SAT MATH CONCEPTS(NO GEO)

FOIL method

Multiply First, Outer, Inner, Last terms in (a + b)(c + d)

Quadratic formula

x = [-b ± √(b² - 4ac)] / (2a)

Sum of roots of quadratic ax² + bx + c = 0

-b / a

Product of roots of quadratic ax² + bx + c = 0

c / a

Discriminant and number/type of solutions

Δ = b² - 4ac; If Δ > 0 → two real solutions If Δ = 0 → one real solution If Δ < 0 → two complex solutions

Exponent rules: a^m × a^n

a^{m+n}

Exponent rules: (a^m)^n

a^{m × n}

Exponent rules: a^m / a^n

a^{m-n}

Exponent rules: a^0

1 (if a ≠ 0)

Simple interest formula

I = P × r × t

Compound interest formula

A = P(1 + r/n)^{nt}

Ratio formula (for part-to-part or part-to-whole)

part / whole = ratio

Density formula

density = mass / volume

Mixture formula

(amount₁ × concentration₁) + (amount₂ × concentration₂) = (total amount × final concentration)

Distance formula between points (x₁, y₁) and (x₂, y₂)

√[(x₂ - x₁)² + (y₂ - y₁)²]

Midpoint formula between points (x₁, y₁) and (x₂, y₂)

(x₁ + x₂)/2, (y₁ + y₂)/2

Slope formula

(y₂ - y₁) / (x₂ - x₁)

Slope-intercept form

y = mx + b

Standard form of linear equation

Ax + By = C

Criteria for parallel lines

Equal slopes (m₁ = m₂)

Criteria for perpendicular lines

Slopes are negative reciprocals (m₁ × m₂ = -1)

Unit conversion example: 1 week = ? days

7 days

Unit conversion example: 1 day = ? minutes

1440 minutes

Probability formula

favorable outcomes / total outcomes

Distance-speed-time relationship

distance = speed × time

Average speed formula

total distance / total time

SOHCAHTOA

sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent

Pythagorean identity

sin²θ + cos²θ = 1

Tangent identity

tanθ = sinθ / cosθ

Reciprocal identities

cotθ = 1/tanθ, secθ = 1/cosθ, cscθ = 1/sinθ

Radian to degree conversion

degrees = radians × (180°/π)

Degree to radian conversion

radians = degrees × (π/180°)

Signs of trig functions by quadrant (ASTC rule)

Quadrant I: All positive Quadrant II: Sin positive Quadrant III: Tan positive Quadrant IV: Cos positive

Coterminal angles

Add or subtract 360° or 2π to find coterminal angles

Complementary angles relationship

sin(90° - θ) = cosθ, tan(90° - θ) = cotθ

Negative angle identities

sin(-θ) = -sinθ, cos(-θ) = cosθ, tan(-θ) = -tanθ