Final Review Accelerated Advanced Algebra
|
|
- Baldwin Elliott
- 5 years ago
- Views:
Transcription
1 Name: ate: 1. What are the factors of z + z z + 25? 5. Factor completely: (7x + 2) 2 6 (z + 1)(z + 5)(z 5) (z 1)(z + 5i) 2 (49x + 1)(x 8) (7x 4)(7x + 8) (7x + 4)(7x 8) (7x + 4)(x 9) (z 1)(z + 5i)(z 5i) (z + 1)(z + 5i)(z 5i) 2. Expand and simplify: (7x + 2i )(7x 2i ) 49x 2 12x x x x Find x 2 + 6x 4 if x = 2a 2 b. 4(a 4 b 6 + a 2 b 1) 4(a 4 b 5 + a 2 b 1) 2(a 4 b 9 + 6a 2 b 2) 2(a 4 b 6 + 6a 2 b 2). ccording to the Fundamental Theorem of lgebra, how many roots does the following equation have? x + 4 = 5x 2 7x Factor: x 4 1 (x + 1)(x 1)(x 2 + 1) (x 2 + 1) 2 (x 2 1) 2 4. What is the greatest monomial factor in 0h 7 k 6 18h 5 k 6 + 0h 4 k 4? (2x 2 + 1)(2x 2 1) 6h 5 k 4 6h 4 k 4 6h 4 k 2 6h k page 1
2 8. Simplify: (x, y 0) 4x 2 y(6x 5xy) + x 4 (4y 8xy) 4x y 2, 11. Simplify: (x 2 8)(x 7x 2 2) x 5 15x x xy 5 x 5y 5 xy 5x y x 5 7x 4 8x + 54x x 6 15x 7 8x + 54x x 5 7x 4 8x + 56x 2 2x Factor: x 6 8 (x 2 2) (x 2 2)(x 2 + 2x + 4) (x 2 2)(x 4 + 2x + 4) (x 2 2)(x 4 + 2x 2 + 4) 12. Write the division statement for 2x 5x 2 10x 6. x + 4 (x + 4)(2x 2 1x + 42) 174 (x 4)(2x 2 + x + 2) 2 (x + 4)(2x 2 + x + 2) + 2 (x + 4)(2x 2 + 1x 42) Find the area of the shaded region in terms of x. 1. What are the zeros of the function f (x) = x + 4x 2 + x 6? x 2 + x + 2 4x 2 x + x 2 + x + 6 x 2 + 9x 2, 2, and 1 2, 1, and 1, 2, and 1, 2, and page 2
3 14. etermine the solution set of the equation x(x 2 + 1)(x 2 4) = 0. { 2, 2} { 2, 1, 1, 2} { 2, 0, 2} {0, 1, 1} 18. Which of the following graphs best illustrates the graph of y = a(x b)(x c)(x d)(x e)(x f )(x g) where a < 0 and b c d e f g? 15. How many terms are in the expansion of (x + 2y) 8? What is the sum of the coefficients of the expansion of (x + y) 7? Which of the following is the graph of y = a(x + 1)(x 2)(x 2), where a > 0? 17. Solve the following system for x and y. y = x x + 14 y x = 4 ( 9, 9), (12, 6) (9, 1), (2, 6) ( 1, 9), (2, 4) ( 9, 1), ( 2, 6) page
4 20. Simplify: (x 2 49)(x 2 81) x x + 56 (x 7)(x 2 81) x + 8 (x 9)(x 2 81) x + 8 (x + 8)(x 2 81) x + 7 (x + 9)(x 2 81) x Simplify: 7xy + 2xy 6 6 7xy + 2x ( 7x 2 ) y 21x 2 6x ( ) 14x 49x 2 4 7xy + 2xy 6y 7xy + 2y Simplify: x + 2 x x 2 x 4 x 2 x 2 5x + 6 x + 2 x does not simplify 25. Simplify: 5x x 1 2x x 2 x 2 8x (x 1)(x 2) x 2 + 8x (x 1)(x 2) 7x x (x 1)(x 2) x x (x 1)(x 2) 22. Simplify: (x 5) 2(x + 5) (x 5) (x + 5) x 15 4 x2 25 2x 10 x 5 4 (x 5) 2(x + 5) 26. Simplify: x x x + 2 x 2 + 4x 16 x 2 4 5x 15 x 2 4 x 15 2x x + 2 x Multiply: x 2 + 6x + 5 x 2 + 2x 8 x 2 5x + 6 x 2 + 2x Solve: 6x + 1 = 5 x + 1 x + 4 x 1 x + 4 x + 1 x 4 x 1 x page 4
