This week in math, we did a review of linear relations. I think the most important thing we learned this week was continuous and discrete variables.

A continuous variable is more of something you can measure or track, for example speed, to get to 100 km/h it will go from 1-100 hitting every number and each decimal and number has a meaning so on a graph we would connect the dots like this:

A discrete variable is basically the opposite of a continuous variable, each decimal dosent have a meaning, for example if you are counting the number of objects, you cant say 1 and a half, there is only 1 or 2 nothing in between. So for this we do not connect the dots and leave them as is like this:

This week in math 10, we started trigonometry, I think by far the most important thing we learned was the mnemonic device known as SOH CAH TOA which helps with finding the angle of a triangle. I will show you 2 examples where SOH CAH TOA shows us which sign to use on our calculator.

Example 1:

The first is to name each line using the letters A, H, and O. You want to put the H on the longest line which in this example would be the line with 16.5. Next, put the O on the opposite side of the angle so in this case, the opposite side of the 38 is on the right line so you would put an O there. Lastly, put the A on the one with no number and in this case, would be the line with the letter D.

After naming each then that is when SOH CAH TOA comes in handy. You want to ignore the letter on a line with no numbers or letters, in this case, O. And then look in SOH CAH TOA for which has an A and an H, which would be CAH. Now you know to use cos (cosine) on your equation and calculator. Now you want to write your equation like this:

Now you want to put the 16.5 on top. But it needs to now go before the COS so you would rewrite your equation like this.

Now put 16.5 cos 38 into your calculator and you should have the answer of 13.

Example 2:

This time let’s do an equation with sin instead of cos. It’s basically the same steps just with different numbers.

First, just like before we want to name each line.

Then using SOH CAH TOA we see that we need one with H and O which is SOH. Now write your equation using sin. Just like before, put the number above and at the front and put it into your calculator and you will have your answer.

And that’s all you need to do

This week in math 10 we learned integral exponents and scientific notation. I think that the integral exponents were the most important this week so here is how to do them.

So here is an example (-2a^3) ^-3 x 3a^12

First, do what’s in brackets on the right side and add the ^-3 to the 2, and then change a^3 to a^-3

Then you want to change it into a fraction

Do the powers again and then you should have -1/8a^-9 x 3a^12

Multiply the equation to get the answer 3/8 a^3

This week in Math 10, I’d say the most important thing we learned was how to find the LCM (lowest common multiple) and the GCF (greatest common factor) of multiple numbers using prime factorization.

Steps to find LCM:

The first step is to find all the factors of both numbers. In my opinion, the easiest way is with a factor tree. Simply write your number and then write beneath it the 2 numbers that multiply into your number, for example:

After finishing the tree, write down all the factors in an equation like this:

Make sure to do the same for both numbers and then you want to compare them and circle each number the 2 have in common but only vertically or diagonally, you can not do sideways

After, make an equation with the numbers that were circled and then put them in brackets, after that you can add the rest of the numbers to the equation but outside of the brackets like this. Multiply them all and you have your answer.\\

For the GCF it is basically the same except after you write the equation you remove any numbers without a pair from the equation, for example: