Category Archives: Math 10

To solve a system using elimination you need to see which number you will need to cancel out.

ex.

3x + 2y = 9

2x + 6y = 6

in order to eliminate either the x or y value you will have to make a zero pair. in order to make a zero pair you must multiple each equation by a certain number to cross one out.

for this equation I am going to multiply the 3x and 2x so that I can cancel it out to find the y value first. In order to make it a zero pair i need to find a number they can both multiply to thats small. But in order to make a zero pair one must be positive and the other must be negative to equal to 0.

for 2 ill multiply that system by -3 and for 3 ill multiply the system by 2 so the gcf can be 6.

2(3x + 2y = 9)

-3(2x + 6y = 6)

this would change the systems to…

6x + 4y = 18

-6x – 18y = -18

then you need to remove the zero pair (-6x, 6x)

so the equation would now look like:

4y = 18

-18y = -18

then you add each number

so it would now look like

-14y = 0

s0 y would =0

(x, 0)

then to find the x you plug in one of the y values with 0 to either system

3x  + 2(0) = 9

3x =9

divide by 3 to put x by itself to = 3

so the answer would be

(3, 0)

The different lines that can be on a graph are vertical lines, horizontal lines, and oblique lines.

vertical

horizontal

oblique

vertical lines go along the y axis so the slope would be y/0 or “undefined” because you cant divide by 0.

horizontal lines go along the x axis so the slope for this line would be 0/x.

To determine if the line is negative or positive you need to look at the direction of the line and the height.

A line that would be negative would be starting on the left and goes higher on the right then the slope would be positive. But if the line is going from the left to right but going down then the slope would be negative.

Domain- x values, figuring out the width of the function

Range- y values, figuring out the height of the function

There are 2 different types of relations:

discrete– count

continuous– measure

Discrete is when the relation does not have a straight line and is labelled with a bunch of dots

Continuous is when the relation is labelled with a line not dots

Vocabulary:

functions

values

domain + range

graph

orgin

product

ordered pair

When writing out the domain and range, if the graph is discrete the domain and range should be listed as numbers (1,2,3,4,5). When writing out a continuous graph the domain and range will be an inequality, so the domain and range will be both the tallest or farthest point on the graph.

This week in math 10 I learned how to graph relations on desmos and how to find each dot. I had to graph these on little charts in my workbook. Then I had to find each coordinate and label where it was on the line.

To do this on desmos I had to type in the relation

one example would be

Then I had to see how the line was on desmos. I needed to check where it went on the x axis, y axis, or sometimes both. Then I found the coordinates that had a dot on the line. For this example, the coordinates (the dots on the line) were…

(-1, 0), (0, -6), and (6, 0)

There are obviously more coordinates, but these were the most noticeable ones that didn’t include a decimal.

Another thing I learned (remembered) this week that relate to this were how to create a coordinate and how to sketch it. First, I learned that the first number to show should be the number that goes along the x-axis. The x axis is the horizontal line on the graph. Then I learned that the second number is the one that goes along the 7-axis. This is the vertical line on the graph.

Most things I have learned this week are just little reminders from last year. I learned a lot about graphing and the s and y intercept and axis. So, most of these things I already learned just not in this much detail and difficulty.

This week during math 10 we have been reviewing linear relations that we learned about last year in math 9. I learned how to label a pattern.

example of an example would be:

2, 4, 6, 8… then you will have to figure out how much it goes up by and what number the pattern starts with.

So, for this one it would go up by 2 and starts at 2

So, the relation would be that it goes up by 2 and across by 2 if I would put it on a graph.

Another thing I learned is how to use a table of relations

example would be:

The left side of this table is going up by 1 and the right side is going down 2 twice then up 4 then down 2 twice and continuing…

In order to graph this you must write it in brackets

Example. (x,x)

In order to make this work you need to put the information from the x table first then the y table

So it would work like (0,4)

We are still learning about this chapter and this is what i’ve taken in so far.

this week we learned how to factor polynomials. We have been doing this for a few days now. the most important part in this chapter is the format

if a question is

ex.

to answer this, you need to find a number that can be added to equal to 5 while using those number to multiply to 6

some number for 5:

1+4, 2+3

multiples for 6:

1×6, 2×3

A similarity for these two numbers is 2 and 3

so the answer this question you need to separate the $x^2$

you can do this by putting them into separate brackets

(x + ) (x+ )

since both of the other number we are going to add them so that the numbers are positive.

now i need to replace the empty space with 2 and 3

(x+2) (x+3)

Now when checking answers…

you need to use the “claw” method.

The way to use this is to distribute all the numbers together then simplify the answer

One thing would be to add the x and the x

so the first part would be $x^2$

Then multiply the same x with the 3

then multiply the 2 with the other x

then lastly multiply the 2 and the three

now add all of those together…

$x^2 + 3x + 2x + 6$

for this you can add like terms together so i would add the 3x and 2x because they have the same variable

so my finalized answer would be $x^2 + 5x + 6$

This week in math 10 I learned how to find area and perimeter of a shape.

For perimeter you need to add all of the sides together

For finding area you need to multiply either the length times the width, or the base times the height.

This is helpful for answering any question when you are trying to find a square inside another square.

This week in period 2 math class, I learned something I’m not really familiar with. I learned about algebra tiles and how to make an equation with them.

In this image orange is positive and blue is negative, but for my class red is negative and blue is positive. But when there is no colour colored in is positive and white is negative.

some ways to use this would be solving an equation…

2x x 3

to answer you would put 2 positive rectangles to equal to 2x, then you would put 3 small squares to equal 3.

For me, these algebra tiles help me understand the question better than just looking at numbers and variables.

another way to use these algebra tiles is by…

so the question was

(2x + 1) (x + 3)

with this you write in a multiplication table, you put one half on top then one on the left side. Next you make a square of the whole thing. Then you use each space between variables to create new numbers. Then you calculate what is in the middle. For this question it would be:

This is what I learned this week and I’m finding it fairly easy and fun!

This week, week 5, we learned how to identify each triangles side in a word problem.

I learned how to tell which number goes where and which angle is which.

These are the notes I took about it on Thursday.