d. What are the steps for finding the y intercepts algebraically?(hint: what is equal to 0?)
|
|
- Gregory Lucas
- 5 years ago
- Views:
Transcription
1 st Semester Pre Calculus Exam Review You will not receive hints on your exam. Make certain you know how to answer each of the following questions. This is a test grade. Your WORK and EXPLANATIONS are graded since the key is provided.. For the data given use a graphing utility to find the type of equation (bonus if you can find the line of best fit!. Write the steps below x y Find the x intercept(s) of: a. 5x y = b. y = (x ) 7 c. y = x 0x using the quadratic formula d. y = x 0x by solving for y, factoring and setting the factors equal to zero (because y=0 at the x intercept) e. How can you check your answer?. Find the y intercept(s) of: a. 5x y = b. y = (x ) 9 c. y = x 0x d. What are the steps for finding the y intercepts algebraically?(hint: what is equal to 0?). Find the vertex of: a. y = (x ) 9 Describe how you found your answer (Hint: what form is it in?) b. y = x 0x using part of the quadratic formula c. y = x 0x by completing the perfect square 5. Are the following functions even, odd, or neither? Explain your answer. a. y = x x b. y = x x c. d. 6. Solve the following algebraically, then graph the solutions on a number line: a. 7(x 8 ) = 7(6 x ) 8 b. 5b 6 b 9 c. x x
2 7. Complete the following by factoring: x x 6 = 0 8. Find f( ) given that a. f (x) = x x x 0 x b. f (x) = x 9. Given f (x) = x and g (x) = x find each of the following: a. ( f g )(x) = b. ( f g )(x) = c. ( fg)(x) = d. ( f/g)(x) = e. ( f g )(x) = f. f (g(x)) = g. g (f(x)) = h. ( g f )(x) = i. ( f g )() = j. f(g( )) = k. g (f()) = l. ( g f)( ) = m. f (x) = n. g (x) = o. f(f (x)) = p. g(g (x)) = q. f (f(x)) = r. f(f (x)) = 0. Show that f and g are inverses using function composition: f (x) = x 9 and g (x) = x 9. Find the value of y when x =. and y = 6x. Write the equation log8 = 5 in exponential form and explain how.. Write the equation ( ) x = 5 in logarithmic form and explain how.. Find the exact answers to the following (use properties) a. log ( 6 ) (hint: rewrite or use change of base) b. log 9 (hint: use the change of base formula) c. log55 0x d. log 5. Use the rules of logarithms to expand the following completely: x(x) a. log x b. og c. log x y 5 l b 9 z 8 x(x 5 ) (x) x 6. Use the rules of logarithms to condense the following completely: a. log(x ) log(x ) log log(x ) log5 b. l og5 log(6x 5) [log(x ) log(x )] 7. Find all real solutions to the following equation using properties of logarithms: a. l og(x ) l og = l og(5x ) b. log x log (x ) = c. ln(x ) l n(x ) = ln(x ) l n(x 7) 8. Find the vertical asymptotes, horizontal/slant asymptotes, holes, and x intercepts of the following, if any, after factoring: x a. f (x) = b. f (x) (x )(x 5) x 6x8 = x 6 x x 7x c. f (x) = x x (omit x intercepts part)
3 x 9. Divide f (x) = x a. Using synthetic division b. Using long division answer: x 8 x 7 x 0. Solve the following systems using the specified methods: a. Substitution: x y = 8 6x 5 y = b. Elimination: x y = x y = 0 c. Matrices: (record your steps) 5x z = 0 x y 5 z = 9 x y z = 0 d. Graphing: x y = x y = 6. Review how to add subtract and multiply matrices. Separate the following into partial fractions (factor first!): a. 5x x x answer: x x b. x x(x ) c. x 7x (x )(x x) answer: x x (x ) answer: 5 x x x x. Prove using mathematical induction: a n = n (n ) n(n) b ( n ) = Using arithmetic and geometric formulas for each of the following write their a) formula for the nth term in the sequence, a n =? b) calculate using the a formula c) formula for the nth term in the series, S n =? d) Calculate using the formula. 5, 8,,... a n = a 8 = S n = S = 5., 6,,... a n = a 8 = S n = S = 0 n=6 6. n Put the following into standard form then graph the equations on your own paper: a 8 s n 7. x y x 6 y = 5 8. y y 8 x = 0 9. x y 8 x 8 y = 0 0. x y 8 x 6 y = 0. Find each of the parts of the graphs below in inequality and interval notation, then describe how to answer these questions below:
4 Maximum(s): Maximum(s): Maximum(s): Maximum(s): minimum(s): minimum(s): minimum(s): minimum(s): To find the domain: To find the range: To find the intervals of increasing: To find the intervals of decreasing: To find the maximums: To find the minimums: ) Use Synthetic division to divide a) x x 5 x 5 by x x 7 x 6 x 5
