Download Final Exam Review

Final Exam Review
Read the directions carefully. I want you to SHOW YOUR WORK for each problem. A solution,
even a correct solution, will not receive full credit if there is no support work or explanation. Partial
credit is always considered, so showing your work is to your advantage.
4.5
Graphs of Rational Functions and Their Applications
 Be able to find the horizontal, vertical and inclined (slant) asymptotes (if they exist) of a
rational function.
 Be able to graph a rational function using x- intercepts, the y-intercept and asymptotes
of the function. (Watch out for holes.)
5.1
Exponential Functions and Their Applications
 Be able to evaluate an exponential function.
 Be able to graph an exponential function.
 Be able to graph translations of an exponential function, including asymptotes.
5.2
Logarithmic Functions and Their Applications
 Be able to switch an equation between logarithmic form and exponential form.
 Be able to evaluate a logarithmic expression with or without a calculator.
 Be able to find the domain of a logarithmic function.
 Be able to graph a logarithmic function, including translations and asymptotes.
 Be able to solve application problems involving logarithmic functions.
5.3
Working with Logarithms and Logarithmic Scales
 Be able to combine logarithms using identities.
 Be able to expand logarithms using identities.
 Be able to evaluate logarithmic expressions using the change of base formula.
 Be able to graph logarithmic functions using a calculator and the change of base
formula.
 Be able to solve application problems involving logarithmic functions.
5.4
Exponential and Logarithmic Equations
 Be able to solve exponential equations by hand.
 Be able to solve exponential equations algebraically by taking a logarithm of both sides.
 Be able to solve logarithmic equations by using identities and switching to exponential
form.
 Be able to solve application problems involving exponential and logarithmic functions.
5.5
Exponential Growth and Decay
 Be able to solve exponential growth applications involving money, and “population”
growth.
 Be able to solve exponential decay applications involving Newton’s Law of Cooling,
medication, carbon dating and radioactive decay.
5.6
Modeling Data with Exponential and Logarithmic Functions (EXTRA CREDIT)
 Be able to make scatter plots using your calculator.
 Be able to find regression equations to fit linear, quadratic, exponential and logarithmic
data using your calculator, including r values.
 Be able to solve application problems related to modeling exponential and logarithmic
data.
5.7
Logistic Growth Models and Their Applications (EXTRA CREDIT)
 Be able to find the logistic growth model, given population information.
 Be able to find the logistic growth model using your calculator, given a table of values.
 Be able to solve application problems related to modeling logistic growth data.
6.1
Systems of Linear Equations in Two Variables
 Be able to determine the number of solutions for a system of linear equations in two
variables and determine whether the system is consistent/inconsistent, and
dependent/independent.
 Be able to solve a system of linear equations in two variables using the substitution
and elimination methods.
 Be able to solve application problems using a system of linear equations in two
variables.
6.2
Systems of Linear Equations in Three Variables
 Be able to determine the number of solutions for a system of linear equations in three
variables.
 Be able to solve a system of linear equations in three variables using the substitution
and elimination methods.
 Be able to solve application problems using a system of linear equations in three
variables.
6.3
Row Operations and Systems of Equations
 Be able to give the order of a matrix.
 Be able to determine the augmented matrix, coefficient matrix, variable matrix, and
constant matrix for a system of equations.
 Be able to solve a system of equations using Gaussian elimination.
 Be able to solve application problems using a system of equations and Gaussian
elimination.
6.4
The Algebra of Matrices
 Be able to multiply a matrix by a constant.
 Be able to add, subtract and multiply two matrices together, if possible.
 Be able to use a graphing calculator to perform matrix operations.
 Be able to write a system of equations given a matrix multiplication equation.
6.5
The Inverse of a Matrix (EXTRA CREDIT)
 Be able check if two matrices are inverses of each other.
 Be able to find an inverse of a 22 or 33 matrix using Gaussian elimination.
 Be able to find an inverse of a larger than 33 matrix using a calculator.
 Be able to solve a system of linear equations using the inverse of a matrix.
Appendix B Determinants and Cramer’s Rule (EXTRA CREDIT)
 Be able to calculate the determinant of a 11, 22 and 33 matrix by hand.
 Be able to calculate determinants of larger matrices using a calculator.
 Be able to determine whether a square matrix has an inverse by calculating a
determinant.
 Be able to use Cramer’s Rule to solve a system of linear equations.
Chapter 4 Review (p. 379)
43, 45, 47, 51, 53
Chapter 4 Test (p. 381)
15, 17
Chapter 5 Review (p. 479)
1, 3, 5, 7, 9, 11, 13, 17, 19, 21, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43,
45, 47, 49, 55, 59, 61, 63, 65*, 69, 71*, 73*, 75, 77, 79, 81
Chapter 5 Test (p. 482)
1, 3, 5, 7, 9, 11, 13, 15, 17*, 19*
Chapter 6 Review (p. 572)
1, 3, 5, 9, 19, 23, 27, 29, 31, 39, 41, 43, 45, 47, 51, 57*, 59, 61*,
65*, 89, 91, 93, 97, 103
Chapter 6 Test (p. 576)
1, 7, 11
Appendix B (p. AP25)
1*, 3*, 5*, 17*, 19*, 23*, 25*, 51*
* This question is from the extra credit section.