# A-level Mathematics/AQA/Pure Core 1

• 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.
• 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
• 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
• 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