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MAT1275FinalReviewFall2019version

These problems are on the topic of angles of elevation or depression, and require you to solve a right triangle for one of its parts.

Resources:

• Angles of elevation or depression  definitions at Math is Fun

• Angles of elevation or depression: five powerful examples from CalcWorkshop

• Video showing a solution to #8

• WeBWorK on SolvingRightTriangles (there are two: one where we use the inverse trig functions to find angles. Use “Show Me Another” if you have already completed these.)

MAT1275FinalReviewFall2019version

This problem requires you to solve a system of two nonlinear equations. You can still usually use substitution or elimination, but with a slightly different strategy than if they were linear.

Realize that a nonlinear system will usually have more than one solution!

Resources:

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

• Various videos on solving nonlinear systems of equations

• A video showing a solution of #7d

 

MAT1275FinalReviewFall2019version

This problem requires you to solve a 3 by 3 system of linear equations.

You may need to review solving a 2 by 2 system of linear equations first.

Resources:

• My handout outlining how to solve a 3 by 3 linear system: MAT12753by3systemsClasswork

• Dr. Math showing how to solve a 3 by 3 linear system (typed)

• The solution to the in-class quiz on solving a 3 by 3 linear system:  MAT1275coQuiz3by3linearSystems

• Solutions to the in-class quiz on 2 by 2 linear systems: MAT1275COQuiz2x2system-19Sept2019-solutions

• WeBWorK on 3X3-systems (Use “Show Me Another” if you have already completed this)

• A video showing a solution to #6a

• VirtualNerd video showing another example of solving a system of 3 linear equations using elimination (our method)

MAT1275FinalReviewFall2019version

This problem requires you to do arithmetic using complex numbers. It’s very much like ordinary algebra, except that you must remember that $i^{2} = -1$, and also to put your final. answer into the standard (“rectangular”) form $a + bi$.

Also remember, since $i$ is a radical (it’s $\sqrt{-1}$), we divide by rationalizing the denominator, which means we have to multiply top and bottom by the conjugate of the denominator. It is helpful to remember that $(a+bi)(a-bi)=a^{2} + b^{2}$.

Resources:

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

• Video showing a solution of #5d

 

MAT1275FinalReviewFall2019version

This problem requires you to do several things:

• Put the equation of the circle into its standard form by completing the squares,

• Read off the center and radius of the circle from the standard form of the equation,

• Find the four “cardinal points” on the graph of the circle and draw the graph.

WARNING: on this problem, as on all the Final Exam problems, you must derive your answers algebraically in order to receive credit. If you graph on your graphing calculator and read off coordinates without doing any algebra, you will receive NO CREDIT!

Resources:

• WeBWorK on Circles:  this shows how to do the first two items above but not how to find the four cardinal points. (Use “Show Me Another” if you have already completed this.)

• Video showing a solution of problem #4a, showing how to find the four cardinal points as well. I recommend putting in the four points BEFORE you try to draw the circle though!

• A longer version of that video

 

MAT1275FinalReviewFall2019version

This problem requires you to simplify a complex fraction. Recall that there are two methods for doing this:

Method 1: simplify the “top” and the “bottom” of the complex fraction by adding or subtracting, if necessary; then turn the division into multiplying by the reciprocal of the “bottom”.

Method 2: Find the LCM of ALL the denominators in the “top” and “bottom” of the complex fraction; multiply the “top” and “bottom” by this LCM to clear all the “little” denominators; simplify and turn the division into multiplying by the reciprocal.

In any case it goes without saying that you must reduce your final answer to lowest terms.

Resources:

• WeBWorK on ComplexFractions:  there are two of them, one for Method 1 and one for Method 2.  (Use “Show Me Another” if you have already completed these.)

• Video showing how to use each of those methods to solve #3a

You may also need to review how to find the LCM. Here is a tutorial from VirtualNerd on finding Least Common Denominators to add/subtract rational expressions

MAT1275FinalReviewFall2019version

This problem requires you to do several things:

• Find the vertex of a parabola from its formula,

• Find the x- and y-intercepts of a parabola from its formula,

• Sketch the graph of the parabola from that information and label the points.

WARNING: on this problem, as on all the Final Exam problems, you must derive your answers algebraically in order to receive credit. If you graph on your graphing calculator and read off coordinates without doing any algebra, you will receive NO CREDIT!

