Hi everyone and welcome to another fabulous week of MathSux! I bring to you the first construction of the back to school season! In this post, we are going to go over the angle bisector definition and example. First, we will define what an angle bisector is, then we’ll take our handy dandy compass and straight edge to construct an angle bisector that will bisect an angle for any size! Check out the video and GIF below for more and happy calculating! ๐

What is an Angle Bisector?

A line that evenly cuts an angle into two equal halves, creating two equal angles.

Angle Bisector Example:

Step 1: Place the point of your compass on the point of the angle.

Step 2: Draw an arc that intersects both lines that stem form the angle you want to bisect.

Step 3: Take the point of your compass to where the lines and arc intersect, then draw an arc towards the center of the angle.

Step 4: Now keeping the same distance on your compass, take the point of your compass and place it on the other point where both the line and arc intersect, and draw another arc towards the center of the angle.

Step 5: Notice we made an intersection!? Where these two arcs intersect, mark a point and using a straight edge, connect it to the center of the original angle.ย

Step 6: We have officially bisected our angle into two equal 35ยบ halves.

*Please note that the above example bisects a 70ยบ angle, but this construction method will work for an angle of any size!๐

What do you think of the above angle bisector definition & example? Do you use a different method for construction? Let me know in the comments below! ๐

Greeting math friends! Today, we are going to dive into statistics by learning how to find the expected value of a discrete random variable. To do this we will need to know all potential numeric outcomes of a “gamble,” as well as be able to repeat the gamble as many time as we want under the same conditions, without knowing what the outcome will be. But I’m getting ahead of myself, all of this will be explained below with two different examples step by step! Don’t forget to check out the video and practice questions at the end of this post to check your understanding. Happy calculating! ๐

What is Expected Value?

Expected Value is the weighted average of all possible outcomes of one โgameโ or โgambleโ based on the respective probabilities of each potential outcome.

Expected Value Formula: Donโt freak out because below is the expected value formula.

In essence, we are multiplying each outcome value by the probability of the outcome occurring, and then adding all possibilities together! Since we are summing all outcome values times their own probabilities, we can re-write the formula in summation notation:

Does the above formula look insane to you? Donโt worry because we will go over two examples below that will hopefully clear things up! Let check them out:

Example #1: Expected Value of Flipping a Coin

Step 1: First letโs write out all the possible outcomes and related probabilities for flipping a fair coin and playing this game. Making the below table, maps out our Probability Distribution of playing this game.

Step 2: Now that, we have written out all numeric outcomes and the probability of each occurring, we can fill in our formula and find the Expected Value of playing this game:

Ready for another? Letโs see what happens in the next example when rolling a die.

Example #2: Expected Value of Rolling a Die

Step 1: ย First letโs write out all the possible outcomes and related probabilities for rolling a die. In this question, we are assuming that each side of the die takes on its numerical value, meaning rolling a 5 or a 6 is worth more than rolling a 1 or 2.ย Making the below table, maps out our Probability Distribution of rolling the die.

Step 2: Now that, we have written out all numeric outcomes and the probability of each occurring, we can fill in our formula and find the Expected Value of playing this game:

Check out the practice problems below to master your expected value skills!

Practice Questions:

(1) An unfair coin where the probability of getting heads is .4 and the probability of getting tails is .6 is flipped. In a game where you win $10 on heads, and lose $10 on tails, what is the expected value of playing this game?

(2) An unfair coin where the probability of getting heads is .4 and the probability of getting tails is .6 is flipped. In a game where you win $30 on heads, and lose $50 on tails, what is the expected value of playing this game?

Solutions:

Still got questions? No problem! Don’t hesitate to comment with any questions below. Thanks for stopping by and happy calculating! ๐

Hi Everyone and welcome to MathSux! Today, I wanted to answer a question I get a lot which is why name your Blog and YouTube channel, “MathSux”? Clearly, I love math, but with the name “MathSux” I wanted to show that it can also be hard and even I can think that it suck sometimes. When we don’t understand something it can be frustrating whether its related to math or really anything! The point is we’ve all gotten frustrated when learning something new at some time, but that’s ok, and that’s exactly what MathSux stands for! ๐

Check out the video below to hear why I chose the name “MathSux” while doodling math art . I hope you enjoy it and happy calculating! ๐

Why is it called “MathSux”?

