# The Ultimate ParaPro Math Formula Cheat Sheet

If you’re preparing for the ParaPro Math test and will take the 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 ParaPro 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 ParaPro Math before the test day?

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

**The Absolute Best Book to Ace the ParaPro Math Test**

**ParaPro** **Math Cheat Sheet**

*Fractions*

*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*

*Decimals*

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

*Mixed Numbers*

*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*

*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*

*Integers*

\( \{…,-3,-2,-1,0,1,2,3,…\} \)

Includes: zero, counting numbers, and the negative of the counting numbers

*Real 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*

*Order of Operations*

PEMDAS

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

*Absolute Value*

*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*

*Ratios*

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

*Percentages*

*Percentages*

Use the following formula to find part, whole, or percent

part \(=\frac{percent}{100}×whole\)

*Proportional Ratios*

*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*

*Percent of Change*

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

*Expressions and Variables*

*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*

*Distributive Property*

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

*Equations*

*Equations*

The values of two mathematical expressions are equal.

\(ax+b=c\)

*Distance from A to B:*

*Distance from A to B:*

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

*Parallel and Perpendicular lines:*

*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:*

*Mid-point of the segment AB:*

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

*Slope of the line:*

*Slope of the line:*

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

*Point-slope form:*

*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:*

*Slope-intercept form:*

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

\(y=mx+b\).

*Factoring:*

*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:*

*Exponents:*

Refers to the number of times a number is multiplied by itself.

\(8 = 2 × 2 × 2 = 2^3\)

*Scientific Notation:*

*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:*

*Square:*

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

*Square Roots:*

*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:*

*Pythagorean Theorem:*

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

*Triangles*

*Triangles*

**All triangles:**

**All triangles:**

Area \(=\frac{1}{2}\) b . h

Angles on the inside of any triangle add up to \(180^\circ\).

*Equilateral:*

*Equilateral:*

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

*Isosceles:*

*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*

*Circles*

Area \(=πr^2\)

Circumference \(=2πr\)

Full circle \(=360^\circ\)

**Rectangles**

**Rectangles**

(Square if *l=w*)

Area=*lw*

**Parallelogram**

**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:*

*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 rectangular/right prism:*

\(SA=ph+2B\)

\(V=Bh\)

**Surface Area and Volume of a cylinder:**

**Surface Area and Volume of a cylinder:**

\(SA =2πrh+2πr^2\)

\(V =πr^2 h \)

**Surface Area and Volume of a Cone**

**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**

**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**:

**Simple interest**

\(I=prt\)

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

**mean**:

**mean**

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

**mode:**

**mode:**

value in the list that appears most often

**range:**

**range:**

largest value \(-\) smallest value

*Median*

*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*

*Average*

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

*Average speed*

*Average speed*

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

*Probability*

*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*

*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*

*Simple Interest*

The charge for borrowing money or the return for lending it.

Interest = principal \(×\) rate \(×\) time

OR

\(I=prt\)

*Powers/ Exponents*

*Powers/ Exponents*

*Positive 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*

*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**

**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**

**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*

*Powers of Powers*

For power of a power: you multiply the exponents.

\((x^a)^b=x^{(ab)}\)

*Dividing Powers*

*Dividing Powers*

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

*The Zero Exponent*

*The Zero Exponent*

Anything to the 0 power is 1.

\(x^0= 1\)

**The Best Book to Ace the ParaPro Test**

## More from Effortless Math for ParaPro Test …

### Can’t find the free ParaPro math test sample practice questions?

We give you the good news that you do not need to search any further !: ParaPro Math FREE Sample Practice Questions

### Have not memorized ParaPro math test formulas and are now worried?

We understand your concerns and have come up with a solution: The Ultimate ParaPro Math Formula Cheat Sheet

### Do you not know how to interpret the ParaPro test scores and this has bothered you?

We know the solution to this problem: How is the ParaPro Test Scored?

**The Perfect Prep Books for the ParaPro Math Test **

## Have any questions about the ParaPro Test?

Write your questions about the ParaPro or any other topics below and we’ll reply!

## Related to This Article

### More math articles

- Top 10 8th Grade Common Core Math Practice Questions
- 6th Grade MCAS Math Practice Test Questions
- SHSAT Math Practice Test Questions
- How to Compare Decimals? (+FREE Worksheet!)
- The Ultimate SIFT Math Course (+FREE Worksheets & Tests)
- Top 10 4th Grade MCAS Math Practice Questions
- The Ultimate 6th Grade RISE Math Course (+FREE Worksheets)
- How to Manage Your Time Effectively on the GED Math Test?
- 10 Most Common 7th Grade FSA Math Questions
- 3rd Grade PARCC Math Worksheets: FREE & Printable

## What people say about "The Ultimate ParaPro Math Formula Cheat Sheet - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.