Study Habits: Efficient or Effective?
Hello there! Welcome to my video on studying habits. Do you ever feel like you are spending a lot of time studying but at the end of the day, you feel like you really weren't that productive? Or maybe reverse, you spent really little time studying but end up being very productive? Today, I'll talk briefly about study habits and how we can balance being efficient vs being effective. These are very important when studying because who doesn't want to optimize their study time? Here's a few key things to note.
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33
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Struggling with Complicated Math Problems?
Hello there! Ever see a really complicated problem and think 💭 "Oh no! How am I supposed to solve that problem?! It's too complicated..." Well sometimes, you can break down the problem into simpler smaller components and tackle it that way. If you break down the problem into smaller components and realize you still can't solve it, then that is your weak spot. There's a quote that says this perfectly from Polya, which is "If you can't solve a problem, then there is an easier problem you can't solve. Find it."
Essentially, what the quote is saying is that a problem is only complicated and difficult to solve because within that problem, there is at least one component that you struggle with. In this video, I won't be solving any of the problems. Instead, I will break down each problem into the "necessary parts" or necessary understanding. If you know how to solve each of those "parts", then you should be able to solve the problem.
For extra credit, you can go ahead and solve the problems and let me know your answers in the comments! :)
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30
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Quick Multiplication (3 digits by 1 digit)
Hello! For today's video, we are continuing the series of quick multiplication. Math tips and tricks to help you look like a boss! We talked about multiplying 2 digits by 1 digit very quickly. This time, we talk about multiplying 3 digits by 1 digit very quickly. The three scenarios you will come across are 1.) no carry multiplication, 2.) simple case: 1 carry, and 3.) harder case: 2 carry.
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4
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Quick Subtraction - 2 Ways
Hello there! For today's video, I will talk about subtraction. It will be a shorter video today given the topic is on the simpler side. Today, I will talk about the 2 ways that we can do quick subtraction. The first way is to over subtract and add the extra that you subtracted. The second way is to under subtract and subtract the amount you missed.
For example:
89 - 11 = 78. You can subtract this normally and get 78. Using the first method, you can rewrite this problem as 89-19 which is 70 and then add back the 8 that you "subtracted too much of" which gives you 78. Using the second method, you can rewrite this problem as 89-10 which is 79 and then subtract the 1 that you "missed" which gives you 78. In simple subtraction, this won't seem significant as a time saver but for bigger numbers, you'll definitely shave off some time from using one of these methods.
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6
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Adding from Left to Right (Quick Estimation)
Hello there! For today, I will be talking about addition. Yup, just plain and simple addition. Traditionally, we are taught to do math from right to left. Add all the numbers in the ones place and carry over the number to the tens place. Add all the numbers in the tens place and carry over the number to the hundreds place and so on. In most real life scenarios, you will only need to estimate the sum of a list of numbers. If you add from the right to left, you don't have an estimate of the number until you add the entire list and go through all the columns. If you add from the left to right, you can get an estimate of what the sum will at least be around.
You'll see 3 separate examples where I estimate the sum of a list of numbers and then solve for the actual.
0:00 Intro to Adding from Left to Right
1:57 Example #1
3:17 Example #2
4:15 Example #3
5:59 Outro and Support my channel
Keep in mind that the further right you add, the more accurate your estimate will be.
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7
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Converting Repeating Decimals to Fractions Correctly (Strategic Shortcut)
Hi there! For today's video, I will be talking about the relationship between decimals and fractions. Previously, I talked about converting finite decimals into fractions and fractions into decimals. This video is specifically on decimals that have a repeating number so the decimal has a bar on top of the repeating numbers. For example, 0.3333..... or 0.9999.... could be represented as 0.3 or 0.9 with a bar on top of the 3 and 9, respectively. I did a video recently about fractions to decimals and you can watch that here: https://rumble.com/vl7v61-converting-fractions-to-decimals-how-to-skill-building-caveman-chang.html
Today, I will show you a different technique to converting this specific group of decimals into a fraction. The repeating number gets troublesome because it goes on forever but with this method, you can get rid of the repeating number and have the exact fraction. Let's take a look to see how!