5 28. Solve: 7x + = 2x 1. How many solutions are shown by the graph of the quadratic function? Ø 29. Solve for x: 2 x x 2 4x + 4 = { 11, 1 } { 4, 1 } { 11, 1 } { 8, 1 } zero one two three 0. Use the graph below to find the point of intersection for the functions. q(x) = 4x r(x) = x + 7 y 2. What are the roots of the function whose graph is shown? x { 1, } {1, 4} {} { 1} ( 4, ) ( 1, 1) ( 2, 5) (1, 7) page 5
6 . What are the solutions to the quadratic function in the graph? 6. When x is a real number, which of the following is the graph of y = x + 2? no real roots 2 and 1 0 and State the range of the function. 4 y 4 2 y 2 y 4 { 2, 1, 0, 1, 2} 5. Given the graph, describe the domain. x 1 y 2 y 2 x 1 page 6
7 7. Which of the following represents the graph of 1 y = x 2 9? 8. Which of the following could be the graph of a rational function that is not a polynomial function? page 7
8 9. Which one of the following sketches is a reasonable graph of y = 2 x +? 41. If 2 x 1 = ( 1 8 )2, then what is the value of x? no solution 42. If 9 x = 27 x+9, then what is the value of x? Solve: 8(8) x = Which one of the following sketches is a reasonable graph of y = 2 x? 44. If y = 10 x, then: y = log x 10 y = log 10 x x = log 10 y x = log y Solve for x: log 5 x = page 8
9 46. Solve for x: log 625 = 4 log x ± Given log x = log a 1 2 log b + 4 log c, determine an expression for x. a b 2 4 c a 4 c b 2 a c 4 b ac 4 b 47. Solve: log 2 (x ) + log 2 (x + 1) = 5 7, 5 7, 5 5, Write log w + log v log z as the logarithm of a single quantity. 48. Simplify: log log wv z log w v z log wv z log w + v z 49. Evaluate log 6 12 to 2 decimal places The expression log M2 2N is equal to: log M 2 log 2N 50. If z = x, then log z is equal to: y2 2 log M log 2 + log N 2 log M log 2 log N log x 2 log y 2 log x y 2 log M log 2 + log N (log x log y) log x 2 log y 2 page 9
10 54. Use the properties of logarithms to expand the expression log x 2y. log x log 2y log x log 2 + log y log + log x log 2 + log y log + log x log 2 log y page 10
11 Problem-ttic format version c Educide Software Licensed for use by fchannor@atlanta.k12.ga.us Terms of Use at 05/19/ N.N PR.5 2. N.N PR.5. N.N REI.7 4. SSE F.IF.7 5. SSE F.IF.7 6. SSE PR.6 7. SSE PR SSE.2 SSE.2 PR.1 PR.1 PR.2 PR. PR PR.7 PR.7 PR.7 PR.7 PR.7 REI.2
12 Teacher s Key Page REI REI.2 0. REI F.IF.4 2. F.IF.4. F.IF.4 4. F.IF.5 5. F.IF.5 6. F.IF.7 7. F.IF.7 8. F.IF.7 9. F.IF.7E 40. F.IF.7E 41. F.IF F.IF.8 4. F.F F.F F.F F.F F.F F.F F.F F.F F.F F.F.5 5. F.F F.F.5
Accel. Geometry FINAL EXAM REVIEW - UNITS 2 AND 3
ccel. Geometry FINL EXM REVIEW - UNITS N 3 Name: ate: 1. Solve: x + 9 = 0 over the set of complex numbers.. ±9i. 3 + i. ±3i. 3 10. The altitude of a triangle is 4 cm more than the base. The area is 36
More informationreview for finals 10. If f (x) = x 2 A If f (x) = x 0 + x x 1, find f (4). 13. If f (x) = (x 0 + x 1 2 ) 2, find f (9).
