 # SAT Math Formulas You Must Know Before the Test Written by Chris Hernandez No contracts. Affordable
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In this article, we will discuss the 12 main formulas that appear on the SAT math exam, along with a number of other formulas you need to commit to memory..

The SAT math exam is unlike any other math assessment you've experienced before. It can appear intimidating; however, if you are adequately prepared, it's totally feasible to achieve a high score.

This test encompasses a broad range of math knowledge — from as early as grade school to your last year of high school. You may have been taught these formulas in the past, but it's likely been a while since you applied them.

Related article: SAT Math Test Overview & Prep Guide

This is one of the aspects of the SAT that makes it difficult since it requires many different types of math. You'll have to move out of the high school math mentality, where you only recall what you've learned recently to ace the test and review what you've learned over time.

The SAT is designed to challenge you and push you to think in new and unusual ways. Paying attention to detail and having a good grasp of the foundational formulas and principles will help you increase your score.

During the exam, you will be given some formulas to use, but not all. In this article, we will discuss the 12 main formulas that appear on the SAT math exam, along with a number of other formulas you need to commit to memory. You can also grab this downloadable PDF reference sheet with the list of formulas:

## Notes Before Starting

Before we get started with the list of formulas, note the following:

• Make sure you thoroughly comprehend the concepts, so you can apply them to any problem.
• Familiarize yourself with the phrasing of the questions, and practice with questions like those on the exam.
• Take a timed test to get used to the time crunch of the actual exam.
• After completing a timed test, identify any mistakes and review the concepts to ensure understanding.

The complexity of SAT Math is due to a combination of content and form:

• Questions, though often based on straightforward ideas, demand multiple steps and can span multiple subjects.
• Many of the math questions and topics are likely topics already encountered in school, however, the Problem-Solving and Data Analysis and Additional Topics sections can involve more novel concepts.
• The no-calculator portion necessitates a more thorough understanding of math topics than many students are used to.
• The pressure of the time limit can put extra strain on test-takers.
• The math sections are at the end of the Sat Test, potentially depleting focus and stamina.

## Primary Areas Covered in the SAT Math Test

### 1. Heart of Algebra

This area focuses on creating, solving, and interpreting linear equations, systems of linear equations, and functions.

These questions ask you to create equations that represent a situation, solve equations and systems of equations, and make connections between different representations of linear relationships.

You’ll have to model situations using linear equations and inequalities and show an understanding of the connections between algebraic and graphical representations of linear equations and inequalities. ### 2. Problem-Solving and Data Analysis

This area includes using ratios, percentages, and proportional reasoning to solve problems in real-world situations, including science, social science, and other contexts. It also includes describing relationships shown graphically and analyzing statistical data.

Questions may require you to read tables and graphs and create summarizing statistics and conditional probabilities.

You must be able to evaluate data collection methods and solve problems involving unit conversions, percentages, ratios, proportions, and rates.

### 3. Passport to Advanced Math

This area requires familiarity with more complex equations or functions, which will prepare you for calculus and advanced courses in statistics.

You must be able to create, solve, and interpret quadratic equations, exponential, radical, and rational functions or equations.

Furthermore, you should be able to recognize and formulate equivalences between rational exponents and radicals, and also between negative exponents and fractions.

Adding, subtracting, multiplying, and factoring polynomial expressions, including those with rational coefficients may feature in the test.

You should also thoroughly understand the relationship between algebraic and graphical representations of nonlinear functions, such as the relationship between zeros and factors of polynomials.

You will encounter Trigonometry, Planar Geometry, and Coordinate Geometry including using area and volume formulas, trigonometric ratios, radians, and degrees, angle measurements

## SAT Math Formulas You Should Know

This article includes a PDF of SAT math formulas, but you are expected to have memorized the twelve formulas that are given on the exam, along with three geometry laws. The other formulas you will need to know for the test depend on which sections you have studied. We have included some additional formulas that may be helpful.

