The Ultimate PSAT 8/9 Math Formula Cheat Sheet

The Ultimate PSAT 8/9 Math Formula Cheat Sheet

If you are preparing for the PSAT 8/9 Math test, you might be anxious about how to remember many different math formulas and topics and recall them during the test. The PSAT 8/9 Math test covers a wide range of math concepts —from as early as elementary school all the way to grade 8 and 9. While you have probably learned many of these math formulas at some point, it may have been a long time since you’ve actually used them. This is where most test takers have a hard time preparing for the test.

So, what formulas do you need to have memorized for the PSAT 8/9 Math before the test day?

Following is a quick formula reference sheet that lists all important PSAT 8/9 Math formulas you MUST know before you sit down for the test. If you learn every formula in this PSAT 8/9 Math Formula Cheat Sheet, you will save yourself valuable time on the test and probably get a few extra questions correct.

Looking for a comprehensive and complete list of all PSAT 8/9 Math formulas? Please have a look at PSAT 8/9 Math Formulas

The Absolute Best Book to Ace the PSAT 8/9 Math Test

Satisfied 142 Students

PSAT 8/9 Math Cheat Sheet


A number expressed in the form \(\frac{a}{b}\)
Adding and Subtracting with the same denominator:
Adding and Subtracting with the different denominator:
Multiplying and Dividing Fractions:
\(\frac{a}{b} × \frac{c}{d}=\frac{a×c}{b×d}\)
\(\frac{a}{b} ÷ \frac{c}{d}=\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ad}{bc}\)    


Is a fraction written in a special form. For example, instead of writing  \(\frac{1}{2}\) you can write \(0.5\).  

Mixed Numbers

A number composed of a whole number and fraction. Example: \(2 \frac{2}{ 3}\) Converting between improper fractions and mixed numbers: \(a \frac{c}{b}=a+\frac{c}{b}= \frac{ab+ c}{b}\)

Factoring Numbers

Factor a number means to break it up into numbers that can be multiplied together to get the original number. Example:\(12=2×2×3\)


\( \{…,-3,-2,-1,0,1,2,3,…\} \)
Includes: zero, counting numbers, and the negative of the counting numbers

Real Numbers  

All numbers that are on number line. Integers plus fractions, decimals, and irrationals  etc.) (\(\sqrt{2},\sqrt{3},π\), etc.)  

Order of Operations  

(parentheses / exponents / multiply / divide / add / subtract)  

Absolute Value

Refers to the distance of a number from, the distances are positive as the absolute value of a number cannot be negative. \(|-22|=22\)


A ratio is a comparison of two numbers by division. Example: \(3 : 5\), or \(\frac{3}{5}\)  


Use the following formula to find part, whole, or percent
part \(=\frac{percent}{100}×whole\)

Proportional Ratios

A proportion means that two ratios are equal. It can be written in two ways:  
\(\frac{a}{b}=\frac{c}{d}\) , \(a: b = c: d  \)

Percent of Change

\(\frac{New \ Value \ – \ Old \ Value}{Old Value}×100\%\)

Expressions and Variables  

A variable is a letter that represents unspecified numbers. One may use a variable in the same manner as all other numbers: Addition: \(2+a\)  : \(2\) plus a
Subtraction: \(y-3\)  : \(y\) minus \(3\)
Division: \(\frac{4}{x}\)  : 4 divided by x
Multiplication: \(5a\)  : \(5\) times a

Distributive Property  



The values of two mathematical expressions are equal.

Distance from A to B:

\(\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2 }\)

Parallel and Perpendicular lines:  

Parallel lines have equal slopes. Perpendicular lines (i.e., those that make a \(90^° \) angle where they intersect) have negative reciprocal slopes: \(m_{1}\) .\(m_{2}=-1\).
Parallel Lines (l \(\parallel\) m)

Mid-point of the segment AB:  

M (\(\frac{x_{1}+x_{2}}{2} , \frac{y_{1}+y_{2}}{2}\))  

Slope of the line:  

\(\frac{y_{2}- y_{1}}{x_{2} – x_{1} }=\frac{rise}{run}\)

Point-slope form:  

Given the slope m and a point \((x_{1},y_{1})\) on the line, the equation of the line is
\((y-y_{1})=m \ (x-x_{1})\).  

