Edexcel FP1

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Each app in this series covers the essential topics for the module, presenting them in short video tutorials and explained in a clear mathematical style so as you can progress quickly and smoothly through the topics. There are further supplementary exercises and worked solutions from past papers for you to try, essential to improving your grade.

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Module Content

Complex numbers:
- Real and imaginary numbers
- Addition, Subtraction and Multiplying complex numbers and simplifying powers of i
- Complex conjugates
- Division of a complex number by a complex number
- Argand diagram
- Modulus and argument of a complex number
- Solving problems with complex numbers
- Square roots of a complex number
- Solving quadratic equations with complex roots (complex conjugate pairs)
- Solving cubic equations
- Solving quartic equations

Numerical solutions to equations:
- Solving equations of the form f(x)=0
- Bisection method
- Linear interpolation
- Newton-Raphson process

Coordinate systems:
- Parabola
- Cartesian Form
- Cartesian equation of a parabola, directrix, focus and locus
- Parametric Form
- Parametric form of a parabola
- Tangents and Normals
- Cartesian Form
- Parametric Form

- Hyperbola (rectangular)
- Cartesian and Parametric Forms
- Introduction - Cartesian and Parametric forms
- Tangents and Normals
- Cartesian Form
- Parametric Form

Matrix algebra:
- Introduction and dimension of a matrix
- Addition and subtraction and multiplying a matrix by a scalar
- Matrix multiplication
- Identity and Inverse of a 2x2 matrix
- Applications
- Simultaneous Equations
- Linear Transformations
- Rotations
- Reflections
- Enlargement
- Transformations Test
- Combinations of Transformations
- Inverse Matrices
- Inverse matrices to reverse linear transformations
- Area Scale Factor
- Determinant as the area scale factor of a transformation
- Proof

Series:
- ∑ notation (revision)
- Sum of the first n natural numbers ∑r and the results for ∑a and ∑(ar+b)
- Harder examples using these results
- Sum of the squares of the first n natural numbers ∑r²
- Sum of the cubes of the first n natural numbers ∑r³
- Using known formulae to sum more complex series

Proof by mathematical induction:
- Series
- Proof of the sum of the series ∑r
- Proof of the sum of the series ∑r²
- Proof of the sum of the series ∑r³
- Further examples
- Divisibility and Multiple Tests
- Proof that an expression is divisible by a certain integer (power type)
- Proof that an expression is divisible by a certain integer (non-power type)
- Recurrence Relations
- Proof of the general term from a recurrence relationship (example 1)
- Proof of the general term from a recurrence relationship (example 2)
- Matrices
- Proof of matrix multiplication statements (example 1)
- Proof of matrix multiplication statements (example 2)