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Algebra 2 Cheat Sheet & Review

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! 🙂

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.

Algebra 2 Playlist:

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.

Algebra 2 Cheat Sheet & Review


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

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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!

Geometry Cheat Sheet & Review

Greeting math peeps! As promised here is the Geometry Cheat Sheet and Review made just for you to prepare for finals. On this page, you’ll also find links to the Geometry lesson playlist, the NYS Geometry 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! 🙂

Geometry 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 shapes, it’s on here.

Geometry Playlist:

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

Geometry 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.

Geometry Blog Posts:

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

Geometry Cheat Sheet & Review

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

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Get everything you need to know with this Geometry Cheat Sheet and Review! Download and print the pdf for reviewing Geometry 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!

Algebra Cheat Sheet & Review

It’s that time of year again, summer is coming, the vacation vibes are calling, but so, unfortunately, are the test cramming and non-stop class reviewing that is coming our way. Nothing like going over topics mentioned at the beginning of the school year to bring us down. How is one supposed to remember everything? Fear not, because I have made a special cheat sheet and review for Algebra, (with Geometry and Algebra 2/Trig. soon to be on the way). I hope you’re staying safe, cool, and calm as the end of the year approaches. Good luck on finals and tests and happy calculating! 🙂

Algebra 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 parabolas, it’s on here.

Algebra Playlist:

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

Algebra 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 Blog Posts:

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

Algebra Cheat Sheet & Review

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

Facebook ~ Twitter ~ TikTok ~ Youtube

Get everything you need to know with this Algebra Cheat Sheet and Review! Download and print the pdf for reviewing Algebra 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!

Finite Arithmetic Series Formula

Happy Wednesday math peeps! Today we are going to go over the Finite Arithmetic Series Formula; What it is, how to use it, and even do a little derivation. Before going any further though, please make sure you know how arithmetic sequences work here. If you have any questions, please don’t hesitate to comment below and to check out the video and practice questions below. Happy calculating! 🙂

What does it mean to find the “Sum of the Finite Arithmetic Sequence”?

We already know what an arithmetic sequence is: a sequence of numbers that forms a pattern when the same number is added or subtracted to each term.

Example:

But when what happens if we wanted to sum the terms of our arithmetic sequence together?

Example:

More specifically, what if we wanted to find the sum of the first 20 terms of the above arithmetic sequence?  How would we calculate that?  That’s where our Finite Arithmetic Series formula comes in handy!

Finite Arithmetic Series Formula:

Finite Arithmetic Series Formula

Looking at the above formula, I have to wonder, what happens if we are not given the value of the last term of the sequence for “a sub n”?  What would we do? Do not worry, because there is another way to use this formula if we expand and simplify it, check it out below:

*Bonus* Arithmetic Series Formula:

Plug in the arithmetic sequence formula for “a sub n,” then combine like terms.

Let’s take a closer look at what each part of our bonus formula represents below:

Finite Arithmetic Series Formula

Now that we have two formulas to work with, let’s take another look at our question now applying our finite arithmetic series formula:

Step 1: First let’s write out our formula and identify what each part represents/what numbers need to be filled in. Since we are not given the value of the last term, “a sub n” we can use the second bonus formula we previously derived.

Finite Arithmetic Series Formula

Step 2: Now let’s fill in our formula and calculate.

Finite Arithmetic Series Formula

Practice Questions:

1) Find the sum of the first 15 terms of the following arithmetic sequence:

4, 8, 12, 16, ….

2) Find the sum of the first 24 terms of the following sequence:

2, 7, 12, 17, ….

3) Find the sum of the first 32 terms of the following arithmetic sequence:

100, 97, 94, 91, ….

4) Find the sum of the first 50 terms of the following arithmetic sequence:

5, 7, 9, 11, 13, ….

Solutions:

1) 480

2) 1,428

3) 1,712

4) 2,700

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

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Looking to learn about Finite Geometric Series? Check out this post here!

Proving Similar Triangles: AA, SSS, & SAS

Happy Wednesday math peeps! TIn today’s post, we are going to go over Proving Similar Triangles, by going over:

1) What it means when two triangles are similar?

2) How to prove two triangles similar?

3) How to find missing side lengths given triangles are similar?

For even more practice, don’t forget to check out the video and practice problems below. Happy calculating! 🙂

What are Similar Triangles?

When two triangles have congruent angles and proportionate sides, they are similar.  This means they can be different in size (smaller or larger) but as long as they have the same angles and the sides are in proportion, they are similar! We use the “~” to denote similarity.

In the Example below, triangle ABC is similar to triangle DEF:

Similar Triangles

How can we Prove Triangles Similar?

There are three ways to prove similarity between two triangles, let’s take a look at each method below:

Angle-Angle (AA): When two different sized triangles have two angles that are congruent, the triangles are similar.  Notice in the example below, if we have the value of two angles in a triangle, we can always find the third missing value which will also be equal.

