Math has been a fun yet challenging class for me this year. I was able to grasp more mathematic vocabulary this year and also further my skills from last year. This post is going to be an array of the top 5 things I learned in Precalculus math 10.

1.) Factoring polynomials

When factoring polynomials, we determine all terms that were multiplied together to get the given polynomial. Let’s say we have this polynomial equation that needs to be factored.

Now as you can see, I took the X squared and I broke it down into two equations each one containing an X. I then figured out what multiplied by what equals to 16. Now although 8 multiple by 2 equals 16, the two smallest number that can multiply to 16 is 4. Of course make sure the equation has one positive 4 and one negative 4 so that the answer will equal -16.

Now we have X to the 4th . To factor this kind of equation we must go through one extra step. We now break the equation into 3 brackets, leaving the first bracket with X squared and the other two with one X each. Now we want to multiply out so we take 4,2 and -2. We now have a factored polynomial equation.

2.) Entire radicals into mixed radicals 

We are going to start out my factoring the entire radicals number. In this case the number is 63 and when we factor 63 out we get 7 multiplied by 9, and then we are able to break 9 down into 3 multiplied by 3. From there we put the prime numbers into where the 63 was. We then find any common pairs. In this equation we have two three’s so these are pulled into the coefficient stop of the radical. and the seven is left inside. We now have 3 root 7.

3.) GCF and LCM 

Although these seem like very basic and simple math skills, I was able to master them and be able to find either of them quickly and efficiently. When dealing with finding the GCF(Greatest common factor) of a two different numbers we must factor out the smallest numbers that multiply to that number.

Now when fiddling the LCM (Lowest common factor) of two numbers you multiply each number out until you find one that they multiply to. For example 6 and 3’s LCM would be 6 because that is the smallest number that they both multiply to. 

4.) All about numbers and number vocabulary 

Numbers come in many different forms. In out first chapter, we learned about all the different kinds that we would be dealing with throughout the course. We learned about 8 different kinds of numbers in math 10. We also learned that numbers can be grouped by their decimal representation. The 8 different kinds of numbers we came across were:

R= Real numbers are all numbers

Q= Rational numbers are numbers that can be made by dividing two integers

Q (with a line on top) = Irrational numbers are real numbers that can NOT be made by dividing two numbers.

Terminating numbers = rational numbers in decimal form that have a finite number of digits. (7.3)

Repeating numbers = 5.121212 a number with a decimal that repeats itself

Integer numbers = Whole numbers not including zero and can be positive or negative

Whole numbers = Only positive numbers with no decimals (10)

Natural numbers = The numbers that came naturally to you, the numbers your parents taught you as a baby. No zero (1,2,3,4,5,6,7,8,9,10)

5.) Trigonometry 

Trigonometry helps us find angles and distances and it is a way of measuring. A right triangle is divided into 3 sides. The hypotenuse, opposite and the adjacent. The adjacent is located by the  refuse angle, the opposite is opposite to the reference angle and the hypotenuse is the longest side. Nicknames for these sides are hyp, opp and adj. To find angles we use three main functions. The functions we used are Sine, Cosine and Tangent. To find any angle we use SOH CAH TOA . SOH CAH TOA stands for:

Here is an example of using Sine to find an angle.

This week in math 10 we learned how to find solutions from systems. A system is when we consider two lines at a time to find a solution. The solution you come up with depends on the systems you have. There is one solution if the system follows m1 does not equal m2. There are 0 solutions if the system is parallel and follows m1=m2 but y1 does not equal y2. There are infinite solutions if the two systems are identical. Now to find a solution between two systems, you can go about it 3 different ways. You can find the solution by graphing , substitution and elimination. My favourite is elimination. These are the steps I like to follow when finding a solution by elimination.

Step 1. 

Multiply one of the two equations to even out the equations so that you can isolate one of the variables.

Step 2. 

Add or subtract the second equation from the first. Depending on what you multiplied the equation by in the first step will determine if you subtract or add.

