This week in Pre Calc we did our final review on rational expressions and equations as we have our unit test on Wednesday. the mistake I wanted to look over this week was on the skills check we did on Thursday.

At first, when doing this question I made a mistake when factoring. It’s important to look over your work cause a simple mistake while factoring can mess up your entire answer. I factored using -8 and 3 instead of -9 and 4. Factoring an expression like this is nothing new and something I’m capable of doing but I made a simple error by just guessing and not checking to make sure those numbers fit the expression and that completely changed my answer. In the end, I caught my mistake and redid the question. Another thing is I forgot to do my non-permissible values. It’s smarter to do these before solving the expression as these values relate to the beginning values.

This is how I ended up solving it. Since it’s a division question I factored everything and then used the reciprocal of the second expression and multiplied everything. This question isn’t difficult but a simple thing like factoring can really change your answer which is why it’s important to not rush and look over your work.

this week in math ten we learned about domain and range. I’d never done anything with domain and range before so I was a little confused at first but after watching some videos on Khan Academy I figured it out.

domain represents the x-axis and range represents the y-axis. domain is all the x values on a graph and range is all the y values. to find the domain and range you can look at a graph or make an equation

an example of one of these equations could be 2<x<8

with that equation, you would get a vertical line starting at 2 and ending with another vertical line that ends at 8

given a function f(x), the values that f(x) can take on constitute the range of the function, while all the possible x values constitute the domain

This week in math ten we learned about slope. I think I had been briefly introduced to this last year but we never went into a lot of detail about it. First slope is represented by the letter M not S and the main way to calculate it by using a graph is by using the formula rise/run. Rise and Run is used to look at how much the slope is going up by on the vertical axis and how much it changes on the horizontal axis. when you connect these dots they should make a diagonal line and if they don’t there are some other options like if there in a straight horizontal line than that means the Y value is equal to zero and if it’s in a straight line on the vertical axis it’s undefined. If the rise goes down it’s negative and if it goes up positive.  if the run goes to the left it’s negative and to the right positive.

You can always figure out the slope of a line if you have 2 points. If you are not given 2 points, you can find 2 points on the graph and use them to find the slope.

Here are some good things to know:
– m = slope
– (x₁, y₁) = point 1
– (x₂, y₂) = point 2
– rise = the difference in the y-values (y₂ – y₁)
– run= the difference in the x-values (x₂ – x₁)

x₁ = 4 and x₂ = 6
y₁ = 2 and y₂ = 1

Now we just need to plug these values into the slope formula:

m = rise / run
= (y₂ – y₁) / (x₂ – x₁)
= (1 – 2) / (6 – 4)
= (-1) / 2
= -1/2

So the slope (m) is -1/2.

this week in math ten I learned more on the topic of linear relations. linear inequalities and equations we’re a big part of math 9 but I did struggle with them a bit. This week we learned about linear patterns and how to plug in a certain number to get the answer for any pattern. you do this by using the x and y axis. I like using a t chart because it’s the most visual and straight forward way to figure out your equations. lets say you have a linear relation that starts at seven and goes up by seven. Your t chart will look something like this

__x__|__y__

1     |     7

2     |     14

3     |     21

now to find the patter we should first identify how much the number is increasing or decreasing by. after that we use x or whatever variable to make the equation

7x = y

this equation is easy because seven times 1 is equal to y 7 and seven times 2 is equal to 14 and so on and so on but sometimes you will need to add or subtract numbers to get the answer you need. you basically just need to find the number that will give you the correct answer every time and you’ll have to go through trial and error to get this answer sometimes.

this week I’ve been reviewing the past three units quite a bit because the midterm is coming up. two things i have reviewed quite a bit is negative exponents because that so far has been my worst unit and trig word problems. i think that trigonometry was my best unit but i still struggled quite a bit with it and I’ve been using the work book and Khan academy to try and improve my skills. I’ve done quite a bit of negative exponent review as well because that was something that confused me quite a bit but i think I’ve got a much better understanding of it now and i feel pretty prepared for the midterm.

This week in math ten i learned some new strategies about factoring polynomials. Mrs Burton taught us the 123 strategy and i found it to be very useful when trying to figure out how to factor different polynomial equations. 1 stands for one thing in common, 2 stands for how many terms and 3 stands for x^2 x and #. I found this strategy of identifying what kind of factoring it is very useful because it can be hard to identify the different kind of factors that your dealing with and how to go about solving the question. anyway i used this a lot while studying for the  upcoming test and i believe it will help me  quite a bit during that.

18^2 + 12x + 6

they all have 3 in common as the gcf

3(6x^2 + 4x + 2)

two is a prime number so you don’t have to do anymore

this week in math I learned about multiplying polynomials. I learned a bit a bit this last year but very little and I found that last week we we’re taught some very good strategies that have helped me a lot when figuring these out. I really liked using the multiplication grid when solving any equations or even when factoring equations. I find its effective and It lets me see the pattern in the numbers which I think has given me a better understanding of polynomials.

I struggled a bit when it came to figuring out area models but I asked some friends for help with that and I think I understand it now. I think that the multiplication table could even be great for multiplying large numbers and I find that once you find different strategies to solve equations polynomials are a lot easier then they seem.

this week in math we started learning about polynomials. From what I remembered from last year I thought polynomials would be pretty easy. but I had forgotten a lot of the terms and the equations you use to solve with. The first day I was confused but then I started to get use to the terms. some examples of that are degree, binomial, coefficient. I feel like the review this week has been good but one thing I learned was a lot of new strategy’s to figure out equations which involve multiplying polynomials. one of those was by using the distribution method of putting everything into smaller sections and multiplying them individually.

here is an example of that method

2(3x-1)

2(3x)    2(1)

answer= 6x-2

This week in math ten I learned how to calculate angles by using trigonometry ratios (sine,cosine,tangent) we had previously learned about this a bit last week but we learned about it more in depth this week! To do this you need to use the two measurements you have on the outside and use the inverse of whatever ratio you are using.

The equations should end up looking something like this

A = sin−1(x/y) 

i also learned about the angles of depression and elevation and how they can help us when solving word problems

This week in math ten I learned a lot of new stuff about right triangles and I learned a lot of new stuff about trigonometry. For me I never practiced anything to do with trigonometry so this was completely new stuff but it was a lot easier then I thought.

I learned about sine, cosine, and tangent ratios and how to put them into my calculator. I also learned that by using these ratios we can figure out the side of any right triangle. You need a calculator for this but I find that once you get the formula down it is a lot easier than I thought it would be.

One other thing I learned is that you can use similar formulas to figure out the inside angle of a triangle which is needed to use the sine, cosine and tangent ratios

example:

• Sin 30° = ½
• Cos 90° = 0
• Tan 45° = 1