Resources:

• WeBWorK on ParabolaVertices: there are two of them, one on CtS (completing the square) and one on Vertex formula. Choose whichever method you prefer.

• Finding the x-intercept: set y=0 in the formula and solve the resulting quadratic equation. Remember that the x-intercept(s) are points of the form $(0,a)$ for some number(s) $a$.

Always try to choose the simplest method that will work for your quadratic equation: Factor and use the Zero Product Property if at all possible!

• Finding the y-intercept: set x=0 in the formula. Remember it is a point $(0, b)$ for some number $b$.

• A video showing a solution to #2c using the Vertex Formula

• A video showing a solution to #2c using Completing the Square to put the equation into vertex form

 

MAT1275FinalReviewFall2019version

This problem requires the use of the Quadratic Formula, although, since no method is specified, you   also use Completing the Square (plus the Square Root Property).

Quadratic Formula resources:

• WeBWorK on QuadraticFormula (you can use “Show Me Another” if you’ve completed this already)

• Videos from the MAT1275 video library on the Quadratic Formula

• Video of solution to #1b

• VirtualNerd video on using the Quadratic Formula

If you prefer to use Completing the Square:

• WeBWorK on SquareRootProperty problems 5-9 (you can use “Show Me Another” if you’ve completed this already)•

I will post a slideshow video on this soon. PLEASE do not “google” this because almost everyone does it wrong!

You may also need to review Simplifying Radicals and/or Reducing Fractions.

Simplifying Radicals:

• Video on simplifying radicals by finding perfect square factors

• Another video from VirtualNerd on simplifying radicals using prime factorization

Reducing fractions:

• PurpleMath on reducing fractions when there is more than one term in the numerator

 

I have posted notes on the Law of Sines and Law of Cosines examples I did in class – the Law of Cosines example continues on to solve the triangle, which I did not get to do Thursday.

Homework:

• Make sure that you do the homework on proving trig identities from last time. The Quiz on Monday will be on trig identities. The Quiz on Wednesday will be on Law of Sines and Law of Cosines.

• Also assigned: see the resource on ramps for accessibility. The largest permitted rise-to-length ratio is 1:12 or $\frac{1}{12}$. What angle of elevation does this give?

• As for the WeBWorK on Law of Sines: for now you only need to do problems 1 and 3-5; you can skip problem 2 for now (or try it if you like, after reading my notes)

• As for the WeBWorK on Law of Cosines: for now you only need to do problems 1 and 4. You may certainly try the others if you like: that will set you up well for what we do on Monday.

• Please go to the Final Exam Review sheet and work on problems 11-16 (which are on trig) for Monday. I will be posting resources specific to each problem on that page over the weekend, and if you find anything useful to share with the class please let me know!

• I have re-opened some of the old WeBWorK assignments for everybody. (It turned out to be too time-consuming to do this on an individual basis.) The assignments I have re-opened are the ones which are closest to the content of the Final Exam. I also arranged their “due dates” so that they appear in the same order as the problems on the Final Exam review sheet.

IMPORTANT: HERE IS WHAT YOU SHOULD DO!

* If you have already completed an assignment, do not redo the problems! We are now in the reduced-scoring period and you. might reduce your score if you do that. Rather, use the “Show me another” button if you want to practice.

* Concentrate on the assignments that you most need to work on. Remember that this is to make you get a good score on the Final Exam which is worth more than twice as much as WeBWorK to your final grade!

* If there are one or more assignments (be reasonable, please!) that you have not completed and you would like re-opened, please let me know BY EMAIL, NOT IN CLASS!, before Sunday 11 PM. After that, sorry, no more.

* The due dates on these are absolutely final and will not be extended for any reason whatever. But you should in any case start working on these assignments NOW if you intend to do them.

* I have also made visible the WeBWorK on Radical Equations. If you are up-to-date on everything else, you may want to do this one for extra credit. But a word to the wise: if you are NOT up-to-date on everything else, your time is better spent working on what will be on the remaining two quizzes and the Final Exam. The extra credit on this one assignment is not enough to make up for poor performance on the Final Exam in particular.

 

See program here.

Honoring the 90th anniversary of Analog magazine.