### Math Test Notes

• The use of a calculator is not permitted.
• All variables and expressions used represent real numbers unless otherwise indicated.
• Figures provided in this test are drawn to scale unless otherwise indicated.
• All figures lie in a plane unless otherwise indicated.
• Unless otherwise indicated, the domain of a given function f is the set of all real numbers x for which f(x) is a real number.

## Math Formulas Provided on the SAT Math Test

Although given on the test, you must be well acquainted with these, and know how to use them well.

### Area of a Circle (A=πr2)

This formula is denoted by: A=πr2

Here is what each of the symbols used in it denotes:

• A refers to the Area of the Circle.
• π is a constant. If you need to fill in its value for any of the questions, it is 3.14 (or 3.14159).
• r in the formula represents the radius of the circle.
• The radius here can be any line drawn from the center of the circle to its edge.

### Circumference of a Circle (C=2πr)

This math formula is denoted by: C=2πr (or C=πd)

Here is what each of the symbols used in it denotes:

• C refers to the Circumference of the Circle.
• π is a constant. If you need to fill in its value for any of the questions, it is 3.14 (or 3.14159).
• d in the formula stands for the diameter of the circle.
• The diameter here can be any line that bisects the circle through the midpoint. It also touches two ends of the circle on opposite sides.
• When compared to the radius mentioned above, it is twice the radius. ### Area of a Rectangle (A=lw)

This formula is denoted by: A=lw

Here is what each of the symbols used in it denotes:

• A refers to the area of the rectangle.
• l in the formula refers to the length of the rectangle.
• w in the formula refers to the width of the rectangle. ### Area of a Triangle (A= ½ b h)

This formula is denoted by: A= ½ b h

Here is what each of the symbols used in it denotes:

• A, here, is the area of the triangle.
• b in the formula refers to the length of the base of the triangle.
• h in the formula refers to the height of the triangle
• Right triangle: If the triangle is a right triangle, it will have the height (h) the same as the side of the ninety-degree angle.
• non-right triangle: If the triangle is a non-right triangle, the height (h) of the triangle will drop down through its interior. ### The Pythagorean Theorem (c2 = a2 + b2)

The formula for the Pythagoras theorem is denoted by c2 =a 2 + b2

Here is what each of the symbols used in it denotes:

• a and b in the formula are the two smaller sides of the triangle.
• c is the longest side of the triangle, or as may call, its hypotenuse.

Here is what this theorem states:

As per this theorem, the sum of the two smaller sides (a, b) of the triangle (which are both squared) is equal to the square of the longest side of the triangle, also called its hypotenuse (c). ### Properties of Special Right Triangle: Isosceles Triangle (x, x, x√2)

Here is what this formula that is present on the SAT test means:

• A triangle that has two sides that are equal in length along with two angles opposite these equal sides that are also equal, is an isosceles triangle.
• This kind of triangle always has two 45-degree angles (equal angles mentioned above), and one 90-degree angle.
• If you have to determine the side lengths of such a triangle, they are determined by the formula: x, x, x√2.
• For this formula, the side opposite 90 degrees (also called the hypotenuse) has a length equal to one of the smaller sides *√2.

For example, if a triangle has side lengths equal to 12, 12, and 12√2, it is an isosceles right triangle. ### Properties of 30, 60, 90 Degree Triangle: Special Right Triangle (x, x√3, and 2x)

Here is what this formula that is present on the SAT test means:

The 30, 60, and 90-degree triangle has 30, 60, and 90 as its three angles. If you have to determine the side lengths of such a triangle, they are determined by the formula: x, x√3, and 2x. Here is what the symbols in this formula mean:

• x is the measurement of the side opposite 30 degrees and is the smallest of all the 3 sides.
• x√3 is the measurement of the side opposite 60 degrees and has the middle length out of all the 3 sides.
• 2x is the measurement of the side opposite 90 degrees, and is the longest of all the 3 sides (hypotenuse).

