Math 205 Study Guide for Quiz #1

Math 205
Study Guide for Quiz #1
Take-home quiz

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Closed-book
Time limit: at most 45 minutes
To be handed out Monday, February 9 and due Tuesday, February 10
Covers HWKs 1 - 2
Covers Sections 12.1 - 12.4
Questions? Send me e-mail or post in the Q&A conference in our FirstClass conference. When applicable, give page or section number, give problem number, and be specific.
Suggestions for Practice Problems:
- 12.1 p566: 9, 12, 15, 17, 18, 27, 29, 30, 31
  Note that in #18 you're graphing the points that satisfy both of the conditions z = 2 and y = 4. So one graph, not two.
- 12.2 p572: 1, 3, 5, 7, 9, 13
- 12.3 p581: 6, 8, 10, 11, 16, 17ab, 19(a), 20
- 12.4 p588: 12, 14, 17, 18, 25
- Ch 12 Review Exercises and Problems p600: 1, 2, 5, 7, 9, 14, 15, 17, 19, 21
- Ch 12 Check Your Understanding p602: any odd-numbered 1 - 49
Material to know or be familiar with
- 3-dimensional or xyz-space
  - plotting points
  - finding distance between points
  - algebraic descriptions for coordinate planes and planes parallel to coordinate planes
  - algebraic descriptions for coordinate axes and lines parallel to coordinate axes
  - equations for spheres
  - recognizing a sphere from its equation (may require completing the square)
  - finding distance between a point and a plane parallel to one of the coordinate planes
  - finding distance between a point and a line parallel to one of the coordinate lines
- graphs for equations involving three variables
  - planes
  - spheres
  - equations with one variable missing (cylinders)
  - z = x²+y², and variations on it
  - z=g(x²+y²) or z=g(sqrt(x²+y²)), where g is a familiar function such as sine, cosine, exponential, etc
  - sketching section of the graph for a fixed value of one of the variables
  - using sections to help identify graphs (won't be quizzed, but good to work on)
  - recognizing symmetry with respect to one of the coordinate planes
  - recognizing symmetry with respect to the origin
  - recognizing circular symmetry (see Example 2 p 569, for instance)
  - from the catalog of surfaces on p593
    - elliptical paraboloids (includes circular paraboloids as special case)
    - ellipsoids (includes spheres as special case)
    - planes
    - cylindrical surfaces (includes circular cylinders, parabolic cyliners)
    - not included this time: hyperbolic paraboloids, hyperboloids, cones
- functions of two variables: z = f(x,y)
  - 4 ways to (re)present such a function
    - graph in 3-space
    - contour diagram in 2-space
    - table
    - formula
  - moving back and forth from one representation to another
  - using such representations in connection with real-world variables
    - weather maps showing isotherms as contour curves for temperature
    - topographical maps showing contour lines or level curves
  - sketching sections of the graph, for fixed x, or fixed y, or fixed z
  - linear functions in particular
    - recognizing linear functions
      - from graph
      - from contour diagram
      - from table
      - from formula
    - working with linear functions
      - finding formula
      - sketching a contour diagram
      - filling in tables
      - sketching the graph
      - slope in the x-direction; in the y-direction
    - simple applications of linear functions
  - graph for the function z = f(x,y) = x²+y² and variations on it
  - not explicitly covered: Cobb-Douglas production functions

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Alexia Sontag, Mathematics
Wellesley College
Date Created: June 28, 1999
Last Modified: February 5, 2004
Expires: June 30, 2004