Step 3. 

Solve for x or y in the new equation.

Step 4. 

Substitute whatever you got for x or y into the original equations and from there you are able to solve for x.

A Solution is found when x and y work for both of the original equations. 

This is a lesson of DOS ( Difference of squares) involving a common factor. Our goal with a question like this is to have two identical binomials that equal what we started with if we evaluated. All you need to do with this question is distribute x squared into two brackets and then find what times what ( YxY) equals – 100. The answer is +10 and -10.

For week 9 I learned who to factor trinomials that have a GCF.

It may look tricky to some but finding a common number that can fit into all the numbers makes it so it is extremely easy. If we have 24, 12 and 36 as our numbers we can all see they have something in common, a 12. You then distribute 12 into each number. 24/12 = 2 12/12= 1 OR x and 36/12 = 3. Now you must rage the equation to have brackets and a 12 in front of the first set of brackets because that is what you distributed.

This week we started Polynomial Operations.  Although we have only done a few lessons, I have already learned a lot.

I have learned all the basics of polynomials.

What is a polynomial made up of ? A polynomial is made up of variables, terms and degrees. Here’s an example of a basic polynomial expression including 3 variables, 4 terms and a degree of 4. 

There are 4 different types of polynomials.

1.) Binomial (a polynomial consisting two terms)

2.) Trinomial ( a polynomial consisting of 3 terms)

3.) Monomial ( a polynomial cosseting of 4 terms)

4.) Anything with more terms is just considered a “Poly” (Polynomial)

What is a term? A term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs.

To figure out how to find the answer to a polynomial equation can be hard for some visual learners like myself, so we can use a chart like way to find the answer of an equation. The chart/diagram looks something like this. 

And here is how I would figure out a question without a diagram/chart 

In trigonometry we use something called “SOH CAH TOA” which stands for Sine, Cosine, and Tangent. SOH CAH TOA also let’s you know what  sides you are going to use for that particular function. To find the missing hypotenuse you must follow these five simple steps.

1.) Draw and Label ( find the opp,adj and hyp) the triangle

2.) Now you will have to use the COSsine since you have the opp but not the hyp. COSsine makes up Opp over Hyp.

3.) Write it into an equation which would look like (Sin = pie /35)

4.) You then use that equation in your calculator.

To find a missing angel you start by labelling the triangle

1.) Label the triangle

2.) Since you have the opposite and the adjacent but no angle you will use tan to find the angle.

3.) The equation you will write and put it into your calculator. (ta(x)=20/5)

4.) To find the angle you have to make tan a negative (tan-1=20/5)

5.) You then put that into your calculator.

During this week of math 10 we started working with spheres. A sphere is a round solid figure, or its surface, with every point on its surface equidistant from its centre. A sphere is 2 hemispheres. The diameter of the sphere which is a straight line passing from side to side through the center of a body or figure, especially a circle or sphere. The radius of a sphere is the diameter divided by two. Radius(r) is half of the diameter(d). In this blog post I’m going to teach you how to get the SA and V of a sphere and then convert it into SA and V of a hemisphere (half a sphere). To find the SA of a sphere the formula we use is 4 x pie x r squared. Let’s say we were told that the d of the circle is 18cm.

Then to find the V of a sphere we use the formula 4/3 x pie x r cubed. Now if we know the r is equal to 9cm then all we need to do is convert the 4/3 into a decimal and follow through with the given formula.

Now to convert the V into a hemisphere you simple divide by tow because the sphere is just two hemispheres. So if our V of the sphere was equal to 3053.62 cm cubed the V for a hemisphere would equal 1526.81cm cubed.

Now to get the SA of the hemisphere form the spheres SA, it isn as easy has just divide by 2 because when you cut the sphere in half you have an extra side which is the flat top. This hemisphere is a dome shape. You use the formula 3 x pie x r squared. So with the formula you can now find the SA of the hemisphere.