∑IGS Maths

VCE Mathematical Methods · 2024 exam feedback

What the markers actually wanted

A direct read of what cost students marks in the 2024 Exam 1 & Exam 2 — and the small habits that get those marks back. Most of these are technique fixes, not new content. You can land most of them this week.

Source: VCAA chief-assessor presentations — Catherine Devlyn (Exam 1, tech-free) and Allason McNamara (Exam 2, CAS), 2024.

Part 1

Top 10 things that cost marks

Tap a card to see the VCAA examples (Exam 1 and Exam 2) and what you should do differently.

1

Brackets and interval notation

Both papers Notation

Brackets around arguments, numerators, coordinates, intervals. Round vs square has to be unambiguous.

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What cost marks Exam 1

Missing brackets around $\cos(3x)$ and around a quadratic numerator made the answer ambiguous (Q1). A "rounded square" bracket on an interval couldn't be marked (Q5c).

What cost marks Exam 2

Flagged everywhere. An interval written $[1,-1]$ without proper brackets reads as two separate terms. Coordinates always need brackets.

Do this: brackets-or-it's-wrong. Be strict on intervals and coordinates. Vinculum too — $\frac{1}{x}+2$ is not the same as $\frac{1}{x+2}$.
2

Exact vs approximate answers

Exam 2 focus Technique

Give exact answers unless the question explicitly asks for a decimal.

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What cost marks Exam 2

$0.5, 5.06$ instead of exact coordinates (Q1). $1.06$ instead of an exact translation. $0.33$ instead of an exact area (Q2).

What cost marks Exam 1

Truncus $x$-intercepts had to be exact surds (Q3).

Do this: set your CAS to "Exact" or use the fraction template. If you do hit a decimal, carry more decimal places than the question asks for and never round mid-working.
3

Command terms — verify / show that / hence

Both papers Language

Each of these words means a specific thing. The working is the mark.

▾

What cost marks Exam 1

A "hence, verify" answered with calculus scored zero — verify means substitute and check (Q7b). Log questions needed every step shown (Q6).

What cost marks Exam 2

Don't skip steps in "show that". The answer is given, so all the marks live in your working (Q2, Q4, Q5).

Do this: learn the three words. Verify = substitute and check. Show that = every line of working, no shortcuts. Hence = use the previous part, don't restart.
4

Transformation language and order

Both papers Language

Use the study-design wording, get the direction right, use the variables the question uses.

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What cost marks Exam 1

"In/on an axis" wasn't accepted — say "parallel to the $x$-axis" or "from the $y$-axis". And use the question's variables ($h$ and $t$), not always $x$ and $y$ (Q5b).

What cost marks Exam 2

Wrong direction or scale (×3 vs ÷3, left vs right) in MC. The safest method is to pick a point on the original graph and track where each transformation sends it (MC, Q1).

Do this: always check a transformation by picking one point and tracking it. If the picture matches the description, you've got it.
5

Function and variable naming

Both papers Notation

Name your answer the way the question names it. A rule (with $=$), not just an expression.

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What cost marks Exam 1

If the question asks for $f'(3)$, write "$f'(3) = \ldots$", not "$y = \ldots$". Don't rename $g(x)$ as $f(x)$ either (Q1b).

What cost marks Exam 2

A tangent answer has to be a rule: $y = mx + c$, not just $mx + c$. Use the variables the question is using.

Do this: when you write the final answer, glance back at the question and copy its notation. Correct expression + wrong name = no mark.
6

Graph work

Both papers Notation

One smooth curve, every key feature labelled, points on the grid.

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What cost marks Exam 1

One continuous smooth curve — no little flicks at the ends. Dashed asymptotes labelled $x = \ldots$ / $y = \ldots$. Show symmetry. A derivative graph must run across the whole domain with labelled endpoints (Q3, Q7c).

What cost marks Exam 2

Use the grid — make coordinates land on grid lines. Bracket key points like $(2, 3)$. Keep the curve continuous through every section (Q1, Q3).

Do this: run a checklist before you move on. Shape → asymptotes → intercepts → key points → endpoints → labels. Every sketch, every time.
7

Solution validity and domain checking

Both papers Technique

Solve, then check the domain. Cross out solutions that don't fit.

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What cost marks Exam 1

If two solutions come out, say which one is valid and why — don't leave both (Q2). Same with infinite-solutions vs no-solution. With domain $x>4$, discard roots that don't satisfy it (Q6).

What cost marks Exam 2

For a composite $f^{-1} \circ g$ to exist, the range of $g$ has to sit inside the domain of $f^{-1}$ (Q5). Exclude any forbidden values cleanly (Q1).

Do this: after every "solve", write one more line: "Domain is $\ldots$, so $x = \ldots$ is the only valid solution." Make it a habit.
8

Setting out and honest working

Both papers Notation

Working that's findable and legible. Never write a false equation to fix a sign.

