SAT Math Formula Sheet

    34 essential formulas organized by topic with examples

    Very High — appears on most tests High — appears frequently Medium — appears occasionally
    Slope Formula
    Very High
    m = (y₂ - y₁) / (x₂ - x₁)

    Calculate slope between two points

    Example: Points (2,3) and (6,11): m = (11-3)/(6-2) = 8/4 = 2
    Slope-Intercept Form
    Very High
    y = mx + b

    m = slope, b = y-intercept

    Example: Slope 3, y-int -2: y = 3x - 2
    Point-Slope Form
    High
    y - y₁ = m(x - x₁)

    Line through point (x₁,y₁) with slope m

    Example: Through (2,5) with slope 3: y - 5 = 3(x - 2)
    Standard Form
    High
    Ax + By = C

    A,B,C are integers, A > 0

    Example: 2x + 3y = 12
    Distance Formula
    Medium
    d = √[(x₂-x₁)² + (y₂-y₁)²]

    Distance between two points

    Example: (1,2) to (4,6): d = √(9+16) = √25 = 5
    Midpoint Formula
    Medium
    M = ((x₁+x₂)/2, (y₁+y₂)/2)

    Midpoint of a line segment

    Example: (2,4) and (6,8): M = (4, 6)
    Quadratic Formula
    Very High
    x = (-b ± √(b²-4ac)) / 2a

    Solve ax² + bx + c = 0

    Example: x² - 5x + 6 = 0: x = (5 ± √(25-24))/2 = 3 or 2
    Discriminant
    Very High
    D = b² - 4ac

    D>0: two real solutions, D=0: one, D<0: none

    Example: x² + 4x + 5: D = 16-20 = -4 (no real solutions)
    Vertex Form
    High
    y = a(x - h)² + k

    Vertex at (h, k)

    Example: y = 2(x-3)² + 1, vertex at (3,1)
    Vertex of Standard Form
    Very High
    x = -b / (2a)

    x-coordinate of vertex for ax² + bx + c

    Example: y = x² - 6x + 8: x = 6/2 = 3
    Factored Form
    High
    y = a(x - r₁)(x - r₂)

    r₁, r₂ are the x-intercepts (roots)

    Example: Roots at 2 and 5: y = (x-2)(x-5)
    Sum/Product of Roots
    Medium
    Sum = -b/a, Product = c/a

    For ax² + bx + c = 0

    Example: x² - 7x + 12 = 0: sum = 7, product = 12
    Area of Triangle
    Very High
    A = ½ × base × height

    Height must be perpendicular to base

    Example: Base 8, height 5: A = ½(8)(5) = 20
    Area of Circle
    Very High
    A = πr²

    r = radius

    Example: r = 4: A = 16π ≈ 50.27
    Circumference
    Very High
    C = 2πr = πd

    r = radius, d = diameter

    Example: r = 5: C = 10π ≈ 31.42
    Pythagorean Theorem
    Very High
    a² + b² = c²

    Right triangle: c is the hypotenuse

    Example: 3² + 4² = 5² → 9 + 16 = 25 ✓
    Special Right Triangles
    Very High
    45-45-90: x, x, x√2 30-60-90: x, x√3, 2x

    Memorize these ratios — they appear constantly

    Example: 45-45-90 with leg 5: hypotenuse = 5√2
    Volume of Cylinder
    High
    V = πr²h

    r = radius, h = height

    Example: r = 3, h = 10: V = 90π
    Volume of Sphere
    Medium
    V = (4/3)πr³

    r = radius

    Example: r = 6: V = 288π
    Arc Length
    High
    s = (θ/360) × 2πr

    θ = central angle in degrees

    Example: 60° arc, r = 9: s = (60/360)(18π) = 3π
    Sector Area
    High
    A = (θ/360) × πr²

    Area of a "pie slice"

    Example: 90° sector, r = 4: A = (90/360)(16π) = 4π
    Mean (Average)
    Very High
    x̄ = Σx / n

    Sum of all values ÷ number of values

    Example: 3,5,7,9,11: mean = 35/5 = 7
    Probability
    Very High
    P(A) = favorable / total

    Probability of event A occurring

    Example: 3 red balls out of 10: P(red) = 3/10
    Percent Change
    Very High
    % change = ((new - old) / old) × 100

    Positive = increase, negative = decrease

    Example: $80 to $100: (100-80)/80 × 100 = 25% increase
    Standard Deviation
    Medium
    σ = √[Σ(x - x̄)² / n]

    Measures spread from the mean

    Example: Higher σ = more spread out data
    Margin of Error
    High
    MoE ≈ 1 / √n

    Approximate margin for sample size n

    Example: n = 400: MoE ≈ 1/20 = 5%
    Product Rule
    Very High
    aᵐ × aⁿ = aᵐ⁺ⁿ

    Same base: add exponents

    Example: x³ × x⁴ = x⁷
    Quotient Rule
    Very High
    aᵐ / aⁿ = aᵐ⁻ⁿ

    Same base: subtract exponents

    Example: x⁵ / x² = x³
    Power Rule
    Very High
    (aᵐ)ⁿ = aᵐⁿ

    Power of a power: multiply exponents

    Example: (x³)⁴ = x¹²
    Negative Exponent
    High
    a⁻ⁿ = 1/aⁿ

    Flip to the denominator

    Example: 2⁻³ = 1/8
    Fractional Exponent
    High
    a^(m/n) = ⁿ√(aᵐ)

    Denominator = root, numerator = power

    Example: 8^(2/3) = ³√(8²) = ³√64 = 4
    SOH-CAH-TOA
    High
    sin = opp/hyp, cos = adj/hyp, tan = opp/adj

    Core trig ratios for right triangles

    Example: If opp = 3, hyp = 5: sin θ = 3/5
    Complementary Angles
    High
    sin(x) = cos(90° - x)

    Sine of an angle = cosine of its complement

    Example: sin(30°) = cos(60°) = 0.5
    Unit Circle Key Values
    Medium
    sin(30°) = ½, sin(45°) = √2/2, sin(60°) = √3/2

    Memorize these — they appear in many problems

    Example: cos(45°) = √2/2 ≈ 0.707
    Pro Tip

    The SAT provides a reference sheet at the start of each Math module with some basic geometry formulas. However, it does NOT include algebra, statistics, or trig formulas — those you must memorize. Focus on the "Very High" frequency formulas first.