## Pure Mathematics

- Extending the Binomial Theorem.
- Arithmetics Sequences and Series
- Geometric Sequences and Series.
- Iterative and Recursive Sequences.

- Radians.
- Small Angle Approximations.
- Reciprocal Trigonometric Functions.
- Inverse Trigonometric Functions

- Simplifying Rational Functions.
- The Modulus Function.
- Composite Functions and Inverse Functions.
- Combining Transformations.

- Differentiate exponentials, logs and trigonometric functions.
- The Second Derivative and Points of Inflexion.
- The Chain Rule.
- The Product Rule.
- The Quotient Rule.

- Integrating Exponentials, \(\frac{1}{x} \), and Basic Trigonometric Functions.
- Integration by Inspection.
- Integration by Substitution.
- Integration by Parts.

- Change of Sign
- Iterative Methods.
- Staircase and Cobweb Diagrams.
- Newton-Raphson Method.
- Trapezium Rule.

- Converting Between Cartesian and Parametric Forms.
- Parametric Differentiation.
- Implicit Differentiation.

- Magnitude and Direction
- Vector Addition and Scalar Multiplication.
- Position Vectors

- Review Proof Methods From Year 1.
- Proof by Contradiction.

- \(\sin (A \pm B),\cos (A \pm B),\tan (A \pm B)\) .
- Double Angle Formulae.
- \(R\sin (x \pm \alpha )\) and \(R\cos (x \pm \alpha )\).
- Trigonometric Proofs.

- Decomposing Rational Functions into Partial Fractions.
- Integrating Using Partial Fractions.

- Construct Differential Equations.
- Solve First-Order Differential Equations.
- Interpret the Solutions to Differential Equations.

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