COLLEGE ALGEBRA



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.

3.4 Fundamental Theorem of Algebra

( Be able to find all of the zeros of a polynomial, (first find any rational zeros by graphing the polynomial on your calculator and using the Rational Zero Theorem and synthetic division), and write the polynomial as a product of linear factors.

( Be able to use known zeros (including complex zeros) and synthetic division to factor a polynomial function and find its zeros.

( Be able to find the complex zeros of a polynomial.

( Be able to use information about the degree of a polynomial and its zeros, including multiplicity, to find the general equation of the polynomial. (Note: If additional information is given, a particular equation can be found.)

3.5 Graphs of Rational Functions and Their Applications

( Be able to find the domain of a rational function.

( Be able to find the horizontal, vertical and slant asymptotes (if they exist) of a rational function.

( Be able to graph a rational function using x- intercept(s), the y-intercept and any asymptotes of the function. (Watch out for holes.)

4.1 Inverse Functions

( Be able to find the inverse of a function or relation represented as a set of points, as a table or as a graph.

( Be able to determine whether two functions are inverses using composition of functions.

( Be able to determine whether a function is one-to-one.

( Be able to find the inverse of a function that is one-to-one, algebraically. (Note: You may need to restrict the domain of the inverse function.)

4.2 Exponential Functions and Their Applications

( Be able to evaluate an exponential function for a given value.

( Be able to graph an exponential function.

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

( Be able to graph an exponential equation using a calculator and determine its horizontal asymptote.

( Be able to solve an applied problem involving a given exponential function.

4.3 Logarithmic Functions and Their Applications

( Be able to switch an equation from logarithmic form to exponential form or vice versa.

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

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

( Be able to find the domain of a logarithmic function.

4.4 Properties of Logarithms and Logarithmic Scales

( 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 application problems involving logarithmic functions (pH, Richter Scale and decibels).

4.5 Exponential and Logarithmic Equations

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

( 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 solve application problems involving exponential functions.

( Be able to solve application problems involving logarithmic functions.

4.6 Exponential Growth and Decay

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

( Be able to solve applied problems involving exponential growth of money (using both models – compounding and continuous).

( Be able to solve applied problems involving exponential growth of populations.

( Be able to solve applied problems involving radioactive decay.

6.1 Systems of Linear Equations in Two Variables (Extra Credit)

( Be able to solve a system of linear equations in two variables using the substitution method.

( Be able to solve a system of linear equations in two variables using the elimination method.

( 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 solve a system of linear equations in three variables using the elimination method.

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

7.1 Gaussian Elimination Method

( Be able to give the order of a matrix.

( Be able to determine the augmented matrix, coefficient matrix and constant matrix for a system of equations.

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

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

( Be able to solve application problems using a system of equations and Gaussian elimination (If you prefer it to the way of 6.1 and 6.2).

7.2 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 find a system of equation given a matrix equation.

7.3 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.

7.4 Determinants (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 3 Review 41 – 55 odd, 59, 65

Chapter 3 Test 11 - 14, 16

Chapter 4 Review Exercises: 1 – 21, 25, 26, 29 – 32, 39 – 62, 67 – 70, 75, 79, 81, 82, 84 – 90

Chapter 4 Test: 1, 3, 4, 5, 8 – 13, 15, 16, 17

Chapter 6 Review Exercises: 9, 14, 16, 73, 75

Chapter 6 Test: 22

Chapter 7 Review Exercises: 1 – 5, 9, 13 – 15, 17 – 23, 35, (37 – 41, 43, 45)

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