This week in math class I have learned how to FOIL when multiplying polynomials as well as using an area diagram.

FOIL is a distributive technique when multiplying polynomials together.

F: First term in each bracket  (a+b)(c+d)   first term:

O: outside terms        (a+b)(c+d)    Outside term:

I: inside terms        (a+b)(c+d)     Inside term:

L: last term in each bracket        (a+b)(c+d)   Last term:

Example:

()()

F: First term in each bracket

You are taking and multiplying it with the other in the other bracket which will then give you because you add the exponents when the bases are the same during multiplication.

I: Inside terms

Make sure to multiply the first term with the other term as well, everything that’s inside the other bracket, so in this case, will be multiplied with (-8) which will be .

You are now left with .

O: Outside terms

Now you have multiplied the first term with everything in the other bracket and the inside term with the other term, you now need to do the same for the outside term. In this case, you now need to multiply 8 with which will give you .

L: Last terms

Then you multiply 8 with the second term in the other bracket.

8(-8) = -64

You now put all the terms together in descending order by the exponents and collect like terms if needed.

and cancel out so you are now left with:

This is Foiling but I learned a quicker technique that you can use depending on each equation.

Example:

Instead of expanding the equation then simplifying, you just need to square x = , then multiply x with +7 and double it = = 14x, then square the last digit which is 7 = = 49.

=

Although this way is quicker, it doesn’t use the same method for every equation. This is just a technique you can use when you are given a polynomial that has an exponent instead of expanding the equation.

The hardest part of this lesson was when I had to find the area of a rectangle/square when it had empty areas, so you had to find out the angles by subtracting then multiplying and other steps which was a little confusing but I managed to understand it.

 

In math class I’ve learned how to find a missing angle as well as finding a missing length of a right angle triangle using trig functions (sin, tan and cos) and learned about how to find the angle of elevation and depression.

To find an angle of a right angle triangle, you always need to have two sides of the triangle. You then start labelling the sides of the triangle so you can see which trig function to use:

Adjacent: the side near the degree.

Hypotenuse: the longest side of the triangle and is opposite to the 90 degree angle.

Opposite: the length that’s opposite to the angle.

After labelling the triangle, you then figure out which sides and angles are given:

Sine:

Cosine:

Tangent:

Punch in the two sides given depending on the trig function you are using, then press 2nd function then the trig function (Sin, Cos, Tan).

If you are given an angle and a side length and you need to solve a missing length, you first label the sides, figure out which length and angle you have then find the function you need to use which includes the side given and the side you are looking for and put it into your calculator depending on the function you are using.

Example:

 

The hardest part about this lesson was the problem solving questions. It’s hard for me to put the information given into a diagram/drawing because I sometimes mix up the sides on where it’s supposed to go.

This week of math class, I’ve learned how to find the volume and the surface area of prisms, cones, pyramids and spheres, as well as learned some new formulas that I can utilize.

Here I am looking for the volume and surface area of a prism. In this example, I needed to use Pythagorean Theorem because the height length was not given to find the area of the triangular base. The whole idea of Surface Area for prisms is to add all the areas of the surfaces/faces. It’s different for cylinders, cones, spheres and pyramids, instead they each have their own formula:

The most challenging part about learning this lesson was finding the Surface Area because it requires a lot of steps and you can accidentally make a small mistake which changes the answer completely. For example, sometimes I would accidentally add the same side of the shape twice or consider the slant height as the height.

There has been quite a few things I’ve learned from Imperial and SI systems. I’ve learned more different conversions in measurements such as converting from feet to miles and meters to yards as well as how to apply them to real life situations. I’ve learned how to do conversions when it includes more than one type of measurement like 2 mi 325 yds to yards. I’ve also learned how to read a vernier caliper in Imperial and metric units and how to read a micrometer in metric units.

When you are given multiple measurements, sometimes you have to do multiple conversions because some of the conversions are not given. For example meters to feet. You have to go through multiple conversions, meters to centimeters then to feet.

The challenges I came across was the problem solving questions because I had a hard time applying the necessary measurements and what to do. It took some time to solve some of them but I managed to figure them out, although I still need some practice.

 

These last few weeks of math have been interesting and educational. I’ve learned more about negative exponents and how to convert them into a positive exponent as well as how to deal with exponents in form of a fraction. I also learned how to find the Lowest Common Multiple and Greatest Common Factor in a quicker way using prime factorization which has helped me a lot in science when I needed to balance chemical equations.