5 b) 5x 6 x 8 by x 5x 0x 6 x ) Use long division to divide a) 6x x 5 x by x x x x b) x x 5 x 5 by x x 7 x 6 5 ) Use f = i and g = 5 i without calculators a) f g = 8 6i b) f g = i c) f * g = 7 6i d) f /g=? in standard form (a bi) /9 i/9 e) conjugate of f= i f) conjugate of g= 5i g) when are conjugates used? 5) Review adding, subtracting, multiplying, dividing, and factoring polynomials x ) Use Synthetic division to divide a) x x 5 x 5 by x x 7 x 6 x 5 b) 5x 6 x 8 by x 5x 0x 6 ) Use long division to divide a) 6x x 5 x by x x x x b) x x 5 x 5 by x x 7 x 6 5 ) Use f = i and g = 5 i without calculators a) f g = 8 6i b) f g = i c) f * g = 7 6i d) f /g=? in standard form (a bi) /9 i/9 e) conjugate of f= i f) conjugate of g= 5i g) when are conjugates used? 5) Review adding, subtracting, multiplying, dividing, and factoring polynomials x x
6 st Semester Pre Calculus Exam Review Key. cubic. a. x = /5 b. x= or x= c. x=, d. x=, e. Graph. a. y=/ b. y = c. y = d. (Hint: x= 0). a. (,9) b. ( 5, 9) c. ( 5, 9) 5 a. even power b. odd power c. odd end behavior d. even end behavior 6. a. 5/7(one solid point) b. b (solid point arrow to right) c. x=7, (hollow points shaded away) 7. x=8, 8. a. b. / 9 a. x x b. x x c. x x x d. x x e. x 9x f. x 9x g. 5 x h. 5 x i. j. 0 k. 7 l. 7 m. f (x) = ± x n. g (x) = x o.through r. = x 0. f(g(x))=g(f(x))=x =. log/ 5 = x. a. b..8 c. 0x d. 6*8=8 5. a. l ogx l og(x ) log(x ) b. 9(logb x glogby 8logbz) c. l og l ogx 5log(x ) l og(x ) log(x ) 6. 5(x ) a. (x ) 5(6x 5) (x ) (x ) b. x 7. a. x = /9 b. x = 6, c. x = / 8. a. vertical: x=⅔, x=5 Holes: none Horizontal: y=0 x intercepts x= b. vertical: x= Holes: x= Horizontal: y= x intercepts: x= c. vertical: x=, Holes: none Slant: y = x 9. a=b= x 8 x 7 x 0 a. ( 5, ) b. (, ) c. rref d. (, ). Review how to add subtract and multiply matrices. a. x x b. x x c. 5 (x ) x x x x. a. True b. True. 5, 8,,... a n = 5 (n ) a 8 = 6 S n = n (5 a n ) S = 8 5., 6,,... a n = * n a 8 = S n = * n S = 5 Put the following into standard form then graph the equations on your own paper: (y ) 7. = 8. x = (y ) (x ) 8 9. ( x ) ( y ) = 8 (x ) 0. (y ) =
7 inequality: y>= Interval: (, ) inequality: y>= 6 Interval: ( 6, ) inequality: y<=75 Interval: (, 75) x>0 Interval: ( 0, ) inequality: x> Interval: (, ) inequality: x<, <x< Interval: (, ) (, ) x<0 Interval: (, 0) inequality: x< Interval: (, ) none inequality: x>, <x< Interval: (, ) (, ) Maximum(s):none Maximum(s):none Maximum(s):none Maximum(s): (,5),(,75) minimum(s): (0, ) minimum(s):(, 6) minimum(s):none minimum(s): (.75, 0) To find the domain: x values minmax To find the range: y values minmax To find the intervals of increasing: up (refers to x values) To find the intervals of decreasing: down (refer to x values) To find the maximums: (highest points, change from increasing to decreasing) To find the minimums: (lowest points, change from decreasing to increasing)
Semester Review Packet
MATH 110: College Algebra Instructor: Reyes Semester Review Packet Remarks: This semester we have made a very detailed study of four classes of functions: Polynomial functions Linear Quadratic Higher degree
More informationf(x) = 2x + 5 3x 1. f 1 (x) = x + 5 3x 2. f(x) = 102x x
1. Let f(x) = x 3 + 7x 2 x 2. Use the fact that f( 1) = 0 to factor f completely. (2x-1)(3x+2)(x+1). 2. Find x if log 2 x = 5. x = 1/32 3. Find the vertex of the parabola given by f(x) = 2x 2 + 3x 4. (Give
More informationQuestion 1. Find the coordinates of the y-intercept for. f) None of the above. Question 2. Find the slope of the line:
of 4 4/4/017 8:44 AM Question 1 Find the coordinates of the y-intercept for. Question Find the slope of the line: of 4 4/4/017 8:44 AM Question 3 Solve the following equation for x : Question 4 Paul has
More informationPreCalculus: Semester 1 Final Exam Review
Name: Class: Date: ID: A PreCalculus: Semester 1 Final Exam Review Short Answer 1. Determine whether the relation represents a function. If it is a function, state the domain and range. 9. Find the domain
More informationH-Pre-Calculus Targets Chapter I can write quadratic functions in standard form and use the results to sketch graphs of the function.
