Free · No sign-up · Year 11 · Specialist Mathematics · Calculus & differential equations

Free Year 11 Calculus & differential equations Quiz — 10 Questions, Instant Results

Want to know whether calculus and differential equations is secure at Year 11 level? Answer 10 questions here, see the score and the correct answers straight away, and then try a new set. Everything is free, part of 3,261 free practice questions RHZ Tutoring publishes, and nothing about your child is collected.

Start the quiz ↓   Or take the free 15-minute Skills Check →

✅ VCE study design aligned⚡ Instant marking + explanations📚 3,261 free practice questions

Free practice quizzesYear 11 Specialist Mathematics quiz › Calculus & differential equations

Calculus & differential equations in Year 11 Specialist Mathematics

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:

  1. Sketch slope fields by hand for simple equations.
  2. Use Euler's method with a spreadsheet.
  3. Practise each integration technique separately, then mixed.

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.

The quiz: 10 questions

Choose one answer for each question, then press Mark my answers. Set 40988 · New set of questions →

Question 1
Calculus & differential equations

The derivative of y = eˣ is?

Question 2
Calculus & differential equations

Solve dy/dx = 2x with y = 5 at x = 0.

Question 3
Calculus & differential equations

The second derivative of y = x³ is?

Question 4
Calculus & differential equations

For dy/dx = 2x, the general solution is?

Question 5
Calculus & differential equations

Differentiate y = 12.

Question 6
Calculus & differential equations

Find ∫ x² dx.

Question 7
Calculus & differential equations

Consider the differential equation dy/dx = y/x for x > 0. Which of the following correctly describes the general solution?

Question 8
Calculus & differential equations

Evaluate ∫₀¹ 3x² dx.

Question 9
Calculus & differential equations

A particle moves along the x-axis with acceleration a(t) = 6t − 4 m/s². At t = 0, velocity is 2 m/s and position is x = 1 m. What is the particle's position at t = 3 s?

Question 10
Calculus & differential equations

A curve passes through the point (1, 0) and satisfies dy/dx = (y + 1)/x for x > 0. Using separation of variables, what is the y-coordinate of the point on the curve where x = e²?

How to read a score out of 10

9 or 10 out of 10
The easy and at-level content is secure. The useful question now is how far above the year level the student can go, which a ten-item quiz cannot show. The free Skills Check adds stretch and challenge questions on every topic so you can see the ceiling as well as the floor.
7 or 8 out of 10
Solid, with one or two specific gaps. Look at which topic the incorrect answers came from (the results panel names the weakest topic) and spend a week on that topic before re-testing with a different seed.
5 or 6 out of 10
Some core ideas are shaky. The pattern matters more than the score: two misses in the same topic is a gap; misses scattered across topics usually means reading the question too fast. Either way, the Skills Check will tell you which.
4 or fewer out of 10
Foundations from an earlier year are probably missing, which is common and fixable. Try the quiz one year level down to confirm, then talk to a tutor about a short catch-up plan rather than more of the same practice.

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.

Start the free Skills Check →

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.

See Specialist Mathematics tutoring → All tutoring →

Questions? Call 03 9509 3293 or book a free consultation. RHZ Tutoring, 17/47 Apex Drive, Truganina VIC 3029.

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.

Other Specialist Mathematics topics for Year 11

Mixed Year 11 Specialist Mathematics quiz (all topics) →

Calculus & differential equations in other year levels

Year 12 Calculus & differential equations

All 3,261 free practice questions, Prep to Year 12 →