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

Free practice quizzes › Year 12 Maths (VCE) quiz › Exam technique

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 75905 · New set of questions →

Question 1

Exam technique

A measurement answer includes?

no units a colour a name units

Question 2

Exam technique

A student is asked to find all values of x in [0, 2π] satisfying sin²(x) − sin(x) − 2 = 0, giving exact answers. They substitute u = sin(x), factor to (u − 2)(u + 1) = 0, obtain u = 2 or u = −1, then write: 'sin(x) = 2 has no solution. sin(x) = −1 gives x = 3π/2. Final answer: x = 3π/2.' They receive full marks. A classmate says they should have presented both solutions from sin(x) = 2. Which response is correct?

The student is incorrect; they should have used the quadratic formula rather than factorisation. The student is partially correct but should have noted x = −π/2 as a second solution from sin(x) = −1. The student is correct; sin(x) = 2 has no real solution because −1 ≤ sin(x) ≤ 1, so no additional solutions exist. The classmate is correct; sin(x) = 2 must yield two solutions since the sine function has two solutions per period.

Question 3

Exam technique

In an exam, a student must find the inverse function of f(x) = (2x + 1)/(x − 3), stating any restrictions. They swap x and y, rearrange correctly to y = (3x + 1)/(x − 2), and write f⁻¹(x) = (3x + 1)/(x − 2). They do not state any domain restriction. The examiner deducts a mark. Which restriction was required and why?

x ≠ 3 must be stated because the original function has a vertical asymptote at x = 3. x ≠ 2 must be stated because the inverse function is undefined when the denominator equals zero. x > 0 must be stated because inverse functions are only defined for positive inputs. x ≠ −1/2 must be stated because f(x) = 0 when x = −1/2, and zero cannot be an input to the inverse.

Question 4

Exam technique

'Show that' questions need?

only the answer nothing full working a guess

Question 5

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?

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

Question 6

Exam technique

A student is asked to sketch the graph of f(x) = 2sin(3x) + 1 for 0 ≤ x ≤ 2π, labelling key features. They correctly identify the amplitude as 2, the period as 2π/3, and the vertical shift as 1. They sketch the graph but do not label axes, scale markings, or the coordinates of any maximum or minimum points. How does this affect their exam mark?

Only the period needs to be shown on the graph; other labels are optional. The examiner cannot deduct marks for missing labels unless the question specifically says 'fully labelled'. Marks are likely deducted because 'key features' in an exam context requires labelled axes, scale, and coordinates of turning points. No marks are lost because the shape of the graph is mathematically correct.

Question 7

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 decimal 0.707 is incorrect and should be rounded to 0.71 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

Question 8

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?

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 Accept the answer, because standard deviation can be negative when the data are negatively skewed

Question 9

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?

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

Question 10

Exam technique

A student solves the equation log₂(x) + log₂(x − 2) = 3 and obtains x = 4 and x = −2. They then write 'both solutions are valid.' Evaluate their conclusion.

The conclusion is wrong; x = 4 must be rejected because it makes the combined logarithm equal to 3, which is outside the domain of log functions The conclusion is wrong; x = −2 is valid but x = 4 should be rejected because it is the extraneous solution introduced by the product rule for logarithms The conclusion is correct; both values satisfy the original equation when substituted back The conclusion is wrong; x = −2 must be rejected because log₂(−2) and log₂(−2 − 2) are undefined, so only x = 4 is valid

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

Other Maths topics for Year 12

Mixed Year 12 Maths (VCE) quiz (all topics) →

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