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What cost marks Exam 1

Don't write $-\frac{10}{3} = \frac{10}{3}$ to force a positive area — that's just wrong. Stop, then write "Area $= \frac{10}{3}$" (Q3b). The right answer has to come from right working.

What cost marks Exam 2

Anything worth more than 1 mark needs working — rule and answer. Make it findable on the page; don't bury it in the margins.

Do this: when you get a negative number for something that has to be positive (area, length, probability), stop. Write "Area $= |\ldots|$" or just take absolute value cleanly. Never fake an equals sign.
9

CAS technique

Exam 2 focus Technique

Define your functions first, then use the right command. Don't grind it by hand.

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What cost marks Exam 2

Define your functions at the start of Section B so you can reuse them. A standard deviation comes straight from normalcdf with $\sigma>0$ — no $Z$-value step needed. Use sliders, fmax, the derivative and bounded-area tools. Always reread your CAS entry before hitting enter.

What cost marks Exam 1

Exam 1 is tech-free — don't try to use calculator-style shortcuts. Show every step the way you would on paper.

Do this: spend the first two minutes of Section B defining $f$, $g$, $h$ etc. on your CAS. Pick the right command (solve, fmax, derivative, normalcdf) instead of doing it by hand.
10

Sense-checking and reading the whole question

Both papers Technique

Does the answer make sense? Did you actually answer every part?

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What cost marks Exam 2

A probability can't be more than 1 (Q4). Read which quantity is actually wanted — maximise $g - f$, not $f - g$; the maximum rate, not the minimum.

What cost marks Exam 1

Transcription slips — changing a sine argument, mis-copying a numerator — turned correct work into lost marks.

Do this: last 30 seconds on each question — re-read what was actually asked, tick off each part, and ask "does this number make sense?" Probabilities $\le 1$, lengths positive, etc.

Part 2

Content to revisit — by strand

Tap a strand to see the recurring mistakes and the specific subtopics worth a refresh.

∫ Calculus & algebra

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  • Trapezium rule: keep the coefficient of $2$ on interior terms; single-term answer; the method is specified, so integration isn't accepted. (E1 Q7)
  • Area under the $x$-axis: correct absolute-value reasoning, ending on a positive area stated cleanly. (E1 Q3b)
  • Log laws + cubic: right combination of laws, solve the cubic, then apply the domain to select the valid root such as $\frac{7+\sqrt{13}}{2}$. (E1 Q6)
  • Rational powers and surds: index form before differentiating; handle $\sqrt[3]{-k}$ and signs carefully. (E1 Q8)
  • Rates and areas: average vs instantaneous rate; recognising when a question needs an area, not a function value. (E2 Q2)

ƒ Functions

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  • Composite functions and range: sketch, then fmax / derivative for the exact extreme; mind the endpoint bracket. (E2 MC, Q5)
  • Inverse functions: get the rule and state/check the domain. (E2 MC)
  • Hybrid functions: domain endpoints and sharp points — e.g. the corner at $f\!\left(\tfrac{1}{3}\right)$. (E2 MC, Q2)

P Probability & statistics

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  • Binomial: identify $n$ and $p$; standard deviation vs variance; cumulative probabilities need $\ge 2$ terms; correct inequality $P(Y\ge 7)$ vs $P(Y>7)$; no normal approximation where binomial is required. (E1 Q4; E2 Q4)
  • Conditional probability: correct numerator and denominator; the result must be $\le 1$. (E2 Q4)
  • With vs without replacement: a common MC trap. (E2 MC)
  • Confidence intervals / sample size: find both bounds for $n$, not just the minimum; bracket the interval; work with $\hat{p}$ and the margin of error. (E1 Q5c; E2 Q4)

∠ Trigonometry

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  • Exact values: $\sin,\cos,\tan$ at $\frac{\pi}{6}, \frac{\pi}{4}, \frac{\pi}{3}$ across $[0, 2\pi]$ from memory — e.g. $\sin\frac{2\pi}{3} = \frac{\sqrt{3}}{2}$, not $-\frac{\sqrt{3}}{2}$. (E1 Q7)
  • Special angles in show-that: $\arccos(0) = \frac{\pi}{2}$; read solutions off turning points. (E2 Q5)
  • General solutions: correct translation direction for the tan family. (E2 MC)

Part 3

If you do only five things this week

The shortest route to picking up the marks most students leave on the table.

1

Brackets everywhere

Around arguments, numerators, coordinates, intervals. Round vs square has to be clear.

2

Exact unless told otherwise

Set your CAS to exact mode. Never round halfway through.

3

Know the three command words

Verify, show that, hence all mean something specific. Your working is the mark.

4

Track a point through transformations

Use study-design wording. Pick a point and follow it through every shift, stretch and reflection.

5

Check validity & domain last

After every solve, write one more line stating which solutions are valid and why.