UniGeniusQCE Maths Methods

Course map

Calculus

  • Calculus of exponential and logarithmic functionsUnit 3: Unit 3 Topic 1: Differentiation of exponential and logarithmic functions
    • Know the graphs of e^x and ln(x) and use their inverse relationship
    • Solve equations involving e and natural logarithms, with and without technology
    • Differentiate exponential and logarithmic functions and model with their derivatives
    LessonPractice
  • Trigonometric derivatives and the differentiation rulesUnit 3: Unit 3 Topic 2: Differentiation of trigonometric functions and differentiation rules
    • Differentiate sine and cosine functions, including composite ones
    • Use the chain, product and quotient rules, giving derivatives in simplest and factorised form
    • Model and solve problems with trigonometric derivatives
    LessonPractice
  • The second derivative and optimisationUnit 3: Unit 3 Topic 3: Further applications of differentiation
    • Interpret the second derivative, including acceleration
    • Find stationary points and points of inflection and classify them with the second derivative
    • Develop and solve optimisation models
    LessonPractice
  • Anti-differentiationUnit 3: Unit 3 Topic 4: Introduction to integration
    • Find indefinite integrals of powers, exponential, reciprocal and trigonometric functions
    • Integrate f(ax + b) and find a function from its derivative and an initial condition
    • Find displacement from velocity or acceleration
    LessonPractice
  • Definite integrals and their applicationsUnit 4: Unit 4 Topic 1: Further integration
    • Use the fundamental theorem of calculus to evaluate definite integrals
    • Find areas under curves and between curves, and approximate them with the trapezoidal rule
    • Find total change and solve motion problems with definite integrals
    LessonPractice

Trigonometry

  • The sine and cosine rulesUnit 4: Unit 4 Topic 2: Trigonometry
    • Use the sine rule, including the ambiguous case
    • Use the cosine rule and the area formula
    • Solve problems with bearings and angles of elevation and depression in two and three dimensions
    LessonPractice

Statistics

  • Discrete random variables and the binomial distributionUnit 3: Unit 3 Topic 5: Discrete random variables
    • Build and use probability functions, including from relative frequencies
    • Find the mean, variance and standard deviation of a discrete random variable
    • Model with Bernoulli and binomial random variables
    LessonPractice
  • Continuous random variables and the normal distributionUnit 4: Unit 4 Topic 3: Continuous random variables and the normal distribution
    • Find probabilities from probability density and cumulative distribution functions
    • Find the mean, variance and standard deviation of a continuous random variable
    • Use z-scores and normal distributions for probabilities and quantiles
    LessonPractice
  • Sampling and sample proportionsUnit 4: Unit 4 Topic 4: Sampling and proportions
    • Recognise random samples and sources of bias
    • Find the mean and standard deviation of a sample proportion
    • Use the approximate normality of the sample proportion for large samples
    LessonPractice
  • Confidence intervals for proportionsUnit 4: Unit 4 Topic 5: Interval estimates for proportions
    • Find approximate confidence intervals for a population proportion
    • Relate the margin of error to the level of confidence and the sample size
    • Interpret intervals and how they vary between samples
    LessonPractice

The external examination

  • The external examinationUnit 3 and Unit 4
    • Know both papers: time, technology, weights and the formula book
    • Write answers that show the working the marking rewards
    • Know that internal assessment is set by your school
    LessonPractice

QCE Mathematical Methods Units 3 and 4. Both papers of the external examination cover Unit 3 and Unit 4. Internal assessment is set by your school, so it is described in a lesson rather than practised here.