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# Summary of AS Specification (Edexcel - Pure)

## 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 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