Mathematics Extension 1
Year 12 · Stage 6 · NSW Mathematics syllabus
Proof by mathematical induction
Use the principle of mathematical induction to prove statements about sums, divisibility, and inequalities for all integers; communicate the base case, inductive hypothesis, and inductive step with rigour.
2 sub-topics
Inverse trigonometric functions
Define the inverse trigonometric functions with their restricted domains and ranges; evaluate exact values; differentiate and integrate involving inverse trigonometric forms.
2 sub-topics
Introduction to vectors
Represent quantities as vectors in component and magnitude–direction form; perform vector arithmetic; apply dot products, projections, and geometric proofs with vectors; model projectile motion using vector components.
3 sub-topics
Further calculus skills
Extend integration technique to include -substitution, the reverse chain rule, inverse-trigonometric and logarithmic standard forms, and integrals of and via double-angle identities.
2 sub-topics
Further applications of calculus
Apply calculus to differential equations, exponential growth and decay models, related rates of change, and volumes of solids of revolution.
3 sub-topics
The binomial distribution
Model repeated independent trials using the binomial distribution; calculate and interpret probabilities; find expected value and variance; use the normal approximation for large samples and understand the sampling distribution of the mean.
2 sub-topics