This week in math we learned about functions and relations and we learned about domain and range.

Here is an example from our workbook of something we learned:

In the question, we are asked to figure out what the answer would be if f=2.

The first thing we have to do in an equation like this is to plug in our given number wherever we see x.

After doing so all you have to do is solve the equation to get your final answer which in this case will be 3.

This week in math we had our big mid term and learned a bit about linear relations!

On behalf of me not doing well on my midterm i will show you a question from a previous unit i struggled on.

This question is from our prime factorization and exponents unit.

Our first step to answering this question is to multiply our exponents.

Since our whole question is inside of brackets that means that the exponent has to be multiplied with everything inside.

In this photo i just multiplied everything together ( which means adding together exponents ) so i could simplify our question.

We aren’t done here though, we have to get rid out our negative exponent.

In this photo all i did was put out simplified form into fraction form. I knew i had to put the 9a to the power of 10 on the bottom because that’s how we turn it positive.

This is a representation of what i did in the previous photo.

This week in math we finished up our polynomials unit.

Here is an example of something we have learned.

The first thing we have to do is see if we have anything in common with each of our terms. If you look at the question you can see that they can all be divided by four. So first we’re going to do is divide each term and then write it out in the simplified form.

After I divided it we always have to bring down the number we divided it by, which in this case it’s four, and then we just place it in front of our bracket with our simplified terms inside.

We aren’t done here. We need to break apart these terms since we have an X squared in our brackets which needs to be simplified.

Seen above, i had to figure out 2 numbers that would both multiply to get out last number and add up to get our middle number. I spread out X squared out into both brackets since we would multiply them together and then i put a negative 8 because our last number is a negative and because -8 added to 1 is -7.

This week in math we looked further into solving and factoring polynomials both positive and negative.

Here is an example:

our first step when we see a question like this is to examine it and see if we can divide anything. So for this question we notice that all three of our terms can be divided by five.

in the image above all I did was divide each term by five and then rewrite the question. The reason that we want to figure out if we can divide first is because it makes our question a lot easier for us to solve. After simplifying the question our next step is to figure out the 2 variables we can use for both our last numbers (4 and 3) This question is a bit easier for figuring this out because our last number which is three is a prime number so we know it only has one set of numbers it’s divisible by. in any other question we would need to figure out which divisors we would use so that they would add up to the first number which in this case is a four so we know that three and one would work for both numbers because 3•1=3 (for our last number) and 3+1 is 4 (for our first number).

in this last photo I took our simplified question and turned it into our answer by pulling out our numbers.

This week in maths we had our unit test on numbers and exponents and we learned a bit about trigonometry. In trigonometry, we learned about the angles of a triangle, sides of a right-angle triangle, ( like the hypotenuse, opposite and adjacent ).

The hypotenuse is always the longest side of the triangle, the opposite side is always the one across from the given angle in an equation. Finally, the adjacent side is the one next to the given angle.

Since we only had a short lesson on this, the one other thing we learned about was ratios.

We have the sine ratio, the cosine ratio, and the tangent ratio. The formulas for the ratios are shown below.

Here is an example of these rules combined in a question:

In this picture, you can see that I labeled the sides with letters instead of using the whole word, as it is easier and helps us keep the question neat. You can also see our given angle which is represented with an a.

The last step for this formula was to figure out our ratios. I plugged in all of the numbers whilst following our rules and came up with the answer this question was asking us which was to figure out each ratio.