Math 10 Top 5

When in math there are a number of things that can help you succeed in the course. Below are my top 5 steps to succeeding in math 10…

1. Do your homework every night

Though our homework was never marked for completion it is essential to your success in math 10. You may think that you don’t have to do it since it’s not for marks but you would be wrong. Each day in math10 you will build on the concepts/ideas that you had learned the previous day. By completing your homework every night  you deepen your understanding of the concepts and allow yourself to practice the same concepts so that you will succeed on the unit test. In math repeating the same steps will allow for you to absorb and master the different skills.

2. Highlight the assigned questions the night before

By highlighting the assigned homework the night before you will save yourself a lot of time in class. Highlighting prior to the class allows for you to get a head start on the homework, this is so that you won’t have as much to do later or, so you can ask as many questions as you can in class while there is help available.

3. Make use of Mrs. Burtons abbreviations

You may think that the abbreviations that Mrs. Burton comes up with are silly and won’t help you at all but that is where you are wrong. The abbreviations make it so that you will have an easier time solving certain questions. The abbreviations such as “SOH CAH TOA”, “Can Divers Pee Easily Underwater”, “King Henry Doesn’t Usually Drink Chocolate Milk”, and “flower power” have allowed me to succeed when doing both my homework and when doing tests. I have used the abbreviations all throughout the semester, they allowed for me to remember the steps to problems that I may have forgotten otherwise.

4. Make sure to ask questions

One of the most important factors to your success in math 10 is making sure that you ask for help. When you don’t understand a question don’t be afraid to ask for help! whether it’s from another classmate, or a teacher don’t be afraid to ask for help. By not asking for help your not helping yourself at all, and are just setting yourself up to not get a good mark on the unit test. Asking questions can help you fix any mistakes your  making or clear up any misunderstandings you have about the concepts.

5. Help people at your table that need it!

By helping those at your table and explaining how to do questions you will improve your own skill. When you assist another classmate it allows for you to deepen your own understanding of the concept since you have to explain to them and possibly demonstrate how to do a question. You wont regret helping another person with their math since it would also be in your best interest to help them.

This week in math 10 we started our last week of learning any new information for our upcoming unit 10 test. This week we learned about how to find the x and y coordinates when given two equations. One way of finding the coordinates is through a process called substitution. Substitution is used to solve for one variable so that you can use that value to solve for another variable in the equation.

Example:

  

Steps:

1. First, you need to pick one of the two equations and rearrange the equation so that it is written as either x = ___ or y = ___ (x + 12y = 3 —> x = -12y + 3)
2. Next, you need to substitute the value of that variable into the other equation using brackets. So wherever there is an x in the other equation we replace it with (-12y + 3)
3. Workout the problem until you have isolated the variable
4. You then put the value of the variable that has just been found into the rearranged equation to solve for the other variable
5. After finding both coordinates make sure to write them as ordered pairs ie. (_,_)
6. Make sure to verify your solutions

How to verify:

1. All you need to do to verify the solutions are by inputting the values of the variables into the equation
2. To know if you have done the solving of the variables correctly, both sides of the equation should be equal/ prove true ie: 7 + 6 = 13 or 13 = 13

This week in math 10 something I learned was how to write 3 different versions of a graphing equation. The first one I learned was called a slope y-intercept form, the second one I learned was called the general form or the “pretty form” and the last one I learned was called point slope form. Today I will be showing how to find the slope y-intercept form.

First in order to write any equation you must know at least two points about the graph. It is also important to know that the formula for slope is  and the formula for slope y-intercept is y=mx+b. In this equation m stands for the slope and b stands for the y intercept.

Example:

How to find slope y-intercept form:

1. First, you need to find the slope using the formula  ,make sure that you simplify if possible.
2. Since we weren’t given the y intercept we need to find what b is equal to. To do this you need to isolate b, to do this you take one of the coordinates given and input it into the equation, in this case I chose (3,4).
3. If there is a fraction in the equation you want to make it into an integer so, you multiply the slope by x and then multiply everything in the equation by the fractions denominator.
4. You then move the integer on the right side of the equation by adding the opposite so that you can isolate b. Remember what you do to one side you have to do to the other.
5. Since we just want to find the value of b you need to divide both sides of the equation by the coefficient in front of b.
6. After finding the value of b you just input all the information that you know about the graph into the equation (This only applies to the slope and y intercept).

This week in math 10 we learned about how to find the slope of a line segment. The slope of a line is used as a way of measuring how steep the line is.

