GRADE 9 MATHEMATICS – LONG NOTES
1. Number Systems
Number systems include natural numbers, whole numbers, integers, rational numbers, irrational numbers,
and real numbers. Rational numbers can be written as fractions, while irrational numbers cannot be
expressed as simple fractions.
Laws of Exponents
• aᵐ × aⁿ = aᵐ⁺ⁿ
• aᵐ ÷ aⁿ = aᵐ⁻ⁿ
• (aᵐ)ⁿ = aᵐⁿ
2. Algebraic Expressions
Algebraic expressions contain variables and constants combined using operations like addition, subtraction,
multiplication, and division.
Examples: - 3x + 5 - 2a − 7b - x² + 4x + 4
Like terms can be combined to simplify expressions.
3. Linear Equations
A linear equation has the highest power of the variable equal to 1.
Example: 2x + 5 = 15 Solution: 2x = 10 x = 5
4. Polynomials
Polynomials consist of terms with variables raised to whole number powers.
Types: - Monomial - Binomial - Trinomial
Factorization Example
x² + 5x + 6 = (x + 2)(x + 3)
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1. Number Systems
Number systems include natural numbers, whole numbers, integers, rational numbers, irrational numbers,
and real numbers. Rational numbers can be written as fractions, while irrational numbers cannot be
expressed as simple fractions.
Laws of Exponents
• aᵐ × aⁿ = aᵐ⁺ⁿ
• aᵐ ÷ aⁿ = aᵐ⁻ⁿ
• (aᵐ)ⁿ = aᵐⁿ
2. Algebraic Expressions
Algebraic expressions contain variables and constants combined using operations like addition, subtraction,
multiplication, and division.
Examples: - 3x + 5 - 2a − 7b - x² + 4x + 4
Like terms can be combined to simplify expressions.
3. Linear Equations
A linear equation has the highest power of the variable equal to 1.
Example: 2x + 5 = 15 Solution: 2x = 10 x = 5
4. Polynomials
Polynomials consist of terms with variables raised to whole number powers.
Types: - Monomial - Binomial - Trinomial
Factorization Example
x² + 5x + 6 = (x + 2)(x + 3)
1
