Here are the Top 5 Things I’ve learned in Math 10.

1. Trigonometry is not necessarily hard, just confusing at first. As long as you know how to use a reference angle to find the cosine, sine, and tangent ratios, it is simple. Just make sure you know which side is the hypotenuse, adjacent and opposite by using the correct angle to reference it. As long as you get the correct angles, you’ll get the right answer. 
2. Know what all the different kinds of numbers are and how to categorize them. Also know your divisibility rules so you don’t spend a lot of time picking numbers that you think might divide in.
3. Remember how to use exponent rules so you don’t get the question wrong or get a really big answer.
4. Use your class time wisely so you can ask questions on topics you don’t understand, and ask to go over questions that were confusing or difficult so you will get them correct on the test.
5. Do all the homework assigned in the workbook because they use questions from there on the test, or finish all un-finished homework before the day of the test so you know what you are doing,

This week we mainly focused on arithmetic sequences and series. These two equations follow a different rule each, and the rule always applies for anything involving them.

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which the change is constant, such as adding by 2 or 3 each time.

What is an arithmetic series?

An arithmetic series is when the terms of arithmetic sequences are added together. This series also follows a specific rule.

Tn=t1 (n-1)d

Tn is the general term or rule. T1 is the first known term which has a specific value. If you get the first three or so terms, you can find out d, which is the difference. N is a number that is multiplied by the difference, but it has to be a natural number.

Sn=n/2 (t1+tn)

Sn is the symbol for the sum. To get this, you can take the answer you got from using the Tn=t1 (n-l)d method, and place the final term in the pattern in the n place.

This week we mainly focused on methods on how to solve equations. We covered 4 different ways, however, the main ones that normally are used to solve algebraically are substituition and elimination.

• Elimination mainly focuses on creating zero pairs. This is very helpful when all the variables have a coefficent that is not equal to 1. I will show an elimination equation below.
• Substitution is used to take numbers of one equation and place them into another equation.

Elimination:

Step 1: Find zero pairs

Step 2: Add zero pairs and other numbers together

Step 3: Continue adding and find the end result

Step 4: Reduce/divide fractions by -13, and here you have your final ‘y’ value

This week we started on our 9th unit of the year, which is the systems of linear equations. Since we just started, let’s just go over the basics.

What are systems of linear equations?

Systems of linear equations are 2 lines that are complete when 2 numbers are placed into the variable spot and makes the equation true.  These can also be called solutions, and are a set of numbers that make the sentence/equation true. There are 3 main kinds of systems that can be used for different kinds of lines.

What are the 3 main kinds of systems? 

• The first one is for a line with different slopes, which means in this case that the slope of m1 does not equal to the slope of m2. This kind of system only has 1 solution, and these lines cross the y-axis at a set point.

• The second system is for a line that has the same slopes. There are infinite solutions, and these are called coincident lines, which mean that they overlap and are on the same lines.

• The last main kind is for parallel lines. These lines will never cross eachother on the Cartesian Plane, and because of that, do not have the same solution. They do have the same slope, so m1=m2. However, they do not have the same y-intercept, and b1 does not equal b2. 

The screenshots/screencaps for my Math 10 Wonky Initials Project using desmos.com are inserted below.

This week, we learned about the different forms in which to represent an equation. There are 3 different kinds of these forms but some are used more or less than others, and I am going to focus on Point-Slope Formula.  Each of these forms is related to linear equations, and are useful for graphing. We also discussed coincident lines, which will be explained more in depth, thought they are pretty simple.

Point Slope Formula

The kind of form I am going to focus on is point-slope form. This has its own formula, which is seen below. This is how you write equations using this formula, and just plug the numbers from your input/output charts into the corresponding places in the sentence. So basically, the slope of the formula is multiplied by x1-x2, and that is equal to y1-y2. During this equation, if we write out the slope in its regular form, it can help us more. Most of these forms rely on us being able to isolate the y variable, so algebra will also be needed to complete this.

How can you find the x and y intercepts using this method? Well, if we have an equation like the one written below, we can pick out which value is in the x2 spot, and the y2 spot, and use this to create an ordered pair to start at. Since the number before the  x value is the slope, we can easily figure out multiple other ordered pairs by using this pattern and starting at the only known ordered pair.

Coincident Lines

What are coincident lines? These are lines that lie exactly on top of one another. It’s a pretty simple concept, but it is important and relative to when we look and observe the slope (rise/run) values of a line segment.