create a checklist for learning content in edexcel further maths

Algebraic Methods

Simplifying algebraic expressions

Solving linear equations

Solving quadratic equations

Solving simultaneous equations

Solving inequalities

Rationalizing denominators

Completing the square

Using the binomial theorem

Working with functions and graphs

Calculus

Differentiating functions

Finding stationary points

Finding maximum and minimum values

Integrating functions

Finding the area under a curve

Solving differential equations

Applying calculus to real-life problems

Vectors

Understanding vector notation

Finding the magnitude and direction of vectors

Adding and subtracting vectors

Scalar multiplication of vectors

Dot product and cross product of vectors

Working with vector equations

Applying vector concepts to geometry and mechanics problems

Complex Numbers

Understanding the imaginary unit

Writing complex numbers in standard form

Adding, subtracting, multiplying, and dividing complex numbers

Finding the modulus and argument of complex numbers

Finding the conjugate of a complex number

Solving equations involving complex numbers

Working with complex numbers in polar form

Matrices

Understanding matrix notation

Adding and subtracting matrices

Multiplying matrices

Finding the determinant of a matrix

Finding the inverse of a matrix

Solving systems of linear equations using matrices

Applying matrix operations to solve real-world problems

Further Algebra and Functions

Simplifying rational expressions

Working with logarithmic and exponential functions

Solving logarithmic and exponential equations

Understanding and applying the properties of logarithms

Understanding and applying the properties of exponentials

Working with hyperbolic functions

Solving equations involving hyperbolic functions

Further Calculus

Differentiating exponential and logarithmic functions

Differentiating trigonometric functions

Integrating exponential and logarithmic functions

Integrating trigonometric functions

Applying calculus to parametric equations

Applying calculus to polar coordinates

Solving differential equations using advanced techniques

Further Vectors and Geometry

Understanding three-dimensional vectors

Finding the scalar and vector product of three-dimensional vectors

Working with lines and planes in three dimensions

Finding the equation of a line or plane

Applying vector concepts to geometry and mechanics problems in three dimensions

Understanding and applying vector calculus concepts

Understanding and applying vector equations of curves and surfaces

Discrete Mathematics

Understanding sets and set notation

Performing operations on sets

Understanding and applying the principles of counting

Understanding and applying the principles of probability

Understanding and applying the principles of permutations and combinations

Understanding and applying the principles of graph theory

Working with algorithms and logic

Mechanics

Understanding and applying the principles of motion

Understanding and applying the principles of forces

Understanding and applying the principles of momentum

Understanding and applying the principles of energy and power

Understanding and applying the principles of circular motion

Solving mechanics problems involving projectiles and collisions

Solving mechanics problems involving statics and dynamics