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Summary of the A-Level Specification

Summary of the A-Level Specification

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

Note that the AS syllabus appears to be a subset of the A-Level syllabus so I have highlighted in bold the material that uniquely belongs to A-Level and not AS. 

Additionally, not all topics have yet been fully cross-referenced in the table below

Pure Maths

Pure maths is split into ten distinct topics. (The additional topic is numerical methods)

Proof

Description Links
Proof by Deduction proof by deduction
Proof By Exhaustion  
Disproof by Counterexample  
Proof by Contradiction  

Algebra and functions

Description Links
Laws of indices surds
manipulate surds, including rationalisation surds
quadratics, graphs, discriminant, complete the square, solve quadratics, disguised quadratics 

quadratics

sketching 1 

disguised quadratics

simultaneous equations of two variables, including one quadratic Simultaneous Eq
linear and quadratic inequalities, interpret graphically. Express answers using 'and', 'or' OR through set notation. 

inequalities

 

Manipulate polynomials, expand brackets, collect terms, factorise, algebraic division, factor theorem

algebraic division

factor theorem

Sketch graphs of polynomials and reciprocals, including horizontal and vertical asymptotes; use graphs to solve equations. Understand proportionality.  sketching 1
Understand the effect of simple transformations (a single stretch or translation)  transformations
Simplify Rational expressions  
The modulus of linear functions modulus function
Composite Functions, inverses and their graphs composite functions
Composites of simple transformations  
Partial fractions partial fractions
Use of functions for modelling  

 

Coordinate geometry

Description Links

equation of straight lines, in multiple forms. Gradient of parallel and perpendicular lines. Use straight line models

straight lines
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
Parametric curves and conversion between parametric and Cartesian parametric curves
Modelling with parametric curves  

 

Sequences and series

Description Links
Understand and use the binomial expansion for positive integers, Extend to any rational $n$ and have awareness of radius of convergence binomial expansion
Manipulate sequences, including those generated by iterative formulae.   
Understand and use sigma notation summation notation
Understand and use arithmetic sequences arithmetic sequences
Understand and use geometric sequences geometric sequences
Use sequences and series in modelling  

Trigonometry

Description Links
understand, use definitions of sin, cos, tan for all arguments; sine and cosine rules; area of a triangle intro trig
use sin, cos, tan functions, graphs, symmetries and periodicity intro trig
use identities $\tan (x)= \frac{\sin(x)}{\cos(x)}$ and Pythagorean identity Pythagorean id
Solve trigonometric equations, in a given interval, including quadratic equations in trig functions, and linear combinations of the unknown.  
Radians  
Small angle approximations small angle approx
Knowledge of exact values Trig values
Reciprocal trig functions  
Trig identities, double angle formula, compound angle formula, R-alpha method, Pythagorean Identities with reciprocal functions

double angle formula

compound angle formula

r-$\alpha$ method

Trig Proofs  
Contextual problems  

 

Exponentials and Logarithms

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

Differentiation

Differentiation Links
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

 

differentiate $x^n$ for rational $n$ and linear combinations differentiation
apply differentiation to find gradients, tangents, normals, maxima, minima and stationary points. Identify where functions are increasing or decreasing.  tangent line
Differentiate $\sin(kx),\;\cos(kx),\;\tan(kx)$ $e^{kx},\ln{x}$ and related linear combinations tangent line
Points of inflection, convex and concave curves tangent line
Product, Quotient and Chain rules

product rule

quotient rule

chain rule

Implicit and parametric differentiation

implicit

parametric

Construction of differential equations tangent line

 

Integration

Integration Links
Know and use the fundamental theorem of calculus ftoc
Integrate $x^n$ (excluding $n=-1$) and related sums, differences and constant multiples intro to integration
Evaluate definite integrals; use integral to find area under a curve intro to integration
Integrate $\frac{1}{x}$, $e^{kx}$, $\sin(kx)$, $\cos(kx)$, $\tan(kx)$ and related functions, including use of identities trig integration
Find the area between two curves  
Understand and use integration as the limit of a sum  
Integration by substitution substitution
Integration by parts by parts
integration using partial fractions partial fractions
first order differential equations separation of vbls

 

Vectors

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