EOCT Review-Analytical Geometry-Questions 1-4

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Analytical Geometry EOCT Review for Georgia
This video answers 1-4

Video Guide
0:17 Problem 1.In this figure l and m the two lines are parallel to each other. Jessie listed the first two steps in a proof that angle 1 + angle 2 + angle 3 = 180 degrees.

1:34 Problem 2. This table defines a function with x values making up the domain and y values making up the range.
Here is my input and here is our output.

4:23 Problem 3. You have the measure of arc QR which is 72 degrees, and you are asked to find the measure of QPR. This is what we call an inscribed angle. The rule is it is half of the arc. So if this is 72 then this angle is half of it which is C 36

5:18 Problem 4. Which of these expressions has a real number value?

Hi welcome MooMooMath
Today we are going to look at questions for the EOCT assessment at the end of Analytical Geometry
Here is item 1 from the state website.
In this figure l and m the two lines are parallel to each other. Jessie listed the first two steps in a proof that angle 1 + angle 2 + angle 3 = 180 degrees. Angles 1,2, and 3 are inside a triangle and you are trying to prove that. In order to justify that we need to show that angle 2 and angle 4 are also congruent. If 1 and 4 and angle 5 create a linear pair that add to 180 and show that 4 and 2 are congruent and 3 and 5 are congruent, we know that the triangle. In order to get there we need to show 2 and 4 are congruent and 1 and 5 are congruent. We are told that lines l and m are parallel so I will mark my diagram. How do we know angles 5,3, and 2, and 4 are congruent? The side vt and the side vu create transversals and these become alternate interior angles. Lets look at our choices.
Which justification can Jessie use for steps 1 and 2. Are they alternate interior angles, corresponding angles, vertical angles, or alternate exterior angles. They are alternate interior angles, because they fall between the two lines, and alternate because they fall on opposite sides of the transversal.
Item 2.
This table defines a function with x values making up the domain and y values making up the range.
Here is my input and here is our output.
Which equation describes this function?
I will zoom in to see the equations.
This is how I would answer it. It is a multiple choice test.
It is one of these 4 choices.
What I need to do is just start plugging in values.
All of these values have to work in these equations.
These are my inputs and these are my outputs.
I will look carefully and pick 0 because it is so easy to plug in. Lets plug in 0 and eliminate some choices. If I plug in 0 in this function I get 4. Lets try b, if I plug in 0. Do I get out 4 no. If I plug in 0 for the third one, it equals -1 and 0 in the last one I get -4.
The only one that works for (0,4) is the first one. So that is my solution. I can double check it by plugging in some other values. If I plug in -2 works out by spot checking these and they are working. So I know A is my answer.
Lets look at the 2nd page which is problem 3 and 4 .
Problem 3 is a circle problem.
This is rally easy.
You have the measure of arc QR which is 72 degrees, and you are asked to find the measure of QPR. This is what we call an inscribed angle. The rule is it is half of the arc. So if this is 72 then this angle is half of it which is C 36
Inscribed angle is equal to 1/2 the measure of the arc.
Problem 4. Which of these expressions has a real number value?
This means it can't be imaginary
Lets look at our choices and it is 1/i. Any time you have an imaginary it is not a real value so it is not this one.
B is negative i, again an imaginary number so it is not the answer.
Next we have the square root of i. i is the value of -1 so we are taking the square root of a negative and that is not real.
So i^2 and the value of i = -1 and if I square it What do I get. I get +1
So there we go.
Opps I wrote thatwrong
i = square root of -1, and if I square that I get i = -1, which is a real number and i^2 =-1 gives me a real number.
Lets go back to c for a second. To evaluate I will take the square root of i and i is the square root of -1 so we are taking the square root of the square root of 1 which is -1 to the 1/4 power which is not a real number. So the only choice is D because when you square the square root of -1 you get -1 which is a real number.
Hope this video was helpful for questions 1-4 on the EOCT Analytical Test

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