Year 12 · VCE / Specialist Mathematics
Flashcards and recall.
Make a short deck from material you need to recall without notes.
Try this with Specialist Mathematics
- Write one prompt per card. Use definitions, explanations or examples from your current topic.
- Answer aloud before turning the card. Split a card if it asks for several unrelated facts.
- Set aside missed cards and revisit them in a later session.
Recall topics
- State the difference between a conjecture, a proof and a counter-example.
- What does the implication P ⇒ Q mean, and what is its converse?
- Explain 'P if and only if Q' (P ⇔ Q) in terms of necessary and sufficient conditions.
- What is proof by cases (proof by exhaustion)?
- Outline the logic of proof by contradiction.
- State the contrapositive of P ⇒ Q and why proving it works.
- What do the quantifiers '∀' and '∃' mean, and how is each disproved?
- State the two steps of a proof by mathematical induction.
- In induction, what exactly is the inductive hypothesis and how is it used?
- How is induction used to prove a divisibility result such as 'n<sup>3</sup> − n is divisible by 6'?
- What is a partial-fraction decomposition and when can a rational function be written as one?
- How do you find a vertical asymptote of a rational function?
- State the rule for the horizontal or oblique asymptote of a rational function based on degrees.
- How is the second derivative used to classify a stationary point and identify concavity?
- Define a point of inflection and the condition for one.
- Write the Cartesian form of a complex number and its modulus.
- State the polar (modulus–argument) form of a complex number.
- How do modulus and argument behave under multiplication of complex numbers?
- State De Moivre's theorem.
- How are the nth roots of unity found and described geometrically?
- How do you find all nth roots of a complex number w = r cis θ?
- State the fundamental theorem of algebra (informal form used in this course).
- State the conjugate root theorem and its use.
- How can the complex equation |z − a| = r be described in the Argand plane?
- What region or curve does arg(z − a) = α describe?
- What does it mean for a set of vectors to be linearly dependent, and the geometric meaning for two/three vectors?
- How do you find the unit vector in the direction of a vector a?
- State the scalar (dot) product formula and what it gives.
- How is the scalar resolute of a in the direction of b calculated?
- What does the vector (cross) product give, and how is its direction found?
- State the derivatives of the three inverse circular functions.
- Describe the relationship between a function's graph and the graph of its antiderivative.
- What is implicit differentiation and when is it used?
- How is the chain rule applied to a related-rates problem?
- Give the antiderivatives that produce inverse circular functions.
- State the antiderivative of 1/x and the related log result.
- How is integration by substitution u = g(x) carried out?
- Which identities convert sin<sup>2</sup>x and cos<sup>2</sup>x for integration?
- State the integration by parts formula.
- Give the formula for the volume of a solid of revolution about the x-axis.
Resource inventory inspected 4 November 2026. The main ATARMAXXING study platform is separate from tutoring. Topic labels show what was found, not a guarantee of complete curriculum coverage or tutor availability.
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