Uni
Genius
Sign in
All learning paths
Pure, second pass
Papers 1 and 2 · 100 marks each, 2 hours each.
30 Lessons
Level 1
Composite/inverse functions and domain/range
Composite and inverse functions with their domains
Core
Level 2
Modulus graphs, equations and inequalities
Modulus graphs, equations and inequalities
Core
Level 3
Rational expressions and partial fractions
Rational expressions and partial fractions
Core
Level 4
Recursive sequences, monotonicity, periodicity and sigma
Recursive sequences, periodicity and sigma notation
Core
Level 5
Arithmetic progressions and proof of their sum
Arithmetic progressions and the proof of their sum
Core
Level 6
Geometric progressions and convergence
Geometric progressions and convergence
Core
Level 7
Sequences and series as financial/physical models
Sequences and series as financial and physical models
Core
Level 8
Rational binomial expansions and approximation
Rational binomial expansions and approximation
Core
Level 9
Reciprocal and inverse trig functions
Reciprocal and inverse trigonometric functions
Core
Level 10
Addition, double-angle and half-angle identities
Addition, double-angle and half-angle identities
Core
Level 11
R-sine/cosine forms and extrema
R forms and their greatest and least values
Core
Level 12
Advanced trig equations and proofs
Harder trigonometric equations and proofs
Core
Level 13
Small-angle approximations
Small-angle approximations
Core
Level 14
Periodic models and realistic domains
Periodic models and realistic domains
Core
Level 15
Linearising power/exponential models with logs
Straight-line log plots for power and exponential models
Core
Level 16
Product, quotient and chain rules
Product, quotient and chain rules
Core
Level 17
Implicit differentiation and parametric curves
Implicit differentiation and parametric curves
Core
Level 18
Parametric models, tangents and parameter domains
Parametric models, tangents and parameter domains
Core
Level 19
Connected rates and setting up differential equations
Connected rates and setting up differential equations
Core
Level 20
Standard advanced integrals and trig rewrites
Standard integrals and trigonometric rewrites
Core
Level 21
Integration by substitution
Integration by substitution
Core
Level 22
Integration by parts, including repeated use
Integration by parts, including repeated use
Core
Level 23
Rational integration and logarithmic forms
Integrating rational functions with partial fractions
Core
Level 24
Area between curves and parametric areas
Areas between curves and under parametric curves
Core
Level 25
Separable differential equations and interpretation
Separable differential equations and what they predict
Core
Level 26
Bracketing roots and failure of sign-change arguments
Locating roots by sign change, and when it fails
Core
Level 27
Fixed-point iteration and staircase/cobweb diagrams
Fixed-point iteration, staircases and cobwebs
Core
Level 28
Newton-Raphson, failure cases and contextual roots
Newton-Raphson, its failures and roots in context
Core
Level 29
Trapezium estimates and bounds
Trapezium rule estimates and bounds
Core
Level 30
Contradiction and first-principles proof clinic
Proof by contradiction and from first principles
Core