Coordinate Geometry in A-Level Maths
When we study shapes in a coordinate plane, we call it Coordinate Geometry. The majority of what we study in Coordinate Geometry, we will do in the Cartesian plane. This is when we have an $x$ and $y$ axis and we describe points by their $(x,y)$ coordinates. At more advanced levels, it is possible to describe shapes with polar coordinates (see more on polar coordinates).
In many cases, a coordinate geometry question will be presented with an accompanying diagram. However, if it is not, it is always a good idea to make your own diagram. Even if there is not enough information to create an accurate diagram, make the best sketch that you can.
You should have actually studied some coordinate geometry before. At GCSE, we learn the equation of a straight line (as well as other curves such as quadratics). Primarily, equations of Straight Lines and equations of Circles and the interesting problems that come with them are covered in the first year of A-Level Maths. Furthermore, we introduce Parametric Equations in the second year.
Other Areas in AS-Maths
- PROOF – proof by deduction, proof by exhaustion, disproof by counterexample
- ALGEBRA & FUNCTIONS – completing the square, cubics, curve sketching, discriminant, indices, inequalities, polynomials, quadratics, simultaneous equations, surds, transformations
- SEQUENCES & SERIES – binomial expansion
- TRIGONOMETRY – non-right-angled triangles, trigonometric equations, trigonometric graphs, trigonometric identities
- EXPONENTIALS & LOGS – exponential & logarithmic graphs, logs, their rules and solving log equations, growth & decay, differentiating e to the kx
- DIFFERENTIATION – differentiation from first principles and differentiating polynomials, increasing & decreasing functions, stationary points, tangents & normals, differentiating e to the kx
- INTEGRATION – fundamental theorem of calculus and integrating powers of x, definite integrals
- NUMERICAL METHODS – (not covered at AS Level)
- VECTORS – two-dimensional vectors, vector arithmetic, vectors in context
Other Areas in A2-Maths
- PROOF – proof by contradiction
- ALGEBRA & FUNCTIONS – modulus of a function, partial fractions, inverse and composite functions, compound transformations
- SEQUENCES & SERIES – arithmetic series (and sigma notation), geometric series, sequences, binomial expansion
- TRIGONOMETRY – radians, arc length & area of a sector, small angle approximations, reciprocal trigonometric functions, inverse trigonometric functions, double & compound angle formulae
- EXPONENTIALS & LOGARITHMS – compound transformations
- DIFFERENTIATION – concavity, convexity & inflection points, derivatives of trigonometric functions, product, quotient & chain rule, parametric & implicit differentiation, differentiating exp/log functions, differential equations & rates
- INTEGRATION – further integration, integration using trigonometric identities, integration by substitution, integration by parts, integration using partial fractions, solving differential equations,
- NUMERICAL METHODS – locating roots using iteration (including Newton-Raphson), trapezium rule
- VECTORS – 3D vectors