MAT 270
Calculus with Analytic Geometry I
Fall 2003
MAT 270 Preliminaries Quiz Outline
Appendix A
Definition of rational numbers
Definition of irrational numbers
Meaning of a repeating decimal (from book and from lecture)
Representation of numbers on a number line
Interval notation (open and closed endpoints)
Solving inequalities -- resulting in intervals
Absolute value (definition, distance between points as |
a
–
b
|)
Triangle inequality
Appendix B
Cartesian coordinates
Distance formula in the plane & Pythagorean theorem
Equation for the midpoint of a line segment (see problems #54-56)
Slope of a line (from book and from lecture, i.e., rate of change framework)
Equations of lines (point-slope, slope-intercept, general/linear equation)
Parallel and perpendicular lines
Appendix C
Equation of a circle
Equation of a parabola
Appendix D
Meaning of radians (arc-length)
Converting between radians and degrees
Length of a sector of a circle
Meaning of trig functions in terms of triangles (sin, cos, tan, csc, sec, & cot)
Meaning of sine and cosine in terms of the unit circle (
x
and
y
coordinates)
Values of trig functions for important angles (multiples of π/6 and π/4).
How to find the value of other trig functions given one trig function and quadrant.
Trig identities (equations 6, 7, 8, 9, 10a, 10b, 11, 16a, 16b, 17a, 17b)
Graphs of trig formulas (sin, cos, tan, csc, sec, & cot)
Section 1.1
Concept of a function that accepts input values to produce output values (see definition on page 12)
Definition of terms (domain, range, composition, even, odd, increasing, decreasing)
Four ways to represent a function (graphically, numerically, algebraically, verbally)
Use each representation to
Determine domain and range
Evaluate a function for a given input
Compose two functions for a given input
Find a function inverse for a given output
Vertical line test – know how it connects to the definition of function.
Piecewise functions (be able to graph, compute compositions)
Section 1.2
Polynomials (coefficients, degree, general shapes of graphs)
Exponential and logarithmic functions (shapes of graphs)
Section 1.3
Vertical and horizontal shifts of functions (p. 38 - be able to apply to any function)
Vertical and horizontal stretching and reflecting (p. 39 – ditto)
Meaning of
f
+
g
,
f–
g
,
fg
,
f/
g
in terms of input and output (also be able to apply)
Meaning of
f
o
g
in terms of input and output (also be able to apply)
Section 1.4
Know how to use your calculator!
Section 1.5
Meaning of exponent as repeated multiplication
Meaning of roots (square root, cube root, etc.)
Meaning of
x
p/q
Laws of exponents
Section 1.6
Meaning of inverse function in terms of input and output
Inverse function notation,
f
-1
Ability to find inverses algebraically
Ability to find specific values for an inverse using a table
Ability to draw the inverse of a function given a graph.
Meaning of one-to-one in terms of input and output (& horizontal line test)
Logarithmic functions as inverses to exponential functions
Laws of logarithms
Inverse trig functions (know the standard restrictions of domains)
Composition of exam (5 questions):
A homework problem you have already done
A definition, property, law, procedure, or the rate or approximation framework
A conceptual problem (involving explaining, drawing a diagram, etc.)
A problem using the standard information in a new way
A problem combining concepts from multiple sections
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