A-Level Maths - Core/Pure 1

- A-Level Maths PURE/CORE 1
- 1.1 and 1.4 Rational Indices Law
- 1.2 Expanding Brackets
- 1.3 Factorising Polynomials
- 1.5 and 1.6 Surds
- 2.1 Solve quad. equ FACTORISE
- 2.2 Square form of quadratic equation
- 2.3 and 2.4 Complete Square Quad. Functs. & graphs
- 2.5 The discriminant
- 2.6 Modelling with Quadratics
- 3.1-3.3 Solving 2 simult. equ. Linear and quad
- 3.4-3.6 Inequals. Linear and quad solving
- 3.6 Inequalities on a graph
- 3.7 Regions bound by quadratics and straight lines
- 4.1 Cubic Graphs
- 4.2 Quartic Graphs
- 4.3 Reciprocal graphs
- 4.4 Points of intersection
- 4.5-4.7 Transformation of graphs
- REVIEW WEEK (1)
- 5.1-5.3 Gradients, straight & parallel lines
- 5.4 Line lengths and areas
- 5.5 Modelling with straight lines
- 6.1-6.2 Circle mid points and equation
- 6.1-6.4 Perpendicular, tangent and chord
- 6.3 Circle line intersections
- 7.1 Factor Theorem
- 7.2 Proof Methods
- Algebraic Division
- Radian measures
- Radian Arc Lengths
- Radian Area of Sector
- Trig in 4 quadrants
- Identities
- Drawing graphs of Sinx Cosx Tanx
- Trig Identities SIN^2 COS^2=1 solving trig equ
- nth term sequences
- Arithmetic Sequences and Series
- Geometric Series
- Differentiation
- Differentiation - 2nd derivative MIN MAX pts
- Integration
- Indefinite Integrals
- Boundary conditions and Definite Integrals
- Integration - Areas under a curve

A geometric series sum_(k)a_k is a series for which the ratio of each two consecutive terms a_(k+1)/a_k is a constant function of the summation index k. The more general case of the ratio a rational function of the summation index k produces a series called a hypergeometric series. For the simplest case of the ratio a_(k+1)/a_k=r equal to a constant r, the terms a_k are of the form a_k=a_0r^k. Letting a_0=1, the geometric sequence {a_k}_(k=0)^n with constant |r|<1 is given by ...

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