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22
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How to Find if a Number is Prime or Not (Strategically)
Hello there! It's been a while since I did a video about prime numbers but today I want to show you how to best utilize your time when you are faced with a problem where you need to find out if the number is prime or not. Imagine a scenario where you don't have a calculator or google. Sometime we have really big numbers and we don't know where to even begin. Testing a bunch of random numbers isn't exactly the best method so we can try to estimate what the top limit of numbers we need to test up to is.
What you're going to do is find the square root of the number or the closest whole number and test the prime numbers until that number. For example, let's take a look at 81. Imagine we didn't know if 81 was a prime number or not. The square root of 81 is 9 so all we need to do is test all the prime numbers up to 9, which are 2, 3, 5, 7. From these tests, we will find that 81 is actually divisible by 3 so it is not a prime number. In this video, I show the steps on finding the "upper limit" for prime numbers to test on two smaller numbers. I will then go over 3 different "bigger numbers" that are 3 digits. For the purposes of this video, I won't use HUGE numbers but you can definitely apply this to the bigger numbers.
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14
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Venn Diagram (2 & 3 Categories)
Hi there! For today's video, I will be talking about venn diagrams. Some people love venn diagrams and some people hate it. Usually, venn diagrams are commonly seen in English or Science contexts. Today, I will be talking about using venn diagrams to help solve problems, specifically math counting problems. I've talked a little about counting numbers in a previous video, if you haven't seen it, check it out here! https://rumble.com/vtanny-fundamental-counting-principle.html
In this video, I go over a number of examples where using a venn diagram is super helpful and allows you to visualize the word problems. For example, in your classroom, there are 15 students that like math, 13 students that like science. 7 students like both math and science, and 3 students hate both. How many students are there in your classroom. Isn't this a confusing problem because you're given so much information? You can use a venn diagram to visually see the problem. Let's jump into the video!
Don't forget, venn diagrams can have more than 2 circles, depending on the categories in the problem.
Practice problems that are covered in this video:
0:00 Introduction to Venn Diagrams
0:53 Practice Problem #1
3:46 Practice Problem #2
10:02 Practice Problem #3
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36
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Fundamental Counting Principle
Hello everyone, I'm super excited about today's video because I talk about the most basic thing that ends up somehow being pretty complex: COUNTING. We will be counting numbers today but not just any numbers, we are covering the fundamental counting principle. You know how sometimes people ask how many numbers are in between 0-100. Your first instinctual answer is 100 but actually, its 101 because we need to remember that 0 is also a number. In most of these types of problems, the main concern is that we need to count accurately. Don't overcount or undercount. Let's jump into the video and check out the different practice problems. The problems get more complex than just asking how many numbers there are. My favorite problem is Practice Problem #5. It tests you on your counting skills but also your understanding of the divisibility rule for 2 and 3.
Practice Problems covered in this video:
0:00 Intro to the Fundamental Counting Principle
0:34 Practice Problem #1
2:26 Practice Problem #2
6:28 Practice Problem #3
9:10 Practice Problem #4
11:25 Practice Problem #5
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33
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CHEATING the Systems of Equations (Unofficial Method)
Hello everyone, for today's video, I will go over the 3rd method which is an unofficial method to solve the systems of equations. This method works on a majority of problems and is the ultimate BRUTE FORCE method to solving systems of equations. There are 3 problems in the video.
Link to Substitution Method: https://rumble.com/vof37u-systems-of-linear-equations-using-the-substitution-method-how-to-examples-c.html
Link to Elimination/Cancellation Method: https://rumble.com/vodcr8-systems-of-linear-equations-using-the-cancellation-method-how-to-examples-c.html
Examples in this video:
0:00 Explaining the methods to solve systems of equations
1:41 Example #1 (Elimination Method)
3:50 Example #1 (Shortcut Method)
5:29 Example #2 (Shortcut Method)
8:57 Example #3 (Shortcut Method)
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26
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Most COMMON Word Problems - Distance Rate Time
Hello all, for this video, I will go over one of the most commonly seen word problem types: distance rate time. These problems are usually something like a painter can paint x number of walls in y number of hours, how long does it take to paint z number of walls. These problems will 100% show up on any algebra test that contains word problems. I will approach the same problems twice using two different methods: 1.) using the formula 2.) intuitively using brute force
Formulas:
1.) d = rt
2.) w = rtm with m being the multiple
Let's jump right into it!
