions. Do a short mixed set daily and a timed paper each fortnight.

About the questions on this page

Every set on this page is a seeded selection of 10 from the 17 functions questions that pass our quality gate. A different seed gives a different set, and there are many more combinations than any one student will need. The correct answers never appear in the page source; the browser asks our server for them after you press Mark my answers.

A single-topic quiz is more precise than a mixed one: if the score here is low, the gap is in functions, not somewhere in Year 12 maths generally. It is still short, though, and it cannot show how a student copes with the stretch and challenge questions that decide a top result. That is what the free Skills Check adds.

Year 12 Functions notes: the key ideas

A one-page summary of functions at Year 12 level, written by RHZ tutors to the VCE study design. Read it before the quiz, or print it for revision.

A composite f(g(x)) exists only when the range of g lies inside the domain of f; g is applied first.
An inverse f⁻¹ swaps x and y; it exists only if f is one-to-one, so restrict the domain if needed.
The domain of f⁻¹ is the range of f, and vice versa; the graph of f⁻¹ reflects f in the line y = x.
Exponential and log functions are inverses: y = eˣ and y = logₑ x; log x needs x above 0.
Circular functions sin and cos have period 2π, tan has period π; transformations alter amplitude and period.
Solve exactly with inverse operations, then check solutions against the original domain.
Worked example: f(x) = e²ˣ + 1. Swap: x = e²ʸ + 1, so f⁻¹(x) = ½ logₑ(x − 1) with domain x above 1.
Common mistake: confusing f⁻¹(x) with 1/f(x); the inverse undoes f, while the reciprocal just divides.
Common mistake: forming g(f(x)) when f(g(x)) is asked; the inner function is applied first, so order matters.

How to revise this: find an inverse by swapping and solving, state its domain, then verify f(f⁻¹(x)) = x by composition.

Prints the notes only; the quiz is hidden.

How to read a score out of 10

What to do with the result

1. Want the full picture?

The free Skills Check takes about 15 minutes, covers every Year 12 topic including stretch and challenge questions, and sends a same-day topic-by-topic report. A tutor calls to walk you through it, no obligation.

Start the free Skills Check →

2. Printable practice with answers

Our Year 12 practice papers are full-length, curriculum-aligned and come with worked answers, so a student can practise on paper the way the real test is sat.

Browse practice papers →

3. Tutoring in Melbourne's west or online

Small groups from $25 an hour and 1:1 from $35 an hour at our Truganina centre, or online anywhere in Australia. Same tutors, same Skills Check, same progress notes either way.

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Frequently asked questions

Is this Year 12 functions quiz free?

Yes, completely: no sign-up, no email, no payment, and you can take it as many times as you like. It is one of 3,261 free practice questions RHZ Tutoring publishes across Prep to Year 12. Press New set of questions, or add ?seed= to the address, for a different selection from the same topic.

Why only 10 questions on one topic?

Because a single-topic set is the most precise free check available: if the score is low, the gap is in functions and nowhere else. There are 17 eligible questions on this topic in our Year 12 Maths bank, so several different sets are available before any repeat.

Where do the functions questions come from?

From RHZ Tutoring's own Year 12 Maths question bank, written to the VCE study design, checked by a tutor and passed through an automated quality gate. The same bank feeds our tutoring sessions and the free Skills Check. The questions on this page sit at the easy and at-level tiers.

What should I do if the score is low?

Read the explanation for each incorrect answer first; most gaps in functions are one of the misconceptions listed on this page. Then try a second set a few days later. If it is still low, the free Skills Check will show whether the gap is confined to this topic, and a tutor can build a short catch-up plan.

Is there a mixed Year 12 Maths quiz?

Yes. The Year 12 Maths quiz spreads ten questions across every topic for the year, and the hub lists topic quizzes for every year level from Prep to Year 12.

Free Year 12 Functions Quiz — 10 Questions, Instant Results

What Year 12 students need to know about functions