Similar Triangles

Side-Side-Side (SSS): When two different sized triangles have three corresponding sides in proportion to each other, the triangles are similar. 

Similar Triangles

Side-Angle- Aside (SAS): When two different sized triangles have two corresponding sides in proportion to each other and a pair of congruent angles between each proportional side, the triangles are similar. 

Similar Triangles

Let’s look at how to apply the above rules with the following Example:

Step 1: Since, we know the triangles ABC and DEF are similar, we know that their corresponding sides must be in proportion! Therefore, we can set up a proportion and find the missing value of length EF by cross multiplying and solving for x.

Similar Triangles

Practice Questions:

1) Are the following triangles similar?  If so, how? Explain.

2) Are the following triangles similar?  If so, how? Explain.

3) Given triangle ABC is similar to triangle DEF, find the side of missing length AB.

4) Given triangle ABC is similar to triangle PQR, find the side of missing length AC.

Solutions:

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

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Check out more posts on Geometry here!

Math + Art: Math Behind Perspective Drawing

Greetings! We are going to do something a little different today and explore Math + Art: Math Behind Perspective Drawing. For all the artists out there who tend to not generally gravitate towards math, this post is for you! There are many ways math can be connected to art, and in this post we will explore the role parallel and perpendicular lines play when it comes to drawing 3-D shapes. And for those who want to learn even more, don’t forget to check out the video below to see how 2-point perspective applies geometry and angles to create 3-D shapes.

What is Perspective Drawing?

Perspective drawing is an art technique that allows us to draw real life objects in 3-D on a flat piece of paper. Notice in the example below that buildings, trees, and power lines get smaller and smaller as we look into the distance just as they would in real life.

Math Behind Perspective Drawing

What are the Basics of Perspective Drawing?

Math Behind Perspective Drawing

There are two main things we need to know about perspective drawing.

1- Horizon Line: A horizontal line that goes across the entire paper. This represents where land and sky meet.

2- Vanishing Point: This is where many of our lines will be directed in order to create that 3-D affect.

Where do I Begin?

Step 1- Now that we have our horizon line and vanishing point, we can start by drawing a road. Use a ruler to draw two lines that lead to the vanishing point, this should resemble a triangle.

Step 2-From here we can start to draw a building by creating two straight lines that are perpendicular to our horizon line.

Math Behind Perspective Drawing

Step 3-Then line up the outermost corner of the building with the vanishing point using a ruler, and draw a line. Do this with each corner of our rectangle for a 3-D effect.

Math Behind Perspective Drawing

Step 3- continued….

Math Behind Perspective Drawing

Step 4- For the remaining lines, use parallel and perpendicular lines to finish off our building.

Math Behind Perspective Drawing

Step 5- Get creative! Add more buildings, windows, antennas, and anything else you might see in a city -scape. Use your imagination! 🙂

This method of perspective drawing is called one-point perspective because there is one vanishing point. But there are also 2-point and 3-point perspectives we can draw!

Want to learn how to do 2-Point Perspective drawing with 2 vanishing points!? Check out the video above to see how geometry and angles are related to this technique of perspective drawing!

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

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For more math + art, check out this post on fractals found in nature here.

NYS Algebra 2 Regents Review Playlist

Algebra 2/Trig. Common Core Regents Jan.2020 Playlist:

Happy Wednesday math friends! In today’s post, I bring to you the latest complete NYS Regents review playlist for Algebra 2/Trig. for January 2020. This is the perfect time to start reviewing for the NYS Regents test so I hope these videos can provide some help before the test cramming begins. Also, be on the lookout for the Geometry Regents review playlist coming out soon. Thanks so much for stopping by and happy calculating!

More NYS Algebra 2/Trig. Regents Review:

1) Synthetic Division

2) The Unit Circle

3) Graphing Trig. Functions

4) Solving Log Equations

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

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If you’re looking for a review on all of Algebra 2/Trig., don’t forget to check out the Algebra 2/ Trig, playlist on Youtube here:

What is the Discriminant?

Hi everyone and welcome to MathSux! In this post, we are going to answer the question, what is the discriminant? Before going any further, if you need a review on what the quadratic equation or imaginary numbers are, check out each related link! Also, don’t forget to check out the video and practice questions below. Happy calculating! 🙂

What is the Discriminant?

The discriminant is a formula we can use that tells us more about a quadratic equation including:

  1. The number of solutions a quadratic equation has.
  2. The “nature” of the roots of the solution (rational/irrational or real/imaginary).

Discriminant Formula:

The discriminant formula may look familiar! It is part of the quadratic formula and we have seen it before, using the very same coefficients a, b, and c from the quadratic equation.

What is the Discriminant?

How does it Work?