Name: ate: 1. If g(x) = (ax 1 x) 2, express g(10) in simplest form. 2. The value of the x-intercept for the graph of x 5y = 0 is 10. 5. 5. What is the inverse of the function y = 2x +? x = 1 2 y 2. y =
More informationSystem of Equations Review
Name: Date: 1. Solve the following system of equations for x: x + y = 6 x y = 2 6. Solve the following systems of equations for x: 2x + 3y = 5 4x 3y = 1 2. Solve the following system of equations algebraically
More informationFunctions and Equations
Canadian Mathematics Competition An activity of the Centre for Education in Mathematics and Computing, University of Waterloo, Waterloo, Ontario Euclid eworkshop # Functions and Equations c 006 CANADIAN
More informationPolynomials. In many problems, it is useful to write polynomials as products. For example, when solving equations: Example:
Polynomials Monomials: 10, 5x, 3x 2, x 3, 4x 2 y 6, or 5xyz 2. A monomial is a product of quantities some of which are unknown. Polynomials: 10 + 5x 3x 2 + x 3, or 4x 2 y 6 + 5xyz 2. A polynomial is a
More informationCommon Core Standards Addressed in this Resource
Common Core Standards Addressed in this Resource.EE.3 - Apply the properties of operations to generate equivalent expressions. Activity page: 4 7.RP.3 - Use proportional relationships to solve multistep
More informationA quadratic expression is a mathematical expression that can be written in the form 2
118 CHAPTER Algebra.6 FACTORING AND THE QUADRATIC EQUATION Textbook Reference Section 5. CLAST OBJECTIVES Factor a quadratic expression Find the roots of a quadratic equation A quadratic expression is
More informationMEMORIAL UNIVERSITY OF NEWFOUNDLAND
MEMORIAL UNIVERSITY OF NEWFOUNDLAND DEPARTMENT OF MATHEMATICS AND STATISTICS Section 5. Math 090 Fall 009 SOLUTIONS. a) Using long division of polynomials, we have x + x x x + ) x 4 4x + x + 0x x 4 6x
More information5.3. Polynomials and Polynomial Functions
5.3 Polynomials and Polynomial Functions Polynomial Vocabulary Term a number or a product of a number and variables raised to powers Coefficient numerical factor of a term Constant term which is only a
More informationCommon Core Standards Addressed in this Resource
Common Core Standards Addressed in this Resource 6.RP.3 - Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams,
More informationPARTIAL FRACTIONS AND POLYNOMIAL LONG DIVISION. The basic aim of this note is to describe how to break rational functions into pieces.
PARTIAL FRACTIONS AND POLYNOMIAL LONG DIVISION NOAH WHITE The basic aim of this note is to describe how to break rational functions into pieces. For example 2x + 3 1 = 1 + 1 x 1 3 x + 1. The point is that
More informationFoundations of Math 2 Final A. Which graph would best represent the graph of this parabola if it is translated 4 units down and 6 units left?
Name: Date: 1. The graph of y = x 2 + is shown below. Which graph would best represent the graph of this parabola if it is translated units down and 6 units left? 2. The roots of a quadratic equation can
More informationVOYAGER INSIDE ALGEBRA CORRELATED TO THE NEW JERSEY STUDENT LEARNING OBJECTIVES AND CCSS.
We NJ Can STUDENT Early Learning LEARNING Curriculum OBJECTIVES PreK Grades 8 12 VOYAGER INSIDE ALGEBRA CORRELATED TO THE NEW JERSEY STUDENT LEARNING OBJECTIVES AND CCSS www.voyagersopris.com/insidealgebra
More informationECM Final Exam Review
Name: Date: 1. Which of the following is the graph of the solution set of the system? y 2 y x 3 2. Three times a number n is greater than 8 more than the number. Which of the following inequalities best
More informationAlgebra 2 - Common Core Summer Assignment
Name: Date: You must answer all questions. Please show works for all questions that need work. You can show the work in the space provided by each question. If you need more room you can do the work on
More informationPARTIAL FRACTIONS AND POLYNOMIAL LONG DIVISION. The basic aim of this note is to describe how to break rational functions into pieces.
