Final exam review



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COLLEGE ALGEBRA

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.


6.1 Rational Functions and Rational Inequalities

Be able to find the horizontal, vertical and oblique (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.)

 Be able to solve rational inequalities.




7.1 Exponential Functions and Their Graphs

 Be able to graph an exponential function.

 Be able to graph translations of an exponential function, including asymptotes.

 Be able to solve an exponential equation by getting the same base on each side of the equation.



7.2 Applications of Exponential Functions

 Be able to solve problems involving exponential functions, given the function.

 Be able to solve exponential growth applications involving money (using both exponential models), and population growth.

 Be able to solve radioactive decay applications.



7.3 Logarithmic Functions and Their Graphs

· Be able to switch an equation between logarithmic form and exponential form.

· Be able to graph a logarithmic function, including translations and asymptotes.

· Be able to evaluate a logarithmic expression without a calculator.

· Be able to solve a logarithmic equation without a calculator (by changing the equation into an exponential equation).

· Be able to solve a logarithmic equation using a calculator.



7.4 Properties and Applications of Logarithms

 Be able to combine logarithms using the logarithmic properties.

 Be able to expand logarithms using the logarithmic properties.

 Be able to simplify exponential and logarithmic expressions using the logarithmic properties.

 Be able to evaluate logarithmic expressions using the change of base formula.

· Be able to solve a logarithmic equation by changing the equation into an exponential equation.

 Be able to solve application problems involving logarithmic functions (pH, Richter Scale and decibels).
7.5 Exponential and Logarithmic Equations

 Be able to solve exponential equations algebraically by taking a logarithm of both sides.

 Be able to solve logarithmic equations by using the logarithmic properties and switching to exponential form.

 Be able to simplify exponential and logarithmic expressions using the logarithmic properties.

 Be able to solve application problems involving exponential functions.


8.1 Solving Systems by Substitution and Elimination

 Be able to solve a system of linear equations in two or three variables using the substitution method. (If the system is dependent, express the solution in terms of one variable.)

 Be able to solve a system of linear equations in two or three variables using the elimination method. (If the system is dependent, express the solution in terms of one variable.).

 Be able to solve application problems using a system of linear equations in two or three variables.



8.2 Linear Systems, Matrices, and Augmented Matrices

 Be able to give the order of a matrix.

 Be able to identify the value of any element of a matrix, given the matrix.

 Be able to determine the augmented matrix for a system of equations.

 Be able to find the system of equations given an augmented matrix.

 Be able to perform any row operation on a matrix.

 Be able to determine whether a matrix is in row echelon form, reduced row echelon form or neither.

 Be able to solve a system of equations using Gaussian elimination and back substitution.

 Be able to solve a system of equations using Gaussian-Jordan elimination.

 Be able to solve application problems using a system of equations and Gaussian elimination.



8.3 Determinants and Cramer's Rule

 Be able to find the minor for any element of a matrix.

 Be able to find the cofactor for any element of a matrix.

 Be able to solve a determinant equation.

 Be able to calculate the determinant of a 11, 22 and 33 matrix by hand.

 Be able to calculate the determinant of a 33 or larger matrix using minors and cofactor expansion along a row or column.

 Be able to calculate determinant of a matrix using a calculator.

 Be able to use Cramer’s Rule to solve a system of linear equations. Note: If the system has 3 or more variables, use the calculator to find the determinants.


8.4 The Algebra of Matrices (*Extra Credit)

 Be able to multiply a matrix by a constant.

 Be able to add, subtract and multiply two matrices together, if possible.

 Be able to solve a matrix equation.

 Be able to use a graphing calculator to perform matrix operations.
8.5 Inverses of a Matrices (*Extra Credit)

 Be able to write a system of equations as a matrix multiplication equation.

 Be able check if two matrices are inverses of each other.

 Be able to find the inverse of a matrix using a calculator.

 Be able to solve a system of linear equations using the inverse of a matrix.

Chapter 6 Test (p. 500) 1, 3, 5, 7, 9, 11, 13, 17, 21, 23, 25, 27, 31, 33, 37


Chapter 7 Test (p. 583) 1, 2, 5 - 27 odd, 31, 33, 37, 39, 41, 43, 47, 49, 53, 55, 61, 63
Chapter 8 Test (p. 695) 1 - 13 odd, 17, 21, 23, 27, 29, 31, 33, 37, 41, 43, 45, 49*, 51*, 55*, 57*, 59*, 61*, 65*, 69*

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