Equations (Copy)

Equations and Formulae Cheat Sheet (IGCSE Mathematics 0580 – CORE)
Topic: Constructing, Solving, and Rearranging

1. Construct Simple Expressions, Equations, and Formulas

• Expressions: No equals sign.
  Example:
  • “2 more than n” → n + 2
  • “3 times a number y” → 3y
• Equations: Has an equals sign.
  Example:
  • “5 less than twice a number equals 11” → 2x – 5 = 11
• Formulas: Show a relationship between different quantities.
  Example:
  • Area of rectangle → A = l × w
  • Speed formula → Speed = Distance ÷ Time

2. Solve Linear Equations in One Unknown

Steps:

1. Simplify both sides if needed (expand brackets, collect like terms).
2. Move all terms with unknowns to one side and numbers to the other side.
3. Divide or multiply to solve for the unknown.

Examples:

• Solve: 3x + 4 = 10
  • 3x = 10 – 4
  • 3x = 6
  • x = 6 ÷ 3 = 2
• Solve: 5 – 2x = 3(x + 7)
  • Expand: 5 – 2x = 3x + 21
  • Bring terms together: 5 – 21 = 3x + 2x
  • –16 = 5x
  • x = –16 ÷ 5 = –3.2

3. Solve Simultaneous Linear Equations in Two Unknowns

Method: Elimination or Substitution

• Elimination: Add or subtract equations to eliminate one variable.
• Substitution: Make one variable the subject from one equation and substitute into the other.

Example (Elimination Method): Solve:

1. 2x + y = 10
2. x – y = 1

Add (1) and (2):
(2x + y) + (x – y) = 10 + 1
3x = 11
x = 11 ÷ 3 ≈ 3.67

Substitute into (2):
3.67 – y = 1
y = 3.67 – 1 = 2.67

Example (Substitution Method): Solve:

1. y = 2x + 3
2. x + y = 13

Substitute y into (2):
x + (2x + 3) = 13
3x + 3 = 13
3x = 10
x = 10 ÷ 3 ≈ 3.33

Then find y:
y = 2(3.33) + 3 = 6.66 + 3 = 9.66

4. Change the Subject of Simple Formulas

Steps:

1. Isolate the term with the new subject.
2. Perform operations to fully make the subject alone.

Examples:

• Formula: A = l × w
  Make w the subject:
  • Divide both sides by l:
  • w = A ÷ l
• Formula: v = u + at
  Make t the subject:
  • v – u = at
  • t = (v – u) ÷ a

Important Rules to Remember

Common Phrases to Equation Translation

Key Exam Tip:
Always check your solution by substituting it back into the original equation or formula.
When changing subject, work step-by-step without skipping moves.