Summary of AS Specification (Edexcel  Pure)
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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  
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  
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 

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 