Slope-intercept form:

given the slope m and the y-intercept b, then the equation of the line is:


\(=x^2+(b+a)x +ab\) “Difference of Squares”
\(a^2-b^2= (a+b)(a-b)\)
\(a^2+2ab+b^2=(a+b)(a+b) \)
\(a^2-2ab+b^2=(a-b)(a-b)\) “Reverse FOIL”
\(x^2+(b+a)x+ab=\) \((x+a)(x+b)\)


Refers to the number of times a number is multiplied by itself.
\(8 = 2 × 2 × 2 = 2^3\)

Scientific Notation:  

It is a way of expressing numbers that are too big or too small to be conveniently written in decimal form.
In scientific notation all numbers are written in this form: \(m \times 10^n\)
Scientific notation:


The number we get after multiplying an integer (not a fraction) by itself. Example: \(2×2=4,2^2=4\)

Square Roots:

A square root of \(x\) is a number r whose square is \(x : r^2=x\)
\(r\) is a square root of \(x\)

Pythagorean Theorem:  



All triangles:

Area \(=\frac{1}{2}\) b . h
Angles on the inside of any triangle add up to \(180^\circ\).


These triangles have three equal sides, and all three angles are \(60^\circ\).  


An isosceles triangle has two equal sides. The “base” angles (the ones opposite the two sides) are equal (see the \(45^\circ\)  triangle above).  


This image has an empty alt attribute; its file name is circ-1.png

Area \(=πr^2\)
Circumference \(=2πr\)
Full circle \(=360^\circ\)


This image has an empty alt attribute; its file name is h-2.png

(Square if l=w)

This image has an empty alt attribute; its file name is jk.png


(Rhombus if l=w)
Regular polygons are n-sided figures with all sides equal and all angles equal.
The sum of the inside angles of an n-sided regular polygon is
\((n-2) .180^\circ\).

Area of a trapezoid:  

\(A =\frac{1}{2} h (b_{1}+b_{2})\)

Surface Area and Volume of a rectangular/right prism:  


Surface Area and Volume of a cylinder:

\(SA =2πrh+2πr^2\)
\(V =πr^2 h  \)

Surface Area and Volume of a Cone  

\(SA =πrs+πr^2\)
\(V=\frac{1}{3} \ πr^2 \ h\)

Surface Area and Volume of a Sphere  

\(SA =4πr^2\)
\(V =\frac{4}{3} \ πr^3\)
(p \(=\) perimeter of base B; \(π ~ 3.14 \))

Simple interest:

(I = interest, p = principal, r = rate, t = time)


mean: \(\frac{sum \ of \ the \ data}{of \ data \ entires}\)


value in the list that appears most often


largest value \(-\) smallest value


Middle value in the list (which must be sorted)
Example: median of
\( \{3,10,9,27,50\} = 10\)
Example: median of
\( \{3,9,10,27\}=\frac{(9+10)}{2}=9.5 \)


\(   \frac{sum \ of \ terms}{number \ of \ terms}\)

Average speed

\(\frac{total \ distance}{total \ time}\)


\(\frac{number \ of \ desired \ outcomes}{number \ of \ total \ outcomes}\)
The probability of two different events A and B both happening is:
P(A and B)=p(A) .p(B)
as long as the events are independent (not mutually exclusive).

Powers, Exponents, Roots

\(x^a .x^b=x^{a+b}\)
\(\frac{x^a}{x^b} = x^{a-b}\)
\(\frac{1}{x^b }= x^{-b}\)
\((xy)^a= x^a .y^a\)
\(\sqrt{xy}=\sqrt{x} .\sqrt{y}\)
\((-1)^n=-1\), if n is odd.
\((-1)^n=+1\), if n is even.
If \(0<x<1\), then

Simple Interest

The charge for borrowing money or the return for lending it.
Interest = principal \(×\) rate \(×\) time

Powers/ Exponents

Positive Exponents

An exponent is simply shorthand for multiplying that number of identical factors. So \(4^3\) is the same as (4)(4)(4), three identical factors of 4. And \(x^3\) is just three factors of x, \((x)(x)(x)\).

Negative Exponents

A negative exponent means to divide by that number of factors instead of multiplying.
So \(4^{-3}\) is the same as \( \frac{1}{4^3}\) and


Factorial- the product of a number and all counting numbers below it.
8 factorial \(=8!=\)
5 factorial \(=5!=\)
2 factorial \(=2!=2× 1=2\)

Multiplying Two Powers of the SAME Base  

When the bases are the same, you find the new power by just adding the exponents
\(x^a .x^b=x^{a+b }\)

Powers of Powers

For power of a power: you multiply the exponents.

Dividing Powers

\(\frac{x^a}{x^b} =x^a x^{-b}= x^{a-b}\)

The Zero Exponent

Anything to the 0 power is 1.
\(x^0= 1\)

College Entrance Tests

The Best Books to Ace the PSAT 8/9 Math Test

Satisfied 110 Students
Satisfied 198 Students
Satisfied 118 Students
Satisfied 235 Students
Satisfied 193 Students
Satisfied 189 Students
Satisfied 57 Students

What people say about "The Ultimate PSAT 8/9 Math Formula Cheat Sheet"?

No one replied yet.

Leave a Reply

30% OFF

Limited time only!

Save Over 30%

Take It Now!


It was $16.99 now it is $11.99

Math and Critical Thinking Challenges: For the Middle and High School Student