Mathematics notes

MATHEMATICS NOTES
Basic Algebra

1. What is Algebra?
Algebra is a branch of mathematics that uses letters and symbols to represent numbers.

Example: x + 5 = 12. Here x is the unknown number.

2. Terms Used in Algebra
• Variable – a letter that represents a number (x, y, a)
• Constant – a fixed number (5, 10, 100)
• Coefficient – number in front of a variable (3x → 3 is coefficient)
• Expression – combination of numbers and variables (2x + 5)
• Equation – two expressions that are equal (2x + 5 = 11)

3. Solving Simple Equations
Example 1: x + 4 = 10
Step 1: Subtract 4 from both sides → x = 6

Example 2: 2x = 14
Step 1: Divide both sides by 2 → x = 7

Example 3: 3x + 5 = 20
Step 1: Subtract 5 → 3x = 15
Step 2: Divide by 3 → x = 5

4. Like Terms
Like terms have the same variable.
Example: 2x + 3x = 5x, 4y − y = 3y

5. Order of Operations (BODMAS)
B – Brackets
O – Orders (powers)
D – Division
M – Multiplication
A – Addition
S – Subtraction

Example: 6 + 2 × 3 = 12

6. HCF Example
Find the HCF of 12 and 18
12 = 2 × 2 × 3
18 = 2 × 3 × 3
HCF = 6

7. Practice Questions
1. x + 7 = 15
2. 2x = 20
3. 5x − 5 = 20
4. Simplify: 3x + 2x
5. Find HCF of 8 and 12

Answers