This year in math I would say I learned a lot academically but I also learned a lot about what works for me and what doesn’t when it comes to getting a good grade that I am proud of.  My top five pieces of advice that helped me a ton is to ALWAYS do the homework.  Throughout this semester I noticed that when I completed the homework I got a better result on my test.  Next tip is to pay attention in class.  A lot of the time if you don’t pay attention and then try to learn it on your own it seems to be a lot harder then it actually is.  Thirdly I would recommend revising every once in a while.  This ensures the marks on your midterm and final are going to be higher.  Fourthly make sure your final answers are always reasonable (this helped me a lot during word problems) and when having trouble I always like to think back to the basics.  Finally, if I were to give only one piece of advice to anyone it would be to ask questions and get help when needed.  I noticed when I did this it helped me tremendously and I did see a better result.  If you take all of these tips and apply them to your habits through anything you do I believe you will see improvement.

This week in math we learned about the elimination method.  Elimination is an important method when it comes to systems of linear equations, and is also quite simple.

When solving an elimination question you can either add or subtract the system. You always want to look for the easier solution and personally, I would add all the time. To solve an elimination question we need to have a zero pair.  So, a pair that cancels out.  In some cases the zero pair is given to us but in most cases you will have to multiple the other line (or sometimes both) with a common number.

After doing this you have a zero pair so all you need to do is add the rest. You then solve for X. So in this example, you will need to divide 88 by -40.  You then have the answer to your X variable.  But to finish the question off to find the solution you then need to go back to the original system and pick one of the equations, replace X with the answer you got and solve for Y.  After doing all this you then have the solution.

This week in math we learned three types of equations.  General form, Y-intercept form, and point-slope form.  They all tell us something different and some don’t tell us anything at all.

First, let’s start with general form. 0=ax+by+c. We like to call this form the pretty form because it is pretty useless. This form doesn’t tell us anything about our slope, Y-intercept or coordinates.  0=2x-5y+10, this is an example of a general form equation.  To tell this apart from the other equations general form always equals 0 and has to have a positive leading coefficient and can never contain fractions.

The second form is Y-intercept form.  Y=mx+b. This form is the most useful in my opinion when graphing.  This form gives you the slope (rise/run) and it also gives us the Y-intercept, which is our starting point on our graph.  Y= -2x/8 + 5, is an example of Y-intercept form.  The numbers paired with X is always going to be our slope, so in this case, the rise is -2 and our run is 8.  In some cases, you might come across an equation where -2 does not have a visible denominator, all this is saying is that the denominator/run is 1.  The equation is also telling us that our Y-intercept (starting point) is +5.  I know this is Y-intercept form because it has a Y on one side of the equal sign.

Lastly, point-slope form.  m(x-x)=y-y.  To use this form we need to know one point/pair of coordinates and the slope.  2(x-5)=y-3, is an example of the point-slope form.  In this example, 2 (2/1) represents the slope and (5, 3) are the coordinates.  I know this is point-slope form because it has brackets and uses only one pair of coordinates.  This form is the fastest to show an equation of a point on the graph.

This week in math we learned how to find the slope of two coordinates without using a graph. First, we should know that the slope is rise over run (rise/run). Another way you can look at it is height over width, Y over X.

To do this we used a thing called slope formula. Slope formula makes it extremely easy and possible when finding a slope with only two coordinates.

When using this formula you have to make sure to always have the Y coordinates as the numerator, and the X coordinates as the denominator as shown below.

You then subtract the coordinates from each other and you will end up with a fraction.  This fraction is representing your slope.  The rise is -6 and the run is 8.

(if it is a negative integer make sure to add it since a negative and a negative form a positive, as shown in the second diagram.)

This week in math we learned the difference between a relation and function. We also learned how to tell them apart when looking at, coordinates, a mapping graph, a chart, and a cartesian graph.

A function is a special relation.  A relation is a number that has two or more Y-variables for one X-variable. A function is a number that has only one other number, so only one Y-variable is associated with an X-variable.  Another way to look at it is that the relation is a friendship and a function is a marriage.  You have many friends at a time, but only one spouse at a time.

Some examples of functions are:

Some examples of relations are:

(reasons are highlighted)

As you can see in the relation examples in every example there is at least one X-variable doubled, or they have more than one partner (y-variable). Now, these are the basics.  In some cases it gets harder and you have to pay attention to if it is opened or closed.

This week in math we learned how to deal with ugly trinomials.  We refer to them as ugly because they are harder to factor.  An easy trinomial is very simple to factor, ugly trinomials involve multiple steps. First, what does an ugly trinomial look like compared to an easy one?

Let’s look at the differences. It’s important to know what type of trinomial it is. When factoring an easy trinomial there is an invisible one as a coefficient beside X squared. Otherwise, in ugly trinomials, their first term can have a coefficient greater than one or as well as an exponent greater than two.

When solving ugly trinomials we have to use a diagram to help us. First, we take the first and last terms and place them in the first and last boxes in the square we have drawn.  Next, we have to find out what two numbers belong in the extra boxes. So, we multiply the first and last terms together to get a number that will help determine what we are looking for.  Then we have to find two numbers that multiply, in this case, to 14 and subtract to -5 (the middle term).  To find these two numbers we have to factor 14.  Make sure you pay attention to the middle term and if it is negative or positive.  If the middle term is positive then the greater number will be positive, otherwise, if the middle term is negative the greater number will be negative.

Finally, we place the two numbers that add/subtract to -5 and multiply to 14 in the empty squares. After this, we add a variable to these numbers, in this case, P. moving from right to left we have to pull out the GCF of the pairs. After, you do the exact same thing top to bottom.  Make sure you acknowledge if it is a negative or positive GCF. When you end with four numbers and two pairs you just found what makes up that ugly trinomial.

This week in math I learned about conjugates.  First of all, a conjugate is a binomial that has a sign that cancels out to make a zero pair.  an example is (X+5)(X-5).  When dealing with conjugates there is a shortcut to solving them. Normally when solving it would look something like this.

After solving it this way we realize that there is a pair that cancels each other out.

So this means if we recognize that the binomial includes a negative and a positive then we can just multiply the first and last pairs.

This week in math we were learning about polynomial operations.  I came across a question with an exponent.  Similar to this question here…

…at first when I saw this question I immediately took the knowledge that I learned from the exponents chapter and applied it here. I multiplied everything inside the bracket by the exponent…

…I then quickly realized that it makes no sense at all, to do that.  Thinking back to exponents, the exponent only applies to what is directly underneath it.  Since x-8 is in brackets, (x-8) is considered as 1.  So this week I learned that when you have a question like this, once there is addition or subtraction in the equation,  you then have to double the equation.  There is still a relation with exponents, when you are squaring you are still doubling everything.