H-Pre-Calculus Targets Chapter Section. Sketch and analyze graphs of quadratic functions.. I can write quadratic functions in standard form and use the results to sketch graphs of the function. Identify
More informationMiller Objectives Alignment Math
Miller Objectives Alignment Math 1050 1 College Algebra Course Objectives Spring Semester 2016 1. Use algebraic methods to solve a variety of problems involving exponential, logarithmic, polynomial, and
More informationLearning Module 1 - Basic Algebra Review (Appendix A)
Learning Module 1 - Basic Algebra Review (Appendix A) Element 1 Real Numbers and Operations on Polynomials (A.1, A.2) Use the properties of real numbers and work with subsets of the real numbers Determine
More information3. Solve the following inequalities and express your answer in interval notation.
Youngstown State University College Algebra Final Exam Review (Math 50). Find all Real solutions for the following: a) x 2 + 5x = 6 b) 9 x2 x 8 = 0 c) (x 2) 2 = 6 d) 4x = 8 x 2 e) x 2 + 4x = 5 f) 36x 3
More information1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.
Math120 - Precalculus. Final Review. Fall, 2011 Prepared by Dr. P. Babaali 1 Algebra 1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.
More informationFinal Exam Review Problems
Final Exam Review Problems Name: Date: June 23, 2013 P 1.4. 33. Determine whether the line x = 4 represens y as a function of x. P 1.5. 37. Graph f(x) = 3x 1 x 6. Find the x and y-intercepts and asymptotes
More informationChapter 2 Polynomial and Rational Functions
Chapter 2 Polynomial and Rational Functions Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Quadratic Functions Polynomial Functions of Higher Degree Real Zeros of Polynomial Functions
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) x 8. C) y = x + 3 2
Precalculus Fall Final Exam Review Name Date Period MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the expression. Assume that the variables
More informationLesson 7.1 Polynomial Degree and Finite Differences
Lesson 7.1 Polynomial Degree and Finite Differences 1. Identify the degree of each polynomial. a. 3x 4 2x 3 3x 2 x 7 b. x 1 c. 0.2x 1.x 2 3.2x 3 d. 20 16x 2 20x e. x x 2 x 3 x 4 x f. x 2 6x 2x 6 3x 4 8
More informationAlgebra 2A Unit 1 Week 1 Day Activity Unit 1 Week 2 Day Activity Unit 1 Week 3 Day Activity Unit 2 Week 1 Day Activity
Algebra 2A Unit 1 Week 1 1 Pretest Unit 1 2 Evaluating Rational Expressions 3 Restrictions on Rational Expressions 4 Equivalent Forms of Rational Expressions 5 Simplifying Rational Expressions Unit 1 Week
More informationAlgebra II Scope and Sequence
1 st Grading Period (8 weeks) Linear Equations Algebra I Review (A.3A,A.4B) Properties of real numbers Simplifying expressions Simplifying Radicals New -Transforming functions (A.7C) Moving the Monster
More informationMission 1 Simplify and Multiply Rational Expressions
Algebra Honors Unit 6 Rational Functions Name Quest Review Questions Mission 1 Simplify and Multiply Rational Expressions 1) Compare the two functions represented below. Determine which of the following
More informationName Advanced Math Functions & Statistics. Non- Graphing Calculator Section A. B. C.