PARTIAL FRACTIONS AND POLYNOMIAL LONG DIVISION NOAH WHITE The basic aim of this note is to describe how to break rational functions into pieces. For example 2x + 3 = + x 3 x +. The point is that we don
More informationMath123 Lecture 1. Dr. Robert C. Busby. Lecturer: Office: Korman 266 Phone :
Lecturer: Math1 Lecture 1 Dr. Robert C. Busby Office: Korman 66 Phone : 15-895-1957 Email: rbusby@mcs.drexel.edu Course Web Site: http://www.mcs.drexel.edu/classes/calculus/math1_spring0/ (Links are case
More informationKing Fahd University of Petroleum and Minerals Prep-Year Math Program Math Term 161 Recitation (R1, R2)
Math 001 - Term 161 Recitation (R1, R) Question 1: How many rational and irrational numbers are possible between 0 and 1? (a) 1 (b) Finite (c) 0 (d) Infinite (e) Question : A will contain how many elements
More informationReview all the activities leading to Midterm 3. Review all the problems in the previous online homework sets (8+9+10).
MA109, Activity 34: Review (Sections 3.6+3.7+4.1+4.2+4.3) Date: Objective: Additional Assignments: To prepare for Midterm 3, make sure that you can solve the types of problems listed in Activities 33 and
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 informationCh 7 Summary - POLYNOMIAL FUNCTIONS
Ch 7 Summary - POLYNOMIAL FUNCTIONS 1. An open-top box is to be made by cutting congruent squares of side length x from the corners of a 8.5- by 11-inch sheet of cardboard and bending up the sides. a)
More informationSection 8.3 Partial Fraction Decomposition
Section 8.6 Lecture Notes Page 1 of 10 Section 8.3 Partial Fraction Decomposition Partial fraction decomposition involves decomposing a rational function, or reversing the process of combining two or more
More informationHow might we evaluate this? Suppose that, by some good luck, we knew that. x 2 5. x 2 dx 5
8.4 1 8.4 Partial Fractions Consider the following integral. 13 2x (1) x 2 x 2 dx How might we evaluate this? Suppose that, by some good luck, we knew that 13 2x (2) x 2 x 2 = 3 x 2 5 x + 1 We could then
More information4.5 Integration of Rational Functions by Partial Fractions
4.5 Integration of Rational Functions by Partial Fractions From algebra, we learned how to find common denominators so we can do something like this, 2 x + 1 + 3 x 3 = 2(x 3) (x + 1)(x 3) + 3(x + 1) (x
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 informationAdding and Subtracting Polynomials Add and Subtract Polynomials by doing the following: Combine like terms
POLYNOMIALS AND POLYNOMIAL OPERATIONS STUDY GUIDE Polynomials Polynomials are classified by two different categories: by the number of terms, and the degree of the leading exponent. Number Classification
More informationUpdated: January 16, 2016 Calculus II 7.4. Math 230. Calculus II. Brian Veitch Fall 2015 Northern Illinois University
Math 30 Calculus II Brian Veitch Fall 015 Northern Illinois University Integration of Rational Functions by Partial Fractions From algebra, we learned how to find common denominators so we can do something
More information7.4: Integration of rational functions
A rational function is a function of the form: f (x) = P(x) Q(x), where P(x) and Q(x) are polynomials in x. P(x) = a n x n + a n 1 x n 1 + + a 0. Q(x) = b m x m + b m 1 x m 1 + + b 0. How to express a
More informationUnit 2 Rational Functionals Exercises MHF 4UI Page 1
Unit 2 Rational Functionals Exercises MHF 4UI Page Exercises 2.: Division of Polynomials. Divide, assuming the divisor is not equal to zero. a) x 3 + 2x 2 7x + 4 ) x + ) b) 3x 4 4x 2 2x + 3 ) x 4) 7. *)
More informationAlgebra II/Math III Curriculum Map
6 weeks Unit Unit Focus Common Core Math Standards 1 Simplify and perform operations with one variable involving rational, exponential and quadratic functions. 2 Graph and evaluate functions to solve problems.
