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Cambridge Senior Maths Methods · Units 3 & 4 · Ranked by VCAA exam probability

Unit 3

Unit 4

Ch.5

Algebra & Polynomials

Current

42%

5A — Polynomial identities

Baseline

68%

Priority 5 — VCAA-mapped questions

Ex.5A Q12 — Identify degree and leading coefficient

68%

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Ex.5A Q14 — Expand and simplify composite polynomial

60%

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5B — Factor Theorem

High yield

92%

Priority 5 — VCAA-mapped questions · Ch.5B Factor Theorem

Ex.5B Q15 — Show that P(2)=0, find a and b (Show That)

92%

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Ex.5B Q18 — Find unknown constants given two factors

88%

Go →

Ex.5B Q20 — Fully factorise cubic using Factor Theorem

85%

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Ex.5B Q22 — Remainder theorem combined with Factor

78%

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Ex.5B Q25 — Prove (x+k) is a factor for all k

72%

Go →

5C — Rational root theorem

The Beast

55%

Priority 5 — Ch.5C

Ex.5C Q8 — Find all rational roots of quartic

55%

Go →

Ch.6

Functions & Relations

88%

Ch.7

Trigonometric Functions

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Maths Methods · Unit 3 & 4

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Unit 3 Application Task

Wed 2 April 2026 · 4 days away

Unit 3 Analysis Task 1

Fri 24 April 2026 · 26 days away

Unit 3 Analysis Task 2

Thu 14 May 2026 · 46 days away

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Cambridge Senior Maths Methods 3&4 · Chapter 5B · Question 15

Factor Theorem — Finding Unknown Constants

High yield Exam 1 Show that · 3 marks

VCAA 10-Year Appearance Probability 92%

Appeared in 9 of 10 Exam 1 papers (2015–2024) Examiner favourite

Question — Show That (Module B: Logic Engine)

The polynomial P(x) = x³ + ax² − 7x + b has a factor of (x − 2) and leaves a remainder of −10 when divided by (x + 1).

Show that a = 1 and b = −6.

3 marks — one mark per demonstrable step

Module B: Logic Engine active — marking focus: communication + rigour + linking terms

Method Breakdown

Your working	Examiner annotation
✓ P(2) = 0 by the Factor Theorem	Correct — Factor Theorem stated explicitly

✓ 4a + b = 6 & a + b = −16	Both equations formed correctly

✗ 3a = 22 → a = 1, b = −6	Subtraction step is not shown. Examiner requires visible intermediate arithmetic to award mark 3.

Examiner's Secret — 2022 Exam 1

In "Show That" questions, the Chief Examiner explicitly noted that students who jumped directly to the answer without showing the subtraction of simultaneous equations were not awarded the final method mark — even when both values of a and b were correct.

Source: VCAA Chief Examiner Report, Maths Methods 2022 Exam 1 · Q6

Next strategic drill

Another 3-mark Show That — Simultaneous Equations · 88% VCAA probability

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Sub-topic

Factor Theorem

Question type

Show That + Find

Module

B — Logic Engine

Inferred marks

4 marks

Difficulty

The Beast

VCAA precedent

2020 Exam 1, Q7

Similar to 2020 Exam 1, Q7 — 78% of students attempted this question type

Method Breakdown

Your working	Examiner annotation
✓ f(3) = 54 − 27 − 33 + 6 = 0	Full arithmetic shown — mark 1 secured

✓ Factor Theorem stated explicitly	Linking term present — mark 2 secured

✓ f(x) = (x−3)(2x²+3x−2)	Quadratic factor correct — mark 3 secured

✓ f(x) = (x−3)(2x−1)(x+2)	Full factorisation — mark 4 secured

Examiner's Secret — 2020 Exam 1

The Chief Examiner noted that only 34% of students secured all 4 marks on this question type. The most common error was omitting the Factor Theorem linking statement after evaluating f(3) = 0. Your working includes this — placing you in the top third of the Victorian cohort on this sub-topic.

Source: VCAA Chief Examiner Report, Maths Methods 2020 Exam 1 · Q7

Caliber verified — advance to Beast Mode

Rational Functions (Ch.9) — 72% VCAA probability · unlocked