1. Compare and contrast the following graphs. Non- Graphing Calculator Section A. B. C. 2. For R, S, and T as defined below, which of the following products is undefined? A. RT B. TR C. TS D. ST E. RS
More informationInternet Mat117 Formulas and Concepts. d(a, B) = (x 2 x 1 ) 2 + (y 2 y 1 ) 2., y 1 + y 2. ( x 1 + x 2 2
Internet Mat117 Formulas and Concepts 1. The distance between the points A(x 1, y 1 ) and B(x 2, y 2 ) in the plane is d(a, B) = (x 2 x 1 ) 2 + (y 2 y 1 ) 2. 2. The midpoint of the line segment from A(x
More informationFinal Exam C Name i D) 2. Solve the equation by factoring. 4) x2 = x + 72 A) {1, 72} B) {-8, 9} C) {-8, -9} D) {8, 9} 9 ± i
Final Exam C Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 7 ) x + + 3 x - = 6 (x + )(x - ) ) A) No restrictions; {} B) x -, ; C) x -; {} D) x -, ; {2} Add
More informationPRINTABLE VERSION. Practice Final. Question 1. Find the coordinates of the y-intercept for 5x 9y + 6 = 0. 2 (0, ) 3 3 (0, ) 2 2 (0, ) 3 6 (0, ) 5
PRINTABLE VERSION Practice Final Question Find the coordinates of the y-intercept for 5x 9y + 6 = 0. (0, ) (0, ) (0, ) 6 (0, ) 5 6 (0, ) 5 Question Find the slope of the line: 7x 4y = 0 7 4 4 4 7 7 4 4
More informationPre-Calculus: Functions and Their Properties (Solving equations algebraically and graphically, matching graphs, tables, and equations, and
Pre-Calculus: 1.1 1.2 Functions and Their Properties (Solving equations algebraically and graphically, matching graphs, tables, and equations, and finding the domain, range, VA, HA, etc.). Name: Date:
More informationFinal Exam A Name. 20 i C) Solve the equation by factoring. 4) x2 = x + 30 A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} -9 ± i 3 14
Final Exam A Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 1 1) x + 3 + 5 x - 3 = 30 (x + 3)(x - 3) 1) A) x -3, 3; B) x -3, 3; {4} C) No restrictions; {3} D)
More informationPrecalculus. How to do with no calculator 1a)
Precalculus UNIT 2 Review NAME PERIOD This assessment covers many concepts which you must be able to understand without the use of your calculator to view the graph. Please complete the following table
More informationBishop Kelley High School Summer Math Program Course: Honors Pre-Calculus
017 018 Summer Math Program Course: Honors Pre-Calculus NAME: DIRECTIONS: Show all work in the packet. Make sure you are aware of the calculator policy for this course. No matter when you have math, this
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. B) 6x + 4
Math1420 Review Comprehesive Final Assessment Test Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Add or subtract as indicated. x + 5 1) x2
More informationReference Material /Formulas for Pre-Calculus CP/ H Summer Packet
Reference Material /Formulas for Pre-Calculus CP/ H Summer Packet Week # 1 Order of Operations Step 1 Evaluate expressions inside grouping symbols. Order of Step 2 Evaluate all powers. Operations Step
More informationA factor times a logarithm can be re-written as the argument of the logarithm raised to the power of that factor
In this section we will be working with Properties of Logarithms in an attempt to take equations with more than one logarithm and condense them down into just a single logarithm. Properties of Logarithms:
More informationRadicals: To simplify means that 1) no radicand has a perfect square factor and 2) there is no radical in the denominator (rationalize).
Summer Review Packet for Students Entering Prealculus Radicals: To simplify means that 1) no radicand has a perfect square factor and ) there is no radical in the denominator (rationalize). Recall the
More informationAlgebra II Double Period Final Exam Review. 3. Solve. 4. Solve.
Algebra II Double Period Final Exam Review Name: Chapter 5 Quadratic Equations and Parabolas 1. Solve. 3. Solve. 2. Solve. 4. Solve. 5. Graph each function. Identify the vertex and zeros for each function.
More informationSection 4.1: Polynomial Functions and Models
Section 4.1: Polynomial Functions and Models Learning Objectives: 1. Identify Polynomial Functions and Their Degree 2. Graph Polynomial Functions Using Transformations 3. Identify the Real Zeros of a Polynomial
More informationPacing Guide Algebra 1
Pacing Guide Algebra Chapter : Equations and Inequalities (one variable) Section Section Title Learning Target(s) I can. Evaluate and Simplify Algebraic Expressions. Evaluate and simplify numeric and algebraic
More information5.6 Logarithmic and Exponential Equations
SECTION 5.6 Logarithmic and Exponential Equations 305 5.6 Logarithmic and Exponential Equations PREPARING FOR THIS SECTION Before getting started, review the following: Solving Equations Using a Graphing
More informationMAT116 Final Review Session Chapter 3: Polynomial and Rational Functions
MAT116 Final Review Session Chapter 3: Polynomial and Rational Functions Quadratic Function A quadratic function is defined by a quadratic or second-degree polynomial. Standard Form f x = ax 2 + bx + c,
More informationThe final is cumulative, but with more emphasis on chapters 3 and 4. There will be two parts.
