Support · Mathematics Extension 2 11–12 – Year 12 · The nature of proof
Support Prove and use results for numbers: if a > b then a±c > b±c; if a > b > 0 then 1/b > 1/a > 0 and vice versa; if (a) > (b) then a² > b² and vice versa; if a > b and b > c then a > c; if a > b and c > d then a + c > b + d; if a > b and c > 0 then ac > bc; if a > b and c then ac
Resources for the prerequisite content of this dot point: earlier-stage (or earlier sub-level) dot points in the same strand that students usually need first. Use these to fill gaps before or alongside the core lesson.
Prerequisite links are draft mappings generated from the syllabus structure (earlier stage, same strand, closest content). They are being reviewed by teachers. Spot a poor match? Tell us.
Prerequisite dot points
Prove that if a cubic P(x) = ax³ + bx² + cx + d has three zeroes α, β, γ, then α + β + γ = - b/a, αβ + βγ + γα = c/a and αβγ = - d/a
Mathematics Extension 1 11–12 – Year 11 · Polynomials Draft mapping
No checked resources on this prerequisite dot point yet.
Prove that if a quartic P(x) = ax^4 + bx³ + cx² + dx + e has four zeroes α, β, γ, δ then α + β + γ + δ = - b/a, αβ + αγ + αδ + βγ + βδ + γδ = c/a, αβγ + βγδ + γδα + δαβ = - d/a and αβγδ = e/a
Mathematics Extension 1 11–12 – Year 11 · Polynomials Draft mapping
No checked resources on this prerequisite dot point yet.
Graph y = cosx for 0 ≤ x ≤ π, then use a reflection in y = x to graph y = cos^(- 1)x with and without graphing applications
Mathematics Extension 1 11–12 – Year 12 · Inverse trigonometric functions Draft mapping
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.