Pure Mathematics Year 1/AS
8. The
Binomial
Expansion
7. Algebraic
Methods
6. Circles
5. Straight Line
Graphs
4. Graphs and
Transformations
3. Equations and
Inequalities
2. Quadratics
1. Algebraic
Topics
Units
1.1
1.2
1.3
1.4
1.5
1.6
2.1
2.2
2.3
2.4
2.5
2.6
3.1
3.2
3.3
3.4
3.5
3.6
3.7
4.1
4.2
4.3
4.4
4.5
4.6
4.7
5.1
5.2
5.3
5.4
5.5
6.1
6.2
6.3
6.4
6.5
7.1
7.2
7.3
7.4
7.5
8.1
8.2
8.3
8.4
8.5
Sub-topics
Index Laws
Expanding Brackets
Factorising
Negative And Fractional Indices
Surds
Rationalising Denominators
Solving Quadratic Equations
Completing The Square
Functions
Quadratic Graphs
The Discriminant
Modelling With Quadratics
Linear Simultaneous Equations
Quadratic Simultaneous Equations
Simultaneous Equations On Graphs
Linear Inequalities
Quadratic Inequalities
Inequalities On Graphs
Regions
Cubic Graphs
Quartic Graphs
Reciprocal Graphs
Points Of Intersection
Translating Graphs
Stretching Graphs
Transforming Functions
Y = Mx + C
Equations Of Straight Lines
Parallel And Perpendicular Lines
Length And Area
Modelling With Straight Lines
Midpoints And Perpendicular Bisectors
Equations Of A Circle
Intersections Of Straight Lines And Circles
Use Tangent And Chord Properties
Circles And Triangles
Algebraic Fractions
Dividing Polynomials
The Factor Theorem
Mathematical Proof
Methods Of Proof
Pascal's Triangle
Factorial Notation
The Binomial Expansion\
Solving Binomial Problems
Binomial Estimation
Revised
Pure Mathematics Year 1/AS
14. Exponentials and
logarithms
13. Integration
12. differentiation
11. Vectors
10. Trigonometric
9. Trigonometric
Identities and
Ratios
Equations
Topics
Units
9.1
9.2
9.3
9.4
9.5
9.6
10.1
10.2
10.3
10.4
10.5
10.6
11.1
11.2
11.3
11.4
11.5
11.6
12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9
12.10
12.11
13.1
13.2
13.3
13.4
13.5
13.6
13.7
14.1
14.2
14.3
14.4
14.5
14.6
14.7
14.8
Sub-topics
The Cosine Rule
The Sine Rule
Areas Of Triangles
Solving Triangle Problems
Graphs Of Sine Cosine And Tangent
Transforming Trigonometric Graphs
Angles In All Four Quadrants
Exact Values Of Trigonometrical Ratios
Trigonometric Identities
Simple Trigonometric Equations
Harder Trigonometric Equations
Equations And Identities
Vectors
Representing Vectors
Magnitude And Direction
Position Vectors
Solving Geometric Problems
Modelling With Vectors
Gradient Of Curves
Finding The Derivative
Differentiating 𝑥 𝑛
Differentiating Quadratics
Differentiating Functions With 2 Or More Terms
Gradients, Tangents And Normal
Increasing And Decreasing Functions
Second Order Derivatives
Stationary Points
Sketching Gradient Functions
Modelling With Differentiation
Integrating 𝑥 𝑛
Indefinite Integrals
Finding Functions
Definite Integrals
Areas Under Curves
Areas Under The 𝑥 -Axis
Areas Between Curves And Lines
Exponential Functions
𝑦 = 𝑒𝑥
Exponential Modelling
Logarithms
Laws Of Logarithms
Solving Equations Using Logarithms
Working With Natural Logarithms
Logarithms And Non-Linear Data
Revised