Year 12 Maths Extension 1

Free interactive notes and timed quizzes for every chapter of NSW Year 12 Maths Extension 1, from mathematical induction and vectors to differential equations and the binomial distribution.

1Pick a chapter below.
2Notes: learn with live graphs, worked examples and practice questions.
3Quizzes: test yourself on the whole chapter.

Extension 1 builds on the Advanced course, so work through the Year 12 Maths Advanced notes as well. Tap Mark as mastered after each section to track your progress on this device. No account needed.

Chapters

1 Mathematical induction 2 sections

Proof by mathematical induction for series in sigma notation and for divisibility, including forming a conjecture and proving it.

Notes Quizzes
2 Vectors 7 sections

Vectors in two and three dimensions: notation, addition and scalar multiples, components and unit vectors, the dot product, angles between vectors, and projections.

Notes Quizzes
3 Vectors and motion 5 sections

Displacement, velocity and acceleration vectors, calculus with vectors, resultant forces and velocities, projectile motion, and the Cartesian equation of a projectile's path.

Notes Quizzes
4 Inverse trigonometric functions 2 sections

The inverse sine, cosine and tangent functions, their restricted domains, ranges and graphs, exact values, transformations, and the symmetries and identities that link them.

Notes Quizzes
5 Further calculus 7 sections

Parametric differentiation, inverse functions and their derivatives, derivatives and integrals involving inverse trigonometric functions, the reverse chain rule, integration by substitution, and integrating sin²x and cos²x.

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6 Further applications of calculus 5 sections

Sketching polynomials from their zeroes, multiple zeroes and the derivative, related rates of change, modified exponential growth and Newton's law of cooling, and volumes of solids of revolution.

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7 Differential equations 5 sections

Differential equations and their solutions, slope fields, separable differential equations, equations of the form dy/dx = g(y), logistic growth, and modelling real situations with differential equations.

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8 The binomial distribution 3 sections

Bernoulli trials, binomial probabilities, the mean and variance of binomial distributions, and the distribution of sample proportions with its normal approximation.

Notes Quizzes