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.

 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.

 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.

 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.

· 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.

 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.

 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.

 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.

 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