Math 10 – Week 8

This week in Math 10 we focussed on slopes. I personally have never done or seen slopes before but after doing them this week I see how simple they are once you know what you are doing.

In this blog post I will focus on on how to find the slope of a line.

There are two different ways to find the slope depending if you have the line in front of you or if you are given coordinates. Those are the two formulas, in which you should know to get the slope.

Let’s take this example for when you are given the line. My first step is to determine the rise and run. To do this I am going to count up first, and then to the side. If you count down then your rise is negative and if you count to the left for your run then the run is negative.

After you find the rise/run you simply just divide the two numbers. If they don’t divide leave it in a fraction and simplify it as far as you can.

Now if you are given the coordinates you are going to follow the formula given above. A common mistake is people mix up the X and the Y, but remember to put the Y on the top of the fraction line.

Once I get to this point in my equation I can subtract 3 and 7, 8 and 3. Once I do that I will divide or simplify my fraction and I have my slope.

Now that we did the basics we will do a harder question.

As you can see in this I followed the exact same steps as I did before. I subtracted Y2 from Y1 and then X2-X1. Finally divided but in this case left it in a fraction.

Just like that you know how to find a slope. It really is very simple you just need to know the formulas and plug in the correct numbers!

Math Blog Post- Week 7

This week in Math 10 we did our Functions & Relations unit. In this unit we quickly covered a few different topics but in this blog post I will focus on functions. I will explain what a function is and how to identify one in any type of graph or table.

What is a function? A function is when none of the input numbers are the same unless they share the same output number. So what’s the difference between a function and a relation? A relation is the relationship between the input and output numbers and a function is just one output for each input. A relation is a vast term, while a function is more specific.

In this example with the coordinates, I can identify that the relationship between these numbers is a function. There is no one way to identify if it is a function. You just need to go through all the input numbers and make sure they all have their own unique output.

In this example using a table of values I can see this is a function because same thing with the coordinates, all in the input numbers have their own individual output numbers. I find a table of values makes it easier to identify because they go down in a row.

In this table of values I can see that one is an input twice. Because they share the same output this is a function. If the 5 were any other number except for 5 this would just be a relation.

If you are given a graph like this the first step is to write down all the coordinates and then identify if it is a function or not.

Now that I have written out all the coordinates I can see this graph represents a function.

Functions are very easy to identify once you understand what one is. Something that confused me when first learning about function was that if an input number is put in twice it is still a function as long as the output is the same. To easily identify is it as a function write it out in way that works best for you. If it is given to you in the form of coordinates write it out as a table of values if that would help you!

 

Math 10 – week 6

This week in Math 10 we finished up our polynomials and factoring unit. In this blog post I am going to explain the third part of factoring 1-2-3, factoring trinomials! I will explain how to do it and then show an example.

There are different ways to approach factoring trinomials but I am going to show the method that works best for me and what I like to do.

Step 1: The first thing I do when I get my question, is write P and S that stand for product and sum. Because I know whatever multiples to equal my product must add to equal my sum. So writing it out can help you see the problem and get the result quicker I find.

Step 2: The next thing I do is figure the two number that are going to work. It can help to write out a list of what multiplies to give you a product of 10.  I can easily identify that 5 and 2 will give me a product fo 10 and sum of 7. But my problem here is that my sum is a negative number. So here I am going to use the multiplication laws that tell me if I have two negatives when multiplied together they must give me a positive answer. And by doing this I will end up with an answer of +10 and -7.

Step 3: When factoring a trinomial the answer is always going to be in two brackets. Because I see I have a squared, I am going to put a in both and the brackets. And my last step is very easy, you put -5 in one bracket and -2 in the other.

Step 4: You don’t have to do this step but you can always take your factored question and solve it to make sure you factored correctly.

Those are the simple steps to factoring a trinomial. I am going to solve another one following the same steps I showed above.

Those are the simple steps to solving a trinomial. I find with practice you don’t even need to write out the product and sum but at the start it really helped me.