The Ultimate SAT Math Cheat Sheet

Master every essential formula and concept for the SAT Math section. This comprehensive guide from CurioLearn covers all the formulas provided in the reference information, plus key strategies and common mistakes to avoid.

Geometry Formulas

Essential area, volume, and geometric relationship formulas

Algebra & Functions

Polynomials, exponents, and function transformations

Test Strategies

Proven strategies and common mistakes to avoid

Essential Geometry Formulas

These formulas are provided in the reference information at the beginning of each SAT math section

Basic Shapes

Circle

Area: A = πr²

Circumference: C = 2πr

Rectangle

Area: A = lw

Triangle

Area: A = ½bh

Pythagorean Theorem

Formula: a² + b² = c²

Special Right Triangles

30-60-90 Triangle

If the short leg = 1, then:

• Short leg = 1
• Long leg = √3
• Hypotenuse = 2

45-45-90 Triangle

If the legs = 1, then:

• Legs = 1
• Hypotenuse = √2

Volume Formulas

Rectangular Prism

Volume: V = lwh

Cylinder

Volume: V = πr²h

Sphere

Volume: V = (4/3)πr³

Cone

Volume: V = (1/3)πr²h

Pyramid

Volume: V = (1/3)lwh

Fractions, Decimals, and Percentages

Basic Conversions

Fraction: part/whole

Percent: (part/whole) × 100

Percent Change

Formula: ((new - old)/old) × 100%

Increase by Percent

Multiply by: (1 + r)

where r is the percent in decimal form

Decrease by Percent

Multiply by: (1 - r)

where r is the percent in decimal form

Interest Formulas

Simple Interest

A = P(1 + rt)

A = final amount, P = principal, r = rate, t = time

Compound Interest (Annual)

A = P(1 + r)ᵗ

Compounded once per year

Compound Interest (n times/year)

A = P(1 + r/n)ⁿᵗ

Compounded n times per year

Rates, Ratios, and Proportions

Conversion Factor

General form: ending units/starting units

Example: (12 inches/1 foot) × 10 feet = 120 inches

Distance Formula

Distance = Rate × Time

Mixture Problems

Concentration A × Volume A + Concentration B × Volume B = Final Concentration × (Volume A + Volume B)

Exponents, Roots, and Polynomials

Exponent Rules

• Multiplication: aᵇ × aᶜ = aᵇ⁺ᶜ
• Division: aᵇ/aᶜ = aᵇ⁻ᶜ
• Power: (aᵇ)ᶜ = aᵇᶜ
• Negative: a⁻ᵇ = 1/aᵇ
• Fractional: aᵇ/ᶜ = ᶜ√(aᵇ)

Imaginary Numbers

• i² = -1
• i³ = -i
• i⁴ = 1
• Pattern repeats every 4 powers

Parabolas

Standard Form

f(x) = ax² + bx + c

Vertex: (-b/2a, f(-b/2a))

y-intercept: c

Factored Form

f(x) = a(x - m)(x - n)

x-intercepts: m and n

Vertex Form

f(x) = a(x - h)² + k

Vertex: (h, k)

Special Factoring Patterns

Difference of Squares

a² - b² = (a + b)(a - b)

Perfect Square Trinomial

a² + 2ab + b² = (a + b)²

a² - 2ab + b² = (a - b)²

Graphing Lines

Slope Formula

m = (y₂ - y₁)/(x₂ - x₁)

Horizontal line: m = 0
Vertical line: m = undefined

Line Forms

• Standard: Ax + By = C
• Slope-Intercept: y = mx + b
• Point-Slope: y - y₁ = m(x - x₁)

Distance & Midpoint

Distance: d = √[(x₂-x₁)² + (y₂-y₁)²]

Midpoint: M = ((x₁+x₂)/2, (y₁+y₂)/2)

Parallel & Perpendicular

• Parallel: equal slopes
• Perpendicular: opposite reciprocal slopes

Data and Probability

Average (Mean)

Average = sum of items/number of items

Median

Median = middle number

(when numbers are in order)

Range

Range = maximum - minimum

Probability

Probability = desired outcomes/possible outcomes

Angles

Angle Relationships

• Vertical angles: are congruent (equal)
• Linear pair: supplementary (add to 180°)
• Circle angles: add to 360°

Parallel Lines

When parallel lines are cut by a transversal:

• All acute angles are congruent
• All obtuse angles are congruent

Triangles

Triangle Properties

• Sum of angles: 180°
• Exterior angle: equals sum of two remote interior angles

Pythagorean Triples

• 3-4-5: 3² + 4² = 5²
• 5-12-13: 5² + 12² = 13²
• Any multiple of these ratios

Circles

Circle Properties

• Radius and tangent: make a right angle
• Central angle: double the inscribed angle

Arc and Sector

Arc length: (x/360) × circumference

Sector area: (x/360) × area of circle

where x = central angle

Circle Equation

(x - h)² + (y - k)² = r²

where (h, k) is the center and r is the radius

Polygons

Trapezoid

Area = ½(b₁ + b₂)h

where b₁ and b₂ are the parallel sides

Regular Polygon

• Sum of interior angles: 180(n - 2)
• Sum of exterior angles: 360°
• One interior angle: 180(n - 2)/n

where n = number of sides

Parallelogram Properties

1. Opposite sides are parallel and congruent
2. Opposite angles are congruent
3. Consecutive angles are supplementary
4. Each diagonal forms a pair of congruent triangles
5. Diagonals bisect each other
6. Area = base × height

• If diagonals are congruent → rectangle

• If diagonals are perpendicular → rhombus

Trigonometry

Basic Trig Ratios

• sin θ = opposite/hypotenuse
• cos θ = adjacent/hypotenuse
• tan θ = opposite/adjacent

Angle Conversions

360° = 2π radians

sin(x) = cos(90° - x)

The sine of an angle equals the cosine of its complement

Parent Graphs & Transformations

Common Parent Functions

• y = x: Linear
• y = x²: Quadratic
• y = x³: Cubic
• y = √x: Square root
• y = |x|: Absolute value
• y = aˣ: Exponential

Transformations

• f(x) + k: Shift up by k units
• f(x) - k: Shift down by k units
• f(x + h): Shift left by h units
• f(x - h): Shift right by h units
• -f(x): Reflect over x-axis
• cf(x): Stretch vertically by c
• f(x)/c: Shrink vertically by c

Math Section Strategies

Key Strategies

Visual Problem Solving

• Draw graphs for intersection point questions
• Draw diagrams for geometry/trigonometry
• Diagrams don't need to be precise, just general

Answer Checking

• Plug in numbers to verify answers
• Use substitution/elimination for systems
• Try factoring vs. quadratic formula

Reading & Time Management

• Read the entire question carefully
• Redo questions instead of just reviewing
• Use alternative solving methods

Function Recognition

• Linear: constant rate of change
• Exponential: increasing/decreasing rates

Common Mistakes to Avoid

Calculation Errors

• Using wrong lengths for sine/cosine
• Reading “3 large and 4 small” as “4 large and 3 small”
• Not dividing by 3 when needed
• Basic operation carelessness

Problem-Solving Errors

• Not reading the entire question
• Missing key information
• Rushing through calculations

Answer Checking Method

Example: If you get x = 2 and y = 3, plug them back into the original equations to verify.

For expression simplification: Set variables to specific values and ensure both expressions give the same result.

Example: For 12xy - 12xy² - 24y, if you chose 12y(x - xy - 2), setting x = 3 and y = 2 should give -120 for both expressions.

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