Edexcel Further Core Maths AS Tutorials

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

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
5. Exam Questions - Loci in the complex plane

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

Simultaneous Equations by Matrix Methods

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

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

View the Playlist of Tutorials below :

1. Relationship between the roots and coefficients of a quadratic equation
2. Relationship between the roots and coefficients of a cubic equation

Standard Summations

1. Sum of the first n natural numbers ∑r and the results for ∑a and ∑(ar+b)
2. Sum of the squares of the first n natural numbers ∑r²
3. Sum of the cubes of the first n natural numbers ∑r³
4. Using known formulae to sum more complex series
5. Exam Questions - Series

Sum of Series

1. Proof of the sum of the series ∑r
2. Proof of the sum of the series ∑r²
3. Proof of the sum of the series ∑r³
4. Proof for other series
5. Exam Questions - Sum of series

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

Applications of Integration – Volumes of revolution

1. Volume of revolution about the x-axis
2. Exam Questions - Volume of revolution about the x-axis
3. Volume of revolution about the x-axis generated between curves
4. Volume of Revolution about the y-axis
5. Exam Questions - Volume of Revolution about the y-axis
6. Volume of Revolution about the y-axis generated between curves

Scalar Product (Dot Product)

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

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

Lines

1. Cartesian form of a line

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. Shortest distance from a point to a plane
6. Angle between a line and a plane
7. The angle between two planes