More informationAlgebra III Chapter 2 Note Packet. Section 2.1: Polynomial Functions
Algebra III Chapter 2 Note Packet Name Essential Question: Section 2.1: Polynomial Functions Polynomials -Have nonnegative exponents -Variables ONLY in -General Form n ax + a x +... + ax + ax+ a n n 1
More informationMathematics High School Algebra
Mathematics High School Algebra Expressions. An expression is a record of a computation with numbers, symbols that represent numbers, arithmetic operations, exponentiation, and, at more advanced levels,
More information(a) Write down the value of q and of r. (2) Write down the equation of the axis of symmetry. (1) (c) Find the value of p. (3) (Total 6 marks)
1. Let f(x) = p(x q)(x r). Part of the graph of f is shown below. The graph passes through the points ( 2, 0), (0, 4) and (4, 0). (a) Write down the value of q and of r. (b) Write down the equation of
More informationMath 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2
Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2 April 11, 2016 Chapter 10 Section 1: Addition and Subtraction of Polynomials A monomial is
More information7th/8th Grade Summer School Post Test
Tindley Preparatory cademy 7th/8th Grade Summer School Post Test Summer Name: Date: 1. Stephanie scored 88, 70, 84, and 72 on her first four science tests. What score does Stephanie need on her fifth science
More information1 Solving Algebraic Equations
Arkansas Tech University MATH 1203: Trigonometry Dr. Marcel B. Finan 1 Solving Algebraic Equations This section illustrates the processes of solving linear and quadratic equations. The Geometry of Real
More informationMultiplication of Polynomials
Summary 391 Chapter 5 SUMMARY Section 5.1 A polynomial in x is defined by a finite sum of terms of the form ax n, where a is a real number and n is a whole number. a is the coefficient of the term. n is
More informationChapter 2.7 and 7.3. Lecture 5
Chapter 2.7 and 7.3 Chapter 2 Polynomial and Rational Functions 2.1 Complex Numbers 2.2 Quadratic Functions 2.3 Polynomial Functions and Their Graphs 2.4 Dividing Polynomials; Remainder and Factor Theorems
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 informationCCSS Math- Algebra. Domain: Algebra Seeing Structure in Expressions A-SSE. Pacing Guide. Standard: Interpret the structure of expressions.
1 Domain: Algebra Seeing Structure in Expressions A-SSE Standard: Interpret the structure of expressions. H.S. A-SSE.1a. Interpret expressions that represent a quantity in terms of its context. Content:
More informationx 9 or x > 10 Name: Class: Date: 1 How many natural numbers are between 1.5 and 4.5 on the number line?
1 How many natural numbers are between 1.5 and 4.5 on the number line? 2 How many composite numbers are between 7 and 13 on the number line? 3 How many prime numbers are between 7 and 20 on the number
More informationQuestion 1: The graphs of y = p(x) are given in following figure, for some Polynomials p(x). Find the number of zeroes of p(x), in each case.
Class X - NCERT Maths EXERCISE NO:.1 Question 1: The graphs of y = p(x) are given in following figure, for some Polynomials p(x). Find the number of zeroes of p(x), in each case. (i) (ii) (iii) (iv) (v)
More informationReading Mathematical Expressions & Arithmetic Operations Expression Reads Note
Math 001 - Term 171 Reading Mathematical Expressions & Arithmetic Operations Expression Reads Note x A x belongs to A,x is in A Between an element and a set. A B A is a subset of B Between two sets. φ
More informationMathematics 136 Calculus 2 Everything You Need Or Want To Know About Partial Fractions (and maybe more!) October 19 and 21, 2016
Mathematics 36 Calculus 2 Everything You Need Or Want To Know About Partial Fractions (and maybe more!) October 9 and 2, 206 Every rational function (quotient of polynomials) can be written as a polynomial
More informationMath 2: Algebra 2, Geometry and Statistics Ms. Sheppard-Brick Chapter 4 Test Review
Chapter 4 Test Review Students will be able to (SWBAT): Write an explicit and a recursive function rule for a linear table of values. Write an explicit function rule for a quadratic table of values. Determine
More informationUnit 2-1: Factoring and Solving Quadratics. 0. I can add, subtract and multiply polynomial expressions
CP Algebra Unit -1: Factoring and Solving Quadratics NOTE PACKET Name: Period Learning Targets: 0. I can add, subtract and multiply polynomial expressions 1. I can factor using GCF.. I can factor by grouping.
