Free Year 11 Calculus (integration) Quiz — 10 Questions, Instant Results

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Calculus (integration) in Year 11 Mathematical Methods

Here is the ground the questions cover. In Units 1 and 2 integration is introduced as anti-differentiation of polynomials, with the constant of integration and simple areas under curves.

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 (integration)

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:

• Area below the axis is not treated separately.
• The limits are substituted in the wrong order.
• Average value is confused with the mean of two function values.

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 (integration) at Year 11

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

1. Practise definite integrals by hand for Exam 1.
2. Use the CAS to verify areas between curves.
3. Check every anti-derivative by differentiating it.

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.

How the 10 questions are chosen

We keep 10 calculus (integration) questions for Year 11 that meet our standard, a few of them at the stretch tier so the set is full, and this page serves 10 of them at a time. The default set is stable, so a teacher or parent can share the link; a fresh set is one click away. Marking happens on our server so the answer key cannot be read from the page.

A single-topic quiz is more precise than a mixed one: if the score here is low, the gap is in calculus (integration), not somewhere in Year 11 Mathematical Methods 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.

The quiz: 10 questions

Choose one answer for each question, then press Mark my answers. Set 87640 · New set of questions →

Question 1

Calculus (integration)

Find ∫ 4 dx.

0 4 + c x⁴ + c 4x + c

Question 2

Calculus (integration)

Find ∫ x² dx.

2x + c 3x² + c x³ + c x³/3 + c

Question 3

Calculus (integration)

Evaluate ∫₀¹ 2x dx.

0 1/2 1 2

Question 4

Calculus (integration)

A function f satisfies f′(x) = 6x² − 4x and f(0) = 3. What is f(2)?

11 19 13 7

Question 5

Calculus (integration)

A particle moves along a straight line with acceleration a(t) = 6t − 2 m/s² at time t seconds. Its initial velocity is 4 m/s and initial position is 1 m from the origin. What is the position of the particle at t = 2 s?

17 m 13 m 9 m 21 m

Question 6

Calculus (integration)

Evaluate ∫₀² 3x² dx.

12 6 4 8

Question 7

Calculus (integration)

Given that ∫₁⁴ f(x) dx = 7 and ∫₁⁴ g(x) dx = 3, what is the value of ∫₁⁴ [2f(x) − 3g(x) + 4] dx?

11 17 25 9

Question 8

Calculus (integration)

Find ∫ (3x² + 2) dx.

x³ + 2 + c x³ + 2x + c 3x³ + 2x + c 6x + c

Question 9

Calculus (integration)

Find ∫ 2x dx.

2x² + c x²/2 + c x² + c 2 + c

Question 10

Calculus (integration)

Find ∫ 6x² dx.

2x² + c 2x³ + c 6x³ + c 12x + c

Mark my answers →

Your result

0 / 10

Take the free full Skills Check →   Try another set

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

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

Frequently asked questions

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