Month: October 2017

Week 6-Pre Calc 11

katelynw2015

This week in Pre Calc 11we learned the 3 ways to solve quadratic equations. The 3 ways are;

1. Factoring

2. Completing the squares

3. Using quadratic equation

Factoring: this is the easiest way to solve quadratic equations

Example:

x^2-9x-22=0> Start off with your equation

 

x^2-11x+2x-22=0> find your 2 numbers that multiply to 22 and add to -9 (-11,2)

 

(x-11)(x+2)> factor by grouping common term (look at week 5 post)

 

x=11 x=-2> when you have your 2 bracketsyou take the opposite of both numbers and those would be what x equals, in this case the opposite of -11 is 11 and the opposite of 2 is -2

 

Completing the square: (b/2)^2

Example:

x^2+4x+1=0> start with your equation

 

(x^2+4x+4)+1-4=0> separate x^2+4x and +1 by using brackets, from there you take whatever number is b (4), divide it by 2 and then square it. For this equation our number will be 4, you then put that number beside 4x and you also put the opposite of that number (-4) and put it beside 1

 

(x+2)^2-3=0> you foil what’s in the bracket and take the copy bracket turn it into (x+2) which is the same as (x+2)(x+2). You also solve outside the bracket so 1-4=-3

 

latex (x+2)^2$ and 3

 

x+2=\sqrt{3} > by squaring (x+2)^2 it just becomes x+2

 

x=-2\sqrt{3} > you then isolate x so you need to move 2 to the other side by making it -2

Week 5- Pre Calc 11

katelynw2015

This week we started a brand new unit, Factoring polynomials. I’m very happy we stared this unit because this was one of my favourite units to do last year in math 10. We spent t most of the day on Friday when we started the unit doing review. Once I did the first question everything came back to me. In my opinion the easiest factoring to do is when you have perfect square binomials like x^2-100  All you need to do is square root both numbers and put them in brackets. Example: x^2-100

(x-10)(x+10)

i got this answer because I put the square root of x^2 (x) at the beginning of each bracket. I then took the square root of 100 which is (10) and I put that at the end of each bracket. x^2-100 has a negative sign, that means that one of the 10 will be positive and the other one will be a negative becasue 10x(-10)=-100

When you are factoring trinomials like x^2+7x+12 This trinomial is an easy trinomial because it has $larex x^2 at the front$ In order Govett solve this trinomial you need to find 2 numbers that multiply to 12amd add to 7. In this case we would use the numbers 3 and 4 because 3×4=12 and 3+4=7. These are the steps I take to get the answer

x^2+7x+12 > we start with the original equation

&$atex x^2+3x+4x+12$ > we take our 2 numbers that multiply to 12 and add to 7 and we put them into our equation in replace of the 7 in order to expand

x(x+3) 4(x+3) > we the night take the common factor out of each equation and put whatever is left over into brackets, in the step we should get the same numbers in both the bracket, I got (x+3)

(x-3)(x+4) > the 2 brackets turn into one and you take the common factor from each equation and put them into a bracket (x+4)

Week 4-Pre Calc

katelynw2015

This week was filled with many new and challenging lessons. We went over Absolute Values, Roots and Radicals, Adding and subtracting Radicals, Multiplying and dividing Radicals, and solving Radical equations. From all these lessons the one I found the most challenging was Multiplying and dividing Radicals.

Generally the idea is to:

1. Multiply coefficients

2. Multiply radicands

3. Simplify

one questin that I struggled with INV the beginning of learning multiplication was

2\sqrt{5}(3\sqrt{45}-8\sqrt{5}+\sqrt{20})

I have to admit, when I first saw the question I had no idea where to start.

I soon learned that you need to multiple the Radical that’s on the outside of the bracket (2\sqrt{5} and multiply it with the Radicals inside the bracket.

after this step is complete you should have: 6\sqrt{5×45}-16\sqrt{5×5}+2(10)

From the last equation all you need to do is solve everything inside the square root sign so you will end up with: 6(15)-16(5)+2(10)

Then all you need to do for the rest of the equation is solve so you should get:

90-80+20

=30

This was one of the first equations that we learned when started our multiply and dividing Radicals lesson. At the start it really confused me and looked very intimmidating, now when I see these types of questions I have no worries becasue I know how to solve them.