Year 12 Maths Advanced

Free interactive notes and timed quizzes for every chapter of NSW Year 12 Maths Advanced, from sequences and series and calculus to finance, the normal distribution and bivariate data.

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

Year 12 builds on the Year 11 Maths Advanced notes, especially differentiation. Tap Mark as mastered after each section to track your progress on this device. No account needed.

Chapters

1 Sequences and series 9 sections

Arithmetic and geometric sequences, their nth terms, partial sums and sigma notation, the sum of an AP and of a GP, limiting sums, and recurring decimals.

Notes Quizzes
2 Curve-sketching using the derivative 11 sections

Use the first and second derivatives to find where a curve increases and decreases, its stationary points and points of inflection, global maxima and minima, optimisation problems, and primitive functions.

Notes Quizzes
3 Integration 9 sections

The definite integral as signed area, the fundamental theorem of calculus, properties of definite integrals, indefinite integrals, areas under and between curves, the trapezoidal rule and the reverse chain rule.

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4 Exponential functions 6 sections

Calculus with the exponential function e^x: tangents, differentiation with the chain, product and quotient rules, curve sketching, integration, areas, and exponential functions with other bases.

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5 Logarithmic functions 6 sections

Calculus with the natural logarithm: log laws and equations, differentiating ln f(x), curve sketching, integrating 1/x and f'(x)/f(x), areas, and logarithms to other bases.

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6 Trigonometric functions 6 sections

Transformations of trigonometric graphs and modelling, differentiating and integrating sine, cosine and tangent, tangents, curve sketching, optimisation, areas, and the proof that the derivative of sin x is cos x.

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7 Motion and rates 5 sections

Displacement, velocity and acceleration as derivatives, motion found by integration, interpreting rates of change and concavity in context, total change from a rate, and exponential growth and decay.

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8 Series and finance 6 sections

Applying arithmetic and geometric sequences to salaries and sales, using logarithms with GPs, simple and compound interest, depreciation, superannuation, loan repayments and pensions.

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9 Discrete probability distributions 3 sections

Discrete random variables and their probability distributions, relative frequency, expected value, variance and standard deviation.

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10 Continuous probability distributions 6 sections

Cumulative frequency, probability density functions and cumulative distribution functions, mean and variance of continuous distributions, the standard normal distribution, z-scores and the empirical rule.

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11 Bivariate data analysis 3 sections

Bivariate data, scatterplots, Pearson's correlation coefficient, correlation and causation, the least-squares regression line, and making predictions with interpolation and extrapolation.

Notes Quizzes