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Maths Extension 1 · Year 12 · NESA ME1-12-04

Further calculus skills

NESA focus area ME1-12-04, 20 lessons.

Syllabus note: this focus area follows the new 2024 NESA syllabus (first HSC 2027). Students sitting the HSC in 2026 study the 2017 syllabus.

20lessons

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Lessons

Integration by Substitution

Substitution: Worked Examples

Choosing the Substitution

Trigonometric Substitutions

Algebraic Manipulation Before Integration

Integrating $\sin^2 nx$ and $\cos^2 nx$

Integrating Powers of Sine & Cosine

Integrating $\tan^2 x$ and $\sec^2 x$

Derivatives of Inverse Functions

Derivative of $\sin^{-1} x$

Derivatives of $\cos^{-1} x$ and $\tan^{-1} x$

Chain Rule with Inverse Trig

Integrating $\dfrac{1}{\sqrt{a^2-x^2}}$

Integrating $\dfrac{a}{a^2+x^2}$

Completing the Square for Integration

Mixed Integration Techniques

Reduction Formulas

Harder Integration Problems

Calculus Exam Techniques

Module 8 Synthesis & Exam Technique