Grade 12 Mathematics

Master the key concepts and formulas you need to excel in your Grade 12 Math exams.

Popular Math Formulas

Quadratic Formula

For equation ax² + bx + c = 0:

x = (-b ± √(b² - 4ac)) / 2a

Used to find the roots of any quadratic equation. The discriminant (b² - 4ac) tells you how many real solutions exist.

Trigonometric Identities

Fundamental identities:

sin²θ + cos²θ = 1

tan θ = sin θ / cos θ

sin(A+B) = sinA·cosB + cosA·sinB

Essential for solving complex trigonometric equations and proving relationships.

Calculus: Derivatives

Basic derivative rules:

d/dx(xⁿ) = n·xⁿ⁻¹

d/dx(sin x) = cos x

d/dx(eˣ) = eˣ

Fundamental for finding rates of change, slopes of curves, and optimization problems.

Calculus: Integrals

Basic integral formulas:

∫xⁿ dx = xⁿ⁺¹/(n+1) + C, n≠-1

∫sin x dx = -cos x + C

∫eˣ dx = eˣ + C

Used for finding areas, volumes, and solving differential equations.

Sequences and Series

Sum formulas:

Arithmetic: Sₙ = n/2·(a₁ + aₙ)

Geometric: Sₙ = a₁(1-rⁿ)/(1-r), |r| < 1

Essential for finding patterns and calculating sums in number sequences.

Analytical Geometry

Distance formula:

d = √[(x₂-x₁)² + (y₂-y₁)²]

Circle equation:

(x-h)² + (y-k)² = r²

Used for solving problems involving points, lines, and curves in a coordinate system.

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