# SAT Math Formula Sheet – Important Formulas for The SAT Exam

Dec 27, 2021 | Turito Team USA

If you are taking the SAT exam to enhance your college application, you might know that math is an important component of the test. This section of the exam tests your understanding of the concepts in mathematics that you have to study further in college. Typically, this exam covers three major areas of the subject:
● Heart of Algebra
● Problem Solving and Data Analysis

For all these areas of the SAT Math exam, one necessary thing is knowing the right Math formulas. If you are looking for the SAT Math Formula Sheet for the same, you are in the right place. In today’s post, we will be telling you all about the 12 important formulas that are there on the SAT math exam sheet. Along with them, there are some other formulas you must memorize.
Let the scrolling begin!

## Important SAT Math Formula Sheet

You can readily find SAT math formula sheet pdf online. However, before that, you should know that 12 formulas are given on the test itself along with three geometry laws. You must know these by heart along with how to use them. The other formulas that you need to learn for the exam depend on the sections you have prepared. Still, we have given some good-to-know formulas at the end.

### SAT Math Formulas Given on The Test

Let us begin with the SAT math formulas already 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 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 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) 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 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 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 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.

#### Given Laws

Along with all the formulas given above, some laws are already given in the SAT math formula sheet. These are as follows:
Law Number 1: The number of degrees of arc in a circle is 360: Which means that a circle has a total of 360 degrees.
Law Number 2: The number of radians of 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.
Law 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.

SAT Math Formulas Not Given on The Test
While the SAT formula sheet provided in the math section has all the important formulas for circles, area, triangles, and volume, there are some others you need to know. Here are some additional formulas that you must memorize to ace the SAT Math Section. Have a look:

### Formulas for Problem Solving and Data Analysis

Firstly, here are some of the formulas you need to solve the Problem Solving and Data Analysis part of the SAT math exam. Have a look:
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
Here are some of the formulas that might come in handy for the areas – Heart of Algebra and Passport to Advanced Math. Make sure to memorize them well, and know how to use them correctly. Have a look:

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 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. Have a look:
● (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 as given 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
After the Heart of Algebra, Problem Solving and Data Analysis, and Passport to Advanced Math, we will cover some other additional topics that are there in the SAT Math exam. Here are some of the formulas you need to remember for the questions that cover these topics. Have a look:

Complex Numbers
i = √ -1, i2 = -1, i3 = -1, i4 = 1

Trigonometric Formulas
The basic trigonometric function formulas that you must keep in mind 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)

#### How to Use the SAT Math Formulas?

Now that you know these SAT Math formulas, let us tell you how to use them to ace the math section of the exam. Instead of learning the question, work by understanding the concepts. In simple words, work to own the material. On the test day, even if you have not seen that question before, you should be able to apply the learned concepts to it and solve it easily.

The wording of the questions is quite important. Familiarize yourself with it, and then think about which formula you can apply to solve it. While there is a standardized test structure, the wording varies, and understanding it is important. Refer to previous year’s questions to understand how the questions are molded.

Lastly, while you are preparing for the SAT math section, always take a timed test. This will help you practice time management and improve your speed for the final test day. These tests are also a great way to check your performance and see if you need to work on certain formulas and concepts. Practice as much as you can and, you are sure to ace your SAT math test.

#### Final Thoughts

Preparing for the SAT exam is undoubtedly a stressful experience. However, do keep in mind that this exam tests you on what you already know. Therefore, when it comes to the SAT Math section, you need not worry. Along with the 12 formulas in the SAT Math Formula Sheet, you do not have to mug up every other formula you come across.

Instead, make sure that, apart from those 12 formulas, whatever formulas you know, you know them well. Be it some trigonometry formulas or geometry formulas, if you focus on them, make sure to learn how to use them well to solve problems. If you study by understanding the use of formulas rather than just learning them, you are sure to ace the SAT math exam. Good luck!