Here is the ground the questions cover. In Specialist Units 1 and 2 calculus is limited to the foundations shared with Methods and an introduction to rates and kinematics; differential equations wait until Units 3 and 4.

The items are tagged to the VCE study design for Year 11, so a score here reflects the standard a Year 11 class is working to, not a generic online level.

Mistakes we see most often in calculus and differential equations

A wrong answer is more useful than a right one if you know why it happened. In sessions with Year 11 students, these are the patterns our tutors see most:

None of these is a sign of low ability. Each is a reasonable idea that worked in an earlier year and needs replacing, which is exactly what a good explanation, or a tutor, does.

Ways to build calculus and differential equations at Year 11

If the quiz shows a gap, more of the same worksheets rarely fixes it. Try these instead:

At VCE, practise by hand for Exam 1 and with the CAS for Exam 2, use past papers under time and mark against the examiners' reports. Fix the errors the same week.

About the questions on this page

Every set on this page is a seeded selection of 10 from the 11 calculus and differential equations 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.

Because every question here is on calculus and differential equations, a low score is a clear signal and a high score is genuinely reassuring for this topic. What it cannot tell you is whether the other Year 11 Specialist Mathematics topics are equally secure, or how far above the year level the student can go; the free Skills Check covers both.

Year 11 Calculus & differential equations notes: the key ideas

A one-page summary of calculus and differential equations at Year 11 level, written by RHZ tutors to the VCE study design. Read it before the quiz, or print it for revision.

Units 1 and 2 calculus shares its foundations with Methods: the derivative as a limit, the power rule, tangents, stationary points and polynomial anti-derivatives.
A rate of change is a derivative with respect to time; the average rate uses a chord and the instantaneous rate uses the tangent gradient.
Where f increases, f′ is positive; at a turning point f′ crosses zero; a sign chart of f′ classifies stationary points.
Anti-differentiation reverses the process: ∫ x^n dx = x^(n+1)/(n + 1) + c, with an initial condition fixing c.
Worked example: a balloon has volume V = 4t³ cm³ at t seconds. dV/dt = 12t², so at t = 2 the volume grows at 48 cm³ per second.
Common mistake: reading the rate from the function value; the rate at t = 2 is dV/dt = 48, not V(2) = 32.
Common mistake: forgetting the constant when anti-differentiating, so the initial condition cannot be applied.

How to revise this: solidify the Methods differentiation and anti-differentiation rules by hand, since Specialist Units 3 and 4 assume them without review.

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 11 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.

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2. Printable practice with answers

Our Year 11 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 11 calculus and differential equations 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 calculus and differential equations and nowhere else. There are 11 eligible questions on this topic in our Year 11 Specialist Mathematics bank, so several different sets are available before any repeat.

Where do the calculus and differential equations questions come from?

From RHZ Tutoring's own Year 11 Specialist Mathematics 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 calculus and differential equations 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 11 Specialist Mathematics quiz?

Yes. The Year 11 Specialist Mathematics 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 11 Calculus & differential equations Quiz — 10 Questions, Instant Results

Calculus & differential equations in Year 11 Specialist Mathematics