For example, if a triangle has side lengths equal to 5, 5√3, and 10, it can be called a 30-60-90 triangle. ### The volume of a Rectangular Solid (V=lwh)

This math formula is denoted by: V=lwh

Here is what each of the symbols used in it denotes:

• V in the formula refers to the volume of the rectangular solid.
• l in the formula refers to the length of one of the sides of the rectangular solid.
• w in the formula refers to the width of one of the sides of the rectangular solid.
• h in the formula denotes the height of the rectangular solid. ### The volume of a Cylinder (V=πr2h)

This math formula is denoted by: V=πr2h

Here is what each of the symbols used in it denotes:

• V in the formula refers to the volume of the cylinder.
• π is a constant. If you need to fill in its value for any of the questions, it is 3.14 (or 3.14159).
• r in the formula refers to the radius of the circular side of the cylinder
• h in the formula refers to the height of the cylinder. ### The volume of a Sphere (V=4/3 πr3)

This math formula is denoted by: V=4/3 πr3

Here is what each of the symbols used in it denotes:

• V in the formula refers to the volume of the sphere.
• π is a constant. If you need to fill in its value for any of the questions, it is 3.14 (or 3.14159).
• r in the formula refers to the radius of the sphere. ### The volume of a Cone (V= 1/3 πr2h)

This formula is denoted by: V= 1/3 πr2h

Here is what each of the symbols used in it denotes:

• V in the formula refers to the volume of the cone.
• π is a constant. If you need to fill in its value for any of the questions, it is 3.14 (or 3.14159).
• r in the formula refers to the radius of the circular side of the cone.
• Lastly, h here refers to the height of the pointed part of the cone. This height is measured from the center of the circular part of the cone. ### The volume of a Pyramid (V=1/3 l w h)

This formula is denoted by: V=1/3 l w h

Here is what each of the symbols used in it denotes:

• V in the formula refers to the volume of the Pyramid.
• l in the formula refers to the length of one of the edges of the given pyramid’s rectangular part.
• w, here, refers to the width of one of the edges of the given pyramid’s rectangular part.
• Lastly, h in the formula refers to the height of the given pyramid at its peak. It is measured from the center of the rectangular part of the figure. ### Laws Given on the SAT Formula Sheet

Along with all the formulas listed above, some laws are already given in the SAT math formula sheet.

These are as follows:

• Number 1: The number of degrees of arc in a circle is 360: Which means that a circle has a total of 360 degrees.
• Number 2: The number of radians of an arc in a circle is 2π: It means that the total number of radians (angle whose corresponding arc in a circle is equal to the radius of the circle) in a circle is equal to 2π.
• Number 3: The sum of the measures in degrees of the angles of a triangle is 180: Which means that a triangle has a total of 180 degrees.

## Math Formulas Not Provided on the SAT Math Test

While the list of SAT formulas provided in the math section has all the important formulas for circles, triangles, area, and volume, below is a list of some others you need to memorize to ace the SAT Math Section.

### Problem-Solving and Data Analysis Formulas

#### Percentages

• Formula to find x percent of a given number n = n(x/100)
• Formula to find out what percent a number n is of another number m = (n100)/m
• Formula to find out what number n is x percent of = (n100)/x
• Formula to find out percent increase or decrease (percent change) = amount of change/original

#### Data Analysis

For the data analysis questions, here is what you should know:

• Mean (Average) = sum of values/total number of values
• Mode = the value that is there are most in the given set
• Median = the middle value when values are in ascending order (least to greatest)
• Range = the total difference between the maximum and the minimum values. #### Standard Deviation

It is used for data points and shows how they spread. This is of two kinds:

• Low standard deviation: This is when the data points are closer to the mean (sum of values/total number of values).
• High standard deviation: This is when the data is spread over a wider range.