Math 141 Review for Final The final is cumulative, but with more emphasis on chapters 3 and 4. There will be two parts. Part 1 (no calculator) graphing (polynomial, rational, linear, exponential, and logarithmic
More informationALGEBRA 2 FINAL EXAM REVIEW
Class: Date: ALGEBRA 2 FINAL EXAM REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question.. Classify 6x 5 + x + x 2 + by degree. quintic c. quartic cubic d.
More informationCURRICULUM CATALOG. Algebra II (3135) VA
2018-19 CURRICULUM CATALOG Algebra II (3135) VA Table of Contents COURSE OVERVIEW... 1 UNIT 1: STRUCTURE AND FUNCTIONS... 1 UNIT 2: LINEAR FUNCTIONS... 2 UNIT 3: INEQUALITIES AND ABSOLUTE VALUE... 2 UNIT
More informationA Partial List of Topics: Math Spring 2009
A Partial List of Topics: Math 112 - Spring 2009 This is a partial compilation of a majority of the topics covered this semester and may not include everything which might appear on the exam. The purpose
More informationUNIT 1 EQUATIONS, INEQUALITIES, FUNCTIONS
UNIT 1 EQUATIONS, INEQUALITIES, FUNCTIONS Act 1 Act 2 A rental car company charges $50.00 per day, plus $0.05 per mile driven. Write a function to model the story. How far did Angie drive if she rented
More informationChapter 2 Formulas and Definitions:
Chapter 2 Formulas and Definitions: (from 2.1) Definition of Polynomial Function: Let n be a nonnegative integer and let a n,a n 1,...,a 2,a 1,a 0 be real numbers with a n 0. The function given by f (x)
More informationAccelerated Advanced Algebra. Chapter 1 Patterns and Recursion Homework List and Objectives
Chapter 1 Patterns and Recursion Use recursive formulas for generating arithmetic, geometric, and shifted geometric sequences and be able to identify each type from their equations and graphs Write and
More informationSolutions to MAT 117 Test #3
Solutions to MAT 7 Test #3 Because there are two versions of the test, solutions will only be given for Form C. Differences from the Form D version will be given. (The values for Form C appear above those
More informationCollege Algebra Notes
Metropolitan Community College Contents Introduction 2 Unit 1 3 Rational Expressions........................................... 3 Quadratic Equations........................................... 9 Polynomial,
More informationALGEBRA 2. Background Knowledge/Prior Skills Knows what operation properties hold for operations with matrices
ALGEBRA 2 Numbers and Operations Standard: 1 Understands and applies concepts of numbers and operations Power 1: Understands numbers, ways of representing numbers, relationships among numbers, and number
More informationCourse Number 432/433 Title Algebra II (A & B) H Grade # of Days 120
Whitman-Hanson Regional High School provides all students with a high- quality education in order to develop reflective, concerned citizens and contributing members of the global community. Course Number
More informationSMSU Mathematics Course Content
Southwest Minnesota State University Department of Mathematics SMSU Mathematics Course Content 2012-2013 Thefollowing is a list of possibletopics and techniques to cover in your SMSU College Now course.
More informationCollege Algebra To learn more about all our offerings Visit Knewton.com
College Algebra 978-1-63545-097-2 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Text Jay Abramson, Arizona State University
More information11 /2 12 /2 13 /6 14 /14 15 /8 16 /8 17 /25 18 /2 19 /4 20 /8
MAC 1147 Exam #1a Answer Key Name: Answer Key ID# Summer 2012 HONOR CODE: On my honor, I have neither given nor received any aid on this examination. Signature: Instructions: Do all scratch work on the
More informationAlgebra II CP Final Exam Review Packet. Calculator Questions
Name: Algebra II CP Final Exam Review Packet Calculator Questions 1. Solve the equation. Check for extraneous solutions. (Sec. 1.6) 2 8 37 2. Graph the inequality 31. (Sec. 2.8) 3. If y varies directly
More informationCollege Algebra and College Algebra with Review Final Review
The final exam comprises 30 questions. Each of the 20 multiple choice questions is worth 3 points and each of the 10 open-ended questions is worth 4 points. Instructions for the Actual Final Exam: Work
More informationfunction independent dependent domain range graph of the function The Vertical Line Test
Functions A quantity y is a function of another quantity x if there is some rule (an algebraic equation, a graph, a table, or as an English description) by which a unique value is assigned to y by a corresponding
More informationA) (-1, -1, -2) B) No solution C) Infinite solutions D) (1, 1, 2) A) (6, 5, -3) B) No solution C) Infinite solutions D) (1, -3, -7)
