QCE Mathematical Methods Syllabus Notes

Original QCE Mathematical Methods notes for syllabus-aligned revision, worked examples, common mistakes and quick checks.

Unit 3: Further calculus and introduction to statistics

Differentiation of exponential and logarithmic functions

  • Calculus of exponential functions

    Learn QCE Mathematical Methods exponential calculus, including why $e$ matters, how to differentiate $e^x$ and how to read exponential growth rates.

  • Calculus of logarithmic functions

    Understand natural logarithms in QCE Mathematical Methods, including ln graphs, inverse relationships, log equations and logarithmic differentiation rules.

Differentiation of trigonometric functions and differentiation rules

  • Calculus of trigonometric functions

    Revise QCE Mathematical Methods trigonometric derivatives, including sine, cosine, radians mode and chain rule applications.

  • Differentiation rules

    Learn when to use the chain, product and quotient rules in QCE Mathematical Methods, with worked examples and exam-style traps.

Further applications of differentiation

  • Second derivative and applications

    Learn how the second derivative connects to concavity, inflection points, acceleration, local extrema and optimisation in QCE Mathematical Methods.

Introduction to integration

  • Anti-differentiation

    Learn QCE Mathematical Methods anti-differentiation, indefinite integrals, constants of integration and motion applications.

Discrete random variables

  • Discrete random variables

    Understand QCE Mathematical Methods discrete random variables, probability functions, expected value, variance and standard deviation.

  • Bernoulli distributions

    Learn Bernoulli distributions for QCE Mathematical Methods, including two-outcome modelling, parameter p, mean and variance.

  • Binomial distributions

    Learn QCE Mathematical Methods binomial distributions, including Bernoulli trials, binomial probabilities, mean, variance and wording traps.

Unit 4: Further calculus, trigonometry and statistics

Further integration

Trigonometry

  • Sine rule and cosine rule

    Learn QCE Mathematical Methods sine rule, cosine rule, area of a triangle, ambiguous case and non-right-triangle modelling.

Continuous random variables and the normal distribution

  • Continuous random variables

    Understand QCE Mathematical Methods continuous random variables, density functions, cumulative distribution functions, expected value and variance.

  • Normal distributions

    Learn QCE Mathematical Methods normal distributions, z-scores, probabilities, quantiles and standardisation.

Sampling and proportions

  • Random sampling

    Learn QCE Mathematical Methods random sampling, bias, procedures for randomness and why samples vary.

  • Sample proportions

    Learn QCE Mathematical Methods sample proportions, $\hat p$ as a random variable, approximate normality and simulation ideas.

Interval estimates for proportions

  • Confidence intervals for proportions

    Learn QCE Mathematical Methods confidence intervals for population proportions, including margin of error, confidence level and interpretation.