Summary of AS Specification (Edexcel - Pure)

The complete AS Syllabus can be found on the Edexcel website; below is an abridged version to facilitate effective use of the site

In this article, we cross reference the AS maths specifications with the website content to help you find the materials you need as quickly as possible!

Pure Maths

Pure maths is split into nine distinct topics.

Proof

Section	Description	Links
1.1	Proof by Deduction	proof by deduction
1.1	Proof By Exhaustion
1.1	Disproof by Counterexample

Algebra and functions

Section	Description	Links
2.1	Laws of indices	surds
2.2	manipulate surds, including rationalisation	surds
2.3	quadratics, graphs, discriminant, complete the square, solve quadratics, disguised quadratics	quadratics sketching 1 disguised quadratics
2.4	simultaneous equations of two variables, including one quadratic	Simultaneous Eq
2.5	linear and quadratic inequalities, interpret graphically. Express answers using 'and', 'or' OR through set notation.
2.6	Manipulate polynomials, expand brackets, collect terms, factorise, algebraic division, factor theorem	algebraic division factor theorem
2.7	Sketch graphs of polynomials and reciprocals, including horizontal and vertical asymptotes; use graphs to solve equations. Understand proportionality.	sketching 1
2.8	Understand the effect of simple transformations (a single stretch or translation)	transformations

Coordinate geometry

Section	Description	Links
3.1	equation of straight lines, in multiple forms. Gradient of parallel and perpendicular lines. Use straight line models	straight lines
3.2	equation of a circle, in geometric and cartesian form. complete square to determine centre and radius, use angle in a semi circle id a right angle. perpendicular from centre bisects a chord. radius is perpendicular to tangent	circle equation

Sequences and series

Section	Description	Links
4.1	Understand and use the binomial expansion for positive integers	binomial expansion

Trigonometry

Section	Description	Links
5.1	understand, use definitions of sin, cos, tan for all arguments; sine and cosine rules; area of a triangle	intro trig
5.2	use sin, cos, tan functions, graphs, symmetries and periodicity	intro trig
5.3	use identities $\tan (x)= \frac{\sin(x)}{\cos(x)}$ and Pythagorean identity	Pythagorean id
5.4	Solve trigonometric equations, in a given interval, including quadratic equations in trig functions, and linear combinations of the unknown.

Exponentials and Logarithms

Section	Description	Links
6.1	know and use graph of the function $a^x$, where $a\gt 0$, know and use the function $e^x$ and its graph	exponentials
6.2	Know that the gradient of $e^{kx}$ is $ke^{kx}$ and hence understand why the exponential model is useful	derivatives
6.3	know and use $\log_ax$ as inverse of $a^x$	exp log inverse
6.4	Know and use laws of logarithms.	laws of logs
6.5	Solve equations of the form $a^x = b$	laws of logs
6.6	Use log graphs to establish parameters in the form $y=ax^n$ and $y = kb^x$
6.7	understand and use exponential growth and decay models

Differentiation

Section	Differentiation	Links
7.1	understand the derivative as the gradient of the tangent to a graph at a general point, sketch gradient curves, find and interpret second derivatives, first principles differentiation	first principles
7.2	differentiate $x^n$ for rational $n$ and linear combinations	differentiation
7.3	apply differentiation to find gradients, tangents, normals, maxima, minima and stationary points. Identify where functions are increasing or decreasing.	tangent line

Integration

Section	Integration	Links
8.1	Know and use the fundamental theorem of calculus	ftoc
8.2	Integrate $x^n$ (excluding $n=-1$) and related sums, differences and constant multiples	intro to integration
8.3	Evaluate definite integrals; use integral to find area under a curve	intro to integration

Vectors

Section	Vectors	Links
9.1	use vectors in two dimensions	intro vectors
9.2	calculate magnitude and direction of a vector and convert between component form and magnitude / direction form	intro vectors
9.3	Add vectors, apply scalar multiplication and understand their geometric interpretations	intro vectors
9.4	Understand and use position vectors; calculate distance between two point represented by position vectors	intro vectors