Free Printable Math Worksheets

Free Printable Math Worksheets

Free printable math worksheets are a terrific way for students to practice math skills.  By utilizing math worksheets, this can free the teacher from needing to take extra time to create practice math questions and problem sets.  Also, with the right math worksheets, students can learn cool math games and learn that math is fun.

This website can be used as a math resource for students and math teachers alike.  Anyone looking to practice their math skills or learn new math concepts should use these free printable math worksheets to practice and get good at solving mathematics problems.  Teachers looking for math worksheets and problem sets for their math students will also find this site to be very valuable to help them teach the mathematics concepts in their math classes.  These can be used as math print out worksheets, if you wish, or can just be copied down and worked out with a pencil and paper, just like students would do in school on a math test or math quiz.  If there is any topic in particular that anyone, teachers or students, would like me to be included, then please leave me a comment below and I will see what I can do.

I have found a great resource at Homeschoolmath.net that has all sorts of automatically generated math worksheets available for several elementary math grades.  Here's a link to their website that is loaded with free printable math worksheets.  There are worksheets specifically appropriate for grade 1 up to grade 6, and then several more worksheets that focus on specific math concepts.  I highly recommend visiting this site!

The following print out worksheets and problem sets are math questions that I have written on my own.  Feel free to download the files and print them out.  I will post answers as well, and I apologize in advance if there are any errors.  Again, please leave me a comment if you find an error and I will make the correction on the worksheet.

I hope that you find these math worksheets useful, and that they help you to more fully understand the topics and math concepts that I have discussed in other blog posts.  Feel free to leave feedback below, especially what you would like to see or what you would like changed.

Here are a few worksheets to get you started.  I will eventually be adding more to this list.  As teachers can agree with, creating math worksheets can take a lot of time... time which frequently could be better used to plan other aspects of their course curriculum.

Addition Worksheet 1 (with answer key)
Addition Worksheet 2 (with answer key)
Addition Worksheet 3 (with answer key)
Subtraction Worksheet 1 (with answer key)
Subtraction Worksheet 2 (with answer key)
Subtraction Worksheet 3 (with answer key)

Trig Identities Cheat Sheet

Trig Identities Cheat Sheet

This is your trig identities cheat sheet!  Trig identities are defined as mathematical expressions that relate various trigonometric functions to others, regardless of what the variables are.  The trig identities are true for all values of the variable.  They are incredibly valuable to understand and to memorize, and their usefulness becomes apparent when you are faced with a complicated trigonometric expression that needs to be simplified.

All you need to do is rearrange the complicated trig expression such that you can express it in terms of the trigonometric identities, substitute in the identity to simplify, and carry on with solving the math problem.  Think of them as a type of "constant" that can be swapped into expressions (that use sine, cosine, tangent, or any of the related trig functions secant, cosecant, or cotangent) to change their appearance without changing the math surrounding the expression.

Trig identities are extraordinarily important in helping you solve your mathematics questions, and so the identities that I list and explain on this trig identities cheat sheet should really be committed to memory.  If you know them and can recognize them automatically, your math homework and trigonometry questions will become a lot easier.

Reciprocal Identities

For the first set of trig identities, I will list the Reciprocal Identities.  These may be familiar to you already, especially if you have been introduced to the trig functions secant, cosecant, and cotangent.  I'll refer you to my post on sine, cosine, and tangent for their basic definitions, as I will build upon those.  If you look at the definition of sine, you see that it is the ratio of opposite over hypotenuse.  (Remember SOHCAHTOA!)  If you invert this ratio to be hypotenuse over opposite, this is the definition of cosecant.  The same thing applies to secant and cotangent: they are the reciprocal ratio of the sides that define the basic trig identity.  So, then you can also say that these trig functions are the reciprocal of the basic trigonometric functions.  Here they are listed for you:

Naturally, you can rearrange these trig identities to isolate the other trigonometry functions as well:

And those are the first set of trig identities I am going to mention here on my trig identities cheat sheet: the Reciprocal Identities.

