Revision notes.

Try this with Mathematics Methods

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.

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Topics in the resource inventory

• Euler's number e, the limit (a^h - 1)/h and the derivative of e^x and Ae^(kx)
• Derivatives of sin x and cos x and their use in practical problems
• The product, quotient and chain rules and composite functions
• Second derivatives, concavity, inflection, the increments formula, curve sketching and optimisation
• Indefinite integrals of x^n, e^x, sin x, cos x and f(ax - b), linearity and initial conditions
• Area as a limit of sums, signed areas, additivity and linearity of definite integrals
• The signed area function and the fundamental theorem of calculus
• Areas under and between curves, total change from a rate, and linear motion
• Discrete random variables: probability functions, expected value, variance and linear changes of scale and origin
• Bernoulli trials and the binomial distribution: probabilities, mean np and variance np(1 - p)
• Logarithms as indices, the log laws and solving index equations
• Graphs of y = log_a x and its translations, logarithmic scales and logarithmic models
• The natural logarithm: derivative of ln x and ln f(x), and integrals of 1/x and f'(x)/f(x)
• Probability density functions, cumulative distribution functions and probabilities as integrals
• Expected value, variance and standard deviation of continuous random variables, including uniform and triangular
• The normal distribution: features, standardisation, and probabilities and quantiles with technology
• Random samples, sources of bias and variability of samples from uniform, normal and Bernoulli distributions
• The sample proportion p-hat as a random variable: mean, standard deviation and approximate normality
• Confidence intervals for a proportion and the margin of error
• Sample size, confidence level and the interpretation of repeated confidence intervals by simulation