*New lessons will be coming your way starting next Wednesday. Also be on the lookout for Regents review questions up on YouTube tomorrow and Friday! ๐

If you are a teacher or student, have you ever thought math sucked at some time in your life? Let me know in the comments below!

Hey math friends and welcome back to MathSux! Back to school season is upon us which means most students (and teachers) will need to review a bit before diving into a completely new subject.ย In order to alleviate some of the back to school whoas, I bring to you, this back to school review! Check out the videos below to get the math juices flowing whether youโre new to Algebra, Geometry, or Algebra 2/Trig! I hope you find these videos helpful and wish everyone the best of luck in their first days at school! Happy calculating! ๐

How to Prepare for Algebra:

Calling all incoming algebra students, Combining Like Terms is a great place to start! You most likely have combined like terms before, but thereโs nothing like sharpening your skills before getting the intense Algebra questions that are coming your way. Check out the video below and try the practice questionshere!

How to Prepare for Geometry:

Geometry students, you have the world of shapes ahead of you! Itโs an exciting time to review basic Area, Perimeter, Circumference, and Pythagorean Theorem rules before moving ahead with this subject. Review the Pythagorean Theorem below from Khan Academy and check out the last page of the review sheet here to review area and perimeter.

How to Prepare for Algebra 2:

Relieve the fond memories of algebra by reviewing all the different ways to Factor and Solve Quadratic Equations! This is a great way to prepare for rational expressions and the harder algebra 2 problems that are right around the corner. Check out the video below and related practice questions here to reinforce these hopefully not yet forgotten algebra skills!

Hope you find this quick review helpful before diving in for the real deal! Besides brushing up on these math topics, what type of new school year routines do like to practice in your classroom or at home? Let me know in the comments and happy calculating! ๐

Greetings and welcome back to MathSux! This week, in honor of the Tokyo Olympics, I will be breaking down some Olympic Statistics. We will look at the top 10 countries that hold the most medals and then look at the top 10 medals earned by country in relation to each country’s total population. Let’s take a look and see what we find! Also, please note that all data used for this analysis was found on the website, here. Anyone else watching the Olympics? Try downloading the data with the link above and see what type of conclusions you can find! Happy Calculating! ๐

Top 10 Countries: Total Olympic Medals

Below shows the top 10 total medals earned by country from the beginning of the Olympics in 1896 to present day July 2021. As we can see in the graph below, the United States is way ahead of the game with thousands more Olympic medals when compared to any other country in the entire world! I always knew the U.S. did well in the Olympics, but did not realize it was to this magnitude!

Top 10 Countries: Total Olympic Medals Based on Population

Below is a different kind of graph. This percentage rate represents total medals earned over time from 1896 to July 2021 divided by the country’s total population. In this case, we can see that Lichtenstein has earned way more medals based on their small population size when compared to any other country in the world! This is amazing and unexpected!

Remember that all data for the above graphs were made from the following website, here. Are you surprised by the above graphs and conclusions? Try downloading the data on your own and see what you can conclude using your own Olympics Statistics skills! Happy calculating! ๐

Looking to apply more math to the real world? Check out how to find volume of the Hudson Yards Vessal in NYC here.

Greetings math peeps and welcome to another week of MathSux! In this post, we will learn how to construct a perpendicular line through a point on the line step by step. In the past, we learned how to construct a perpendicular bisector right down the middle of the line, but in this case we will learn how to create a perpendicular line through a given point on the line (which is not always in the middle). Following along with the GIF or check out the vide below. Thanks for stopping by and happy calculating! ๐

What are Perpendicular Lines ?

Lines that intersect to create four 90ยบ angles about the two lines.

What is happening in this GIF?

Step 1: First, we are going to gather materials, for this construction we will need a compass, straight edge, and markers.

Step 2: Notice that we need to make a perpendicular line going through point B that is given on our line.

Step 3: Open up our compass to any distance (something preferably short though to fit around our point and on the line).