Word Problems:
0:00 Introduction to Distance Rate Time Word Problems
2:45 Rate Problem #1 (Formula Method)
6:10 Rate Problem #1 (Brute Force/Intuitive Method)
8:36 Rate Problem #2 (Formula Method)
12:27 Rate Problem #2 (Brute Force/Intuitive Method)
14:16 Rate Problem #3 (Formula Method)
17:02 Rate Problem #3 (Brute Force/Intuitive Method)
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33
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Common Algebra Tests Word Problems
Hello everyone, as you can guess from the title of this video, yes...we are talking about word problems today. Do you dislike word problems just like everyone else? It's ok, today in this video I will guide you through the word problems. Your goal is to recognize what the word problem is asking you to find then you write out an algebraic equation that helps you find it. You will first need to identify the steps you take to find the variable that the word problem wants. When you have that, slowly write out the steps and it becomes your equation. I have 3 examples for you today and they're all pretty easy once you get the hang of it.
Word Problems:
0:00 Common Algebra Tests Word Problems
1:43 Word Problem #1
4:30 Word Problem #2
9:13 Word Problem #3
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34
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Properties of Logarithms
Hello, today I will continue the topic of logarithms. In a previous video, I went over some skill building practice examples that go over the definition of a logarithmic equation. If you haven’t seen that video, you can check it out here https://rumble.com/vqtcmu-logarithmic-equations-and-exponential-form.html
In today's video, I will go over the four properties of logarithms and explain a little bit about the history of logarithms. Let's jump into it!
The four properties of logarithms:
logb(xy) = logb(x) + logb(y)
logb(x/y) = logb(x) - logb(y)
logb(x^n) = nlogbx
logb(a) = logc(a) / logc(b)
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32
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Vertex Formula vs Vertex Form
Hello everyone! Today, I will go over the difference between the vertex formula and the vertex form. In this video, we will go over several practice problems together that help us understand how to find the x-coordinate of the vertex from a given equation in standard form. In order to find the y-coordinate, take the x-coordinate and plug it back into the standard form to solve for y.
Check out my video here where I talk about Vertex Form https://rumble.com/vqd122-completing-the-square-vertex-form.html
Standard form: y = ax^2 +bx + c
Vertex form: h = (-b)/2a
Vertex formula: a(x-h)^2 + k
The a and b in the vertex form are found from the standard form. The h and k in the vertex formula are the x and y coordinate from solving the vertex form and standard form for x and y.
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72
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Logarithmic Equations and Exponential Form
Hello, in today's video, I will be going over practice problems to work on your understanding of logarithmic equations. In this video, you will be given logarithmic equations with a variable and your goal is to solve the equations. You will need to put the logarithmic equation into exponential form so you can easily see what values you have and what variable you are looking for.
Logarithmic Equation: logb x = y
Exponential Form: b^y = x
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33
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Quadratic Formula and the Discriminant
Hello, in this video, I will talk about the quadratic formula. The quadratic formula is used to solve quadratic equations. There are 2 key components of the quadratic formula, the plus or minus sign and the (b^2-4ac). The b^2-4ac is called the discriminant and it helps us determine what the x-intercepts are if there are any.
If you haven't seen my other video on a quadratic formula practice problem, check it out here https://rumble.com/vnxi78-solving-equation-using-the-quadratic-formula-practice-problem-caveman-chang.html
Let's jump into the video, I hope you enjoy it. If you enjoyed this video, please give me a thumbs up, click the subscribe button.
Don’t forget to let me know in the comments below if you have any questions!
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28
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1
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Graphing Quadratics In Vertex Form
Hello everyone, for today I will be covering the topic of graphing quadratics. In this video, you will see the quadratic equations either shown in vertex form or converted to vertex form.
If you haven’t seen my previous video on vertex form, check it out here https://rumble.com/vqd122-completing-the-square-vertex-form.html
There are a few components of the vertex form. The parent function of the quadratic parabola is y = x^2. The variables in the vertex form tell us different things about the quadratic.
a: whether the parabola opens facing upwards or downwards (positive or negative) and if the parabola is skinnier or wider
h: horizontal shift
k: vertical shift
Let me know if you have any questions in the comments below.
