Grade 10 Mathematics Study Notes
1. Algebra
Laws of Exponents:
- a^m × a^n = a^(m+n)
- a^m ÷ a^n = a^(m-n)
- (a^m)^n = a^(mn)
- a^0 = 1
- a^-n = 1/a^n
Algebraic Expressions:
Like terms: 3x + 5x = 8x
Expanding: a(b+c)=ab+ac
Factorising:
- Common factor: 6x+12=6(x+2)
- Difference of squares: a²-b²=(a-b)(a+b)
2. Equations
Linear equations are solved by isolating the variable.
Example:
3x+5=20
3x=15
x=5
Simultaneous equations contain two unknowns and can be solved by substitution or elimination.
3. Functions
Straight line equation:
y=mx+c
1. Algebra
Laws of Exponents:
- a^m × a^n = a^(m+n)
- a^m ÷ a^n = a^(m-n)
- (a^m)^n = a^(mn)
- a^0 = 1
- a^-n = 1/a^n
Algebraic Expressions:
Like terms: 3x + 5x = 8x
Expanding: a(b+c)=ab+ac
Factorising:
- Common factor: 6x+12=6(x+2)
- Difference of squares: a²-b²=(a-b)(a+b)
2. Equations
Linear equations are solved by isolating the variable.
Example:
3x+5=20
3x=15
x=5
Simultaneous equations contain two unknowns and can be solved by substitution or elimination.
3. Functions
Straight line equation:
y=mx+c
