Category: Grade 10

This week in polynomials we covered many different methods for ways to solve different polynomial questions. I had one question I was meaning to ask, it was “what method do we use in certain situations, and know do we know when to use each different one”. Before asking I was determined to try my best to figure it out myself. I took a bit of extra time to look at these different methods and investigate my question. After a bit of extra work I answered my own question, making a few notes of what to look for when trying to figure out what method to use. I made a video explaining only a few of the methods I looked into. I tried to explain my way of knowing how you know when to use each different method.

Different solving methods:

• the pattern
• GCF (greatest common factor)
• conjugates (zero pairs or difference of squares)

The pattern:

1. has to factor to a simple binomial
2. no leading coefficient (GCF first to reduce and simplify)
3. has to have x² in front (no exponent higher than 2)  if so reduce with GCF first
4. the last term has to have a factor that adds up to the middle term

GCF (greatest common factor)

1. all numbers have to have something in common
2. all numbers have to be divisible by the same # or variable
3. used to simplify the polynomial so you can do the pattern after

Conjugates:

1. no middle term
2. a factor of the negative last term has to equal 0
3. can use the pattern if you recognize that the middle term has t0 add to 0

This week in math 10 we learned how to find missing angles, which was differs from last week where we had to find the opposite, missing side lengths. Here is a short video I made explaining how to find a missing angle when only given 2 side lengths.

The unit we started this week was trigonometry. The main idea of this unit is to find side lengths and angles of right triangles when just given either the reference angle and or side lengths. The thing that was most interesting to me was finding missing side lengths of right angle triangles. When doing these questions the first 2 thing you want to do are label the triangle and have SOH CAH TOA written down as a referance. The next this is you need to figure out what one out of sin, cos, and tan uses the letters you need. In this case we are looking for what one used A and H, this would be CAH so therefor we are using cos.The next step is to just write your equation and solve,making sure to isolate the variable in this case its a. In the question I chose to show the variable is on the bottom, which means we have to reciprocate the fraction, therefor we have to do that to the other side also. Putting the cos and 39 degrees over one and then flipping it. Because what you do to one side you have to do to the other. (use the photos below to understand better)

This week I learned how to find a surface area and volume of a bunch of new shapes. But, the most interesting to me was the surface area and volume of a sphere. the formula is different than any other shapes. The cool thing is that the diameter is equal to the diameter or the radius x2, because it is the same all the way around.  If you roll it than it says the same. Another thing to add onto this is that the shape of a hemisphere is equal to half of a sphere, the word hemi meaning half. But when finding the surface area of a hemisphere you cannot just divide it by two, you actually have to add the area of the base to the final answer.

This week was one of the most challenging weeks of math ten so far. Full of new concepts and easy to fall behind. But it was also a big time for learning, completely new things. The most interesting things I learned this week was conversions. There are 2 ways to do this, either with the number line or multiplying the fractions. First, the number line. The sentence I use to remember all of the symbols is (Good Man king henry doesn’t usually drink chocolate milk usually never). All of these letters stand for a prefix, for example k stands for kilo and c stands for centi. The k,h,da,u,d,c,m all are just one apart on the number line and the 2 on either side, G M and n u, are 3 apart. You can use this just like you would a number line. Say you want to find how many cm are in a km. you want to only look at the first letter, the prefix. So you start at the first one, k, and then count how many spaces till you arrive at c, making sure to remember what way you are going, in this case it would be to the right. So you are moving the decimal 5 spaces to the right.

* something to note* if a letter is alone it starts at U because it has no prefix so it it just a unit // example 1000ml to L move on the number line from m to U.

The second way to do conversions is my multiplying fractions. The main idea for this is to get cancel out the units. For example, your trying to convert 3ft and 11 inches to inches. First you need to establish what you know. I know that there are 12inches in a foot. So you add it into a fraction, putting the ft on opposite sides of the fraction so they cancel out leaving you with only inches. Don’t forget to add the remaining 11 inches at the end!

This week we learned all about rational exponents. More specifically we learned how to change an power that has a exponent thats a fraction, to a root. These two things, a root and a exponent can be equal to each other. At first I was confused about where the denominator and the numerator go on the root. Which one is the index and what one stays an exponent. The phrase, flower power really helped me with this. Because in a flower the root is on the bottom, therefor the denominator, the number at the bottom of the fraction is the root/index .

root= bottom number of fraction

exponent= top number of fraction

The last part to this is if the fraction thats the exponent is negative. Because last week it was all about negative whole numbers as exponents, now we have negative fractions. There really isn’t much to do when the fraction as a negative. all you have to remember is that the root is never the negative one, it is always the exponent.

This week was all pretty much review except for one completely new concept, negative exponents. When I first was introduced to negative exponents I thought it was going to be the same answer, but just negative. For example I thought… (this is wrong)

When actually a negative exponent just means its a reciprocal of the answer with positive exponents. (right answer)

This whole week was filled with completely new concepts that I have never been introduced to before, even though there were things I learnt last year woven into it, the main ideas were new

to me. The coolest thing I learned this week was hard to choose because there was so many. Finally I came the conclusion that prime factorization was the biggest thing I learned. Prime factorization is one of the key parts to this chapter, used in almost all questions so far. The idea that you can break down a number by using prime factorization but it still means the same thing was the main thing that was cool to me.

Here is my example:

the prime factorization of 1,260…

1,260 is the same as 2∗2∗3∗3∗5∗7

therefor, 2∗2∗3∗3∗5∗7 can be a representation of 1,260