Algebra st Semester Final Exam Review Multiple Choice. Write an equation that models the data displayed in the Interest-Free Loan graph that is provided. y = x + 80 y = -0x + 800 C) y = 0x 00 y = 0x +
More informationSecondary Math 3 Honors - Polynomial and Polynomial Functions Test Review
Name: Class: Date: Secondary Math 3 Honors - Polynomial and Polynomial Functions Test Review 1 Write 3x 2 ( 2x 2 5x 3 ) in standard form State whether the function is even, odd, or neither Show your work
More informationScope and Sequence Mathematics Algebra 2 400
Scope and Sequence Mathematics Algebra 2 400 Description : Students will study real numbers, complex numbers, functions, exponents, logarithms, graphs, variation, systems of equations and inequalities,
More informationAlgebra 2 Honors Curriculum Pacing Guide
SOUTH CAROLINA ACADEMIC STANDARDS FOR MATHEMATICS The mathematical processes provide the framework for teaching, learning, and assessing in all high school mathematics core courses. Instructional programs
More informationChapter 2 Polynomial and Rational Functions
Chapter 2 Polynomial and Rational Functions Overview: 2.2 Polynomial Functions of Higher Degree 2.3 Real Zeros of Polynomial Functions 2.4 Complex Numbers 2.5 The Fundamental Theorem of Algebra 2.6 Rational
More informationPolynomial Functions and Models
1 CA-Fall 2011-Jordan College Algebra, 4 th edition, Beecher/Penna/Bittinger, Pearson/Addison Wesley, 2012 Chapter 4: Polynomial Functions and Rational Functions Section 4.1 Polynomial Functions and Models
More informationMath 137 Exam #3 Review Guide
Math 7 Exam # Review Guide The third exam will cover Sections.-.6, 4.-4.7. The problems on this review guide are representative of the type of problems worked on homework and during class time. Do not
More informationFundamental Theorem of Algebra (NEW): A polynomial function of degree n > 0 has n complex zeros. Some of these zeros may be repeated.
.5 and.6 Comple Numbers, Comple Zeros and the Fundamental Theorem of Algebra Pre Calculus.5 COMPLEX NUMBERS 1. Understand that - 1 is an imaginary number denoted by the letter i.. Evaluate the square root
More informationFinal Exam Study Guide Mathematical Thinking, Fall 2003
Final Exam Study Guide Mathematical Thinking, Fall 2003 Chapter R Chapter R contains a lot of basic definitions and notations that are used throughout the rest of the book. Most of you are probably comfortable
More informationAlgebra 2 Khan Academy Video Correlations By SpringBoard Activity
SB Activity Activity 1 Creating Equations 1-1 Learning Targets: Create an equation in one variable from a real-world context. Solve an equation in one variable. 1-2 Learning Targets: Create equations in
More informationAlgebra 2 Khan Academy Video Correlations By SpringBoard Activity
SB Activity Activity 1 Creating Equations 1-1 Learning Targets: Create an equation in one variable from a real-world context. Solve an equation in one variable. 1-2 Learning Targets: Create equations in
More informationAlgebra 2 CP Curriculum Pacing Guide
SOUTH CAROLINA ACADEMIC STANDARDS FOR MATHEMATICS The mathematical processes provide the framework for teaching, learning, and assessing in all high school mathematics core courses. Instructional programs
More information1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.
Math120 - Precalculus. Final Review Prepared by Dr. P. Babaali 1 Algebra 1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents. (a) 5
More informationIdentify the graph of a function, and obtain information from or about the graph of a function.
PS 1 Graphs: Graph equations using rectangular coordinates and graphing utilities, find intercepts, discuss symmetry, graph key equations, solve equations using a graphing utility, work with lines and
More informationReview 1. 1 Relations and Functions. Review Problems
Review 1 1 Relations and Functions Objectives Relations; represent a relation by coordinate pairs, mappings and equations; functions; evaluate a function; domain and range; operations of functions. Skills
More informationMath 0031, Final Exam Study Guide December 7, 2015
Math 0031, Final Exam Study Guide December 7, 2015 Chapter 1. Equations of a line: (a) Standard Form: A y + B x = C. (b) Point-slope Form: y y 0 = m (x x 0 ), where m is the slope and (x 0, y 0 ) is a
More informationReview questions for Math 111 final. Please SHOW your WORK to receive full credit Final Test is based on 150 points
Please SHOW your WORK to receive full credit Final Test is based on 150 points 1. True or False questions (17 pts) a. Common Logarithmic functions cross the y axis at (0,1) b. A square matrix has as many
More informationSection 5.1 Determine if a function is a polynomial function. State the degree of a polynomial function.
