Summary of the ALevel Specification
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Summary of the ALevel Specification
The complete ALevel 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 ALevel syllabus so I have highlighted in bold the material that uniquely belongs to ALevel and not AS.
Additionally, not all topics have yet been fully crossreferenced 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  
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. 

Manipulate polynomials, expand brackets, collect terms, factorise, 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, Ralpha method, Pythagorean Identities with reciprocal functions  
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 

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  
Implicit and parametric differentiation  
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 