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 |
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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 |