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26
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Completing the Square (Vertex Form)
Hello there! For today’s video, I will be talking about completing the square. This is essential in understanding how to graph a quadratic equation. We will be using a formula to complete the square and manipulate the equation around to be in the vertex form. The vertex is the midpoint of the parabola ( the shape of the graphed quadratic equation). Once we find the vertex, we know where the parabola “starts”, all the points after are equidistant from each other which creates the U shape of the parabola.
Formulas used in this video:
1.) y = (x-h)^2 + k
2.) y = x^2 + bx + (b/2)^2
3.) y = (x + (b/2))^2
Notice that formula 3 is a variation of formula 2. Formula 3 will help you get to the vertex form (formula 1)
Don’t forget to let me know in the comments below if you have any questions!
Sections of the video:
00:00 Introduction to Completing the Square
00:43 Changing the quadratic equation to vertex form
01:22 What is the vertex?
02:00 The formula for Completing the Square
03:53 Manipulating the quadratic equation into vertex form
06:21 Example #2
09:05 Example #3
13:34 Example #4
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82
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How to Graph Linear Inequalities
Hello everyone! I hope you had a wonderful thanksgiving with your friends and family!
Today, I will talk about how to graph linear inequalities. A key thing you need to note is the inequality sign (greater than, greater than or equal to, less than, and less than or equal to) If the sign has a "or equal to", then the line you draw on the coordinate plane will be a solid line. If the sign is just a greater than or less than, the line you draw on the coordinate plane will be a dashed line. Regardless of the sign, you will need to shade one side on the line. You can find out which side to shade by picking a point on either side and plugging it into the inequality. Shade in the side where the point plugged into the inequality makes it true. Usually, the easier point to pick is (0,0) unless the line has a point (0,0) then just pick a different point.
Thanks for reading! I hope you enjoy my video! Let me know in the comments below if you have any questions.
Timestamps:
00:00 Intro to graphing linear inequalities
01:19 Practice Problem #1
04:33 Practice Problem #2
07:06 Practice Problem #3
08:35 Practice Problem #4
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26
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Slope: Parallel vs. Perpendicular Lines
Hello, in this video I talk about 2 different types of lines: parallel and perpendicular. For parallel lines, the slopes are the same because these are lines that never intersect at any point. Perpendicular lines are lines that intersect at a 90 degree angle so the slopes will be negative reciprocals of each other.
In this video, you will work through practice problems with me so you can understand the relationship between slope and point slope forms. You will be given the slope of a line and a point that the other line passes. From the information given, find the line in point slope form. Let's jump right in!
Let me know below in the comments if you have any questions.
Timestamps:
00:00 Introduction to Parallel vs Perpendicular Lines
01:51 Practice Problem #1 - Parallel
04:50 Practice Problem #2 - Perpendicular
07:16 Practice Problem #3 - Parallel
10:54 Practice Problem #4 - Perpendicular
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17
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Finding Line Using Only Slope - Point Slope Form
Hi everyone! For this video, I will tell you that all you need to know is the formula for slope.
m = (y2-y1)/(x2-x1)
From this formula, you actually can find out the other two formulas: the point slope form and the slope intercept form. If you could only memorize one formula to find lines with slope, you should remember the slope formula. At the beginning of the video, I explain how to get from m = (y2-y1)/(x2-x1) to y-y1 = m(x-x1) and y = mx + b. For the second part of the video, I go over a few examples on how to find the line in point slope form when given the slope and a point that the line passes.
Let me know in the comments below if you have any questions. Thanks for watching!
Timestamps:
00:00 How to convert slope formula to point slope and slope intercept
00:39 Covert slope to point slope formula
02:24 Covert point slope formula to slope intercept formula
04:22 Practice problem #1 (solve together)
06:16 Practice problem #2 (solve together)
07:40 Practice problem #3 (try yourself)
09:17 Practice problem #4 (try yourself)
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Finding Slope (m)
Hello there! Today I will be going more in detail about slope because I only briefly talked about it in my last video. Slope is the relationship between two different points. If you haven't seen my last video, check it out! https://youtu.be/xjIZE2MunNU I talk about graphing basic linear equations using the slope intercept method.
