Category Archives: Math 11

Top 5 things I learned in Precalculus 11

This week I will be talking about the top 5 things I learned in Precal 11, not everything here will be about math.

My first topic is to be more prepared for my test. On the first test, I got a rude awakening with a very low mark, I think it is the lowest mark I have ever gotten. So knowing that I had to put in a lot of work after that and get back on track, even though on most of my tests this year I haven’t done my best. But I  learned a lot of good tricks on test taking. Some tricks I learned is to never erase on ur scrap paper and just cross it out. and if you skip a question write it at the top of the paper so you know where to find it and save time.

My second topic is on completing the square. Completing the square when an equation is a quadratic and is in general form: (y = ax^2 + bx + c)

My third topic is the Quadratic formula. The quadratic formula is also used when an equation is quadratic and in a general form. The reason I like the quadratic formula is that it was very new to me I haven’t learned anything like it before. The formula is :

It’s pretty simple you just plug the numbers in and solve like you normally would.

My fourth topic is the sine Law. I found this a cool way to find the sides and angles of a triangle.

The formula for the sine law is:

sin a/A = sin b/B = Sin c/C

In this question, we’re gonna be looking for a side.

So what we do is look for opposites. so A>70 is the opposite of 50.3 and B>49 is the opposite of x

So it will be sin70/50.3 * sin49/x were going to cross multiply which ends up being:

sin49*50.3/sin70*x we take out x and we are left with

sin49*50.3/sin70 = x

then we punch in the numbers and we get 40.4.

and to find an angle you do the same thing but the number you get you have to put it through inverse sine to get ur answers.\\

My Fifth topic is the cosine law. Like the sine law, it is a cool and easier way of finding the sides and angles of a triangle.

The formula for the cosine law is

: a^2= b^2+c^2-2ab*cosA

Given this question

First, we input the numbers that we know into the formula.

a^2= 50^2 + 63^2 -2(50)(63)cos(48)

a^2= 2253

we square then we get

a= 47

Precalculus 11 started off with a really rough start and a not-so-smooth finish. But I did learn that for the next semester and years to come, I need to step my game up and can’t be doing the same thing I’ve done since middle school. I need to put a lot more effort into m school work for a better outcome. But I’m glad I took this class it was able to learn a lot of stuff and explore a whole different area of math.

 

 

Week 14 – Pre-Calculus 11- Sine Law

This week in math 11 we learned about the sine law. The sine law helps us fine an angle or side if a triangle.

The formula for the sine law is:

Sin a/A = Sine b/B = Sin c/C

Let’s do an easy question to start.

In this question, we’re gonna be looking for a side.

So what we do is look for opposites. so A>70 is the opposite of 50.3 and B>49 is the opposite of x

So it will be sin70/50.3 * sin49/x were going to cross multiply which ends up being:

sin49*50.3/sin70*x we take out x and we are left with

sin49*50.3/sin70 = x

then we punch in the numbers and we get 40.4.

and to find an angle you do the exact same thing but the number you get you have to put it through inverse sine to get ur answers.

 

 

 

Week 13 – Pre-Calculus 11 – Multiplying and dividing rational expressions

This week in pre-calculus 11 we learned multiplying and dividing rational expressions.

Let’s start off with a easy question. 3/n divided by 6/n
we can cross multiply here so we multiply 3 with n and 6 with n.

Now we can cancel out the n because there is 1 in the numerator and denominator.  so it will be 3/6

then we can simplify it to 1/2. But that’s not it, we have to add restrictions so that the n in the denominator won’t end up being 0. so in our case N cant equal 0.

 

Week 10 – precalculus 11 – How to graph a parabola

This week in pre-cal 11 we learned how to graph a parabola.

If given an equation like this.

then we use complete the square and stop at the standard form

So knowing how to complete the square we end up with this

since we have a stretch of 2 our pattern of 1, 3 and 5 multiples by 2 looks like 2, 6, 10.

and will have a vertex of (-2,-12)

and have a LOS of (-2,0)

the graph will look like this

Week 9 – Precalculus 11 – Finding the vertex

This week in Precal 11 we learned how to find the Vertex of a parabola

When given an equation like this:

2 is the stretch so the pattern 1, 3, and 5 would multiply by 2 but this doesn’t help us find the vertex just helps us graph the parabola.

-2 is what tells us what number it is on the x-axis. the origin is always (0,0) – numbers move right + numbers move left so -2 would move to 2 on the graph.

3 tells us how many spaces it moves up and down positives go up negatives go down.

so the vertex of this number would be (2,3)

here is a cheat sheet I like to use