SAT Math Reference Sheet: Conquer the 800

Mastering the SAT Math section requires a solid understanding of key concepts and formulas. This comprehensive reference sheet serves as an indispensable guide for students preparing for the exam.

Arithmetic

Integers

• Positive: Greater than zero
• Negative: Less than zero

Fractions

• Rational: Can be expressed as a/b, where a and b are integers
• Improper: Numerator is greater than or equal to the denominator
• Mixed: Combination of a whole number and a proper fraction

Decimals

• Decimal point separates whole number from fractional part
• Decimal notation: 0.d1d2d3...

Exponents

• a^n = a multiplied by itself n times
• a^0 = 1 (except when a = 0)
• a^-n = 1/a^n

Logarithms

• Logarithm: Inverse function of exponential function
• Log(a^b) = b

Algebra

Variables

• Symbols representing unknown values
• Equations: Relationships between variables

Linear Equations

• Equation in the form ax + b = c
• Slope-intercept form: y = mx + b
• Point-slope form: y - y1 = m(x - x1)

Quadratic Equations

• Equation in the form ax^2 + bx + c = 0
• Factoring
• Square completing
• Quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a

Inequalities

• Relations that establish an order between values
• Types:

  • (greater than)

  • < (less than)
  • ≥ (greater than or equal to)
  • ≤ (less than or equal to)

Functions

• Relation that assigns each input value to exactly one output value
• Types:
  • Linear
  • Quadratic
  • Polynomial
  • Rational
  • Exponential
  • Logarithmic

Geometry

Triangles

• Equilateral: All sides equal
• Isosceles: Two equal sides
• Scalene: No equal sides
• Angle sum: 180 degrees

Quadrilaterals

• Parallelogram: Opposite sides parallel
• Rectangle: Parallelogram with four right angles
• Square: Parallelogram with four equal sides
• Trapezoid: One pair of parallel sides

Circles

• Radius: Distance from center to any point on circle
• Diameter: Double the radius
• Circumference: 2πr
• Area: πr^2

Statistics

Measures of Central Tendency

• Mean (average): Sum of all values divided by the number of values
• Median: Middle value when arranged in order
• Mode: Value that appears most frequently

Measures of Dispersion

• Range: Difference between the largest and smallest values
• Variance: Average squared distance from the mean
• Standard deviation: Square root of variance

Probability

Outcomes

• Possible results of an experiment

Events

• Sets of outcomes

Probability

• Chance that an event will occur
• P(E) = Number of outcomes in E / Total number of outcomes

Tables

Exponents of Powers

Properties of Logarithms

Triangles

Quadrilaterals

FAQs

What is the most important skill for SAT Math?

• A strong foundation in algebra and geometry.

How much time should I spend studying for SAT Math?

• The College Board recommends at least 100 hours of preparation.

What is the average SAT Math score?

• 531 out of 800 (as of 2021).

How can I improve my SAT Math score quickly?

• Focus on practicing commonly tested concepts.

What are some tips for the day of the test?

• Get a good night's sleep.
• Stay calm and focused during the exam.
• Use all the time allotted to complete the test.