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Introduction
1. SAT Reading and Writing
2. SAT Math
2.1 Intro to SAT Math
2.2 SAT Math Tools and Strategies
2.2.1 The UnCLES Method for SAT Math
2.2.2 SAT Math Formula Sheet
2.3 SAT Algebra
2.4 SAT Geometry
2.5 SAT Advanced Math
2.6 SAT Problem Solving and Data
Wrapping Up
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2.2.2 SAT Math Formula Sheet
Achievable SAT
2. SAT Math
2.2. SAT Math Tools and Strategies

SAT Math Formula Sheet

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Although the SAT provides a generous list of formulas accessible on test day, there are quite a few relevant formulas, properties, and strategies not included on that list. The Achievable course formula sheet provides a comprehensive list, with explanations where necessary, of quite a few other formulas relevant to the SAT. The last page of this sheet simply repeats the formulas provided by SAT on test day; we include it here so you can compare and contrast the formulas included on the test with those that aren’t.

We highly recommend making physical flashcards to memorize these formulas and concepts, as research and experience suggest that writing down the information and interacting physically with the cards provides the best retention. But if you prefer online flashcard sites such as Quizlet, please use those; the format that feels most accessible to you is the one that is likely to work best.

If you do use physical flashcards, we recommend the “Leitner Box” method, which separates the cards into four or five boxes, ranging from boxes labeled Every Day to a box with some lesser frequency, such as Every Week or Every Other Week. When you answer a card correctly, move it toward the “less frequent” box. When you answer a card incorrectly, move it toward the “more frequent” box. The formulas that stump you the most should remain in the Every Day box until you begin gaining consistent traction with them.

If you apply yourself faithfully to retaining these formulas in your working memory, you will see significant fruit of your labors on the SAT math section!

Download: Achievable SAT Math Formula Sheet

Achievable SAT problem solving and data sheet

Achievable SAT algebra sheet a

Achievable SAT algebra sheet b

Achievable SAT algebra sheet c

Achievable SAT geometry sheet

Achievable SAT formulas provided on the SAT sheet

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SAT Math Formula Sheet

Although the SAT provides a generous list of formulas accessible on test day, there are quite a few relevant formulas, properties, and strategies not included on that list. The Achievable course formula sheet provides a comprehensive list, with explanations where necessary, of quite a few other formulas relevant to the SAT. The last page of this sheet simply repeats the formulas provided by SAT on test day; we include it here so you can compare and contrast the formulas included on the test with those that aren’t.

We highly recommend making physical flashcards to memorize these formulas and concepts, as research and experience suggest that writing down the information and interacting physically with the cards provides the best retention. But if you prefer online flashcard sites such as Quizlet, please use those; the format that feels most accessible to you is the one that is likely to work best.

If you do use physical flashcards, we recommend the “Leitner Box” method, which separates the cards into four or five boxes, ranging from boxes labeled Every Day to a box with some lesser frequency, such as Every Week or Every Other Week. When you answer a card correctly, move it toward the “less frequent” box. When you answer a card incorrectly, move it toward the “more frequent” box. The formulas that stump you the most should remain in the Every Day box until you begin gaining consistent traction with them.

If you apply yourself faithfully to retaining these formulas in your working memory, you will see significant fruit of your labors on the SAT math section!

Download: Achievable SAT Math Formula Sheet

Achievable SAT problem solving and data sheet

Achievable SAT algebra sheet a

Achievable SAT algebra sheet b

Achievable SAT algebra sheet c

Achievable SAT geometry sheet

Achievable SAT formulas provided on the SAT sheet

Key points

SAT Math Formula Memorization Strategies

  • Use physical or digital flashcards for retention
  • Leitner Box method: organize cards by review frequency
  • Focus on formulas not provided on the SAT reference sheet

Algebra: Linear Equations and Systems

  • Slope formula: ( m = \frac{y_2 - y_1}{x_2 - x_1} )
  • Slope-intercept form: ( y = mx + b )
  • Standard form: ( Ax + By = C )
  • Point-slope form: ( y - y_1 = m(x - x_1) )
  • Parallel lines: same slope
  • Perpendicular lines: slopes are negative reciprocals

Algebra: Quadratics and Polynomials

  • Quadratic formula: ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} )
  • Vertex form: ( y = a(x - h)^2 + k )
  • Factoring quadratics: ( ax^2 + bx + c = 0 )
  • Difference of squares: ( a^2 - b^2 = (a + b)(a - b) )
  • Sum/difference of cubes formulas

Algebra: Exponents and Radicals

  • Product rule: ( a^m \cdot a^n = a^{m+n} )
  • Power rule: ( (a^m)^n = a^{mn} )
  • Negative exponents: ( a^{-n} = \frac{1}{a^n} )
  • Radical to exponent: ( \sqrt[n]{a^m} = a^{m/n} )

Algebra: Functions

  • Function notation: ( f(x) )
  • Domain and range concepts
  • Composition: ( f(g(x)) )
  • Inverse functions: ( f^{-1}(x) )

Algebra: Absolute Value and Inequalities

  • Absolute value definition: ( |a| = a ) if ( a \geq 0 ), ( -a ) if ( a < 0 )
  • Solving absolute value equations and inequalities

Algebra: Systems of Equations

  • Substitution and elimination methods
  • Solutions: one, none, or infinitely many

Algebra: Word Problems and Translating

  • Setting up equations from word problems
  • Units and dimensional analysis

Statistics and Probability

  • Mean, median, mode definitions
  • Range and standard deviation basics
  • Probability: ( P = \frac{\text{favorable outcomes}}{\text{total outcomes}} )
  • Counting principle, permutations, combinations

Geometry: Triangles

  • Triangle sum theorem: angles sum to ( 180^\circ )
  • Area: ( \frac{1}{2} \times \text{base} \times \text{height} )
  • Pythagorean theorem: ( a^2 + b^2 = c^2 )
  • Special triangles:
    • 45-45-90: sides ( x, x, x\sqrt{2} )
    • 30-60-90: sides ( x, x\sqrt{3}, 2x )
  • Similarity and congruence criteria

Geometry: Circles

  • Area: ( \pi r^2 )
  • Circumference: ( 2\pi r )
  • Arc length: ( \frac{\theta}{360} \times 2\pi r )
  • Sector area: ( \frac{\theta}{360} \times \pi r^2 )
  • Equation: ( (x - h)^2 + (y - k)^2 = r^2 )

Geometry: Polygons and Quadrilaterals

  • Sum of interior angles: ( (n - 2) \times 180^\circ )
  • Area of rectangle: ( l \times w )
  • Area of parallelogram: ( b \times h )
  • Area of trapezoid: ( \frac{1}{2}(b_1 + b_2)h )

Geometry: Coordinate Geometry

  • Distance formula: ( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} )
  • Midpoint formula: ( \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} ) )

Geometry: Volume and Surface Area

  • Rectangular prism volume: ( lwh )
  • Cylinder volume: ( \pi r^2 h )
  • Sphere volume: ( \frac{4}{3}\pi r^3 )
  • Cone volume: ( \frac{1}{3}\pi r^2 h )
  • Surface area formulas for common solids

SAT-Provided Reference Sheet (Formulas Given on Test Day)

  • Area and circumference of circle
  • Area of triangle and rectangle
  • Pythagorean theorem
  • Volume formulas for rectangular prism, cylinder, sphere, cone, pyramid
  • Special right triangle side ratios

General Test-Taking Strategies

  • Memorize formulas not on the SAT sheet
  • Practice applying formulas to different problem types
  • Use process of elimination and estimation when unsure