The whole year, readable in five minutes.

1Subject

1. 01

   Functions and Limits

   State what a limit is, and evaluate one — including where a function is undefined.

   • Functions, domain and range
   • Graphs and transformations
   • The idea of a limit
   • Evaluating limits algebraically
   2 more lessonsShow fewer

   • One-sided limits, and limits at infinity
   • Continuity

   6 practice classes

2. 02

   The Derivative

   Differentiate from first principles, and know what the derivative measures.

   • Rate of change, and the tangent problem
   • The derivative from first principles
   • Differentiating powers and polynomials
   • The product and quotient rules
   2 more lessonsShow fewer

   • The chain rule
   • Higher-order derivatives

   5 practice classes · An assessment

3. 03

   Differentiating Everything

   Differentiate trigonometric, exponential, logarithmic and inverse functions.

   • Trigonometric functions
   • Exponential and logarithmic functions
   • Inverse trigonometric functions
   • Implicit differentiation
   2 more lessonsShow fewer

   • Logarithmic differentiation
   • Parametric differentiation

   6 practice classes

4. 04

   Applications of the Derivative

   Find tangents, stationary points, maxima and minima, and justify which is which.

   • Tangents and normals
   • Increasing, decreasing and stationary points
   • Maxima, minima and the second derivative
   • Curve sketching
   2 more lessonsShow fewer

   • Optimisation problems
   • Lesson 24

   5 practice classes · An assessment

5. 05

   The Integral

   Integrate by substitution and by parts, and recognise which to reach for.

   • Antiderivatives and the indefinite integral
   • Integration by substitution
   • Integration by parts
   • Partial fractions
   2 more lessonsShow fewer

   • Trigonometric integrals
   • Choosing a method, reliably

   6 practice classes

6. 06

   The Definite Integral

   Use the fundamental theorem of calculus to find an exact area under a curve.

   • Area under a curve, and the Riemann sum
   • The fundamental theorem of calculus
   • Properties of definite integrals
   • Area between two curves
   2 more lessonsShow fewer

   • Volumes of revolution
   • Improper integrals

   5 practice classes · An assessment

7. 07

   Differential Equations

   Classify and solve a separable differential equation.

   • What a differential equation is
   • Order, degree and general solutions
   • Variables separable
   • Homogeneous equations
   2 more lessonsShow fewer

   • Linear first-order equations
   • Modelling growth, decay and cooling

   6 practice classes

8. 08

   Calculus in Use

   Apply calculus to related rates, motion and linear approximation.

   • Related rates
   • Motion problems with calculus
   • Approximation and linearisation
   • Reading a calculus question correctly
   2 more lessonsShow fewer

   • Exam technique, and the common errors
   • Lesson 48

   5 practice classes · An assessment

Practice classes go over the lesson before them: worked problems, revision and doubts. Assessments sit at the midpoint and the end of the year.