This week, we learned about arithmetic sequences and the different formulas to solve these sequences. In this blog post, I am going to show you the different formulas to simplify these arithmetic sequences.

Let’s say we have this sequence:

1, 4, 7, 10, 13…

First we need to find the difference in this pattern.

Look at the amount that this sequence jumps each time, we know that the difference is 3

To find the general rule, we use this formula:

Tn= + (n=1)(d)

Now all you need to do is plug in the information and do the algebra.

Tn=1+(n-1)(3)

Tn=1+3n-3

Tn=3n-2

Now, let’s say we wanted to find out what would be.

Then we add the first term to the difference 11 times.

= 1+(11)(3)

= 34

In this blog post, I am going to show you how to use the substitution to solve system of equation questions.

So let’s say that we have two equations that look like this:

y=x+2 and 3x+4y=1

So first we are going to take the equation that has a variable with a coefficient of 1.

Then we are going to make sure that the variable is isolated. Then we are going to take the other part of the equation and substitute it into our second equation.

3x+4(x+2)=1

In this equation, we are only left with one one variable shown. Then from here we are going to distribute, sort and simplify.

3x+4x+8=1

3x+4x=1-8

7x/7=-7/7

x=-1

Then we check our results to see if they are correct and to find our Y value.

(y)=(-1)+2

y=1

(-1,1) are our coordinates.

This week, we learned about system of equations. In this blog post, I am going to talk about these equations and demonstrate some information.

First of all, what is system of equations?

A system of equations is a collection of two or more equations with a same set of unknowns.

Let’s say we had the two equations: 4x-2y=8 and 2x-y=4

We need to find an X value and a Y value that would work perfectly for both equations. We need to find the two coordinates that are true.

In this case (0,-4) would be the values that would make the statement true.

In this blog post, I am going to show you how to write an equation in slope point form using the information we have from a graph and y-intercept form.

So let’s say we had this graph:

We can see that there are two visible nice points where we can take information from to help us write this equation. (2,0) and (0,3)

Before we construct this equation, we have to determine the slope by using the change in y over the change in x method. (which is equal to 3/2)

Once we know our slope, then we can use the information shown the graph and plot it into our equation.

3/2(x-_)=y-_

(Where the blanks are, you would plot in the x1 and y1 coordinates.

3/2(x-2)=y-0

Then you have your completed point slope equation.

In this blog post, I am going to show you how to find the slope of a line using the X and Y coordinates.

The equation we can use to solve this is:

So let’s say you have the coordinates (3,4) and (8,7)

You would then take the information given from these coordinates and place it into the equation.

Which would look like this: 4-7/3-8

Which would equal to -3/-5

Which is equivalent to 3/5

Knowing this method is really easy and will help you figure out slopes by using the coordinates.

This week, we learned about function notation. In this blog post, I am going to demonstrate how to understand and solve function notation.

Let’s say we had an equation that looked like this:

F(x) = 3x+4    F(3)

The F(x) notation is another way of showing the y value of a function. Because F(x) = y.

This is showing that we need to find the answer for the equation if X is equal to three.

The equation would end up looking like this:

(3)(3)+4

Which is equal to 13

Now 13 is representing our Y value. Because writing F(x) = 13 is the same thing as writing y = 13

Once you understand the steps of function notation, it is easy to solve these questions.

This week, we started to learn about relations. I thought that Domain and Range was really interesting and easy to understand once you have learned about it. In this blog post, I am going to talk about Domain and Range.

Domain: The domain of a function is the complete set of possible values of the independent variable.

Range: he range of a function is the complete set of all possible resulting values of the dependent variable.

Domain is always the X value and range is always the Y value. ( X is red and Y is blue).

If the relation is discrete, the domain and range would look something like this:

{X|0,3,-3,2} {Y|2,4,-2,}

If the relation is continuous but had a determined end the domain and range would look something like this:

{X|-3<X<3, XER} {Y|-2<Y<4, YER}

If the relation is continuous but didn’t have a determined end the domain and range would look something like this:

{X| XER} {Y| YER}

This week, we finished our polynomial unit test and learned how to solve “ugly trinomials”. These are expressions that are not are not able to be easily solved by just looking at them or using any of the four hints to factoring polynomials. In this blog post, I am going tok show you some tips and tricks to help you efficiently find the answer to these difficult expressions.

Step 1: Lets say you have an expression that looks like this

First thing first, we can see that there is a 3 to the power of 2 at the start of the expression. Draw out your two bracketed areas, place a 3x at the start of the first bracketed area and an x at the start of the second bracketed area. Example: (3x    )(x     )

Step 2: Looking at the last number of the expression, we are going to find any multiples of that particular number. In this case, the only multiples of 8 would be 1,8 and 2,4.

Step 3: This step is basically trial and error. You take each pair of numbers and try them in different orders in the blank areas within the brackets. You also need to figure out whether the numbers you are using should be negative of positive. You will know if you have chosen the right pair and placed them correctly by using the claw method to then expand the equation. if the two new numbers you get from expanding the equation equal to the middle monomial in the equation (in this case it is -2x), then you know that you have correctly solved the question.

The answer to this equation is (3x+4)(x-2)