Study Archives - Math Lessons

Holiday Discount at the Math Shop!

Seasons greetings math friends! Tis’ the season of giving, celebrating, and of course, glitter! And in honor of the holiday season, I’m here to take a break from providing math lessons this week, to instead, provide a holiday discount at the Math Shop! Did you know we have an exclusive math shop, just for us MathSux nerds? Check out the one-of-a-kind MathSux merchandise designs located in the Math Shop, found in the link below. Don’t forget to use the discount code, ‘CHEERSMATH‘ for a whopping 20% off! Also, check out my my top 3 favorite picks below for a quick preview of what you’ll find in the store. Does anyone else have nerdy math gear that they use in their lives and in their classroom? Let me know in the comments below!

Holiday Discount:

Math Shop: https://mathsux.creator-spring.com/

Discount: ‘CHEERSMATH‘

Top 3 Gifts (for the Math Nerd in your Life):

The Math Shop has one-of-a-kind math themed designs on t-shirts, stickers, and posters in a variety of colors for all the math nerds in your life. These items are perfect for math fans, teachers, and students to keep studying the subject light and positive! This can be perfect for those frustrated learning moments, for example, quotes like “Keep Calm and Calculate on” will carry any math learner through to the more enlightened side of math. Although this was hard to do, check out my personal top 3 favorites from the Math Shop:

1) Peace, Love, Pi T-Shirt in Pink:

2) MathSux Stickers

3) Keep Calm and Calculate on Stickers

Hoping you’re all having a wonderful holiday season and a Happy New Year! Last but not least, of course I also want to wish you happy calculating! Be back with more math lessons in 2022!

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NYS Regents Review – Algebra June 2021

Greetings math friends! Today we are going to break down the NYS Regents, specifically the Algebra NYS Common Core Regents from June 2021, one question at a time. The following video playlist goes over each and every question one step at a time. I’ve been working on this playlist slowly adding new questions and videos every week and now that it is complete, it is time to celebrate (and/or study)! Please enjoy this review along with the study aids and related links that will also help you ace the NYS Regents. Happy calculating!

NYS Regents – Algebra June 2021 Playlist

Study Resources:

Looking to ace your upcoming NYS Regents!? Don;t forget to check out the resources below, including an Algebra Cheat Sheet, and important topics and videos to review. Good luck and happy calculating!😅

Algebra Cheat Sheet

Combing Like Terms and the Distributive Property

How to Graph an Equation of a Line

Piecewise Functions

NYS Regents – Algebra 2020

How to Study Math?

How is one supposed to study math!? Well, there is usually only one way, and that is to practice, practice, practice! But don’t get too stressed, because you can also make practice fun (or at least more pleasant).

Add some background music to your study session and make a nice cup of tea before diving in for the brain marathon. Another idea is to study only 1 hour at a time and to be sure to take breaks. Can’t seem to get that one question? Take a break and walk a way, or even better find a new study spot! It’s been scientifically proven that studying in different places can boost your memory of the very information you’re trying to understand.

What study habits do you have that have worked for you in the past? Let me know in the comments and good luck on your upcoming test!

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** Be sure to check out the full list of Algebra lessons and old Regents questions review!**

How to Construct an Equilateral Triangle?: Geometry

Happy Wednesday math peeps! This post introduces constructions by showing us how to construct an equilateral triangle by using a compass and a ruler. For anyone new to constructions, this is the perfect topic for art aficionados since there is more drawing than there is actual math.

What is an Equilateral Triangle?

Equilateral Triangle: A triangle with three equal sides. Not an easy one to forget, the equilateral triangle is super easy to construct given the right tools (compass+ ruler). Take a look below:

how to construct an equilateral triangle

Now, for our Example:

Solution:

What’s Happening in this GIF?

1. Using a compass, measure out the distance of line segment .

2. With the compass on point A, draw an arc that has the same distance as .

3. With the compass on point B, draw an arc that has the same distance as .

4. Notice where the arcs intersect? Using a ruler, connect points A and B to the new point of intersection. This will create two new equal sides of our triangle!

