Free Year 12 Calculus Quiz — 10 Questions, Instant Results

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Calculus at Year 12: what the curriculum expects

Year 12 calculus covers the rules of differentiation including the chain, product and quotient rules, applications to tangents, rates and optimisation, anti-differentiation, definite integrals and areas under and between curves.

This topic sits inside the VCE study design for Year 12 maths; the questions stay at the easy and at-level tiers so the result is a fair check of the foundations.

Common calculus misconceptions tutors see

The distractors in this quiz are built from real misconceptions rather than random wrong numbers, so a specific wrong answer usually points to a specific gap. The ones we see most at Year 12:

• Maximum and minimum are not distinguished from the derivative being zero.
• The chain rule is missed when differentiating a composite function.
• The constant of integration is dropped.

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.

Practising calculus with a Year 12 student

The habits that move calculus from shaky to secure at Year 12:

1. Differentiate a mixed set daily so rule selection is automatic.
2. Sketch the curve before finding an area.
3. Check anti-derivatives by differentiating them.

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 this calculus quiz works

The 10 questions are drawn from 21 eligible items on calculus in our Year 12 maths bank, all at the easy and at-level tiers. The selection is fixed for this address so a shared link shows the same quiz; press New set of questions or add ?seed= to the address for a different mix. Options are shuffled, no two questions share a stem, and the answer key is fetched from our server only after you submit, so it is not hidden in the page.

A single-topic quiz is more precise than a mixed one: if the score here is low, the gap is in calculus, 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.

The quiz: 10 questions

Choose one answer for each question, then press Mark my answers. Set 72524 · New set of questions →

Question 1

Calculus

Let f(x) = x · ln(x) for x > 0. Which of the following correctly gives f′(x)?

f′(x) = ln(x) f′(x) = x · (1/x) = 1 f′(x) = 1/x f′(x) = 1 + ln(x)

Question 2

Calculus

Evaluate ∫₁³ (2x − 1/x²) dx. Give your answer as a fraction if necessary.

8 − 2/3 8 − 4/3 6 − 2/3 8 + 2/3

Question 3

Calculus

Find ∫ 6x dx.

3x² + c 6x² + c 6 + c x² + c

Question 4

Calculus

The function f(x) = x³ − 3x² − 9x + 2 is decreasing on the interval where f′(x) < 0. Which of the following correctly identifies that interval?

−1 < x < 3 x < −1 or x > 3 x < 0 or x > 6 0 < x < 2

Question 5

Calculus

A curve has gradient function f′(x) = 3x² − 12x + 9. At the point where the curve has a local minimum, what is the second derivative f′′(x)?

−6 0 6 9

Question 6

Calculus

The rate at which a population P grows is modelled by dP/dt = kP, where k is a positive constant. At t = 0, P = 200 and at t = 3, P = 1600. What is the exact value of k?

k = (1/3)·ln(2) k = 8/3 k = ln(8)/3 k = ln(8)

Question 7

Calculus

The function f(x) = 2x³ − 9x² + 12x − 3. At which x-value does f have a local minimum, and what is the value of f′′(x) there?

x = 2, f′′(2) = −6 x = 1, f′′(1) = 6 x = 2, f′′(2) = 6 x = 1, f′′(1) = −6

Question 8

Calculus

Differentiate y = x⁴.

4x³ 4x x³ x⁵/5

Question 9

Calculus

Differentiate y = 8.

8 8x 1 0

Question 10

Calculus

Find ∫ x² dx.

x³/3 + c 2x + c 3x² + c x³ + c

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Your result

0 / 10

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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

Other Maths topics for Year 12

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