#### Probability

• Probability of an Event, denoted by (P event) = favorable outcomes/possible outcomes
• Joint or conditional probability P (event1 AND event2) = Pevent1 x Pevent2
• Mutually exclusive probability P (event1 OR event2) = P event1 + P event2

#### Fundamental Counting Principle

It is calculated by picking one from each group and then multiplying the number of options in each of them.

#### Permutation

This is the combination of events that take place when order matters. For this, any of the items cannot be repeated. Here is how you can denote it:

P (n, r) = n! / (n-r)!

For example, if the values of “n” and “r” are 15 and 3, here is what you get:

P (15, 3) = 15! / (15-3)! = 2,730

#### Combination

This is the combination of events that take place when order doesn’t matter at all. Here is how you can denote it:

C (n, r) = n! / r! (n-r)!

For example, if the values of “n” and “r” are 15 and 3, here is what you get:

C (15, 3) = 15! / 3! (15-3)! = 455

#### Arithmetic Sequences (tn = t1 + d (n-1))

This math formula is denoted by: tn = t1 + d (n-1) where t is the previous term and d is a common difference. Their sum can find the nth difference.

#### Geometric Sequences (tn = t1 r(n-1))

This math formula is denoted by: tn = t1 r(n-1) where t is the previous term and r is the common ratio.

## Formulas for Heart of Algebra and Passport to Advanced Math

### Lines (m = y2 – y1 / x2 – x1)

Slope of the line, denoted by m = y2 – y1 / x2 – x1

Here, you should know that parallel lines have the same slope. As for the perpendicular lines, their slopes are negative reciprocals.

### Domain (x)

It is the set of possible values of x.

### Range (y)

It is the set of possible values of y.

### Slope-Intercept Form (y = mx + b)

It is denoted by: y = mx + b

### Point-Slope Form (y – y1 = m (x – x1))

It is denoted by: y – y1 = m (x – x1)

### Midpoint Formula (X1 + x2 / 2, y1 + y2 / 2)

It is denoted by: x1 + x2 / 2, y1 + y2 / 2

### Distance Formula (d = √ (x1 – x2)2 + (y1 – y2)2)

It is denoted by:

d = √ (x1 – x2)2 + (y1 – y2)2

### Direct Variation (y = kx)

It is denoted by: y = kx

Here, k depicts the constant of variation or proportionality.

### Indirect Variation (y = k/x)

It is denoted by: y = k/x or y x = k

Here, k depicts the constant of variation or proportionality.

### Standard Form of a Quadratic (ax2+ bx + c = y)

It is denoted by: ax2+ bx + c = y

### Quadratic Formula (x = -b +- √b2 – 4ac / 2a)

It is denoted by: x = -b +- √b2 – 4ac / 2a ### Formulas To Find the Vertex

• x – coordinate = – b / 2a
• Vertex form of a quadratic y = a (x – h)2 + k; here, the vertex is h, k
• Factored form of a quadratic 0 = (x – p) (x – q); here, x-intercepts/solutions/zeros are x = p and x = q

### Exponential Functions

The exponential functions are represented as f (x) = ab x

Here, b > 0, and b is not equal to 1.

Thus, this will show growth if b > 1. It will decay if 0 < b < 1.

Growth/Decay is represented as A (t) = A0 (1 +- r) t

In the above formula, r is a percent, A0 is the initial value, and t denotes time.

For the time (t), you have to add 1 if it represents growth, and in the case of decay, you need to subtract one.

### Exponents & Roots

Here are the basic SAT math formulas that you can use to solve questions on exponents.

