## Welcome to LearnFM Unit 1!

Below you will find a list of topics that have been released we are aiming to get Unit 1 released by the end of September so stay tuned

Section 1

$$\begin{bmatrix}a & b\\c & d\end{bmatrix}$$

### Matrices

Learn how a matrix works and discover how to add, subtract, multiply and divide them

$$\begin{bmatrix}1 & 0\\0 & -1\end{bmatrix}$$

### Matrices Transformation

Learn to transform matrices through multiplication

$$\begin{bmatrix}x\\y\end{bmatrix} = \begin{bmatrix}x'\\y'\end{bmatrix}$$

### Invariant Points

Learn about matrices that stay the same even after transformations

Section 2

### Polynomials

Learn how to find the roots of a quadratic equation using the quadratic formula

$$x + iy$$

### Complex Numbers

Learn about complex numbers and there conjugates and discover how to add, subtract, multiply and divide them

$$x + iy$$

$$r∠θ$$

### Changing Complex Forms

Learn how how to change complex forms and to use geometry with complex numbers

$$arg(z+2)$$

### Complex Numbers Contd.

Harder questions about complex numbers to expand your understanding

$$α+β$$

### Polynomials Contd.

Learn how to find polynomials using their roots and discover ways of finding roots of longer polynomials

Section 3

$$\sum_{r=1}^{n}r$$

### Sum and Series and Method of Difference

Learn to add long series quickly using summation and how to represent a series in a sum equation

$$\frac{x+2}{x^2(x-4)}$$

### Partial Fractions

Learn to seperate fractions into smaller denominations to easily be used in other equations

$$✓$$

### Proofs

Learn how to prove a mathematical statement is correct through equations

Section 4

$$2\underline{i} + 3\underline{j}$$

### Vectors

Learn about vectors which are applied throughout mathematics to represent distances

### Vectors on a Plane (3D Vectors)

Learn about vectors in 3D and how they can interact with planes