Test Instructions Objectives Section 5.1 Section 5.1 Determine if a function is a polynomial function. State the degree of a polynomial function. Form a polynomial whose zeros and degree are given. Graph
More informationAlgebra I. Course Outline
Algebra I Course Outline I. The Language of Algebra A. Variables and Expressions B. Order of Operations C. Open Sentences D. Identity and Equality Properties E. The Distributive Property F. Commutative
More informationDear Future Pre-Calculus Students,
Dear Future Pre-Calculus Students, Congratulations on your academic achievements thus far. You have proven your academic worth in Algebra II (CC), but the challenges are not over yet! Not to worry; this
More informationevaluate functions, expressed in function notation, given one or more elements in their domains
Describing Linear Functions A.3 Linear functions, equations, and inequalities. The student writes and represents linear functions in multiple ways, with and without technology. The student demonstrates
More informationPolynomial and Rational Functions. Chapter 3
Polynomial and Rational Functions Chapter 3 Quadratic Functions and Models Section 3.1 Quadratic Functions Quadratic function: Function of the form f(x) = ax 2 + bx + c (a, b and c real numbers, a 0) -30
More informationRational Exponents. Polynomial function of degree n: with leading coefficient,, with maximum number of turning points is given by (n-1)
Useful Fact Sheet Final Exam Interval, Set Builder Notation (a,b) = {x a
More informationPreCalculus Notes. MAT 129 Chapter 5: Polynomial and Rational Functions. David J. Gisch. Department of Mathematics Des Moines Area Community College
PreCalculus Notes MAT 129 Chapter 5: Polynomial and Rational Functions David J. Gisch Department of Mathematics Des Moines Area Community College September 2, 2011 1 Chapter 5 Section 5.1: Polynomial Functions
More informationAlgebra and Trigonometry
Algebra and Trigonometry 978-1-63545-098-9 To learn more about all our offerings Visit Knewtonalta.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Jay Abramson, Arizona State
More informationINTERNET MAT 117. Solution for the Review Problems. (1) Let us consider the circle with equation. x 2 + 2x + y 2 + 3y = 3 4. (x + 1) 2 + (y + 3 2
INTERNET MAT 117 Solution for the Review Problems (1) Let us consider the circle with equation x 2 + y 2 + 2x + 3y + 3 4 = 0. (a) Find the standard form of the equation of the circle given above. (i) Group
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Calculus I - Homework Chapter 2 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the graph is the graph of a function. 1) 1)
More informationRational Functions. Elementary Functions. Algebra with mixed fractions. Algebra with mixed fractions
Rational Functions A rational function f (x) is a function which is the ratio of two polynomials, that is, Part 2, Polynomials Lecture 26a, Rational Functions f (x) = where and are polynomials Dr Ken W
More informationGeometry Placement Exam Review Revised 2017 Maine East High School
Geometry Placement Exam Review Revised 017 Maine East High School The actual placement exam has 91 questions. The placement exam is free response students must solve questions and write answer in space
More informationCathedral Catholic High School Course Catalog
Cathedral Catholic High School Course Catalog Course Title: Pre-Calculus Course Description: This course is designed to prepare students to begin their college studies in introductory Calculus. Students
More informationSection 6.6 Evaluating Polynomial Functions
Name: Period: Section 6.6 Evaluating Polynomial Functions Objective(s): Use synthetic substitution to evaluate polynomials. Essential Question: Homework: Assignment 6.6. #1 5 in the homework packet. Notes:
More informationLesson 7.1 Polynomial Degree and Finite Differences
Lesson 7.1 Polynomial Degree and Finite Differences 1. Identify the degree of each polynomial. a. 1 b. 0.2 1. 2 3.2 3 c. 20 16 2 20 2. Determine which of the epressions are polynomials. For each polynomial,
More informationMuskogee Public Schools Curriculum Map
Muskogee Public Schools Curriculum Map 2009-20010 Course: Algebra II Grade Level: 9-12 Nine- 1 st Nine Standard 1: Number Systems and Algebraic Operations - The student will perform operations with rational,
More informationAlgebra 2 Honors: Final Exam Review
Name: Class: Date: Algebra 2 Honors: Final Exam Review Directions: You may write on this review packet. Remember that this packet is similar to the questions that you will have on your final exam. Attempt
