Revision notes.

Try this with Mathematics Extension 2

1. Close your notes and write the main idea in two sentences from memory.
2. Reopen the source and correct the first mistake or omission you find.
3. Add one example and one question to test whether you can apply the idea.

View Mathematics Extension 2 resources on ATARMAXXING ↗

Topics in the resource inventory

• The language of proof: implication, converse, contrapositive and proof by contradiction
• Proving inequalities from a > b and the non-negativity of squares
• The triangle inequality and the AM–GM inequality for two numbers
• Induction for series in sigma notation and for non-standard base cases or steps
• Divisibility and inequality proofs by induction
• Induction in calculus, geometry, the binomial theorem and recursive formulae
• Vectors in three dimensions: components, magnitude, the dot product and spheres
• Vector equations of lines: r = a + λb, parallel and perpendicular lines, and points on a line
• Complex numbers in Cartesian form: arithmetic, the conjugate, square roots and the Argand plane
• Polar and exponential form: modulus, argument, Euler's formula and the geometry of multiplication
• De Moivre's theorem: induction proof, powers and trigonometric identities
• Quadratics and polynomials over the complex numbers, and the conjugate root theorem
• Geometry of complex arithmetic: vectors, the parallelogram law and rotation by i
• nth roots of unity, nth roots of a complex number, and regions of the Argand plane
• Integration by substitution and rational functions with a quadratic denominator
• Partial fractions and integrating rational functions
• Integration by parts and reduction (recurrence) formulae
• Simple harmonic motion: equations, the defining property and graphs
• Straight-line motion with variable acceleration and resisted motion
• Projectile motion: parametric equations, the Cartesian path and resisted projectiles