OCR Further Pure Core Maths AS

It is advisable to check the official OCR Further Pure Core Maths AS specification in case of any changes.

Contents

Complex Numbers
Matrix Algebra
Proof by Mathematical Induction
Vectors
Roots of Polynomial Equations
Past Papers

Complex Numbers

Complex Numbers

  1. Real and imaginary numbers
  2. Addition, subtraction and multiplying complex numbers and simplifying powers of i
  3. Complex conjugates
  4. Division of a complex number by a complex number
  5. Argand diagrams
  6. Modulus and argument of a complex number
  7. Solving problems with complex numbers
  8. Square roots of a complex number
  9. Solving quadratic equations with complex roots
  10. Solving cubic equations
  11. Solving quartic equations
  12. Exam Questions - Complex numbers
  13. Geometrical effects of conjugating a complex number
  14. Exam Questions - Finding roots
  15. Modulus-argument form of a complex number
  16. Multiplication and division rules for mod and argument of two complex numbers
  17. Exam Questions - Further complex numbers

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Loci in the Complex Plane

  1. The locus of a point moving in a circle
  2. The locus of a point moving along a perpendicular bisector
  3. The locus of a point moving along a half-line
  4. Using complex numbers to represent regions on an Argand diagram

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Matrix Algebra

Matrices

  1. Introduction and dimension of a matrix
  2. Addition and subtraction and multiplying a matrix by a scalar
  3. Matrix multiplication
  4. Identity and Inverse of a 2x2 matrix
  5. Exam Questions - Identity and inverse of a 2x2 matrix
  6. Transposed and symmetric matrices
  7. Finding the determinant of a 3x3 matrix
  8. Finding the inverse of a 3x3 matrix where it exists

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Simultaneous Equations by Matrix Methods

  1. Solving simultaneous linear equations in 2 unknowns
  2. Solving three linear simultaneous equations

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Matrix Linear Transformations

  1. Linear transformations - rotations
  2. Linear transformations - reflections
  3. Linear transformations - enlargement
  4. How well do you know your transformations?
  5. Combinations of transformations
  6. Inverse matrices to reverse linear transformations
  7. Determinant as the area scale factor of a transformation
  8. Exam Questions - Matrix transformations
  9. 3D matrix transformations
  10. Invariant points

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Proof by Mathematical Induction

Various Types of Proofs

  1. Divisibility and multiple test proofs
  2. Exam Questions - Divisibility and multiple tests
  3. Matrix proofs
  4. Exam Questions - Matrix proofs

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Vectors

Scalar Product (Dot Product)

  1. Scalar product
  2. Perpendicular vectors
  3. Exam Questions - Scalar product

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Vector Equations of Lines

  1. Vector equation of a line
  2. Angle between two lines
  3. Parallel lines
  4. Intersecting and skew lines
  5. Exam Questions - Parallel intersecting and skew lines
  6. Closest point to a line and shortest distance from the origin
  7. Shortest distance of a point to a line

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Exam Questions – Vectors

  1. Exam Questions - Vectors

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Lines: Vector to Cartesian form

  1. Cartesian form of a line

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Vector Product

  1. Vector product (cross product)

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Roots of Polynomial Equations

Roots of Polynomial Equations

  1. Relationships between the roots and coefficients of a quadratic equation
  2. Relationships between the roots and coefficients of a cubic equation
  3. Relationships between the roots and coefficients of a quartic equation

Past Papers for OCR Further Pure Core Maths AS

For further revision and practice I have past papers, some with worked solutions – Check them out.

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