MAT1275CO College Algebra and Trigonometry FA2019

Important information about the Final Exam:

Our Final Exam is scheduled for Thursday 19 December at our usual class meeting time and in our usual room. All students, without exception, are expected to show up for the Final Exam, which is required in order to pass the course.

There will be assigned seating, different from the assigned seating in the previous tests. Please try to arrive early so that we can get everyone seated and start on time.

If you arrive late or while I am directing students to their seats, please DO NOT SEAT YOURSELF. Wait until I tell you where your assigned seat is.

Additional instructions may be written on the blackboard during the Exam. You are responsible for following all instructions, whether on the board or on the exam paper.

You will need a calculator for the exam. It does not need to be a graphing calculator. If you need to borrow a calculator from the Library, please make sure you arrive in time to do that. You will not be permitted to leave the classroom and go to the Library once the exam has begun.

While I am distributing the exam papers and other materials at the start of the exam, the door to the classroom will be shut and a sign posted asking you to wait. Please wait outside the room until I call you in.

You may not use a cellphone, Apple watch or any other smart watch, or any device which can connect to the internet for any reason. The presence of such a device in my or your eyesight during the exam will be regarded as evidence of intent to violate Academic Integrity Policy and your exam papers may be collected at that point.

You do not need a watch because I will project the internet clock onto the screen as usual.

You may not communicate with another student for any reason in any way during the exam. Both of your papers may be taken away. If you need a pen, pencil, or eraser, or anything else, raise your hand and ask me.

Please make a restroom visit before the exam begins. No one may leave the classroom before the end of the exam without speaking to me, except that after 1 hour has passed, if you handed in your papers, you may leave.

Please see the City Tech Academic Integrity Policy.

Also, please review my course policies.

 

———————————————–

The resource pages linked below have been updated so that they all link the new Fall 2019 version of the Final Exam review sheet – the only change is that the instructions to some of the problems have been changed for clarity. Nothing has changed about what you have to do.

I have also added in the missing resources, including two slideshows: one on solving exponential equations and one on proving identities. Look for them in the relevant problems.

 

MAT1275FinalReviewFall2019version

Below are links to resource pages for each of these problems. This page will be updated as new resources are added. Please also let me know by email or by leaving a comment on this post (NOT in class!) if you find something useful online.

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problems 8-10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

 

The resource pages linked below have been updated so that they all link the new Fall 2019 version of the Final Exam review sheet – the only change is that the instructions to some of the problems have been changed for clarity. Nothing has changed about what you have to do.

I have also added in most of the missing resources; the only thing still remaining to be uploaded are two slideshows, one on solving exponential equations and one on proving identities. Look for a second update later today!

 

MAT1275FinalReviewFall2019version

Below are links to resource pages for each of these problems. This page will be updated as new resources are added. Please also let me know by email or by leaving a comment on this post (NOT in class!) if you find something useful online.

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problems 8-10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

 

MAT1275FinalReviewFall2019version

This problem requires you to solve a simple exponential equation using logarithms. You will need to use your calculator for this one. When you take the logarithm of each side, you can use either the log base 10 on both sides or the natural logarithm on both sides: you get the same result either way!

Resources:

• WeBWorK ExponentialEquations-CalcBase10

• Video of a solution to problem 17a

• Slideshow MAT1275coSolvingSimpleExponentialEquationsUsingLogsShort

MAT1275FinalReviewFall2019version

This problem requires you to find an exact value of a logarithm without using a calculator. In order to receive credit for this problem you must show how you arrived at your answer: merely writing an answer with no work shown will result in 0 points! So pay attention to how I recorded my work on the board in class.

Resources:

• WeBWorK LogarithmicFunctionsExactValues

 

• Here are two videos which you may find useful: they give a method that is similar to what I did in class but a bit “formal”.

Finding exact values of logs 1

Finding exact values of logs 2

•  And here is a video showing a solution to #16c, using that somewhat formal method

MAT1275FinalReviewFall2019version

This problem requires you to solve a trig equation for exact solutions in the interval $[0, 2\pi)$. This means that you are not supposed to use a calculator to solve this equation and you will have to show how you arrived at your answer without using a calculator in order to receive credit!

