AQA A-Level Maths
Selection of pages and worksheets relating to AQA A-Level Course
Table of Contents
- Core 1
- Surds
- Coordinate Geometry
- Quadratics
- Circles
- Simultaneous Equations and Quadratic Inequalities
- Factors, Remainders and Cubic Graphs
- Differentiation
- Integration
- Core 2
- Trapezium Rule
- Trigonometry
- Arithmetic and Geometric Series
- Core 3
- Core 4
- Binomial Expansion (C4)
Surds
Key Facts
You need to know the following:[br][br][list][*]A square root such as[math]\sqrt{2}\text{ or }\sqrt{5}[/math] is a surd. (But not, eg.[math]\sqrt{4}=2[/math] )[/*][*]Surds multiply and divide as normal: [math]\sqrt{a}\times\sqrt{b}=\sqrt{ab}[/math] and [math]\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}[/math][/*][*]Surds simplify by decomposing them into a product with a square number, and applying the root to that square - eg. [math]\sqrt{75}=\sqrt{25}\times\sqrt{3}=5\times\sqrt{3}=5\sqrt{3}[/math][/*][/list]
Test Yourself: Simplifying Surds
[list][*]You can [b]rationalise[/b] surds of the form [math]\frac{1}{\sqrt{2}}[/math] by multiplying by [math]\frac{\sqrt{2}}{\sqrt{2}}[/math] - this keeps the fraction the same value, but 'eliminates' the surd from the bottom: [math]\frac{1}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{1\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{\sqrt{2}}{2}[/math][/*][/list]
Step-by-Step: Rationalising (simple) denominator
Rationalising the Denominator (Complex)
Trapezium Rule
Key Facts
The trapezium rule is defined as:[br][math]\int_a^bf(x)\mathrm{dx}\approx\frac{1}{2}h\left\{\left(y_0+y_n\right)+2\left(y_1+y_2+\ldots+y_{n-1}\right)\right\}[/math], where [math]h=\frac{b-a}{n}[/math].[br]This gives an [b]approximation [/b]to an integral, and is made more accurate by increasing [math]n[/math], the number of strips.[br][br]A common way of remembering the bit within { ... } is to treat it as [i]both of the ends and two times the middle values.[/i][i][br][/i]
Binomial Expansion (C4)
Intro