Further Pure 1

Edexcel A Level Further Pure 1.

Further Pure 1

Further Pure 1 topics

Trigonometry

The t-formulae

  1. The t-formulae (Proof)
  2. Solving trigonometric equations using the t-formulae

Further Calculus

Taylor’s Series

  1. Taylor's series
  2. Solution to differential equations using Taylor's series
  3. Exam Questions - Taylor’s series
  4. Using Series Expansions to Find Limits : still to do

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Leibnitz’s theorem

  1. Leibnitz’s theorem

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L’Hospital’s Rule

  1. L'Hospital's Rule - Still to be made

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The Weierstrass substitution

  1. The Weierstrass substitution

Further Differential Equations

First Order Substitution Types

  1. Using substitution to reduce a differential equation to a known form
  2. Exam Questions - Substitution types

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Second Order Substitution Types

  1. Using substitution to reduce a differential equation to a known form

Coordinate Systems

Conic Sections

  1. The conic sections of a circle, parabola, ellipse and hyperbola

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Parabola

  1. Coordinate geometry: Parabola directrix, focus, locus and equation
  2. Parabola parametric form
  3. Tangents and normals: Cartesian types
  4. Tangents and normals: parametric types
  5. Exam Questions - Parabola

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Hyperbola (Rectangular)

  1. Cartesian and parametric type
  2. Tangents and normals : Cartesian type
  3. Tangents and normals: parametric type
  4. Exam Questions - Hyperbola (rectangular)

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The Ellipse

  1. The Ellipse - Cartesian and parametric forms
  2. Tangents and normals to an ellipse
  3. Equation of the directrix and coordinates of the focus

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The Hyperbola

  1. Cartesian and parametric equations and asymptotes for a hyperbola
  2. Cartesian equation, focus and directrices
  3. Finding equations of tangents and normals to a hyperbola
  4. Finding equations of simple loci

Further Vectors

Vector Product

  1. Vector product (cross product)
  2. Applications : Area of a triangle and parallelogram

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Triple Scalar Product

  1. Triple scalar product
  2. Applications: volume

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Lines

  1. Cartesian form of a line
  2. Vector product form of a line
  3. Shortest distance between two skew lines

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Planes

  1. Parametric vector form of a plane
  2. Scalar product forms of a plane
  3. Cartesian form of a plane
  4. Finding the point of intersection between a line and a plane
  5. The equation of the line of intersection between two non parallel planes
  6. Shortest distance from a point to a plane
  7. Angle between a line and a plane
  8. The angle between two planes
  9. Intersection of three planes

Further Numerical Methods

Numerical Solution of First Order and Second Order Differential Equations

  1. First Order Differential Equations - Still to be done
  2. Second Order Differential Equations - Still to be done

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Numerical Integration

  1. Simpson's Rule
  2. Exam Questions - Simpson's Rule

Inequalities

Fractional Inequalities

  1. Fractional inequalities

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Modulus Inequalities

  1. Modulus inequalities
  2. Exam Questions - Modulus inequalities
  3. Modulus inequalities fractional type
  4. Exam Questions - Modulus inequalities fractional type