Step 4: Place the compass end-point on Point B, and draw a semi-circle around our point, making sure to intersect the given line.

Step 5: Open up the compass (any size) and take the point of the compass to the intersection of our semi-circle and given line. Then swing our compass above the line.

Step 6: Keeping that same length of the compass, go to the other side of our point, where the given line and semi-circle connect. Swing the compass above the line so it intersects with the arc we made in the previous step.

Step 7: Mark the point of intersection created by these two intersecting arcs we just made and draw a perpendicular line going through Point B!

Still got questions? No problem! Don’t hesitate to comment with any questions below or check out the video above. Thanks for stopping by and happy calculating! ๐

Greetings and happy summer math peeps! In honor of the warm weather and lack of school, I thought we’d have a bit of fun with origami and volume! In this post, we will find the volume of a box and the volume of a square base pyramid. We will also be creating each shape by using origami and following along with the video below. For anyone who wants to follow along with paper folding tutorial, please note that we will need one piece of printer paper that is 8.5″ x 11″and one piece of square origami paper that is 8″ x 8″. If you’re interested in more math and art projects check out this link here. Stay cool and happy calculating! ๐

Volume of Box (or Rectangular Prism):

To get the volume of our origami box (video tutorial above), we are going to multiply the length times the width times the height. All the values and units of measurement were found by measuring the box we made in inches in the video above with 8.5 x 11 inch computer paper.

Volume of Square Base Pyramid:

Below is a diagram of the square base pyramid we created via paper folding (watch video tutorial above to follow along!). Please note that if you used a different sized paper (other than 8 X 8 inches), you will get a different value for measurements and for volume.

For step by step instruction, don’t forget to check out the video above to see how to paper fold a box and square base pyramid. I hope this post made math suck just a little bit less and finding volume a bit more fun. Still got questions or want to learn more about Math+ Art? No problem! Don’t hesitate to comment with any questions below. Thanks for stopping by and happy calculating! ๐

Happy Summer everyone! Now that school is out, I thought we could have a bit of fun with Math and Art! In this post, we will go over how to make a the original spirograph (by hand) step by step using a compass and straight edge. Follow along with the video below or check out the tutorial in pictures in this post. Hope everyone is off to a great summer. Happy calculating! ๐

What is a Spirograph?

The childhood toy we all know and love was invented by Denys Fisher, a British Engineer in the 1960’s.But the method of creating Spirograph patterns was invented way earlier by engineers and mathematicians in the 1800’s.

The Original Spirograph (by hand):

Step 1: Gather materials, for this drawing, we will need a compass and straight edge.

Step 2: Using our compass, we are going to open it to 7 cm and draw a circle.

Step 3: Next, we are going to open the compass to 1cm, making marks all around the circle, keeping that same distance on the compass.

Step 4: Draw a line connecting two points together (any two points some distance apart will do).

Step 5: Now, we are going to move the straight edge forward by one point each and connect the two points with another line.

Step 6: Continue this pattern of moving the ruler forward by one point and connecting them together all the way around.

Step 7: We have completed our Spirograph drawing! Try different sized circles, points around the circle, colors, and points of connections to create different types of patterns and have fun! ๐

Still got questions or want to learn more about Math+ Art? No problem! Don’t hesitate to comment with any questions below. Thanks for stopping by and happy calculating! ๐

Hi there and welcome to MathSux! Today we are going to break down dilations; what they are, how to find the scale factor, and how to dilate about a point other than the origin. Dilations are a type of transformation that are a bit different when compared to other types of transformations out there (translations, rotations, reflections). Once a shape is dilated, the length, area, and perimeter of the shape change, keep on reading to see how! And if you’re looking for more transformations, check out these posts on reflections and rotations. Thanks so much for stopping by and happy calculating! ๐

What are Dilations?

Dilations are a type of transformation in geometry where we take a point, line, or shape and make it bigger or smaller, depending on the Scale Factor.

