SAT Math Formulas You Should Know

SAT Math Formulas

When you take the SAT, you’ll have access to SAT Math formulas within the Bluebook software. Don’t get too excited: these formulas only cover some high-school geometry topics. While it’s certainly useful to have those formulas during the exam (especially if it’s been a few years since you’ve taken geometry), there are many other formulas that can be helpful for achieving your goal SAT Math score. These formulas, along with the ones you will be given, are covered in this article.

Categories of SAT Math Formulas

Here are two ways to think about how urgent it is to learn a formula. Each formula covered in this article has been sorted into one of these two groups:

• Must Understand: Formulas that make some SAT questions possible to solve or significantly easier.
• Nice to Understand: Formulas that provide another way to answer questions (in addition to using tools like the built-in graphing calculator).

Memorizing Formulas

To memorize SAT Math formulas, first evaluate how well you know each one.

• Know: You understand this formula and can use it.
• Sorta Know: You may have seen the formula, but you either don’t clearly remember the formula or have difficulty applying the formula.
• Don’t Know: You’ve never seen this formula.

The formulas you know are done—don’t spend any time memorizing or working on something you’ve already mastered!

Next, start learning the Sorta Know and Don’t Know formulas included in the Must Understand category. Use flashcards (real or digital), write down the formulas, or practice with whatever memorization technique works best for you.

Once you’ve mastered the formulas in the Must Understand category, move on to the Nice to Understand formulas.

Must Understand Formulas

Algebra

“Algebra” is the College Board’s term for algebra without exponents or radicals—in other words, algebra with lines. Many questions can be solved by plugging in numbers or graphing with the built-in calculator.

However, not every algebra concept can be addressed with these strategies. Here are two equations that are required to answer certain questions on the SAT:

• Slope: y₂ - y₁ x₂ - x₁ , where (x1, y1) and (x2, y2) are points on the line.
• Slope-intercept form of a line: y = mx + b
  • m is the slope.
  • b is the y-intercept.
  • (x, y) is any point on the line.

Advanced Math

“Advanced Math” is the College Board’s term for algebra with exponents. The class in school that covers these topics is often called Algebra II.

As with Algebra, many of these questions can be solved with strategies or tools, but listed below are the formulas worth memorizing.

Quadratics

Equations with an exponent of 2 on the variable (often x). This topic is heavily tested on the SAT, so you want to be confident with these formulas.

• Standard form: ax² + bx + c = 0 or y = ax² + bx + c
  • If a > 0, the parabola opens up
  • If a < 0, the parabola opens down
  • c is the y-intercept
• Factored form: a(x – r)(x – s) = 0, where r and s are the solutions
• Vertex form: y = a(x – h)² + k, where the vertex is at the point (h, k)

Growth and Decay

Many growth and decay questions can be answered using the graphing calculator (often along with strategies such as Plugging In), but these questions are typically far more efficient to solve with formulas.

• When the growth is a percent of the total population, final amount = original amount(1 ± rate)ⁿ, where the rate is expressed as a decimal
• When the growth is a multiple or ratio of the total population, final amount = original amount(multiplier)ⁿ

Problem Solving and Data Analysis

• Mean: Total = Average × Number of things, or T = AN
• Range: greatest value – least value
• Ratio: part part or part:part
• 
• 

Geometry and Trigonometry

Most of the formulas you need for these questions will be provided, so you don’t need to memorize these formulas, but you do need to know how to use them.

Geometry Formulas to Understand but Not Memorize (Reference Sheet Formulas)

• Circles:
  • A = πr²
  • C = 2πr
• Rectangles:
  • A = lw
• Triangles:
  • Pythagorean theorem: a² + b² = c², when the triangle is a right triangle and c is the hypotenuse
• Volume of a rectangular solid: V = lwh
• Volume of a cylinder: V = πr²h
• Volume of a sphere:
• Volume of a cone:
• Volume of a pyramid:
• Number of degrees of an arc in a circle: 360°
• Number of radians of arc in a circle: 2π
• The sum of the measurements in degrees of angles of a triangle: 180°

Geometry Formulas to Memorize

• Diameter of a circle: d = 2r
• Arcs and sectors of a circle:
• SOHCAHTOAH:
• Parallel lines: When parallel lines are intersected by the same line, two kinds of angles are created—BIG and small:
  • BIG angles = BIG angles
  • small angles = small angles
  • BIG + small = 180°
• 180° = π radians

Nice to Understand Formulas

Algebra

• If |x| = c, then x = c or x = –c
• Standard form of a line: Ax + By = C
  • is the slope.
  • is the y-intercept.

Advanced Math

“Advanced Math” is the College Board’s term for algebra with exponents. The class in school that covers these topics is often called Algebra II.

As with Algebra, many of these questions can be solved with strategies or tools, but listed below are the formulas worth memorizing.

Quadratics

• The solutions can be determined using the quadratic equation:
• The sum of the solutions is
• The product of the solutions is
• The x-coordinate of the vertex is
• The y-coordinate of the vertex is best determined by plugging the x-coordinate of the vertex into the original equation.
• The number of distinct real solutions can be determined by using the discriminant (which is the expression under the radical of the quadratic equation): D = b² – 4ac
  • If D > 0, there are two distinct real solutions.
  • If D = 0, there is one distinct real solution.
  • If D < 0, there are no real solutions.

Problem Solving and Data Analysis

• Mean:
• Median: Middle value when the values are in consecutive order.
• Mode: The most commonly occurring element.

Geometry and Trigonometry

• Circumference of a circle: C = πd
• Diameter of a circle: d = 2r
• Arc length: s = r, where  is the central angle in radians.
• Area of a square: A = s²
• Perimeter of a square: P = 4s
• Area of a parallelogram: A = bh
• Perimeter of a rectangle: P = 2(l + w)
• Sum of the angles in an n-sided polygon: (n – 2)180°
• Angle measure of each angle in a regular n-sided polygon:
• Surface area of a rectangular solid: S = 2(lw + lh + wh)
• Surface area of a cube: S = 6s²
• Surface area of a right circular cylinder: S = 2πr² + 2πrh
• Surface area of a sphere: S = 4πr²
• Volume of a cube: V = s³

Remember: the test-makers do not care how you solve a question so long as you come up with the correct response. Because you have a limited amount of time on the test, choose the fastest, most accurate methods at your disposal. Knowing when to use the SAT Math formulas provided or which you’ve memorized will go a long way in improving your score!