The Ultimate SIFT Math Formula Cheat Sheet

The Ultimate SIFT Math Formula Cheat Sheet

If you’re taking the SIFT Math test in a few weeks or months, you might be anxious about how to remember ALL the different formulas and math concepts and recall them during the test. The SIFT Math covers a wide range of topics—from as early as elementary school all the way to high school. While you have probably learned many of these 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 SIFT Math before the test day?

Following is a quick formula reference sheet that lists all important SIFT Math formulas you MUST know before you sit down for the test. If you learn every formula in this SIFT 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 SIFT Math formulas?Please have a look at: SIFT Math Formulas

The Absolute Best Book to Ace the SIFT Math Test

SIFT Math Cheat Sheet

Fractions  

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

Decimals  

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:\(12=2×2×3\)

Integers  

\( \{…,-3,-2,-1,0,1,2,3,…\} \)
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  

PEMDAS
(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. \(|-22|=22\)

Ratios

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

Percentages

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  

\(a(b+c)=ab+ac\)

Equations  

The values of two mathematical expressions are equal.
\(ax+b=c\)

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:
\(y=mx+b\).

Factoring:

“FOIL”
\((x+a)(x+b)\)
\(=x^2+(b+a)x +ab\) “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”
\(x^2+(b+a)x+ab=\) \((x+a)(x+b)\)

Exponents:  

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:
\(5×10^0\)
\(-2.5×10^4\)
\(5×10^{-1}\)
\(2,122456×10^3\)

Square:  

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:  

\(a^2+b^2=c^2\)

Triangles

All triangles:

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

Equilateral:  

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

Isosceles:

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

Circles

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

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

Rectangles

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

(Square if l=w)
Area=lw

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

Parallelogram

(Rhombus if l=w)
Area=lh
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:  

\(SA=ph+2B\)
\(V=Bh\)

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:

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

mean:

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

mode:

value in the list that appears most often

range:

largest value \(-\) smallest value

Median  

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

Average

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

Average speed

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

Probability

\(\frac{number \ of \ desired \ outcomes}{number \ of \ total \ outcomes}\)
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

\(x^a .x^b=x^{a+b}\)
\(\frac{x^a}{x^b} = x^{a-b}\)
\(\frac{1}{x^b }= x^{-b}\)
\((x^a)^b=x^{a.b}\)
\((xy)^a= x^a .y^a\)
\(x^0=1\)
\(\sqrt{xy}=\sqrt{x} .\sqrt{y}\)
\((-1)^n=-1\), if n is odd.
\((-1)^n=+1\), if n is even.
If \(0<x<1\), then
\(0<x^3<x^2<x<\sqrt{x}<\sqrt{3x}<1\).

Simple Interest

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

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
\(x^{-3}=\frac{1}{x^3}\)

Factorials  

Factorial- the product of a number and all counting numbers below it.
8 factorial \(=8!=\)
\(8×7×6×5×4×3×2×1=40,320\)
5 factorial \(=5!=\)
\(5×4×3×2×1=120\)
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.
\((x^a)^b=x^{(ab)}\)

Dividing Powers

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

The Zero Exponent

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

The Best Books to Ace the SIFT Math Test

Related to "The Ultimate SIFT Math Formula Cheat Sheet"

10 Most Common SIFT Math Questions
10 Most Common SIFT Math Questions
Top 10 SIFT Math Practice Questions
Top 10 SIFT Math Practice Questions
SIFT Math FREE Sample Practice Questions
SIFT Math FREE Sample Practice Questions
SIFT Math Practice Test Questions
SIFT Math Practice Test Questions
How to prepare for SIFT Math Test
How to prepare for SIFT Math Test
SIFT Math Formulas
SIFT Math Formulas
SIFT Math Worksheets
SIFT Math Worksheets
The Ultimate SIFT Math Course
The Ultimate SIFT Math Course

Leave a Reply

Your email address will not be published. Required fields are marked *

52% OFF

Download Instantly

X

How Does It Work?

Find Books

1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

add to cart

2. Add to Cart

Add the eBook to your cart.

checkout

3. Checkout

Complete the quick and easy checkout process.

download

4. Download

Immediately receive the download link and get the eBook in PDF format.

Why Buy eBook From Effortlessmath?

Save money

Save up to 70% compared to print

Instantly download

Instantly download and access your eBook

help environment

Help save the environment

Access

Lifetime access to your eBook

Test titles

Over 2,000 Test Prep titles available

Customers

Over 80,000 happy customers

Star

Over 10,000 reviews with an average rating of 4.5 out of 5

Support

24/7 support

Anywhere

Anytime, Anywhere Access

Find Your Test

Schools, tutoring centers, instructors, and parents can purchase Effortless Math eBooks individually or in bulk with a credit card or PayPal. Find out more…