A1 - Expansion $-$ 1 variable, degree 1 $-$ Very easy

Examples :   $2\left(4x+1\right);4\left(x-3\right)-3\left(4x+3\right)$

A2 - Expansion $-$ 1 variable, degree 1 $-$ Easy

Example :   $3\left(6x+4\right)+4\left(-3+3x\right)-3\left(4x+2\right)$

A3 - Expansion $-$ 2 ou 3 variables, degree 1 $-$ Easy

Example :   $2\left(4x-4y+2\right)-4\left(3x+2y+4\right)$

A4 - Expansion $-$ Degree 2 $-$ Medium

Examples :   $x\left(2x+4\right)-2x\left(3+3x\right);{\left(3x+2\right)}^2$

A5 - Expansion $-$ Degree 2 $-$ A bit difficult

Examples :   ${\left(-2x+2y+2\right)}^2;{\left(x-3\right)}^2\left(1-4x\right)$

B1 - Factorizations - Very easy

Examples :   $-4x^2+3x;x\left(x-3\right)+\left(3x-2\right)\left(x-3\right)$

B2 - Factorizations - Easy

Examples :   $x^2-16;9x^2-12x+4$

B3 - Factorizations - Medium

Example :   $\left(5+4x\right)\left(2x-1\right)+{\left(5+4x\right)}^2$

B4 - Factorizations - Common factor - Difficult

Example :   $4x^2-25+\left(4x+3\right)\left(2x+5\right)$

B5 - Factorizations - Discriminant $-$ Easy

Example : $x^2+3x-4$

B6 - Factorizations - Discriminant $-$ Medium

Examples :   $x^2-x-3;-3x^2-3x+4$

B7 - Factorizations - Degree 3 - Without discriminant - Medium

Examples :   $x^3-27;x^3-4x^2+4x$

B8 - Factorizations - Degree 3 and 4 - Difficult

Examples :   $\left(2x-3\right){\left(4x-1\right)}^2-\left(4x+3\right)\left(2x-3\right);x^4-10x^2+9$

C1 - Linear equations $-$ Immediate

Examples :   $3x=5;2x-1=0$

C2 - Linear equations $-$ Like terms

Examples :   $5x=3x+2;-x+3=4x+5+2x$

C3 - Linear equations $-$ Like terms

Examples :   $2.3x+3.4=-2.6x-1;\frac{4x-5}{3}=\frac{-x-1}{6}$

C4 - Linear equations $-$ Expansion

Examples : $3x+2-3x=4x+x-5$     $2\left(2x+1\right)=3\left(-2x+5\right)$

C5 - Linear equations $-$ Expansion

Examples :   $5\left(1.3x+3.4\right)=4\left(-2.9x-5\right);3\left(\frac{x}{3}+2\right)=5\left(\frac{x}{6}-5\right)$

C6 - Linear equations $-$ Expansion

Examples : $\frac{5x}{3}+5=\frac{4x}{3}+5;\frac{2x+2}{3}=\frac{4x-5}{6}-\frac{3x+3}{2}$

C8 - Equations with 0, 1 or an infinity of solutions  

Examples : $2x=2-2x+4x;4\left(3x-5\right)=4\left(x-4\right)$

C10 - Fractional equations transforming into linear equations  

Example : $\frac{5}{-3x+1}=\frac{2}{4x+2};\frac{-3x-2}{-x-3}=2$

D1 - Linear inequalities $-$ Immediate

Examples :   $3x\le 5;2x-1>0$

D2 - Linear inequalities $-$ Like terms

Examples :   $5x\ge 3x+2;-x+3<4x+5+2x$

D3 - Linear inequalities $-$ Like terms

Examples :   $2.3x+3.4>-2.6x-1;\frac{4x-5}{3}\le \frac{-x-1}{6}$

D4 - Linear inequalities $-$ Expansion

Examples : $3x+2-3x<4x+x-5$     $2\left(2x+1\right)\ge 3\left(-2x+5\right)$

D5 - Linear inequalities $-$ Expansion

Examples :   $5\left(1.3x+3.4\right)>4\left(-2.9x-5\right);3\left(\frac{x}{3}+2\right)\le 5\left(\frac{x}{6}-5\right)$