More information) = nlog b ( m) ( m) log b ( ) ( ) = log a b ( ) Algebra 2 (1) Semester 2. Exponents and Logarithmic Functions
Exponents and Logarithmic Functions Algebra 2 (1) Semester 2! a. Graph exponential growth functions!!!!!! [7.1]!! - y = ab x for b > 0!! - y = ab x h + k for b > 0!! - exponential growth models:! y = a(
More informationAlgebra II Honors Final Exam Review
Class: Date: Algebra II Honors Final Exam Review Short Answer. Evaluate the series 5n. 8 n =. Evaluate the series (n + ). n = What is the sum of the finite arithmetic series?. 9+ + 5+ 8+ + + 59. 6 + 9
More informationA VERTICAL LOOK AT KEY CONCEPTS AND PROCEDURES ALGEBRA I
A VERTICAL LOOK AT KEY CONCEPTS AND PROCEDURES ALGEBRA I Revised TEKS (2012): Building to Algebra I Linear Functions, Equations, and Inequalities A Vertical Look at Key Concepts and Procedures Determine
More informationFinal Review. Non-calculator problems are indicated. 1. (No calculator) Graph the function: y = x 3 + 2
Algebra II Final Review Name Non-calculator problems are indicated. 1. (No calculator) Graph the function: y = x 3 + 2 2. (No calculator) Given the function y = -2 x + 3-1 and the value x = -5, find the
More informationAlg Review/Eq & Ineq (50 topics, due on 01/19/2016)
Course Name: MAC 1140 Spring 16 Course Code: XQWHD-P4TU6 ALEKS Course: PreCalculus Instructor: Van De Car Course Dates: Begin: 01/11/2016 End: 05/01/2016 Course Content: 307 topics Textbook: Coburn: Precalculus,
More informationPart I: Multiple Choice Questions
Name: Part I: Multiple Choice Questions. What is the slope of the line y=3 A) 0 B) -3 ) C) 3 D) Undefined. What is the slope of the line perpendicular to the line x + 4y = 3 A) -/ B) / ) C) - D) 3. Find
More informationAlgebra 2 Segment 1 Lesson Summary Notes
Algebra 2 Segment 1 Lesson Summary Notes For each lesson: Read through the LESSON SUMMARY which is located. Read and work through every page in the LESSON. Try each PRACTICE problem and write down the
More informationSUMMER REVIEW PACKET. Name:
Wylie East HIGH SCHOOL SUMMER REVIEW PACKET For students entering Regular PRECALCULUS Name: Welcome to Pre-Calculus. The following packet needs to be finished and ready to be turned the first week of the
More informationPRECALCULUS BISHOP KELLY HIGH SCHOOL BOISE, IDAHO. Prepared by Kristina L. Gazdik. March 2005
PRECALCULUS BISHOP KELLY HIGH SCHOOL BOISE, IDAHO Prepared by Kristina L. Gazdik March 2005 1 TABLE OF CONTENTS Course Description.3 Scope and Sequence 4 Content Outlines UNIT I: FUNCTIONS AND THEIR GRAPHS
More informationCOLLEGE ALGEBRA FINAL REVIEW 9) 4 = 7. 13) 3log(4x 4) + 8 = ) Write as the sum of difference of logarithms; express powers as factors.
Solve. 1) x 1 8 ) ( x ) x x 9 ) x 1 x 4) x + x 0 ) x + 9y 6) t t 4 7) y 8 4 x COLLEGE ALGEBRA FINAL REVIEW x 8) 81 x + 9) 4 7.07 x 10) 10 + 1e 10 11) solve for L P R K M + K L T 1) a) log x log( x+ 6)
More informationSample Final Exam. Math S o l u t i o n s. 1. Three points are given: A = ( 2, 2), B = (2, 4), C = ( 4, 0)
Math 0031 Sample Final Exam S o l u t i o n s 1. Three points are given: A = ( 2, 2), B = (2, 4), C = ( 4, 0) (a) (5 points) Find the midpoint D of the segment with endpoints B and C. ( 2 + ( 4) D =, 4
More informationAlgebra 2 - Semester 2 - Final Exam Review
Algebra 2 - Semester 2 - Final Exam Review Your final exam will be 60 multiple choice questions coving the following content. This review is intended to show examples of problems you may see on the final.
More informationINTERNET MAT 117 Review Problems. (1) Let us consider the circle with equation. (b) Find the center and the radius of the circle given above.
INTERNET MAT 117 Review Problems (1) Let us consider the circle with equation x 2 + y 2 + 2x + 3y + 3 4 = 0. (a) Find the standard form of the equation of the circle given above. (b) Find the center and
More informationAP Calculus AB Summer Math Packet
Name Date Section AP Calculus AB Summer Math Packet This assignment is to be done at you leisure during the summer. It is meant to help you practice mathematical skills necessary to be successful in Calculus
More informationCollege Algebra with Corequisite Support: Targeted Review
College Algebra with Corequisite Support: Targeted Review 978-1-63545-056-9 To learn more about all our offerings Visit Knewtonalta.com Source Author(s) (Text or Video) Title(s) Link (where applicable)
More information