Math 230, Spring 1999
Review for Exam 1
Basic Rules:
1. No TI-92, TI-89, or any other calculators with symbolic calculation features
are allowed.
2. A basic formula sheet of space curves and 3D motions will be given to you for
the test.
What can you do to improve your performance?
1. Read the instruction very carefully. Many problems are NOT like the
problems from the textbook.
2. Avoid arithmetic, algebra and calculus mistakes.
3. Don't let the fear of complicated problems blind you. When you have the
confidence of you algebra and calculus skills, you'll be quicker to detect your
small mistakes, correct and simplify thing before it gets too messy. When you
are not overwhelmed by calculation details, you'll know when to look for
short cuts.
4. A formula can be used in many different ways. It usually represents a
"relationship" between different quantities. Sometimes more than one
formulas are used in solving a problem.
5. Visualize if you can.
Subjects covered
1. Vectors and their operations (20-30%)
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components of i, j, k
magnitude and direction (unit vector)
operations: scalar multiple, sum and difference
operations: dot and cross products
scalar projection and vector projection
parallel and orthogonal vectors
angle between vectors
other applications: area of triangle and parallelogram, volume of parallelepiped
There are unlimited ways to ask questions about the basic concepts. The concepts of
the magnitude and the unit vector of any given vector are essential. Most interesting
questions are related to the two products, dot and cross product, and two kinds of
projections.
2. Lines and planes (20-30%)
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equations for lines
equations for planes
find the equation of a line from its description
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find the equation of a plane from its description
relations between a point and a line
relation between two lines (intersecting, parallel, and skew)
relation between a point and a plane
relation between a line and a plane
relation between two planes
angle between intersecting lines, a line and a plane, and planes
distance between points, lines, and planes
3. Space curves and 3D motion (40-50%)
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position, velocity, speed, and acceleration
unit tangent vector
principal unit normal vector
arc length and distance
curvature and radius of curvature
osculating plane, binormal vector, and normal plane
tangential and normal components of acceleration