Expressions and Linear Equations Cheat Sheet

This cheat sheet covers the fundamental concepts of algebraic expressions, linear equations, inequalities, formulas, and simultaneous equations, providing a concise overview for quick reference and problem-solving.

Core Principles

• Algebraic expressions use pronumerals (variables) to represent unknown quantities.
• Like terms can be combined through addition and subtraction; unlike terms cannot.
• Linear equations are solved by isolating the variable using inverse operations.
• Inequalities represent a range of values and are solved similarly to equations, with a key rule about reversing the inequality sign when multiplying or dividing by a negative number.
• Formulas are equations that relate variables; they can be evaluated by substitution or transposed to solve for a specific variable.
• Simultaneous equations involve two or more equations with multiple variables, solved using substitution or elimination to find a common solution.

Formulas

• Area of a circle: $A = \pi r^2$
• Celsius to Fahrenheit: $F = \frac{9}{5}C + 32$
• Distance, velocity, time: $d = vt$
• Area of a trapezium: $A = \frac{1}{2}(a+b)h$