Numerical Methods in A-Level Mathematics
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Numerical Methods
When we cannot solve an equation, for example, using the normal analytical techniques we often use Numerical Methods. This usually requires the use of computers but at A-Level Maths we learn the fundamentals of these processes by doing the calculations by hand (or with a calculator). Recall that we first saw numerical methods in GCSE Maths when using iteration.
We do not study Numerical Methods in AS-Maths. However, in Year 2, we take a look at various numerical methods for finding roots. We also explore ways of estimating the area beneath graphs which up until now we have found using definite integrals.
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- (not covered in AS Maths)
Other Topic 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
- COORDINATE GEOMETRY – straight lines, equation of a circle
- 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
- VECTORS – two-dimensional vectors, vector arithmetic, vectors in context
Other Topic Areas in A2-Maths
- PROOF – proof by contradiction
- ALGEBRA & FUNCTIONS – modulus of a function, partial fractions, inverse and composite functions, compound transformations
- COORDINATE GEOMETRY – parametric equations
- 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,
- VECTORS – 3D vectors