# A-level Mathematics/AQA/Pure Core 1

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< A-level Mathematics | AQA

- Co-ordinate Geometry
- Equation of a line, y = mx + c
- Finding a line
- two points
- gradient, one points
- etc.

- When are lines perpendicular or parallel?

- Surds
- Simplification -
- Rationalising the Denominator.

- Quadratics
- Diff b/w expression and equation
- Factorising
- Completing the square
- Vertex of, line of symmetry of

- Formula
- Sketching
- Discriminant of
- Implications made by discriminant value

- Inequalities
- Three-part inequalities
- Quadratics
- Solution by sketch and completing square

- Circles
- Circle Theorems
- Tangents are perpen. to radii
- Tangents from an external point are equal, etc.
- MORE

- Co-ordinate Geometry Form of
- Circle from three points, finding tangents to a point

- Circle Theorems

- Other algebra
- Factor Theorem
- Remainder Theorem
- Simultanoues Eq.
- Elimination
- Substitution

- Curve Sketching
- Intersections of curves as sol'n to sim. eq.
- Translations of curves.

- Diff'n
- IDEA: finding the gradient of the tangent to a curve
- As a limit
- function (f'(x), f
*(x)) and Liebniz notation (dy/dx)* - Diff'n polynomials
- Higher Derivatives
- Maxima and Minima

- Increasing and decreasing functions
- Practical Applications

- Int'n
- Inverse process
- Net Area b/w curve and x-axis
- Idea that below x-axis is NEGATIVE

- Diff b/w definite and indefinite int'n
- Area b/w curve and x-axis
- Are b/w two curves b/w two points

- MASHUPS