Still got questions? No problem! Don’t hesitate to comment with any questions. Happy calculating! 🙂

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Looking to learn more about triangles? Check out this post on right triangle trigonometry here!

Expanding Cubed Binomials: Algebra 2/Trig.

Greetings math friends! This post will go over expanding cubed binomials using two different methods to get the same answer. We’re so used to seeing squared binomials such as, , and expanding them without a second thought. But what happens when our reliable squared binomials are now raised to the third power, such as,? Luckily for us, there is a Rule we can use:

But where did this rule come from? And how can we so blindly trust it? In this post we will prove why the above rule works for expanding cubed binomials using 2 different methods:

Why bother? Proving this rule will allow us to expand and simplify any cubic binomial given to us in the future! And since we are proving it 2 different ways, you can choose the method that best works for you.

Method #1: The Box Method

Step 1: First, focus on the left side of the equation by expanding (a+b)³:

Step 2: Now we are going to create our first box, multiplying (a+b)(a+b). Notice we put each term of (a+b) on either side of the box. Then multiplied each term where they meet.

Step 3: Combine like terms ab and ab, then add each term together to get a²+2ab+b².

Step 4: Multiply (a²+2ab+b²)(a+b) making a bigger box to include each term.

Step 5: Now combine like terms (2a²b and a²b) and (2ab² and ab²), then add each term together and get our answer: a³+3a²b+3ab²+b³.

Screen Shot 2020-08-18 at 10.21.05 PM.png

Method #2: The Distribution Method

Screen Shot 2020-08-18 at 10.17.54 PM.png

Let’s expand the cubed binomial using the distribution method step by step below:

Now that we’ve gone over 2 different methods of cubic binomial expansion, try the following practice questions on your own using your favorite method!

Practice Questions: Expand and simplify the following.

Solutions:

Screen Shot 2020-08-18 at 10.22.19 PM.png

Still, got questions? No problem! Check out the video above or comment below! Happy calculating! 🙂

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**Bonus: Test your skills with this Regents question on Binomial Cubic Expansion!

How to use Recursive Formulas?: Algebra

Welcome to Mathsux! This post is going to show you everything you need to know about Recursive Formulas by looking at three different examples. Check out the video below for more of an explanation and test your skills with the practice questions at the bottom of this page. Happy calculating! 🙂

What is a Recursive Formula?

A Recursive Formula is a type of formula that forms a sequence based on the previous term value. What does that mean? Check out the example below for a clearer picture:

Example #1:

-> First, let’s decode what these formulas are saying.

-> We found the sequence 2, 6, 10, 14, 18. Since we only needed the fifth term to answer our question, we know our solution is 18.

Example #2:

-> First, let’s decode what these formulas are saying.

***Note this was written in a different notation but is solved in the exact same way!

-> We found the sequence 1,3,9. Since we only needed to find the third term to answer our questions, we know our solution is 9.

-> First, let’s decode what these formulas are saying.

-> We found the sequence 4,10, 28. Since we only needed to find the third term to answer our question, we know the solution is 28.

Practice Questions:

Solutions:

Still got questions? No problem! Check out the video above for more or try the NYS Regents question below, and please don’t hesitate to comment with any questions. Happy calculating! 🙂

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***Bonus! Want to test yourself with a similar NYS Regents question on Recursive Formulas? Click here!

Reflections: Geometry

Greetings and welcome to Mathsux! Today we are going to go over reflections, one of the many types of transformations that come up in geometry. And thankfully, it is one of the easiest transformation types to master, especially if you’re more of a visual learner/artistic type person. So let’s get to it!

What are Reflections?

Reflections on a coordinate plane are exactly what you think! When a point, a line segment, or a shape is reflected over a line it creates a mirror image. Think the wings of a butterfly, a page being folded in half, or anywhere else where there is perfect symmetry.

Example:

Step 1: First, let’s draw in line x=-2.

Step 2: Find the distance each point is from the line x=-2 and reflect it on the other side, measuring the same distance. First, let’s look at point C, notice it’s 1 unit away from the line x=-2, to reflect it we are going to count 1 unit to the left of the line x=-2 and label our new point, C^|.

Step 3: Next we reflect point A in much the same way! Notice that point A is 2 units away on the left of line x=-2, we then measure 2 units to the right of our line and mark our new point, A^|.