You can see slope written as many different forms. M is the variable that represents slope. You may also see the notation of "triangle y" over "triangle x". The triangle is actually a delta which represents the change in y over the change in x. The slope is the ratio between the change in y in relation to the change in x. Breaking it down even more, you see (y2-y1)/(x2-x1). To find the slope, you can just take the two points on the coordinate plane and plop them into the equation. You can also learn how to pick points that will satisfy slopes that are given in the problem.
Thanks for checking out this video! I hope you enjoy it.
Timestamps:
00:00 Introduction to finding slope
01:28 Formula to find slope
02:26 Finding out which points to label as (x1,y1) and (x2,y2)
03:27 Finding out slope between 2 points
04:20 Practice finding slope
07:09 Points given on a line all have the same slope
09:28 Find points that satisfy the slopes given
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18
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Graphing Basic Linear Equations
Hello! Today, I will be talking about how to graph basic linear equations. There are two methods that I will go over. The first one is using a "t-table" where we plug in x and solve for y. We make a table of the x and y then we plot them onto the coordinate plane and draw a line. This method is extremely tedious. The second method is the slope intercept method.
Slope Intercept Method: y=mx+b
In this equation, m is the slope and b is the y-intercept. By definition, slope is the change in y (how high from the point ) over the change in x (how wide from the point). The y-intercept is the point where it crosses the y-axis. The x-intercept is the point where it crosses the x-axis. Using the slope intercept method, it will be much easier to graph these basic linear equations. Let's jump right into it! I hope you enjoy this video, let me know in the comments if you have any questions.
Timestamps:
00:00 Intro to Graphing Basic Linear Equations
00:14 First Method to Graph Basic Linear Equations
00:34 T Table
02:03 Second Method to Graph Basic Linear Equations (Slope Intercept)
03:30 What is a slope?
04:18 What is an intercept?
05:56 2nd Example to practice the slope intercept method
07:30 3rd Example to practice the slope intercept method
09:04 Final Example to try on your own!
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133
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Plotting and Identifying Points on a Coordinate Plan
Hello! For this video, it will be broken into two parts: 1.) Plotting Points on a Coordinate Plane(All Quadrants) and 2.) Identifying Points on a Coordinate Plane.
Coordinates of a point will be written in (x,y) form. The x represents its value on the x axis. The y represents its value on the y axis. The center point of the coordinate plane is (0,0) which we call the origin. Values on the x axis that are to the right of the origin are positive and to the left are negative. Values on the y axis that are above the origin are positive and below are negative. I have included the timestamps below so you can jump right to the problems. Let me know in the comments if you have any questions!
Timestamps:
00:00 Intro to video
00:11 What is a coordinate plane?
01:09 Notation for point (x,y)
01:36 Plotting Point A
02:27 Plotting Point B
03:25 Plotting Point C
03:50 Plotting Point D
04:38 Plotting Point E
05:04 Plotting Point F
05:53 Part 2: Identifying coordinates when given points
06:35 Identifying coordinates for Points A, B, C with me
08:00 Identifying coordinates for Points D, E, F by yourself
For more math videos like this, be sure to subscribe to my channel https://rumble.com/user/CavemanChang
Hope you enjoyed my video! Thank you for watching!
Credits:
Custom Titles: Simple Video Making
Link: https://www.youtube.com/channel/UCOsP...
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Finding Area and Perimeter of Triangles in a Square
Hello! For this video, I will be teaching you about area and perimeter, specifically for triangles that are within a square. Pay close attention because this might be similar to problems that appear on standardized math tests.
Problem of the Video: ABCD is a square. Find the sum of the perimeter and the sum of the area of the four small triangles. The square is drawn on the board in the video.
Let me know in the comments if you have any questions!
Timestamps:
00:00 introduction to the problem
00:36 What do we know about the problem?
00:51 Finding sum of area
01:59 Using the Pythagorean Theorem
02:45 Finding sum of perimeter
For more math videos like this, be sure to subscribe to my channel
https://rumble.com/user/CavemanChang
Hope you enjoyed my video! Thank you for watching!
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