 

How to find the slope of a line segment:

1. First, the formula to find the slope of a line segment is , the formula can also be written as
2. We then input the numbers into the formula so:
3. You then subtract the numbers on both parts of the fraction:
4. If the fraction that is leftover can be simplified then you simplify it, if it can’t be simplified then you leave the fraction as is and that is your slope

 

NOTE:

• If the line segment is a straight horizontal line then the slope will be zero
•  If the line segment is a straight vertical line the slope can’t be defined so you would write undefined

This week in math 10 one of the things we learned was how to calculate the length of a line segment using the x and y coordinates on the graph. In this blog post I will focus on finding the length of diagonal line segments.

Example:

 

How to find the length of a line segment:

*Note: A  and B *

When looking at the diagonal line segment one could notice that the line segment makes up part of a right triangle (shown in red), in other words think of the diagonal line segment as the hypotenuse of a right triangle. One of the ways of finding the hypotenuse of a triangle is by using the Pythagorean theorem (  ). In some cases you can count how long both side a and b are but, if you are not able to then in order to find what  and  are equal to you can use the formula  in which a =  and b =  . you then square and add the values of  and  together to get .  The last step to finding the length of the line segment is to square root both  and its value. If the square root of  and  isn’t a whole number you may leave it as a radical unless the question asks you otherwise.

This week in math 10 we learned about linear relations. This week we learned a bit more about the X and Y intercepts.

•  We learned hat when graphing there is a dependent variable (y) and an independent variable (x)
• We also learned how to solve for the x and y intercepts
• When solving for the x intercept y = 0
• When solving for the y intercept x = 0

Example:

How to solve for the x or y intercepts:

1. If solving for the x intercept replace all y’s with zero. If solving for the y intercept replace all x’s with zero. In this case we will be solving for the x intercept
2. next you need to isolate the variable so you + or –  the constant to cancel it out. What you do to one side of the = sign you do to the other so in this case you add 33 to both sides of the equation.
3. Next to isolate the x you divide both sides of the equation by the coefficient (number beside the variable) to get the value of x.

This week in math 10 we mostly reviewed for our polynomials test on Friday. Although it was review one thing I learned this week was how to factor difference of squares.

Every difference of squares can be factored as:  = (a + b)(a – b), due to the + and – having the same value the middle term gets cancelled out.

When factoring a difference of squares there are 3 things you need to make sure of

1.You need to make sure the equation is a binomial

2.There is a negative sign ( – )

3.Both terms are perfect squares

Example:

Further Examples:

 

How to Factor:

1. Decide if the terms have anything in common or have a GCF. If so factor out the GCF
2. Since every difference of squares can be factored as  = (a + b)(a – b), to get this you just need to find what numbers squared will produce the results that you want. In this case you want to find what number squared will produce   [x (x)] and what numbers squared will produce 16 [4 (4)]
3. Check to see if the remaining factors can be factored even further

 

 

This week in math 10 we talked about the different ways of factoring polynomials. One thing that I learned this week was how to factor simple trinomials.

When factoring a simple trinomial there will always be a pattern in the equation ( + bx + c ). In order to factor the trinomial you need to find two integers that when multiplied together will be of equal value with c and when added together will be of equal value of b, in other words you list the multiples of the constant that represents c and pick the integers from those numbers. If there are no two set of integers that make this possible then the equation can’t be factored. You must also be sure to check whether the product is a positive or negative number as well as the sign in front of he sum since it will effect if the integers are positive or negative.

Example:

However, if the  has a coefficient greater than one the equation is no longer simple. In that case you need to check and see if the terms have a GCF that they can be divided by, if not then you just have to factor them out. In this case there is a GCF that the terms can be divided by. After dividing the terms by the GCF, you write the quotient inside brackets and the GCF as a coefficient outside of the brackets. Lastly, you factor as normally would factor a trinomial.

Example:

This week we learned more about polynomials, from working with multiplication questions with multiple terms to learning how to factor polynomials. This week I will explain how to solve a polynomial multiplication question that has multiple terms.

Example:

How to Simplify:

1. First, you want to lessen the amount of brackets so in this case you would multiply the brackets in each term by one another. The product will need to be written in brackets since it hasn’t been multiplied by the coefficient outside the brackets yet.
2. Next, you want to get rid of the brackets so you multiply the brackets by the coefficients that are directly beside them.
3. Lastly, you look at the products and collect any like terms to simplify it. Like terms are those that have the same variable and exponent ie. -10x, and +5x, if you were to combine these two like terms you would be left with -5x.