Category: Math 10

Week 8- Math 10

Ahhh solving triangles. You get one angle and one side, figure out the rest.

Once you get the hang of it, it’s quite fun. You’re given a triangle like this

To start, label the sides and list what you need to find.

Find everything that is missing (aka the stuff you just listed). We’ll start with angle F here. Since we know angle E is 90°, angle D is 50° and that the sum of the angles in a triangle must be 180°, we can just do 180-(90+50) to find angle F.

We can solve side EF and DE with the information we now have and SOH CAH TOA like so:

Week 7- Math 10

The most fun and interesting part of this week was learning how to find missing angles using sin, cos and tan on my calculator.

If I had a question like this (I labeled each side already and written SOH CAH TOA to figure out which one to use):

Just having sin, cos or tan would not be helpful because I am not given the degree of the angle inside. Instead, I would use each of those to the power of -1. Since I now know which sides I’m given and which formula to use, I can start to write my equation and solve it, like so:

Week 6- Math 10

Dear Math Blog Post,                                                                                                                          Week 6

My brain has gotten stuffed with more information. Every day, it’s something new. Do I always remember what I learned after the lesson? Not always but then they force me to use it the next day so I am forced to remember, and the information gets drilled into my head. This week, I remember learning how to find the volume and surface area of a hemisphere.

To find the volume of a hemisphere, you will use this formula:

For example, if you wanted to find the volume of a hemisphere with a radius of 2, this is what you would do:

When you do the surface area, it gets slightly more math-y. There are 2 exposed parts in the surface area of a hemisphere; the bottom half and the circle on top. When you calculate the surface area, the two must be added together.

The formula and an example question for finding the surface area of a hemisphere are in the picture below.

Week 5- Math 10

In math 10 this week, I learned how to convert units such as feet to inches or imperial to metric.

For example, I had a question where the I got was in meters cubed but the question asked me to have it in liters. The answer was 689.64^2m. To convert it into meters I did this:

Because the m^2 cancels each other out and the L is left which is the only unit so the answer would be, in this case, 78.37L.

However, it is not simply that. In the picture above, the units were already in m^2. If it were not, I would have to multiply the unit twice (or three times if it is cubed) to match up to the squared (or cubed).

Like this,

Math 10- Week 4

This week, my ah-ha moment was while I was working on this question:

((64a)^\frac{1}{3})^\frac{1}{2}

At first, I got the answer to the left. I then checked the answer only to realize that it was wrong but I could not figure out why. A few moments later, I realized that 64 was a coefficient and that \frac{1}{6} also had to be distributed to that as well. So then I redid my work and got the right answer (the work on the right).

Math 10- Week 3

Week 3 was almost like a review of exponents from grade 9 but with a bit more “pizazz” because we learned about negative exponents, which was entirely new to me.

I understood it quickly and got the hang of it after a few examples, however, I did still have some trouble with the assignments. Mainly this one: Simplify. Write the final answer with positive exponents. (5 a^3 b^2)(-2a^-2b)^-3 ÷ (-5a^8b^-9)^-2

At first, I got confused while I was simplifying and ended up with this:

I realized where I went wrong- the exponents inside do not change when you move it “upstairs” or “downstairs.” So then I changed how I did my work and got this:

which was correct. I learned to be extremely careful with negatives because I can be forgetful with the rules.

Week 2- Math 10

This week, we covered more prime factorization and a few square and cube root related questions.

One question I had a bit of trouble with was this one:

The mixed radical \frac{1}{12} \sqrt[3]{128} can be converted to a mixed radical in simplest form a \sqrt[3]{b} . The value of a+b to the nearest tenth is ______. 

At first, I did this:

Then I checked the answer and it wasn’t right. I realized what I did wrong so I redid my math which resulted in this:

And it was the right answer.

Math 10 Week 1

The first week of class we did numbers- more specifically, we did prime numbers, prime factorization, lowest common multiple and greatest common factors (and roots). It was a lot like a review of what we did in grade 9.

One question I had a slightly hard time with was this one:

5. Twin primes are defined to be consecutive odd numbers that are both prime. List the seven other twin primes less than 80.

I counted until 23, which is a prime number, and assumed that it should be on the list paired with 29. However, after a long period of thinking and not seeing 23 in the answer, I realized that 25 was the next odd number but 25 is not a prime number so the next twin pair would be 29 and 31.