Rich – AAT(H)
Name: _________________________________
FINAL EXAM REVIEW
Date: _____________________ Period: _______
Some things to remember when studying for the final exam:
1. This final exam is designed to be taken during one 75 minute class period.
2. This final exam will be multiple choice (with calc) and short answer (part calc, part non-calc).
3. In addition to these example problems, you should also review all previous tests, quizzes, & WINKs as
well as the midterm (Unit 1 parts A and B).
4. This final exam will cover all of the topics in Unit 1 and Unit 2.
Final Exam Review Book Problems
Unit 1 Part A: Simplifying Expression & Solving Equations & Inequalities
Unit 1 Part B: Functions and their Graphs
For Unit 1, use the abbreviated midterm review listed below:
 pg. 70 #27 – 40, 47 – 49, 55 – 64, 67 – 78
 pg. 165 #5 – 12, 21 – 28, 43 – 46, 99 – 100, 111, 112, 121 – 130 (write your answers in interval notation), 132, 150
 pg. 253 #23 – 28, 39 – 51, 55 – 65 (skip 62, 64), 69, 71, 72, 81, 83, 84, 97, 98, 100, 101, 107 – 112, 115 – 122
Unit 2 Part A: Quadratic Functions
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pg. 167 #65 – 74, 77 – 94
pg. 255 #81
pg. 326 #3 – 12, 15 – 18, 20, 21, 23
Unit 2 Part B: Polynomial Functions of Higher Degree
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pg. 167 #95, 97, 98
pg. 255 #62, 64, 66 – 68, 82
pg. 327 #25 – 30, 31 – 34, 36 – 44, 49 – 60, 63 – 82
Unit 2 Part C: Rational Functions
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pg. 71 #79 – 84
pg. 167 #107 – 110
pg. 255 #85, 86
pg. 376 #1 – 10, 13 – 30 (identify excluded values, VA, HA, SA, Holes, domain, range, y-int, zeros and graph).
Unit 2 Part D: Exponential and Logarithmic Functions
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pg. 168 #145
pg. 437 #7 – 13, 15 – 26, 31 – 34, 35, 36, 38 – 58, 65 – 68, 71 – 74, 79 – 85, 87 – 94, 97 – 112, 119 – 130, 135, 145 – 148,
153, 154
Learning Targets for Semester 1 Final Exam 2012
Essential Questions: Think of these EQs as you are studying for the midterm.
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What is the important information?
What do I need in order to start the problem?
How is this similar or different from what I have done before?
What can I do to retain what I have learned?
How can I use this and how does it apply to my life?
How do I remember this?
Do I need help and where do I go to find it?
How would a calculator make this problem easier to do?
How do I tell which method to use and how do I apply it?
Is there another way to do the problem and which is better?
What should this function look like?
Learning Targets: These are all of the LTs that have appeared in Unit 1 and Unit 2. They are all fair game, though it would be
impossible for all LTs to appear on the final exam. I would recommend using this as a checklist of skills to help you identify the
topics you need help on, and the topics in which you are confident.
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1.A.1: solve equations in one variable.
1.A.4: solve one-variable inequalities and graph the solution set.
1.A.5: solve one-variable absolute value inequalities and graph the solution set.
1.A.2: find x- and y-intercepts of graphs algebraically.
1.A.3: use linear equations to model and solve real life problems.
1.A.6: use properties of exponents.
1.A.7: use scientific notation to represent real numbers.
1.A.11: use properties of rational exponents.
1.A.8: use properties of radicals.
1.A.9: simplify and combine radicals.
1.A.10: rationalize denominators.
1.A.12: write polynomials in descending order (standard form).
1.A.13: add, subtract, and multiply polynomials
1.A.14: use polynomials to solve real life problems.
1.A.15: use rate of change to graph lines.
1.A.16: find the rate of change of lines.
1.A.17: write the equation of a line
1.A.18: use rate of change to identify parallel and perpendicular lines.
1.A.19: use lines to model and solve real life problems
1.A.20: use tables to graph equations (absolute value, square root, linear, quadratic, cubic).
1.A.21: sketch graphs of equations.
1.A.22: find the x- and y-intercepts of graphs of equations.
1.A.23: determine if an equation or graph is symmetric with respect to the x-axis, y-axis, or origin.
1.A.24: use graphs and equations in a real world situation.
1.A.25: graph an equation of a circle.
1.A.26: write equations of circles.
1.A.27: use mathematical models to solve real-life problems.
1.A.28: use common formulas to solve problems.
1.A.29: factor by taking out the greatest common factor (GCF).
