Complete SAT Math Notes
Master every concept tested on the SAT Math section with CurioLearn's comprehensive study guide. This complete resource covers all four major content areas with detailed explanations, step-by-step examples, and proven strategies to help you achieve your target score.
19 of 58 questions
Linear equations, inequalities, systems, and function notation
17 of 58 questions
Ratios, percentages, statistics, and data interpretation
16 of 58 questions
Polynomials, quadratics, radicals, and rational expressions
6 of 58 questions
Geometry, trigonometry, circles, and complex numbers
Linear equations and inequalities, interpreting linear functions, systems of equations, basic function notation, and absolute value functions.
Order of Operations
Simplifying Expressions
Simplify expressions using PEMDAS: Parenthesis, Exponents, Multiplication or Division, Addition or Subtraction.
4(8 - 5) + 9
= 4(3) + 9
= 12 + 9
= 21
Solving for a Variable
Use SADMEP (reverse of PEMDAS): Subtraction or Addition, Division or Multiplication, Exponents, Parenthesis.
(3x - 12)/2 = 9
3x - 12 = 18
3x = 30
x = 10
Forms of Linear Equations
Slope-Intercept Form
y = mx + b
m = slope, b = y-intercept
Standard Form
Ax + By = C
Slope = -A/B
Slope Formula
m = (y₂ - y₁)/(x₂ - x₁)
Rise over run
Systems of Linear Equations
Combination Method
Multiply equations to make coefficients opposite, then add equations to eliminate one variable.
Substitution Method
Solve one equation for a variable, then substitute into the other equation.
Function Notation
f(x) represents the output when x is the input. For example, if f(x) = 2x - 5, then f(3) = 2(3) - 5 = 1.
Linear Inequalities
One Variable
Solve like equations, but reverse inequality sign when multiplying/dividing by negative numbers.
Two Variables
Graph the line, then shade above (for > or ≥) or below (for < or ≤). Use solid lines for ≤/≥, dotted for </>.
Absolute Value
|x| represents distance from 0. For |x + 6| = 2, set up two equations: x + 6 = 2 or x + 6 = -2.
Ratios, rates, proportions, percentages, units, linear and exponential growth, reading data, and statistical analysis.
Ratios and Proportions
Ratios
A ratio compares two quantities. Can be written as a fraction (3/4) or with a colon (3:4).
Proportions
Two ratios that are equal. Solve by cross-multiplying: if a/b = c/d, then ad = bc.
Rates
Ratios comparing different units (miles per hour, dollars per item). Unit rates have denominator = 1.
Percentages
Basic Percentage Formula
Part = (Percent/100) × Whole
What is 42% of $280? → 0.42 × 280 = $117.60
Percent Change
Percent Change = (New - Original)/Original × 100%
If price increases from $800 to $920: (920-800)/800 × 100% = 15%
Statistics
Mean (Average)
Sum of values ÷ number of values
Median
Middle value when arranged in order
Mode
Most frequently occurring value
Range
Maximum - Minimum
Scatterplots and Data Analysis
Best-fit Line
Line that best represents the trend in data. Equation form: y = mx + b
Correlation
Strong positive: points close to line with positive slope. Strong negative: points close to line with negative slope.
Unit Conversions
Use conversion factors to change units. Set up fractions so unwanted units cancel out.
1 km = 0.621 miles
1 mile = 5280 feet
Convert 1.5 km to feet:
1.5 km × (0.621 mi/km) × (5280 ft/mi) = 4920 ft
Polynomial operations, quadratic equations, radical and rational expressions, exponential functions, and advanced function notation.
Polynomial Operations
Adding/Subtracting
Combine like terms (same variable and exponent).
Multiplying
Use FOIL for binomials: First, Outside, Inside, Last. For larger polynomials, multiply each term.
Factoring
Find two numbers that multiply to the constant term and add to the coefficient of x.
Quadratic Equations
Standard Form
y = ax² + bx + c
Vertex: x = -b/(2a)
Vertex Form
y = a(x - h)² + k
Vertex: (h, k)
Factored Form
y = a(x - p)(x - q)
Zeros: x = p, x = q
Quadratic Formula
x = (-b ± √(b² - 4ac)) / 2a
Exponents and Radicals
Exponent Rules
Multiplying: add exponents
Dividing: subtract exponents
Power to power: multiply
Any number to 0th power
Radical Rules
Product rule
Quotient rule
Rational Expressions
Adding/Subtracting
Find common denominator, then add/subtract numerators.
Multiplying
Multiply numerators and denominators, then simplify.
Dividing
Multiply by the reciprocal (flip the second fraction).
Exponential Functions
Basic Form
y = a · bˣ
a = initial amount, b = growth/decay factor
Compound Interest
A = P(1 + r/n)^(nt)
P = principal, r = rate, n = compounds per year, t = time
Geometry, trigonometry, circles, complex numbers, and advanced mathematical concepts.
Geometry
Area Formulas
Volume Formulas
Triangle Properties
• Sum of angles = 180°
• Triangle inequality: sum of any two sides > third side
• Pythagorean theorem: a² + b² = c² (for right triangles)
Right Triangle Trigonometry
Basic Ratios
Complementary Angles
sin θ = cos(90° - θ) and cos θ = sin(90° - θ)
Circles
Circle Equations
(x - h)² + (y - k)² = r²
Center: (h, k), Radius: r
Arc Length and Sector Area
Arc Length = (θ/360°) × 2πr
Sector Area = (θ/360°) × πr²
θ = central angle in degrees
Circle Theorems
• Central angle = arc measure
• Inscribed angle = ½ × arc measure
• Tangent perpendicular to radius at point of contact
Complex Numbers
Basic Form
a + bi
a = real part, b = imaginary part, i = √(-1)
Operations
• Adding: (a + bi) + (c + di) = (a + c) + (b + d)i
• Multiplying: Use FOIL, remember i² = -1
• Dividing: Multiply by conjugate to rationalize
Radians
Conversion
180° = π radians
To convert: multiply degrees by π/180 or radians by 180/π
Common Values
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