# Pure Mathematics with FP1 and FP2

Mind Map by , created over 4 years ago

## A-Levels Pure Mathematics Mind Map on Pure Mathematics with FP1 and FP2, created by Alex Burden on 11/03/2014.

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 Created by Alex Burden over 4 years ago
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Pure Mathematics with FP1 and FP2
1 Core 1
1.1 Factor/Remainder Theorem
1.1.1 If, when you factorise a quadratic equation, the remainder is 0 then this is the Factor Theorem.
1.1.1.1 Use the factor theorem to factorise the polynomial 2x³ - 7x² - 28x - 12

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1.1.2 The Remainder Theorem is when the remainder from factorising is not 0
1.1.2.1 When x³ + ax² - x - 2 is divided by x - 4, the remainder of 74. Find the value of a

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1.2 Binomial Expansion
1.3 Surds
1.4 Simultaneous Equations
1.5 Coordinate Geometry
1.6 Completing the Square
1.7 Differentiation from First Principles
1.8 Rules of Differentiation
1.9 Stationary/Turning Points
1.10 Normals and Tangents
1.11 Inequalities
1.12 Transformations
1.13 Lines and Curves
1.14 Roots of Equations
2 Core 2
2.1 Logarithms
2.2 Arithmetic Progressions
2.3 Geometric Progressions
2.4 Circles
2.5 Trigonometry - Sine and Cosine Rule
2.6 Trigonometry Equations
2.7 Trigonometry Identities
2.9 Integration
2.10 Area Under a Curve
2.11 The Trapezium Rule
3 Core 3
3.1 Secx, Cosecx and Cotx
3.2 Pythagorean Identities
3.3 Exponential and Log Functions
3.4 Differentiating a Bracket
3.5 The Quotient Rule
3.6 Differentiation of Inverse Trigonometry Functions
3.7 Implicit Differentiation
3.8 Parametric Differentiation
3.9 Disproof by Counter Example
3.10 Simpson's Rule
3.11 Functions
3.12 The Modulus Function
3.13 Integration
3.14 Approximate Solutions
3.15 Multistep Transformations
3.16 Intersecting Lines and Curves
3.17 The Product Rule
3.18 Trigonometry Differentiation
4 FP1
4.1 Matrices

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4.1.1 Row Reduction

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4.2 Roots of Equations

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4.2.2 Cubic Equations

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4.3 Complex Numbers

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4.4 Number Systems

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4.5 Differentiation

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4.6 Isometry in the Plane

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4.7 Mathematical Induction

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4.8 Triangular Numbers

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5 FP2
5.1 Further Partial Fractions

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5.2 Complex Numbers

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5.3 Factor Formulae

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• A+B=x        A-B=y To write a product as a sum/difference; - Write in descending order - A=sum     B=difference If cos2x+cos3x+cos4x, use factor formulae on 2 extreme angles and then factorise result with the middle

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5.4 The t Formulae

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5.5 Further Integration

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5.6 General Solutions

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5.7 Functions

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5.8 Conics
5.8.1 Conic Sections
5.8.1.1 Properties of Conic Sections