MAC 2313 - University of North Florida



MAC 2313

Review - Exam 1

May 27, 2010

When: June 3, 2010, in Room 14/2743, 12:40-2:50 (if you clear it with me first, you can start the exam early)

What Material: Sections 10.2-10.5, 11.1-11.7.

Procedure: The exam will be closed book. You will be allowed one sheet of notes, 8-1/2 by 11 inches, front and back. A graphing calculator will be expected, though TI-89's and TI-92's will not be allowed.

How to Study: My exams are very straightforward, focusing on standard problems as opposed to tricks. I have a tendency of putting several problems of the same type on an exam, ranging from easy to difficult. I do like to put word problems on exams, but we did not see any word problems in these chapters.

You WILL be expected to show your work on all problems.

You should go over every homework problem assigned, as well as all problems from the chapters that are similar. Continue to practice until you can do the problems comfortably in a test situation (one page of notes and a calculator, no additional notes, no back of the book, no CalcChat, etc). Also focus on quiz problems. If I found a type of problem important enough for a quiz, it is probably important enough for an exam. Finally go over the practice problem sets at the end of the chapter. Even though it includes some material that I did not cover, it is good in that the topics are mixed together, just like on the exam.

Previous Knowledge: All of precalculus is fair game. You need to be able to differentiate anything. You need to be able to integrate any basic function, or anything that requires u-substitution. Polar integration often requires standard trig substitutions. I will not require any integration technique more complicated than that.

Specific Topics:

• Parametric Curves: Be able to graph them (figure out how to do it on your calculator – don’t forget to change your t-range and t-step if necessary), get rid of the parameter (if possible), find the slope at a point, the tangent line at a point, the concavity at a point, the arclength of the curve, or the surface area of revolution. These all boil down to a plug-n-chug equation, but you still need to know how to do it. Be extra careful with your algebra: one mistake could keep you from being able to integrate. Expect problems where you need to find horizontal or vertical tangencies. Practice Problems: 10.2, 3-32, 39-42, 55-62; 10.3, 1-56, 67-72.

• Polar Coordinates: Make sure you can convert from rectangular to polar and from polar to rectangular. Remember that there is some extra concern when going from rectangular to polar. You should also be able to convert between polar equations and rectangular equations. Practice Problems: 10.4, 1-21, 27-42.

• Graphing in Polar Coordinates: I will give you an equation; you will supply the graph. Just make sure you know how to use that graphing calculator. As with parametric curves, make sure your theta range and theta step are appropriate for your graph. Practice Problems: 10.4, 43-52, 81-90.

• Slope of Polar Curves: It's an equation. Plug everything in correctly, and you get the correct answer. I could combine one of these problems with an intersection problem (first find the point of intersection, then find the slope there), or I could require you to find points where the curve has horizontal/vertical slope. Practice Problems: 10.4, 59, 60, 65-88.

• Area of Polar Curves: This one can be tricky, especially if I ask you to give me area between two curves. Make sure you graph the functions, make sure you get the right range to integrate (i.e., find points of intersection), and make sure you do the integration formula correctly. Practice Problems: 10.5, 1-26, 31-44.

• Vectors: Many different things to ask about them: add, subtract, multiply by a scalar, find the unit length vector in the same direction, find its norm, dot product, angles, determine if two vectors are orthogonal, determine if two vectors are parallel, cross product, find a vector perpendicular to two given vectors, area of parallelograms, volumes of parallelepipeds. You should know how to do all of these things, and you should know what they mean geometrically. Lots of stuff to worry about here, so make sure you have it all straight in your head. Practice Problems: 11.1, 1-74; 11.2, 53-88; 11.3, 1-50; 11.4, 1-24, 27-36, 41-48.

• Lines and Planes: Be able to find the equation for a line given a point and a vector, or the equation of a plane given a point and a normal. Expect questions where you have to do work first to figure out the point or vector, then you can write out the equation. I can also ask questions like "do the lines intersect" or "are they parallel" or "where does the line and the plane intersect". Practice Problems: 11.5, 3-86 (especially 13-20 and 41-52).

• Cylindrical and Spherical Coordinates: Most of this is just converting from one coordinate system to another. I can also ask you to convert an equation from one coordinate system to another. All of this boils down to the sets of conversion equations. Practice Problems: 11.7, 1-104.

• Surfaces: You should know the names of the various surfaces, but there will not be any problems specifically from Section 11.6 on the exam.

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