When we find the value of the discriminant of any quadratic equation, it will give us a value that tells us how many solutions (or roots) a quadratic equation has.  Remember when we say “roots” what we really mean are the x-value(s) of the quadratic equation that hit the x-axis. This value will also tell us if the solutions to the quadratic equation are rational/irrational or real/imaginary. Take a look at how it all breaks down below:

Now that we are familiar with the rules, let’s take a look at an Example:

Step 1: First let’s write out our quadratic equation and identify the coefficients a, b, and c so they are ready to be plugged into our discriminant formula.

Step 2: Now let’s write out and fill in our formula using the coefficients and solve.

What is the Discriminant?

Step 3: Now let’s analyze our answer! Since, we got a discriminant value of 36, notice that it is a positive perfect square! If we look back at our discriminant table, this tells us that our quadratic equation is going to have 2 real and rational solutions.

Practice Questions:

Find the discriminant, number of solutions and nature of the roots of the following quadratic equations:  

Solutions:

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! 🙂

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Finite Geometric Series Formula: Algebra 2

Happy Wednesday math friends! In today’s post we are going to go over what finding the sum of a finite geometric series means and then use the finite geometric series formula to solve an example step by step. If you need a refresher on geometric sequences before tackling these types of questions, don’t hesitate to check out this post here. Also, don’t forget to check out the video that explains everything you see here as well as practice questions below. Happy calculating! 🙂

What does it mean to find the “Sum of the Finite Geometric Sequence”?

We already know what a geometric sequence is: a sequence of numbers that form a pattern when the same number is multiplied or divided to each term.

Example:

But when what happens if we wanted to sum the terms of our geometric sequence together?

Example:

More specifically, what if we wanted to find the sum of the first 20 terms of the above Geometric Sequence?  How would we calculate that?  That’s where our Finite Geometric Series Formula will come in handy!

Finite Geometric Series Formula:

Finite Geometric Series Formula

Now that we have a formula to work with, let’s take another look at our question and apply our finite geometric series formula to answer the solution:

Step 1: First let’s write out our formula and identify what each part represents/what numbers need to be fill in.

Finite Geometric Series Formula

Step 2: Now let’s fill in our formula and solve with the given values.

Finite Geometric Series Formula

Try the similar practice questions below!

Practice Questions:

1) Find the sum of the first 15 terms of the following geometric sequence:

4, 12, 36, 108, ….

2) Find the sum of the first 12 terms of the following sequence and round to the nearest tenth:

128, 64, 32, 16, ….

3) Find the sum of the first 18 terms of the following geometric sequence and round to the nearest tenth:

400, 100, 25, 6.25, ….

4) Find the sum of the first 12 terms of the following geometric sequence:

3, 6, 12, 24, ….

Solutions:

1) 28,697,812

2) 255.9

3) 533.3

4) 12,285

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

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Check out similar posts for Algebra 2/Trig. here!

How to Construct a 45 Degree Angle with a Compass

Greeting math friends and welcome to another wonderful week of MathSux! In today’s post we are going to break down how to construct a 45 degree angle with a compass. We will take this step by step starting with a simple straight edge, then we will create a 90 degree angle, and finally we will bisect that 90 degree angle to get two 45 degree angles. If you have any questions please don’t hesitate to check out the video and step-by-step GIF below. Thanks so much for stopping by and happy calculating! 🙂

How to Construct a 45 degree Angle with a Compass

How to Construct a 45 Degree Angle with a Compass:

Step 1: Using a straightedge, draw a straight line, labeling each point A and B.

Step 2: Using a compass, place the point of the compass on the edge of point A and draw a circle.

Step 3: Keeping the same length of the compass, take the point of the compass to the point where the circle and line AB intersect. Then swing compass and make a new arc on the circle.

Step 4: Keeping that same length of the compass, go to the new intersection we just made and mark another arc along the circle.

Step 5: Now, take a new length of the compass (any will do), and bring it to one of the intersections we made on the circle.  Then create a new arc above the circle by swinging the compass.

Step 6: Keep the same length of the compass and bring it to the other intersection we made on our circle.  Then create a new arc above the circle.

Step 7: Mark a point where these two lines intersect and using a straight edge, connect this intersection to point A. Notice this forms a 90º angle.

Step 8: Now to bisect our newly made 90º angle, we are going to focus on the pink hi-lighted points where the original circle intersects with line AB and our newly made line.

Step 9: Using a compass (any length), take the compass point to one of these hi-lighted points and make an arc.

Step 10: Keeping that same length of the compass, go to the other hi-lighted point and make another arc.

Step 11: Now with a straight edge, draw a line from point A to the new intersection of arcs we just made.

Step 12: Notice we split or 90º angle in half and now have two equal 45º angles?!

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! 🙂

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Looking for more constructions? Check out how to construct a square inscribed in a circle and an equilateral triangle by clicking on their respective links!