Pythagorean Identities

The next set that I would like to mention are the Pythagorean Identities.  Allow me to direct you to a recent post I put up on my In Mathematics blog that had a lengthy explanation about Pythagorean Identities.  I recommend giving that a read to better understand where these trig identities are coming from and how they can be derived.  However, for completeness, I will list them here as well, like above.

Quotient Identities

The Quotient Identities are another set of trig identities that are fairly easy to remember, especially when you understand how to derive them.  Start with the basic trig definitions for sine and cosine.  Sine is opposite over hypotenuse, cosine is adjacent over hypotenuse.  Now, divide sine by cosine:

sine / cosine = [opposite / hypotenuse] / [adjacent / hypotenuse] = opposite / hypotenuse

The hypotenuse in the numerator and denominator expressions cancel out, and you are left simply with the basic trigonometric definition of tangent!  Similarly,divide cosine by sine to get the second quotient identity.

The identities that I have explained above are sometimes considered to be the 8 fundamental trigonometric identities, including the Reciprocal (x3), Pythagorean (x3), and Quotient (x2) identities. Hopefully my explanations have helped you to understand the logic behind these identities, which will ideally make them easier for you to memorize and work with!

Please remember to +1 me if this was useful!

Mental Math Secrets

Have you ever wanted to learn Mental Math Secrets?  Wouldn't it be amazing if you could do all of your math questions in your homework or on tests without ever having to use your calculator, or even having to write it down, because you could quickly and accurately find the answers in your head?  If you improve mental math techniques, this could very easily happen for you!

Math and Multimedia Carnival #21

Welcome to the 21st edition of the Math and Multimedia Carnival!  I hope you enjoy the selection of mathematics-related topics that have been included in the carnival this month, which have either been submitted via the blog carnival submission site, emailed to me, or are of my personal choosing.  Before we get to those though, as is tradition for the Math and Multimedia Carnival, let's learn some trivia about the number 21!

Triva about the Number 21:

• 21 is a Fibonacci number, whereby is it the sum of the preceding two numbers (8 and 13) in the Fibonacci sequence.
• We are currently living in the 21st century.
• The element with the atomic number 21 is Scandium.
• The name of pop singer Adele's second album is titled "21".
• In most US states, 21 is the legal drinking and gambling age.
• Coincidentally enough, 21 is another name for the popular card game, Blackjack.
• A popular restaurant in New York City is named "21 Club".
• A standard, 6-sided die has a sum of 21 total spots.
• Here's a strange one.  According to Dr. Duncan MacDougall, a 20th century American physician, a person's soul is a physical component of the body, and has a weight of 21 grams.

And now, on to my collection of math articles!  I hope you enjoy them!

Technology and Mathematics

Colleen Young has submitted a list of some of the best online tools to help learning, in her post "Top 100 Tools 2012 - voting open."  The article is hosted on her site Mathematics, Learning and Web 2.0, and contains a link to vote for your favorite learning tools of the year.

Amongst several other great articles on the subject of technology in education, Mark Gleeson has a very interesting read up on his site, titled "The iPad and Maths - Are We There Yet? Pt 2 (non-Math apps do the job?)," which he has up on his website Mr G Online.


Mathematics Education

John Golden has submitted a post titled "Two Teacher Tech Topics" from his math hombre site.  This article takes a look at teachers' attitudes towards the use of calculators in mathematics, and also shares some thoughts on reflective writing or blogging as a means to strengthen learning.

Diana Clerk has provided a nice round up of some extremely useful sites and resources in her post titled "20 Best Sites for Helpful Dissertation Tips."  You can find plenty of tips and advice from these sites to help you complete one of the most difficult parts of a Ph.D. program.  This submission is hosted on the Online Ph.D. Program website.


General Mathematics

Guillermo Bautista, the creator of the Math and Multimedia Carnival, submitted a pair of blog entries.  The first is titled "Divisibility by 8" and outlines a shortcut for dividing large numbers by 8.  This entry is posted on his website, Mathematics and Multimedia.  Speaking of large numbers, his second post provides a commentary on "The Use of Large Numbers," which is posted on his Mathematical Palette blog.

Kalid Azad provides a very helpful article that undoubtedly will be of use to many students: "Vector Calculus: Understanding the Dot Product."  I wish my physics class (back in the day) explained vector math as well as this post.  He even throws in a reference to the speed boost pads found in Nintendo's Mario Kart, to keep things current!  He has this posted on his site, Better Explained.

Warren Davies has provided an answer to a common question asked by students in the field of statistics: "What the hell is Bonferroni correction?"  This short post explains the Bonferroni correction and its role in data error analysis, and is hosted on his "Generally Thinking Data Blog."

Rick Regan has a fantastic four-part series on binary arithmetic up on his website Exploring Binary.  The latest in his series is "Binary Multiplication," which follows articles on addition and subtraction, among other incredibly informative works on the topic of binary numbers.

One of my submissions to this blog carnival is titled "Inverse Trig Functions," in which I discuss how to find an unknown angle when given the value of the standard trigonometric function.  This article is posted elsewhere on this site, Math Concepts Explained.  My second submission is a post about "Pythagorean Identities" and how you can derive them, which I have up at the In Mathematics blog.


And that concludes the 21st edition of the Math and Multimedia Carnival!

I hope that you have enjoyed the variety of articles, and perhaps learned a little something new as well!  Thank you to all of the authors who submitted their works, and also to those who gave me permission to repost their pages.  The 22nd edition is just around the corner, so here's to the continued success of the Math and Multimedia Carnival!

Inverse Trigonometric Functions - Arcsine, Arccosine, Arctangent

Inverse trig functions are a core concept in trigonometry.  Specifically, they are named arcsine, arccosine, and arctangent.  We have already discussed how to find things such as the sine of 25 degrees, or cosine of 71 degrees.  However, we need to introduce a new math concept to figure out such problems as "what angle gives a sine value of 0.2?"  This is where inverse trig functions come in. Think of their relationship to the standard basic trig functions as being comparable to that between multiplication and division.  You do one operation, and then the opposite to go the other way and undo the first operation.

You may be taught these in school slightly differently.  Instead of using the names arcsine, arccosine, and arctangent (arcfunctions!), it is also very common to see these represented as the basic trig notation with a -1 exponent, like these:

arcsine = sin^-1

arccosine = cos^-1

arctangent = tan^-1

These are likely the symbols that you will see on your calculator.  Typically, they are the shifted function of the regular sin, cos, and tan buttons.  It is important to note the distinction between the basic trigonometric functions and these new inverse trig functions.  When using the basic trig functions, the value you are obtaining is the ratio of the two relevant sides of the triangle for the given angle.  When using the inverse trig functions, what you are solving for is the actual angle that produces the given ratio of sides.  So, make sure you push the right button on the calculator!

The most basic way of finding an inverse function, in general, is to take your given function and switch the x and y, and then rearrange.

f(x) = x² + 5
y = x² + 5.... now switch x and y
x = y² +5.... and rearrange
y² = x - 5
y = sqrt(x-5)

And there you have determined the inverse function.  This is the same strategy that is being applied when we are talking about inverse trig functions.  However, having the inverse trig buttons on our calculators really take all of this extensive and possibly difficult rearranging and calculating out of the picture.

Here is a basic example of one of these inverse trigonometric functions.  Hopefully you will see that they are extremely easy to work with.

Find the angle for the given trig ratio:
sin(θ) = 1 /√2
θ = sin^-1(1 /√2)
θ = 45°

Hopefully this introduction to the inverse trig functions has been useful for you.  There is a lot more information about this math concept that is probably quite beyond the scope of what is necessary to actually solve most of the basic trigonometry questions you will find in your maths homework.  I have found several good resources, if you would like to learn more about inverse trigonometric functions.  They can be found on the ubc.ca math website, or on The Math Page (among many other great math resources out there).  Please leave a comment below if you know of any other great sites that you would like to share with other readers. Also, once again, please hit the +1 if you've enjoyed this post!