Burtonmath10

Week 16 – Math 10

This week i learned about solving systems using substitution

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All I really had to do was substitute x with 3y+2 for the second equation and when i solve for y, i can substitute it again for the first equation and find x.

Step 1: re-arrange an equation to x= ____ or y=____ if necessary

Step 2: substitute the equation into the second equation of x or y

Step 3: Solve equation

Step 4: substitute the found number back into the first equation and solve for the other variable

It is actually really just substituting for substituting because the equation already gives you the what x equals and you have to substitute in the other equation and find it and substitute again

 

Patterns in Polynomials

There are 3 patterns that can be found in polynomials:

  1. Multiply 2 Binomials

First term = multiply both terms together – x^2

second term = sum of last two terms together – 7x

 

third term = multiply both terms together – 12

this saves you time from double distributing and allows you to solve it quicker.

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2. Multiplying Conjugates

Ex. (x-2)(x+2)

 

Here is algebra tiles to show you how it works.

We can multiply the first term and last term to get the answer.

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If you look at the algebra tiles, the negative x and positive x cancels each other out and you are left with x^2 – 4

3. Perfect Square

If there is a question like x^2-25, it would be easy to solve as we know that since 25 is a perfect square we can find the square root, which is 5, and multiply it twice because we are just splitting the numbers. Therefore, (x-5)(x+5) is the factored form of x^2-25 by using perfect squares.

 

Week 9 – Math 10

I did not understand how to factor polynomials at first but I learnt that it is actually very easy.

week 9

First, I have to find the GCF. I made a venn diagram and to find the GCF of the two terms.

Then, I would divide the GCF to both terms. I would write the GCF as the coefficient and put the factored form in the brackets. To check, multiply the coefficient back into the equation to see if it matches up.

Week 8 – Math 10

mathI had problems multiplying polynomials that have more than one term within a bracket. I realized that I can separate the terms in the first bracket and multiply it to the second bracket. This is easier since all i have to do now is add them together and simplify it. This is called double distributive

 

Week 6 – Math 10

One of the questions i didn’t understand was finding missing sides of a right triangle.

I did not know how to use SOH CAH TOA to solve the missing lengths

First you have to find the reference angles. Then you plug in the corresponding ration SOH CAH TOA and you put it in the equation.

Here I solved using the ratio sin :

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Week 5 – Math 10

There was one question i found particularly challenging.

the question was convert 8 ft 3 inches to inches and then convert from inches to cm.

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I realized that i had to use the unit conversions that was given to convert from one unit to another.

What I determined was:

1ft = 30.48cm

1in=2.54cm

 

From here, we used these statements to create fractions with either side as the numerator or the denominator.

I have to cancel out the units by using fractions so that at the end we have the unit converted so in this case for the first part, 8ft was converted through a process of cancellation to 96in and i made sure to add on the extra 3in. And then I did the same for converting inches to cm. Through this process, it is easy to determine the equivalent unit conversion.

 

Week 4 – Math 10

I didn’t know how to write an equivalent expression when there is two square roots together.  I use to just square root it separately but i learnt that there was a shortcut to find the equivalent expression.

Example: √√ x^5

Instead of doing it separately, I could change make two \frac{5}{2} exponents like this ((x^\frac{5}{2})^\frac{5}{2}) because x^\frac{5}{2} = √ x^5

Now i know that since i have two exponents, i can use the power law and multiply it with each other. \frac{5}{2} x \frac{5}{2}=x^\frac {5}{4}

the answer is x^\frac{5}{4}