D6 - Linear inequalities $-$ Expansion  

Examples : $\frac{5x}{3}+5\le \frac{4x}{3}+5;\frac{2x+2}{3}\ge \frac{4x-5}{6}-\frac{3x+3}{2}$

D8 - Inequalities witt 0, 1 or an infinity of solutions

Examples : $2x>2-2x+4x;4\left(3x-5\right)\le 4\left(x-4\right)$

E1 - Quadratic equations - Immediate

Examples : $16x^2-9=0;\left(-2x+4\right)\left(5x-1\right)=0;{\left(5x-2\right)}^2=0$        

E2 - Quadratic equations- Immediate

Examples : $\frac{x^2}{4}=16;\left(\frac{x}{3}-4\right)\left(3x+\frac{4}{3}\right)=0;{\left(\frac{x}{2}-5\right)}^2=0$

E3 - Quadratic equations - Factorization

Examples : $x^2-9-\left(5x+2\right)\left(x-3\right)=0;\left(3x+2\right)\left(x-3\right)+\left(x-4\right)\left(x-3\right)=0$

E4 - Quadratic equations - Factorization

Examples : $4x^2+12x+9+\left(x-4\right)\left(2x+3\right)=0;\left(4x+4\right)\left(-4x+12\right)+\left(-x+3\right)\left(x-4\right)=0$

E5 - Quadratic equations - Discriminant

Examples : $x^2-3x+4=0;-2x^2+2x+1=0;x^2+2x+1=0$

E6 - Quadratic equations - Discriminant

Examples :   $-x^2+\frac{4}{5}x-4=0;4x^2+\frac{2}{5}x+\frac{3}{5}=0$

E7 - Quadratic equations - Calculations and discriminant

Examples :   $\left(4x+2\right)\left(3x-6\right)=3x\left(6x-3\right);-2x^2-x+3=4x^2+4x+2$

E8 - Quadratic equations - Calculations and discriminant  

Examples : ${\left(4x+5\right)}^2={\left(5x-1\right)}^2;{\left(2x+2\right)}^2-\left(3x-2\right)\left(4x-1\right)=0$

E9 - Fractional equations transforming into quadratic equations  

Example : $\frac{1}{x+3}+\frac{1}{x-1}=\frac{2}{x};\frac{2x+3}{-3x-1}=\frac{4x-1}{2x-1}$

F1 - Simultaneous equations $2\times 2$ $-$ Very easy

Examples :   $\left\{\begin{array}{l}2x+1=4\\ 2y-1=1\end{array}\right.$   $\left\{\begin{array}{l}x+y=1\\ x+2y=5\end{array}\right.$

F2 - Simultaneous equations $2\times 2$ $-$ Easy

Examples :   $\left\{\begin{array}{l}4x+2y=5\\ -3x+2y=-4\end{array}\right.$     $\left\{\begin{array}{l}-3y=-x+5\\ 4x=2y+4\end{array}\right.$

F3 - Simultaneous equations $2\times 2$ $-$ Like terms

Examples :   $\left\{\begin{array}{l}5y+2z-2=-3y+z+4\\ -3y+2z-2=3y+4z-3\end{array}\right.$

F4 - Simultaneous equations $2\times 2$ $-$ Decimals and fractions

Examples :   $\left\{\begin{array}{l}5.1x-2.7y=3\\ 2.9x+5y=-4\end{array}\right.$     $\left\{\begin{array}{l}\frac{2}{3}x+\frac{5}{6}y=3\\ x+4y=3\end{array}\right.$

F5 - Simultaneous equations with 2 unknowns $-$ 0, 1 or an infinity of solutions

Examples :   $\left\{\begin{array}{l}3x+2y=5\\ 9x+6y=15\end{array}\right.$   $\left\{\begin{array}{l}3x+3y=-4\\ 4x-3y=2\\ 2x+9y=-10\end{array}\right.$

F6 - Simultaneous equations $3\times 3$ $-$ Medium

Examples :   $\left\{\begin{array}{l}3x-2y-2z=2\\ y-z=1\\ 2x+3y+2z=1\end{array}\right.$     $\left\{\begin{array}{l}-x+y-z=-2\\ 2x+y+2z=-1\\ -x+2y+3z=0\end{array}\right.$