Free Year 12 Exam technique Quiz — 10 Questions, Instant Results

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Exam technique at Year 12: what the curriculum expects

Exam technique for Year 12 covers reading the question, showing working that earns method marks, allocating time across a paper, the difference between Exam 1 (technology-free) and Exam 2 (CAS), and reviewing answers for reasonableness.

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 exam technique 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:

• Units and domains are left off final answers.
• Working is skipped on Exam 1, so method marks are lost.
• Too long is spent on the first multiple-choice section.

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 exam technique with a Year 12 student

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

1. Do timed past papers under exam conditions.
2. Mark your own work with the examiners' report.
3. Write a list of formulas you must know for Exam 1.

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

The 10 questions are drawn from 27 eligible items on exam technique 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 exam technique, 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 15785 · New set of questions →

Question 1

Exam technique

A student is asked: 'Find the equation of the tangent to y = x³ − 4x at the point where x = 2.' They correctly find y = 0 and f′(x) = 3x² − 4, giving f′(2) = 8. They write the equation as y = 8x + c, substitute (2, 0) to get c = −16, and present the answer y = 8x − 16. An examiner awards full marks. A classmate argues they should have also verified the point lies on the curve. Which response best reflects good exam technique?

The student should re-derive the gradient using first principles to guarantee correctness. The student's work is complete and the classmate's suggestion, while good practice, would not earn additional marks in this context. The classmate is correct; verifying the point lies on the curve is a required step without which marks could be deducted. The student must also find the normal to the curve at that point before the answer is complete.

Question 2

Exam technique

In an exam, a student is asked to find the exact value of sin(135°). They write sin(135°) = sin(45°) = √2/2 ≈ 0.707. Which part of their working contains an error that would cost marks?

The exact value √2/2 is incorrect; it should be √3/2 Using the related angle of 45° — this reference angle is wrong for 135° Writing sin(135°) = sin(45°) without noting the correct quadrant sign, then using the decimal approximation instead of the exact value √2/2 The decimal 0.707 is incorrect and should be rounded to 0.71

Question 3

Exam technique

A student solves a quadratic equation and obtains x = −3 and x = 5. The original problem states that x represents the width of a rectangular paddock in metres. What must the student do before writing their final answer?

Report both solutions because a quadratic always has two valid answers Reject x = −3 because a width cannot be negative, and state x = 5 m Average the two solutions to obtain x = 1 m Substitute both values back into the quadratic to check for arithmetic errors

Question 4

Exam technique

An exact answer avoids?

π surds rounding fractions

Question 5

Exam technique

A student is solving an exam problem: 'A particle moves so that its velocity is v(t) = t² − 5t + 4 m/s for t ≥ 0. Find the total distance travelled in the first 4 seconds.' The student computes ∫₀⁴ (t² − 5t + 4) dt, obtains −8/3, and writes 'total distance = −8/3 m'. What is wrong with this approach?

Distance must be found using ∫₀⁴ |v(t)| dt; the student must split the integral at the zeros of v(t) and add the absolute values of each piece. The antiderivative of t² − 5t + 4 is incorrect; the student has made an algebraic error leading to a negative result. A negative answer for distance is acceptable because the particle travels in the negative direction for part of the interval. The student should have used the displacement formula s = ut + ½at² instead of integration.

Question 6

Exam technique

0.02048 to 3 significant figures is?

0.020 0.0205 0.021 0.02

Question 7

Exam technique

A student uses their CAS calculator to find the intersection of y = e^x and y = 3 − x², and the calculator returns x ≈ 0.9282 and x ≈ −1.8257. The question asks for answers correct to 2 decimal places. The student writes x ≈ 0.93 and x ≈ −1.83. Have they rounded correctly?

No — x ≈ −1.8257 rounds to −1.83 correctly, but x ≈ 0.9282 rounds to 0.93 incorrectly; it should be 0.93. Actually both are correct: 0.9282 → 0.93 and −1.8257 → −1.83. Yes — both values are correctly rounded to 2 decimal places No — for negative numbers, rounding away from zero means −1.8257 should be reported as −1.82 No — 0.9282 rounds to 0.92 (the third decimal is 8, so round the second decimal up gives 0.93, which is correct, but the student made an error with the negative)

Question 8

Exam technique

A student is asked to 'show that the derivative of f(x) = x·ln(x) is 1 + ln(x).' They write: 'f′(x) = 1·ln(x) + x·(1/x) = ln(x) + 1. ✓'. An examiner deducts marks. Why?

The answer must be left as ln(x) + 1 rather than 1 + ln(x) to match the target expression exactly A 'show that' response must present each differentiation rule used (product rule, derivative of ln(x)) explicitly as separate steps before combining them The student should have used logarithm laws to expand ln(x) before differentiating The student differentiated incorrectly; the derivative of x·ln(x) is not 1 + ln(x)

Question 9

Exam technique

A student is asked to find all solutions to 2cos²(x) − cos(x) − 1 = 0 for x ∈ [0, 2π], giving exact answers. They factorise to (2cos(x) + 1)(cos(x) − 1) = 0, obtaining cos(x) = −½ and cos(x) = 1. They then write: cos(x) = −½ gives x = 2π/3, and cos(x) = 1 gives x = 0, and present {0, 2π/3} as the complete solution set. What is the most significant exam technique error in their final answer?

They should not have included x = 0 because the domain [0, 2π] uses a closed interval and 0 is a boundary point. They factorised incorrectly; the correct factors are (2cos(x) − 1)(cos(x) + 1) = 0. They needed to verify each solution by substituting back into the original equation before writing the final answer. They omitted x = 4π/3, which is the second solution in [0, 2π] for cos(x) = −½, making the solution set incomplete.

Question 10

Exam technique

When checking work on a multiple-choice exam, a student notices that their answer to a statistics question gives a standard deviation of −4.2. What is the most important action to take?

Accept the answer, because standard deviation can be negative when the data are negatively skewed Report the answer as |−4.2| = 4.2 without reworking, because the sign error is a known rounding artifact Report the answer as −4.2 and note that it indicates the data are below the mean Rework the calculation entirely, because standard deviation is always non-negative and a negative result indicates a computational error

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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

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