We always multiply the value of the scale factor by the original shape’s length or coordinate point(s) to get the dilated image of the shape. A scale factor greater than one makes a shape bigger, and a scale factor less than one makes a shape smaller. Letโs take a look at how different values of scale factors affect the dilation below:

Scale Factor >1 Bigger

Scale Factor <1 Smaller

Scale Factor=2

In the below diagram the original triangle ABC gets dilated by a scale factor of 2. Notice that the triangle gets bigger, and that each length of the original triangle is multiplied by 2.

Scale Factor=1/2

Here, the original triangle ABC gets dilated by a scale factor of 1/2. Notice that the triangle gets smaller, and that each length of the original triangle is multiplied by 1/2 (or divided by 2).

Properties of Dilations:

There are few things that happen when a shape and/or line undergoes a dilation. Letโs take a look at each property of a dilation below:

1. Angle values remain the same.

2. Parallel and perpendicular lines remain the same.

3. Length, area, and perimeter do not remain the same.

Now that we a bit more familiar with how dilations work, letโs look at some examples on the coordinate plane:

Example #1: Finding the Scale Factor

Step 1: First, letโs look at two corresponding sides of our triangle and measure their length.

Step 2: Now, letโs look at the difference between the two lengths and ask ourselves, how did we go from 3 units to 1 unit?

Remember, we are always multiplying the scale factor by the original length values in order to dilate an image. Therefore, we know we must have multiplied the original length by 1/3 to get the new length of 1.

When it comes to dilations, there are different types of questions we may be faced with. In the last question, the triangle dilated was done so about the origin, but this wonโt always be the case. Letโs see how to dilate a point about a point other than the origin with this next example.

Example #2: Dilating about a Point other than the Origin

Step 1: First, letโs look at our point of dilation, notice it is not at the origin! In this question, we are dilating about point m! To understand where our triangle is in relation to point m, letโs draw a new x and y axes originating from this point in blue below.

Step 2: Now, letโs look at coordinate point K, in relation to our new axes.

Step 3: Letโs use the scale factor of 2 and the transformation rule for dilation, to find the value of its new coordinate point. Remember, in order to perform a dilation, we multiply each coordinate point by the scale factor.

Step 4: Finally, letโs graph the dilated image of coordinate point K. Remember we are graphing the point (6,4) in relation to the x and y-axis that stems from point m.

Check out these dilation questions below!

Practice Questions:

1) Plot the image of Point Z under a dilation about the origin by a scale factor of 2.

2) Triangle DEF is the image of triangle ABC after a dilation about the origin. What is the scale factor of the dilation?

3) Point L is dilated by a scale factor of 2 about point r. Draw the dilated image of point L.

4) Line DE is the dilated image of line AB. What is the scale factor of the dilation?

Solutions:

Still got questions? No problem! Don’t hesitate to comment with any questions below. Thanks for stopping by and happy calculating! ๐

Ahoy and welcome math friends! For the latest installment, here is the Algebra 2 Cheat Sheet & Review made just for you to prepare for finals. On this page, you’ll also find links to the come math friends! For the latest installment, here is the Algebra 2 lesson playlist, the NYS Algebra 2 Common Core Regent’s Playlist, and the library of Geometry blog posts. Hope you find these resources helpful as the end of the school year approaches. Good luck on finals and happy calculating! ๐

Algebra 2 Cheat Sheet:

Download and print the below .pdf for a quick and easy guide of everything you need to know for finals; From formulas to graphs, it’s on here.

Looking for a more detailed review? Check out the Youtube playlist for Algebra 2 below. It includes every MathSux video related to Algebra 2 and will be sure to help you ace the test!

Algebra 2 Common Core Regents Review:

This playlist is made especially for New York State dwellers as it goes over each and every question of the NYS Common Core Regents. Perfect if you are stuck on that one question! You will surely find the answer here.

Algebra 2 Blog Posts:

For anyone in search of blog posts and practice questions, check out MathSux’s entire Algebra 2 library organized by topic here.

Still got questions? No problem! Don’t hesitate to comment with any questions below. Thanks for stopping by and happy calculating! ๐

Get everything you need to know with this Algebra 2 Cheat Sheet and Review! Download and print the pdf for reviewing Algebra 2 or check out the video playlists for a more in-depth review of each topic. If you are living in NYS, you also might want to check out the NYS Regents Common Core Video as needed!