1.A.30: factor by grouping.
1.A.31: factor trinomials.
1.A.32: solve by factoring.
1.B.1: determine if a relation is a function.
1.B.2: evaluate functions.
1.B.5: add and subtract functions.
1.B.6: multiply and divide functions.
1.B.7: find the composite functions.
1.B.3: find the domain and range of functions.
1.B.4: use functions to model real-life problems.
1.B.8: use combinations and composite functions to solve real-life problems.
1.B.9: find the inverse of a function algebraically.
1.B.10: verify that 2 functions are inverses of one another.
1.B.11: use the graph of a function to determine if it has an inverse.
1.B.12: use the Horizontal Line Test to determine if functions are one-to-one.
1.B.13: use the Vertical Line Test for functions.
1.B.14: find zeros of a function.
1.B.15: determine increasing and decreasing intervals of functions.
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1.B.16: determine relative maximum and minimum of functions.
1.B.17: determine the average rate of change of a function.
1.B.18: can identify even and odd functions.
1.B.19: can identify and graph parent functions of linear, quadratic, cubic, square root, absolute value and piecewise functions.
1.B.20: use vertical and horizontal shifts to sketch graphs of functions.
1.B.21: use reflections to sketch graphs of functions.
1.B.22: use nonrigid transformations to sketch graphs of functions.
2.A.1: use the imaginary unit i to write complex numbers.
2.A.2: add, subtract, and multiply complex numbers.
2.A.3: use complex conjugates to write the quotient of two complex numbers in standard form.
2.A.4: solve a quadratic equation by factoring.
2.A.5: solve a quadratic equation by graphing.
2.A.6: solve a quadratic equation by extracting the square roots.
2.A.7: solve a quadratic equation using the Quadratic Formula.
2.A.8: Find complex solutions of quadratic equations.
2.A.9: solve a quadratic equation by completing the square.
2.A.10: use quadratic equations to model real life problems.
2.A.11: write a quadratic equation with the given roots.
2.A.12: graph a quadratic equation from vertex form.
2.A.13: graph a quadratic equation from standard from.
2.A.14: identify the y-intercept, vertex, and axis of symmetry of a quadratic equation in standard form
2.A.15: write the vertex form of the quadratic function given a graph.
2.A.16: write the vertex form of the quadratic function given a vertex and a point on the graph.
2.B.1: use the leading coefficient test to determine end behavior of graphs of polynomials.
2.B.2: determine if polynomial functions are even or odd degree.
2.B.3: sketch the graph of a function using the leading coefficients, zeros, and other needed solution points.
2.B.4: find zeros of polynomial functions.
2.B.5: use the zeros of a polynomial to write an appropriate equation.
2.B.6: use polynomial equations to model real life problems.
2.B.7: use long division to divide polynomials.
2.B.8: use synthetic division to divide polynomials by binomials in the form (x – k).
2.B.9: use the Factor Theorem.
2.B.10: find all of the zeros of a polynomial by using the graphing utility to find one real zero and polynomial division to find the rest.
2.B.11: find conjugate pairs of complex zeros.
2.C.1: simplify rational expressions.
2.C.2: add, subtract, multiply, and divide rational expressions
2.C.3: solve rational equations.
2.C.4: determine the domain and range of a rational function.
2.C.5: determine the horizontal asymptotes, vertical asymptotes, slant asymptotes, and "holes" (if any) on graphs of rational function.
2.C.6: find zeros (if any) of a rational function.
2.C.7: Write a rational function with its given characteristics.
2.C.8: sketch the graph of rational functions.
2.C.9: sketch graphs of rational functions that have slant asymptotes.
2.D.1: recognize and evaluate logarithmic and natural logarithmic functions.
2.D.2: convert logarithm functions to exponential functions and vice versa.
2.D.3: use the properties of logs and natural logs to simplify expression.
2.D.4: graph logarithmic and natural logarithmic functions.
2.D.5: use the change of base formula to rewrite and evaluate logarithmic expressions.
2.D.6: use the properties of logarithms and natural logarithms to evaluate, rewrite, or simplify expressions.
2.D.7: use properties of logarithms to expand and condense logarithmic expressions.
2.D.8: use logarithmic functions to model and solve real-life problems.
2.D.9: solve logarithmic and exponential equations.
2.D.10: Use exponential and logarithmic equations to model and solve real-life problems.
2.D.11: use an exponential model to solve real-life problems. (specifically exponential growth and decay problems)
2.D.12: graph an exponential function and determine the y intercept, domain, range, and any asymptotes.
2.D.13: use an exponential model to solve real-life problems.