Download 2011-2012 CP Precalculus Final Exam Topics

2011-2012 CP Precalculus Final Exam Topics
Delaware Military Academy
Chapter P & Chapter 1 NOT included on Final Examination
The Final Exam will cover information from Chapters 2, 3, 4, and 10.
Chapter 2
Section 2.1 Quadratic Functions
Sketch the graph of a quadratic function
Identify the axis of symmetry, vertex, and concavity
Show familiarity with standard and vertex form of a quadratic
Section 2.2 Polynomials of Higher Degree
Identify the equations, degrees, and graphs of linear, quadratic, cubic,
quartic, and quintic functions
Complete a sign chart to sketch a polynomial written in factored form
Section 2.4 Complex Numbers
Apply operations on complex numbers
Show understanding of the conjugate of a complex number
Section 2.6 Rational Functions and their Asymptotes
Understand and sketch transformations of the graph of y=1/x
Given the graph of a rational function, describe the behavior of the graph
Interpret the equation to find the vertical/horizontal asymptotes
Discuss the domain and range of a rational function
Chapter 3
Section 3.1 Exponential Functions and Their Graphs
Sketch the graph of exponential functions, Identify the (horizontal)
asymptote
Use the formulas for Compound Interest [formulas given on final exam].
Section 3.2 Logarithmic Function and Their Graphs
Evaulate a Logarithm without a calculator
Converting between exponential and logarithmic form
Sketch the graph of a logarithmic function
Section 3.3 Properties of Logarithms
Use the properties of logarithms to condense or expand a logarithmic
expression
Section 3.4 Solving exponential and Logarithmic Equations
Solve simple or complex equations containing exponential or logarithmic
functions
Chapter 4
4.1 Radian and Degree measure
Converting between radians and degrees
Sketch and find angles that are coterminal
4.2 Trigonometric Functions: The Unit Circle
Show your knowledge of all the degree, radian, and coordinates around
the unit circle
Show understanding of the ratios of sine, cosine, tangent, cosecant, secant,
and cotangent
Given one of the 6 trig functions, find one of the remaining 5 trig
functions
Evaluate any of the 6 trig functions for increments of 30, 60, 45, and 90
degrees around the unit circle.
4.3 Trigonometric Functions
Use inverse trig functions to find a missing angle of a right triangle
Use one of the 6 trig functions to find the missing side of a triangle.
4.5 Sketching Sine and Cosine waves
Given an equation, sketch the sine or cosine wave
Identify the amplitude and period
Chapter 10
10.1 Circles
Identifying the center and radius from a circle equation
Given the equation, sketch the circle
10.2 Ellipses
Identifying the major axis, minor axis, foci, vertices, co-vertices, and
center of an ellipse
Give the equation, sketch the ellipse
10.3 Hyperbolas
Given the equation, sketch the hyperbola
Identify the center and vertices
FINAL EXAMINATION REVIEW QUESTIONS
Section 2.1 Review Questions
1.) Locate the axis of symmetry of the quadratic f ( x)   x 2  4 x  10 . Then find the
vertex.
2.) Write the equation of a quadratic that is concave down.
3.) Rewrite the quadratic in standard from f ( x)  4( x  3) 2  5 .
4.) Identify the vertex of the following quadratic f ( x)  4( x  3) 2  5 .
Section 2.2 Review Questions
5.) Write an example equation and graph of a linear, quadratic, cubic, and quartic
function.
6.) Complete the sign chart for the following polynomial. f ( x)   x( x  3)( x  1)
x
-∞<x<-3
-3
-3<x<0
0
0<x<1
1
1<x<∞
f(x)
7.) Sketch the polynomial that corresponds to the following sign chart.
x
-∞<x<-4
-4
-4<x<-1
-1
-1<x<1
f(x)
1
1<x<∞
Section 2.4 Review Questions
8.) Write the imaginary number, i, as a radical.
9.) Complete the operation: (2+2i)-(3+4i)
10.) Complete the operation: (4i)(-2i)
11.) What is the conjugate of (2+3i)?
12.) Rationalize the denominator by multiplying by the conjugate of the denominator:
3
(2 + i)
Section 2.6 Review Questions
1
1
1
1
13.) Sketch the graphs of y  , y   1 , y 
, and y 
. List the asymptotes
x
x -1
x 1
x
of each
4x 2 - 16
14.) Find the vertical and horizontal asymptote of the rational function. y  2
x 9
x
15.) Write the end behavior model of the rational function y  2
. Explain why this
x 9
graph has no horizontal asymptote.
16.) Describe the behavior of the rational function graphed below.
Section 3.1 Review Questions
17.) Sketch the graph of y  3 x , y  3( x 2) , and y  3 x  2 . Identify the horizontal
asymptote of each.
18.) Suppose that $500 is compounded continuously for 5 years in an account with an
interest rate of 2%. How much money will be left in the account after 5 years? 10
years?
19.) Suppose that $500 is compounded weekly for 5 years in an account with an interest
rate of 2%. How much money will be left in the account after 5 years? What if the
money is compounded monthly?
Section 3.2 Review Questions
20.) Evaluate each logarithm without using a calculator.
1
log e 1
log 4 16
log 3
9
log 10 10
21.) Write the equation in logarithmic form. 2 x  256
22.) Sketch the graphs of y  log 2 x , y  log 2 ( x  2) , y  log 2 ( x)  2 Label and
identify the asymptotes of each
Section 3.3 Review Questions
23.) Use the properties of logarithms to expand the following term into the
xy
sum/difference of logarithms. ln( 3 )
z
24.) Use the properties of logarithms to condense the following expression into a single
term logarithm. log 4 ( x)  2 log 4 (2 y)  3 log 4 ( x)
Section 3.4 Review Questions
25.) Solve the following logarithmic equations.
log x 16  4
2  log 2 ( x  4)
2  3  ln( x)  5
26.) Solve the following exponential equations.
4 ( 2 x 1)  64
10 x  .001
Section 4.1 Review Questions
27.) Convert 410 to radians
5
28.) Convert
into degrees.
8
29.) Find two angles that are coterminal to each other.
Section 4.2 Review Questions
30.) Fill in the following portion of the unit circle.
31.) Evaluate the following trig expressions.
tan( 0)
sin(  )
sec( )
3
4
32.) If sin(x)=3/4, then cot(x)=____.
Section 4.3 Review Questions
33.) Use inverse trig to find the missing angle.
34.) Find the identified missing side length of the each triangle.
cos( )
2
Section 4.5 Review Questions
35.) Sketch each function. Label the axii. y  sin( x) , y  cos(x) , and y  5 cos( x) .
2
36.) Identify the period and amplitude of the following: y  5 cos(2 x) , y   sin( 1 x)
8
Section 10.1 Review Questions
37.) Identify the center and radius of the following. ( x  3) 2  y 2  1
38.) Sketch the following circle. y   x 2  9
Section 10.2 Review Questions
39.) Sketch the following ellipse. Label the minor axis, major axis, foci, center, vertices,
( x  3) 2
and co-vertices of the ellipse.
 y2  1
25
Section 10.3 Review Questions
40.) Sketch the following hyperbola. Label the center and vertices.
( x  1) 2 y 2

1
9
4