Algebra 2 Semester 2 Final Exam Study Outline Semester 2 Final Exam Study Tips and Information

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1 Algebra 2 Semester 2 Final Exam Study Outline 2013 Semester 2 Final Exam Study Tips and Information The final exam is CUMULATIVE and will include all concepts taught from Chapter 1 through Chapter 13. However, the exam will PRIMARILY focus on the concepts covered from Chapters 6.3 through Chapter 13, as well as vectors. This guide will outline concepts IN THE CHRONOLOGICAL ORDER that we covered them this year! Your binder is an excellent study tool. Review all notes to decide what material has been emphasized. Look at and REDO homework problems with which you struggled! Use the homework solutions on my website to check your answers! Do EVEN numbered problems in the book from sections that we covered. Use the homework solutions on my website and come to extra help to check your answers! Study your old quizzes and tests and practice CORRECTING mistakes that you made on them! REDO quiz and tests problems with which you had trouble! Know the meaning of all math vocabulary. Be able to explain them to someone else who knows nothing about math! Additional practice is available within the online book website- if you click on the Additional Practice tab for each chapter, under the Student Resources heading you can complete the Interactive Practice Test for each chapter. Under the Lesson Resources heading, you can do interactive practice quizzes and extra practice worksheets for each lesson. REMEMBER- the more you practice each type of problem, the more you will feel confident and succeed on the exam! LASTLY BUT MOST IMPORTANT- do NOT wait until the night before the semester final exam to study! A least a COUPLE OF WEEKS before the exam, you should divide up your studying so that you focus on 2 or 3 sections of a chapter each night. Eventually, figure out what concepts you struggle with the most, and focus on practicing those problems the last night or two before the exam. 1

2 Algebra Semester 2 Final Concepts and Problems You Must Know! *I recommend that you start with Chapter 6 when utilizing this outline, since the final exam will mostly emphasize Chapters 6 through 13!* 1) Chapter 1 a) Know how to express a given set using interval or set-builder notation. b) Know how to classify numbers by the subsets of the real number system. c) Know how to identify Commutative, Associative and Distributive properties. d) Know the quotient and product properties of square roots, and know how to simplify square roots by using those properties. e) Know how to simplify a square root by rationalizing the denominator. f) Know how to write and simplify algebraic expressions. g) Know how to simplify expressions using properties of exponents and properties of scientific notation. h) Know how to identify whether or not a relation is a function by using mapping diagrams. i) Know how to evaluate and graph functions using function notation and tables. 2) Chapter 2 a) Know how to solve and graph solutions to linear equations and inequalities. Also, study your special cases! b) Know how to set up and solve proportions. c) Know how to identify and graph linear functions. 2

3 d) Know how to find the x and y intercepts when given a linear equation. e) Know how to write the equation of a line in slope-intercept form that passes through two points. f) Know how to determine whether lines are parallel, perpendicular, or neither. g) Know how to properly solve and graph (and shade!) linear inequalities. h) Know how to make a scatter plot when given a data set, and know how to draw a best-fit line. i) Know how to solve absolute-value equations and inequalities. Know when to use AND or OR! j) Know how to graph absolute-value functions, and know how to describe and perform their possible transformations when given an equation. 3) Chapter 3 a) Know how to use a graph and table to solve a system of two equations with two variables. b) Be able to classify a system of equations as independent or dependent, and consistent or inconsistent. c) Know how to solve a system of two equations using substitution method. d) Know how to solve a system of two equations using elimination method. e) Know how to solve and graph systems of linear inequalities (including shading!). f) For a linear programming problem, know the 6 steps to completing the problem. Make sure to define variables, write the objective function, write inequalities for constraints, find the vertices, and plug them into the objective function! g) Know how to use elimination to solve linear systems with 3 equations and 3 variables. 3

