UniGeniusQCE Specialist Maths

Course map

Complex numbers and proof

  • Further complex numbersUnit 3: Unit 3 Topic 1: Further complex numbers
    • Multiply, divide and raise complex numbers to powers in polar form
    • Find and place the nth roots of unity and of other complex numbers
    • Factorise polynomials and solve polynomial equations over the complex numbers
    LessonPractice
  • Mathematical induction and trigonometric proofsUnit 3: Unit 3 Topic 2: Mathematical induction and trigonometric proofs
    • Write a complete proof by induction for sums and divisibility
    • Use sigma notation for sums
    • Prove multiple-angle identities with De Moivre's theorem and the binomial expansion
    LessonPractice

Vectors and matrices

  • Vectors in two and three dimensionsUnit 3: Unit 3 Topic 3: Vectors in two and three dimensions
    • Work with vectors in three dimensions: magnitude, unit vectors, scalar products and projections
    • Find vector, parametric and Cartesian equations of lines, planes and spheres
    • Use the vector product for normals and areas, and vectors to prove geometric results
    LessonPractice
  • Vector calculusUnit 3: Unit 3 Topic 4: Vector calculus
    • Find the Cartesian equation of a path given as a vector function of time
    • Decide whether two particles' paths cross and whether the particles meet
    • Differentiate and integrate vector functions to model motion, including projectiles and circular motion
    LessonPractice
  • Further matricesUnit 3: Unit 3 Topic 5: Further matrices
    • Find determinants and inverses and solve matrix equations
    • Solve systems of linear equations by elimination and interpret the three cases
    • Model with dominance and Leslie matrices
    LessonPractice

Calculus

  • Integration techniquesUnit 4: Unit 4 Topic 1: Integration techniques
    • Integrate with trigonometric identities and by substitution
    • Differentiate and integrate with the inverse trigonometric functions
    • Integrate with partial fractions and by parts
    LessonPractice
  • Applications of integral calculusUnit 4: Unit 4 Topic 2: Applications of integral calculus
    • Find areas between curves and volumes of solids of revolution
    • Approximate definite integrals with Simpson's rule
    • Model with the exponential random variable
    LessonPractice
  • Rates of change and differential equationsUnit 4: Unit 4 Topic 3: Rates of change and differential equations
    • Differentiate implicitly and solve related rates problems
    • Solve first-order differential equations, including by separating variables, and read slope fields
    • Model with logistic growth, Newton's law of cooling and radioactive decay
    LessonPractice
  • Modelling motionUnit 4: Unit 4 Topic 4: Modelling motion
    • Use momentum and resultant forces, including on a smooth inclined plane
    • Choose the form of acceleration that suits the problem
    • Model straight-line motion, including simple harmonic motion and motion with air resistance
    LessonPractice

Statistical inference

  • Statistical inferenceUnit 4: Unit 4 Topic 5: Statistical inference
    • Find the distribution of a sample mean and use the central limit theorem
    • Find and interpret approximate confidence intervals for a population mean
    • Relate the margin of error to the level of confidence and the sample size
    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 Specialist Mathematics 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.