Precalculus Fall Final Exam Review 2013
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Precalculus Fall Final Exam Review Topics 2013
1. Parabolas (2.1)
a. Write in vertex form given the expanded form.
b. Write the equation for the parabola given the vertex and a point on the
parabola.
c. Find the max or min value.
2. Functions (Ch. 1)
a. Given a graph, use transformations to identify the function.
b. Determine whether a function is Even/Odd/Neither
c. Determine whether a function One to One
d. Find the Inverse of a function
e. Evaluate functions for specific values.
f. Perform operations with functions algebraically and graphically (addition,
subtraction, multiplication, division).
g. Evaluate Composition of Functions (including those that have domain
changes due to the composition)
h. Shift, Reflect(x and y directions), and Stretch any function
i. Determine End Behavior of a function (falls, rises)
j. Determine the intervals on which a function is increasing, decreasing or
constant.
k. Graph a Piecewise Function
l. From a graph, determine what the piecewise function is.
m. Determine the Domain and Range of a Function given:
i. Numerical data (ordered pairs)
ii. An equation for a function
iii. Graph
3. Polynomials (2.2, 2.3, 2.5)
a. Find all zeros of a polynomial
b. Use division to factor a polynomial
c. Given the zeros, write the polynomial function.
d. Graph polynomials using zeros and end behavior
4. Complex Numbers (2.4)
a. Perform operations with Complex Numbers (Add, Subtract, Multiply,
Divide)
b. Raise “i” to a power
c. Absolute Value
5. Rational Functions (2.6 and 2.7)
a. Find the following information for a Rational Function
i. Intercepts
ii. Horizontal Asymptotes
iii. Vertical Asymptotes
iv. Slant Asymptote
b. Sketch the graph of a rational function
c. Solve Rational Functions
6. Angles/Trigonometry (4.1-4.4)
a. Estimate angle measures.
b. Find complementary angles, supplementary angles, reference angles and
coterminal angles.
c. Convert between radians and degrees.
d. Determine the quadrant for the terminal side of an angle.
e. Given two of these measures, find the other: arc length, radius, central
angle.
f. Find the angles that have a given trig value
g. Evaluate trig functions given
i. The angle
ii. A point on the terminal side of the angle
iii. A triangle with the angle and two side lengths
iv. The value of another trig function.
h. Use trigonometry to find angle of elevation or depression or triangle side
lengths for applications.
7. Law of Sines and Cosines (6.1-6.2)
a. Use the Law of Sines and Cosines to solve a triangle.
b. Solve equations using Law of Sines and Cosines.
c. Find the area of an oblique triangle.
8. Graphing Trigonometric Functions (4.5-4.7)
a. Graph all 6 trigonometric functions with and without transformations.
b. Determine the period, amplitude, phase shift and vertical shift for graphs
of trig functions (if applicable).
c. Sinusoidal Application
d. Trigonometric Inverses