Resources:

• WeBWorK TrigEquations problems 6-9

• Video showing a solution for problem 15d

• My slideshow MAT1275-SolvingBasicTrigEqns-slideshow

and my handout MAT1275SolvingTrigEquationsActivitiesHandout

MAT1275FinalReviewFall2019version

This problem requires you to prove a trig identity. I strongly recommend you use the method that we developed to make this easier!

Resources:

• Handout  Proving trig identities made easier: trig_deliv

• Slideshow with the proof of $\cos(x) + \sin(x)\tan(x) = \sec(x)$: ProvingTrigIdentitiesMadeEasier

[which is the problem proved in the handout and also is essentiqally the problem in today’s Quiz!]

MAT1275FinalReviewFall2019version

This problem requires you to find the values of trig functions given the value of one of them, plus information about the quadrant. You may need to review: the coordinate plane definitions of the trig functions; the signs of the trig functions in the four quadrants. (People insist on using a mnemonic for that, but it’s really not necessary: think about the unit circle.)

Resources:

• WeBWorK CoordinatePlaneTrig problems 4, 5 (Use “Show Me Another” if you have already completed this)

 

 

MAT1275FinalReviewFall2019version

This problem requires you to use the Coordinate Plane and/or the Unit Circle definitions of the trig functions. We did this extensively while reflecting the basic triangles over the axes to find the important points on the unit circle in all four quadrants. (Remember I kept asking you, “What’s the reference angle?”)

If the angle in given in degrees, continue to work in degrees (or you can switch to radians if you like). If a problem is given in radians, do not translate it to degrees! but stay in radian measure.

IMPORTANT: When you are asked to find exact values, it means you must not use your calculator to compute them: rather, in this problem, use your knowledge of the important points on the unit circle and draw a picture to explain your answer – that is how you show your work! You may also need to draw a picture of one of the two important right triangles. But if you show nothing at all and just write down the answer, you receive 0 points!

Resources:

• WeBWorK  UnitCircle (Use “Show Me Another” if you have already completed this.)

• Here are four videos from Patrick’s Just Math Tutorials which may be helpful:

Finding a reference angle using degrees

Finding a reference angle using radians

Using reference angle to evaluate trig functions, using degrees

Using reference angle to evaluate trig functions, using radians

 

 

Topics:

• Using Law of Sines and Law of Cosines to find angles
• Exponential functions and logarithms
• Solving logarithmic equations

Definition of logarithms (Math is Fun) – this goes all the way back to the very basics.

Introduction to logarithms (Math is Fun)

Here is the slideshow on what is a logarithm and how to find exact values for certain logs: MAT1275-LogarithmBasics-slideshow

I also have a slideshow for solving exponential equations, but it needs some work.

Homework:

• Read through the comments I wrote on your Test 4 papers and write down or remember any questions you have: either email me asap or bring them to class on Wednesday.
• Finish the WeBWorks on Law of Sines and Law of Cosines by Tuesday night!
• Do the remaining problems from the Final Exam Review MAT1275FinalReview, at least one of each type. Next time I will ask for volunteers to “teach” at least one of each type, NOT the ones which have videos already, and this is your last opportunity for extra credit! Make extra sure that you do the last two problems (on logs and solving exponential equations) – I will post more practice on the Final Exam review page soon.
• Read about the “old” WeBWorK assignments in the post from last time.

 

MAT1275FinalReviewFall2019version

This problem requires you to use either the Law of Sines or the Law of Cosines to find an unknown angle or side in a triangle which is not assumed to be a right triangle! Please avoid using anything that only applies to right triangles!

Resources:

• WeBWorK LawOfSines and LawOfCosines (Use “Show Me Another if you have already completed these)

• Videos from Patrick’s Just Math Tutorials:

Law of Sines Example 1

Law of Sines Example 2

Law of Sines Example 3

And yes, I know that the examples below seem to be out of their correct order, but trust me on this:

Law of Cosines Example 5

Law of Cosines Example 2

Law of Cosines Example 3