Pure Year 1

1.1 Index laws

1.2 Expanding brackets

1.3 Factorising

1.4 Negative and fractional indices

1.5 Surds

1.6 Rationalising denominators

2.1 Solving quadratic equations

2.2 Completing the square

2.3 Functions

2.4 Quadratic graphs

2.5 The discriminant

2.6 Modelling with quadratics

3.1 Linear simultaneous equations

3.2 Quadratic simultaneous equations

3.3 Simultaneous equations on graphs

3.4 Linear inequalities

3.5 Quadratic inequalities

3.6 Inequalities on graphs

3.7 Regions

4.1 Cubic graphs

4.2 Quartic graphs

4.3 Reciprocal graphs

4.4 Points of intersection

4.5 Translating graphs

4.6 Stretching graphs

4.7 Transforming functions

5.1 y = mx + c

5.2 Equations of straight lines

5.3 Parallel and perpendicular lines

5.4 Length and area

5.5 Modelling with straight lines

6.1 Midpoints and perpendicular bisectors

6.2 Equation of a circle

6.3 Intersections of straight lines and circles

6.4 Use tangent and chord properties

6.5 Circles and triangles

7.1 Algebraic fractions

7.2 Dividing polynomials

7.3 The factor theorem

7.4 Mathematical proof

7.5 Methods of proof

8.1 Pascal's triangle

8.2 Factorial notation

8.3 The binomial expansion

8.4 Solving binomial problems

8.5 Binomial estimation

9.1 The cosine rule

9.2 The sine rule

9.3 Areas of triangles

9.4 Solving triangle problems

9.5 Graphs of sine, cosine and tangent

9.6 Transforming trigonometric graphs

10.1 Angles in all four quadrants

10.2 Exact values of trigonometrical ratios

10.3 Trigonometric identities

10.4 Simple trigonometric equations

10.5 Harder trigonometric equations

10.6 Equations and identities

11.1 Vectors

11.2 Representing vectors

11.3 Magnitude and direction

11.4 Position vectors

11.5 Solving geometric problems

11.6 Modelling with vectors

12.1 Gradients of curves

12.2 Finding the derivative

12.3 Differentiating x^n

12.4 Differentiating quadratics

12.5 Differentiating functions with two or more terms

12.6 Gradients, tangents and normals

12.7 Increasing and decreasing functions

12.8 Second order derivatives

12.9 Stationary points

12.10 Sketching gradient functions

12.11 Modelling with differentiation

13.1 Integrating x^n

13.2 Indefinite integrals

13.3 Finding functions

13.4 Definite integrals

13.5 Areas under curves

13.6 Areas under the x-axis

13.7 Areas between curves and lines

14.1 Exponential functions

14.2 y = e^x

14.3 Exponential modelling

14.4 Logarithms

14.5 Laws of logarithms

14.6 Solving equations using logarithms

14.7 Logarithms and non-linear data