Grade 12 Mathematics – Short Notes
1. Functions
A function assigns each input exactly one output. Written as f(x). Example: f(x) = 2x + 3.
1 Linear: f(x) = mx + b
2 Quadratic: f(x) = ax² + bx + c
2. Slope of a Line
Formula: m = (y2 - y1) / (x2 - x1). Measures steepness of a line.
1 Positive slope: rising
2 Negative slope: falling
3. Quadratic Functions
Formula: x = (-b ± √(b² - 4ac)) / 2a. Graph is a parabola.
1 b² - 4ac > 0: two solutions
2 b² - 4ac = 0: one solution
3 b² - 4ac < 0: no real solution
4. Exponents Rules
1 a■ × a■ = a■■■
2 a■ / a■ = a■■■
3 (a■)■ = a■■
4 a■ = 1
5. Distance Formula
d = √((x2 - x1)² + (y2 - y1)²). Finds distance between two points.
6. Basic Trigonometry
1 sin θ = opposite / hypotenuse
2 cos θ = adjacent / hypotenuse
1. Functions
A function assigns each input exactly one output. Written as f(x). Example: f(x) = 2x + 3.
1 Linear: f(x) = mx + b
2 Quadratic: f(x) = ax² + bx + c
2. Slope of a Line
Formula: m = (y2 - y1) / (x2 - x1). Measures steepness of a line.
1 Positive slope: rising
2 Negative slope: falling
3. Quadratic Functions
Formula: x = (-b ± √(b² - 4ac)) / 2a. Graph is a parabola.
1 b² - 4ac > 0: two solutions
2 b² - 4ac = 0: one solution
3 b² - 4ac < 0: no real solution
4. Exponents Rules
1 a■ × a■ = a■■■
2 a■ / a■ = a■■■
3 (a■)■ = a■■
4 a■ = 1
5. Distance Formula
d = √((x2 - x1)² + (y2 - y1)²). Finds distance between two points.
6. Basic Trigonometry
1 sin θ = opposite / hypotenuse
2 cos θ = adjacent / hypotenuse