4 4) Chapter 4 a) Know how to locate an entry in a matrix, and know how to state the dimensions of a matrix. b) Know how to add, subtract, and multiply matrices. Make sure you know WHEN you can perform these operations. c) Know how to calculate the determinant of a 2x2 and 3x3 matrix. d) Know how to find the inverse of a matrix, and how to determine whether or not a matrix has an inverse. e) Know how to solve systems of 2 equations and 2 variables (BY HAND) using matrices. 5) Chapter 5 a) Know how to graph quadratic equations when presented in vertex form. b) From a description, know how to write the equation for a quadratic function in vertex form, and know how to describe the transformations. c) Know how to identify important aspects of a parabola from a quadratic equation written in standard form. d) Know how to find the maximum or minimum of a quadratic function. e) Know how to factor and find roots (zeros) of quadratic equations. f) Know how to solve quadratic equations by completing the square. g) Know how to define and use imaginary and complex numbers. h) Know how to solve quadratic equations with complex roots. i) Know how to solve quadratic equations using the quadratic formula. j) Know how to classify roots using the discriminant. k) Know how to solve quadratic equations by using tables and graphs. 4

5 l) Know how to perform operations with complex numbers, such as finding absolute-value, adding, subtracting, multiplying, dividing, and evaluating powers of complex numbers. 6) Chapter 6 a) Know how to classify and graph polynomials. b) Know how to identify, evaluate, add, and subtract polynomials. c) Know how to multiply polynomials. d) Know how to use synthetic division to determine whether a binomial is a factor of a polynomial. e) Know how to solve a polynomial equation by factoring. f) Know how to identify the multiplicity of a root when solving a polynomial equation. g) Know how to identify the leading coefficient, degree, and end behavior of a polynomial function. h) Be able to perform and identify transformations of polynomial functions. i) Know how to use finite differences to determine the degree of a polynomial that best fits data. 7) Chapter 7 a) Know how to identify and graph exponential growth and decay functions. (Also know how to identify their asymptotes). b) Know how to find the inverse of a function both graphically and algebraically. c) Know how to convert expressions in logarithmic form to exponential form, and vice versa. d) Know how to evaluate logarithmic expressions. e) Know how to evaluate expressions using the different properties of logarithms, including the Change of Base formula. 5

6 f) Know how to solve exponential and logarithmic equations. g) Know how to graph and simplify expressions/equations that include the natural base e. h) Know how to identify and find transformations of exponential functions. 8) Chapter 8 a) Know how to write and graph a direct variation. b) Know how to solve a joint variation. c) Know how to simplify, multiply, and divide rational expressions. d) Know how to solve rational equations using the least common denominator (LCD). e) Know how to solve rational inequalities. f) Know how to simplify radical expressions and rewrite them using rational exponents. g) Know how to graph radical functions and their transformations. h) Know how to solve radical equations. 9) Chapter 9 a) Know how to write, evaluate, and graph piecewise functions. b) Know how to add, subtract, multiply, and divide functions. c) Know how to evaluate composite functions. 10) Chapter 11 a) Know how to calculate permutations and combinations by hand AND using your calculator. b) Know how to calculate theoretical and experimental probability. c) Know how to calculate the probability of the complement. 6

7 11) Chapter 13 a) Know how to calculate the six trigonometric functions for a right triangle. b) Know how to draw an angle with a given measure in standard position, as well as how to find its coterminal angles. c) Know how to find a reference angle for a given angle. d) Know how to convert degrees to radians, and vice versa. e) Know how to calculate arc length using the appropriate formula. f) Know the unit circle, as well as how to calculate values of sine, cosine, tangent, and their inverses by using the unit circle as well as your calculator. g) Know how to calculate inverse trigonometric functions when they have capital letters (like Sin, Cos, Tan). h) Know the Laws of Sines and Cosines and how/when to use them 12) Chapter 10 a) Know how to write and graph an equation for a circle. b) Know how to write an equation in standard form for an ellipse when the center is at the origin and when it is not at the origin. Also know how to graph and label and ellipse with its foci, vertices, and co-vertices. c) Know how to write an equation in standard form for a hyperbola when the center is at the origin and when it is not at the origin. Also know how to graph and label and ellipse with its foci, vertices, co-vertices, axes, and asymptotes. d) Know how to write an equation in standard form for a parabola when the vertex is at the origin and when it is not at the origin. 13) Chapter 12 a) Know how to find the first few terms of a sequence by using recursive and explicit formulas. b) Know how to write a series in summation notation. 7

8 c) Know how to evaluate a series that is written in summation notation. d) Know how to identify and find the nth term of an arithmetic sequence. e) Know how to identify and find the nth term of a geometric sequence. f) Know how to determine whether a series converges or diverges. 8