• (am)n = (an)m = am n
• am.an = am + n
• a-m = 1/am
• am/an = am-n = 1/an-m
• (ab)n = an bn
• (a/b) n = an/bn
• a0 = 1

To solve the question on roots, the basic SAT math formulae used to solve questions are listed below:

• n√ a = a1/n
• n√ ab = n√ a* n√ b
• n√(a/b) = n√ a / n√ b
• (n√ a) n = a

## Formulas for Additional Topics in SAT Math

### Complex Numbers

i = √ -1, i2 = -1, i3 = -1, i4 = 1

### Trigonometric Formulas

The basic trigonometric function formulas that you must remember are the following:

• 1/cos = secant (or sec)
• 1/sin = cosecant (or csc)
• 1/tan = cotangent (or cot)

Trigonometric identities you should know by heart are:

• sine/cosine = tangent
• sin^2 x + cos^2 x =1
• tan^2 + 1 = sec^2 x
• cot^2 + 1 = csc^2 x

• 360 degrees = 2pi radians
• Degrees = Radians times (180/pi)
• Radians = Degrees times (pi/180) It is essential to not just rely on your classroom materials for preparation for the SAT. It is important to familiarize yourself with the College Board's specific types of questions in your test prep, which can be done by utilizing questions from official tests and study guides. This will help you gain an understanding of what the SAT is expecting from you, which is critical to doing well on the exam.

• It is essential to comprehend the concepts behind the questions in the no-calculator section of the SAT, rather than simply memorizing equations. You must have a solid understanding of why the strategies you have learned in school are the correct methods and be able to adjust them to fit the questions given on the SAT.
• Before committing equations to memory, take the time to comprehend their meaning, application, and structure. Doing this will not only help with comprehension and usage but will also make the equations easier to remember.
• To be successful, it is important to have a timeline that is both practical and efficient. Breaking up work into shorter, more frequent periods of study over a longer period of time is the ideal way to learn.
• Amikka Learning recommends a minimum of three months of studying and preparation before taking an official test; however, many students prefer to plan for a longer period of time. Since mastering the SAT requires a lot of practice and hard work, it is important to make sure you give yourself enough time and practice regularly to maximize your chances of success.
• To do well on standardized tests like the SAT, you need to become familiar with the time and format restrictions of the test. The best way to do this is to simulate a testing environment by taking full-length, timed practice tests to determine your average speed.
• This is especially important for the math sections which appear at the end of the test, as it will help you build the speed and endurance to complete them. Amikka Learning offers mock testing and diagnostic services which include comprehensive score reports.
• It is important to set objectives as you study for the SAT. This will help you evaluate your progress and provide motivation and direction. Keep in mind that you are taking the SAT to gain admission to college, so make sure to know the SAT scores the colleges you are applying to are expecting.
• Creating a study plan is key to successful sat prep. It's important to start with the most important concepts and systematically identify areas that need improvement to create a practice plan. Having a plan will help make sure that all topics are accounted for and provide a way to track progress.
• Having an expert SAT tutor to assist you can prove invaluable in your academic journey. Not only will they help you understand the subject matter, but they can also develop a plan of study and objectives, and measure your progress as you go. The mission of Amikka's SAT tutors is to help students become more confident learners by pairing students with coaches that they can relate to, as well as providing them with enough resources to succeed.

More SAT Math Tips are available here.

## Bottom Line

Overall, mastering the essential SAT Math Formulas is a crucial part of succeeding on the SAT exam and preparing for the future. It can be a daunting process to learn all the necessary formulas, but with Amikka Learning's Online SAT Tutoring, high school students have access to the tools and resources needed to become proficient and confident in their math abilities. There is even a free trial available if you are unsure about whether this is the best option for you. With the right guidance and support, students can be prepared to approach the SAT Math section with confidence and success. Written by Founder
Chris Hernandez

Christopher Hernandez, the founder of Amikka Learning, couldn’t afford expensive SAT tutoring so he spent hundreds of hours studying on his own.

After improving over 400 points and attending an Ivy League school he realized how unfair the playing field was with tutoring: no matter how smart you were, if you couldn’t afford tutoring you were stuck.
His dream was to change this.

He began tutoring for the SAT and quickly realized that he was a gifted tutor. His students were loving his program and improving very fast.

Fast forward 8 years, Amikka is a leader in the education industry and has helped thousands of students get into their dream schools.

If you’d like a free consultation for 1-on-1 tutoring schedule a call with our team here.

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