Quadratic Formula: x = (−b ± √(b²−4ac)) / 2a
Discriminant: Δ = b²−4ac
Δ > 0 → 2 real roots
Δ = 0 → 1 repeated root
Δ < 0 → no real roots
Vertex form: y = a(x−h)² + k → vertex (h, k)
Laws of Exponents: aᵐ·aⁿ = aᵐ⁺ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁻¹ = 1/a
Factor or use quadratic formula for ax²+bx+c=0
Function notation: f(x), domain & range
Inverse function: swap x and y, solve for y
Example
Solve 2x²−5x+3=0 using the quadratic formula.
Δ = 25−24 = 1 → x = (5±1)/4 → x = 1.5 or x = 1
📊 Unit 2 · Linear & Simultaneous Equations
Slope: m = (y₂−y₁)/(x₂−x₁)
Slope-intercept: y = mx + b
Point-slope: y−y₁ = m(x−x₁)
Parallel lines: same slope (m₁=m₂)
Perpendicular lines: m₁ × m₂ = −1
Simultaneous equations: substitution or elimination
Graphical solution: intersection point
Example
Line through (2,3) and (4,7). Find slope and equation.
m = (7−3)/(4−2) = 2 → y−3 = 2(x−2) → y = 2x−1
📐 Unit 3 · Geometry & Trigonometry
SOH-CAH-TOA:
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
Sine Rule: a/sin A = b/sin B = c/sin C
Cosine Rule: c² = a²+b²−2ab·cos C
Circle: A = πr², C = 2πr
Pythagorean Theorem: a²+b²=c²
Example
In right triangle: opposite = 5, hypotenuse = 13. Find sin θ.
sin θ = 5/13 ≈ 0.385 → θ ≈ 22.6°
📈 Unit 4 · Statistics & Probability
Mean = Σx/n
Median = middle value (sorted data)
P(A) = favourable outcomes / total outcomes
P(A∪B) = P(A)+P(B)−P(A∩B)
P(A|B) = P(A∩B)/P(B)
Standard Deviation: σ = √(Σ(x−x̄)²/n)