Step 4: Lastly, we reflect point B. This time, point B is 1 unit away on the right side of the line x=-2, we then measure 1 unit to the opposite side of our line and mark our new point, B^|.

Step 5: Finally, we can now connect all of our new points, for our fully reflected triangle A^|B^|C^|.

Practice Questions:

Solutions:

Still got questions? No problem! Check out the video above or comment below! Happy calculating! 🙂

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Looking to review rotations about a point? Check out this post here!

Algebra 2: Rational Exponents

Piecewise Functions: Algebra

Greetings, today’s post is for those in need of a piecewise functions review! This will cover how to graph each part of that oh so intimidating piecewise functions. There’s x’s, there are commas, there are inequalities, oh my! We’ll figure out what’s going on here and graph each part of the piecewise-function one step at a time. Then check yourself with the practice questions at the end of this post. Happy calculating! 🙂

What are Piece-Wise Functions?

Exactly what they sound like! A function that has multiple pieces or parts of a function. Notice our function below has different pieces/parts to it. There are different lines within, each with their own domain.

Now let’s look again at how to solve our example, solving step by step:

Translation: We are going to graph the line f(x)=x+1 for the domain where x > 0

To make sure all our x-values are greater than or equal to zero, we create a table plugging in x-values greater than or equal to zero into the first part of our function, x+1. Then plot the coordinate points x and y on our graph.

Screen Shot 2020-07-21 at 10.05.00 AM.png

Translation: We are going to graph the line f(x)=x-3 for the domain where x < 0.

To make sure all our x-values are less than zero, let’s create a table plugging in negative x-values values leading up to zero into the second part of our function, x-3. Then plot the coordinate points x and y on our graph.

Ready to try the practice problems below on your own!?

Practice Questions:

Graph each piecewise function:

Solutions:

Still got questions? No problem! Check out the video above or comment below for any questions. Happy calculating! 🙂

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***Bonus! Want to test yourself with a similar NYS Regents question on piecewise functions? Click here.

Intersecting Secants Theorem: Geometry

Ahoy! Today we’re going to cover the Intersecting Secants Theorem! If you forgot what a secant is in the first place, don’t worry because all it is a line that goes through a circle. Not so scary right? I was never scared of lines that go through circles before, no reason to start now.

If you have any questions about anything here, don’t hesitate to comment below and check out my video for more of an explanation. Stay positive math peeps and happy calculating! 🙂

Wait, what are Secants?

Intersecting Secants Theorem: When secants intersect an amazing thing happens! Their line segments are in proportion, meaning we can use something called the Intersecting Secants Theorem to find missing line segments. Check it out below:

Let’s now see how we can apply the intersecting Secants Theorem to find missing length.

Screen Shot 2020-07-14 at 10.45.29 PM.png

Step 1: First, let’s write our formula for Intersecting Secants.

Step 2: Now fill in our formulas with the given values and simplify.

Step 3: All we have to do now is solve for x! I use the product.sum method here, but choose the factoring method that best works for you!

Step 4: Since we have to reject one of our answers, that leaves us with our one and only solution x=2.

Screen Shot 2020-07-14 at 10.14.41 PM.png

Ready to try the practice problems below on your own!?

Practice Questions: Find the value of the missing line segments x.

Solutions:

Screen Shot 2020-07-20 at 9.30.55 AM.png

Still got questions? No problem! Check out the video above or comment below for any questions and follow for the latest MathSux posts. Happy calculating! 🙂

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To review a similar NYS Regents question check out this post here.

Absolute Value Equations: Algebra

Happy Wednesday math friends! Today, we’re going to go over how to solve absolute value equations. Solving for absolute value equations supplies us with the magic of two potential answers since absolute value is measured by the distance from zero. And if this sounds confusing, fear not, because everything is explained below!

Also, if you have any questions about anything here, don’t hesitate to comment. Happy calculating! 🙂

Absolute Value measures the “absolute value” or absolute distance from zero. For example, the absolute value of 4 is 4 and the absolute value of -4 is also 4. Take a look at the number line below for a clearer picture: