This week in math 10 we were reviewing polynomials. Though it was all review one thing that I learned how to do was how to make an area model.

An area model is one way to help solve a multiplication question. When multiplying polynomials in a sense you are also calculating the area of a rectangle.

Example:

How to make an area model:

1. first, you need to draw a rectangle and separate it into four squares
2. You then need to take the first term and separate it into two parts ex. 24 could also be written as 20 + 4, in this case you would separate the first term into  and +8. After you separate the first term you write the first part on the top of the first rectangle and the second half of the term on top of the rectangle right beside it.
3. Then you do the same thing to the second term but place the first half of the term (x) on the side of the first rectangle and the second half (-2) beside the rectangle directly under the first part of the term. (-2 would be written beside the rectangle under the rectangle that is beside x)
4. You then find the area of each of the individual rectangles
5. Add all of the areas together, collecting an like terms if there are any to get your answer

This week in math 10 we learned about trigonometry. We learned how to solve for missing lengths and how to identify different parts of the triangle, as well as an acronym to remember the different ratios (SOH CAH TOA).

For each equation solve for “X” and round your answer to the nearest whole number

Problem 1: 

1. First, you should label all sides of the triangle to help you write the equation (opposite, adjacent, hypotenuse)
2. Look at the lengths given and decide which of the tree signs you will be most appropriate (sin, cos, tan)
3. You need to isolate the variable in the equation. To isolate the variable you divide the sign by itself.
4. You the multiply the fraction on the right side by the sign in your equation. Since we don’t know the angle we have to invert the sign when we write it. Signs should always be written with an angle.
5. Solve the equation. Make sure to ado a degree symbol to the answer since you were solving for the angle and not side length.

 

Problem 2:

1. First, you should label all sides of the triangle to help you write the equation (opposite, adjacent, hypotenuse)
2. Look at the lengths given and decide which of the tree signs you will be most appropriate  (sin, cos, tan)

3. You need to isolate the variable in the equation. To do this you Multiply both sides of the problem by the denominator on the right side, in this case it would be 21.

4. Solve the equation.

 

Problem 3:

1. First, you should label all sides of the triangle to help you writ the equation (opposite, adjacent, hypotenuse)

2. Look at the lengths given and decide which of the tree signs you will be most appropriate (sin, cos, tan)

3. You need to get the variable on the top of the fraction so you reciprocate both sides of the equation.

4. You then want to isolate the variable so you multiply both numerators by the denominator of the fraction that contains the variable. In this case you multiply both sides by 28.

5. Solve the equation.

 

This week in math one thing that I learned how to do was how to calculate the surface area and the volume of a sphere. I also learned that two cones can fit inside a sphere, and one cone can fit inside a hemisphere, only if they have the same radius.

 

Surface area:

1. The formula for the surface area of a sphere is 4
2. If we know that the radius of the sphere is 11.5cm then we just input it into the  formula ie. 4(11.5)^{2}
3. You then square the radius ie. 4(132.25) and multiply across to get your answer
4. Round to the nearest 1oth of a cm

volume:

1. The formula for the volume of a sphere is
2. Since we know the radius, again, we just input it into the equation ie.
3.  To help you may want to rewrite the equation so 3 is the denominator and  is the numerator, it means the same thing as  
4. You then cube the radius ie.   and multiply across to get your answer, if you rewrote the equation as one fraction the you multiply across the top and divide by 3 to get your answer
5. Round answer to nearest 10th of a cm

 

This week in math we learned about measurement. Although I’ve never loved the measurement unit I learned some tricks when converting which helped me learn to enjoy the unit more.  One thing that I learned this week was how to convert measurement from imperial to metric and vise versa using unit analysis. Being able to convert from metric to imperial and imperial to metric is an important skill to have since we live so close to the United States and still measure some things using the imperial system ex. height.

Example: 

How To Solve The Problem:

1. You write down the number you are converting, which in this case would be 12ft.
2. You then analyze and see if there are any known conversions. If we know that we are trying to convert from imperial to metric, and we know that 1in = 2.54cm, then it would be best to convert the 12ft to inches and then convert that to centimeters and so on.
3. You write the know conversion as a fraction. We know that 1ft is equal to 12in so we write that as a fraction with 12in as the numerator and 1ft as the denominator. we write it like this because we are trying to cancel out the feet so that we are left with only inches. note: the unit you are trying to cancel out should always be written opposite to that of the fraction in front of it.
4. You continue with the previous step until you are left with the unit of measurement you are trying to convert to.
5. then you multiply across and divide and you should be left with your answer.

 

This week we didn’t really learn anything new involving exponents, we mostly reviewed for our exponents test on Thursday. I may not have learned anything new but I found that both unit 1: Radicals and unit 2: Exponents are closely related.

When you look closely at both of the units one could see that some of the components of the lessons like radicals and fractional exponents are alternate ways of expressing the same thing. If you wanted the square root of a number not only could it be expressed as a radical but, it could also be written as a power to one-half. Another way the two units are related to one another is that in the exponents unit it involves things from the first unit like radicals, coefficients, and index’s.

         

This week in math 10 we learned all about exponents. Although the beginning of this unit was review I learned quite a bit about solving equations involving exponents. This week one of the things that I learned was how to solve fraction exponents. I also learned a phrase to remember when solving these types of equations, “flower to the power, root to the root”.

Example:

How to solve the problem:

• You look at the fraction exponent and determine which number is the flower and which number is the root of the flower, the numerator will always be the flower and the denominator will always be the root. the flower will act as the power of the radicand and the root will go in front of the root sign acting as the index.
• Next, you find the root of the radicand, after finding the root you should be left with the root of the radicand and an exponent. You then multiply the number by itself as many times as the exponent calls for. what you should be left with is the answer to your equation.

 

This week in math 10 we learned about mixed radicals and entire radicals. Something that I learned how to do was how to covert mixed radicals into entire radicals.

1. To turn a mixed radical into an entire radical you need to covert the coefficient into a square root. to do this you must square the coefficient.
2. Next, you multiply the two square roots by one another to get the entire radical

Example:

This week in math 10 we learned about numbers. Though it was mostly a review of things that I’ve done in my previous years of math one thing I learned is that if you are only given the prime factors of a number it can tell you quite a bit about that number. With only its prime numbers you can find both your mystery number and ALL of its factors.

1. You start by writing down the prime factors that are already given
2. Then, you would cover one of the prime numbers and multiply the other prime numbers together to find what the covered numbers pair (the number that you would multiply the covered number by to equal the mystery number) is. Repeat for the other prime numbers.
3. Next, you multiply the prime numbers in pairs, making sure that you multiply each number by all the other prime numbers given.
4. Make sure you don’t forget to add 1 and the original number (multiply all the prime numbers together) on the list of factors