More informationEssential Mathematics
Appendix B 1211 Appendix B Essential Mathematics Exponential Arithmetic Exponential notation is used to express very large and very small numbers as a product of two numbers. The first number of the product,
More informationSolutions to Exercises, Section 2.5
Instructor s Solutions Manual, Section 2.5 Exercise 1 Solutions to Exercises, Section 2.5 For Exercises 1 4, write the domain of the given function r as a union of intervals. 1. r(x) 5x3 12x 2 + 13 x 2
More informationAFDA Unit 1 Practice Test
F Unit 1 Practice Test Name: ate: 1. Which inequality is represented by the accompanying graph? 4 3 1 0 1 3 4. < x 3. x 3. x < 3. < x < 3. Which inequality is represented by the accompanying graph? 1 0
More informationsum(seq(1/(2^x), x, 3, 6, 1)= 15 64
SEQUENCE & SERIES Summation Notation sum(seq(1/(2^x), x, 3, 6, 1)= 15 64 Arithmetic- SUBTRACT to find d (common difference) Geometric- DIVIDE to find r (common ratio) EXAMPLES REAL/COMPLEX NUMBERS Complex
More information10/22/16. 1 Math HL - Santowski SKILLS REVIEW. Lesson 15 Graphs of Rational Functions. Lesson Objectives. (A) Rational Functions
Lesson 15 Graphs of Rational Functions SKILLS REVIEW! Use function composition to prove that the following two funtions are inverses of each other. 2x 3 f(x) = g(x) = 5 2 x 1 1 2 Lesson Objectives! The
More informationCourse: Algebra MP: Reason abstractively and quantitatively MP: Model with mathematics MP: Look for and make use of structure
Algebra Cluster: Interpret the structure of expressions. A.SSE.1: Interpret expressions that represent a quantity in terms of its context (Modeling standard). a. Interpret parts of an expression, such
More informationBeginning Algebra. 1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions
1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions Beginning Algebra 1.3 Review of Decimal Numbers and Square Roots 1.4 Review of Percents 1.5 Real Number System 1.6 Translations:
More informationYou try: What is the equation of the line on the graph below? What is the equation of the line on the graph below?
1 What is the equation of the line on the graph below? 2 3 1a What is the equation of the line on the graph below? y-intercept Solution: To write an equation in slope-intercept form, identify the slope
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 informationComplex Numbers: Definition: A complex number is a number of the form: z = a + bi where a, b are real numbers and i is a symbol with the property: i
Complex Numbers: Definition: A complex number is a number of the form: z = a + bi where a, b are real numbers and i is a symbol with the property: i 2 = 1 Sometimes we like to think of i = 1 We can treat
More informationx y x y ax bx c x Algebra I Course Standards Gap 1 Gap 2 Comments a. Set up and solve problems following the correct order of operations (including proportions, percent, and absolute value) with rational
More informationSOL Warm-Up Graphing Calculator Active
A.2c (a) Factoring polynomials SOL Warm-Up 1. Which of the following represents 12x 2 + 6x + 3 in simplified form after factoring out the greatest common factor? A 12(x 2 + 2x + 4) B x(12x 2 + 6x + 3)
More informationCalculus II. Monday, March 13th. WebAssign 7 due Friday March 17 Problem Set 6 due Wednesday March 15 Midterm 2 is Monday March 20
Announcements Calculus II Monday, March 13th WebAssign 7 due Friday March 17 Problem Set 6 due Wednesday March 15 Midterm 2 is Monday March 20 Today: Sec. 8.5: Partial Fractions Use partial fractions to
More informationThese are the skills you should be proficient in performing before you get to Pre-AP Calculus.
Fort Zumwalt School District PRE-AP CALCULUS SUMMER REVIEW PACKET Name: 1. This packet is to be handed in to your Pre AP Calculus teacher on the first day of the school year. 2. All work must be shown
More informationUnit 7: Functions. 3. Which diagram shows a relation that is not a function? 1. Which graph represents a function? A. B. A. B. C. D. C. D.
Name: ate: 1. Which graph represents a function? 3. Which diagram shows a relation that is not a function? 2. Which diagram is not the graph of a function? 4. Which graph of a relation is also a function?
More informationPolynomial Functions
Polynomial Functions Equations and Graphs Characteristics The Factor Theorem The Remainder Theorem http://www.purplemath.com/modules/polyends5.htm 1 A cross-section of a honeycomb has a pattern with one
More informationAlgebra II Mathematics N-CN The Complex Number System
GRADE HS Algebra II Mathematics N-CN The Complex Number System K-2 3-5 6-8 9-12 Perform arithmetic operations with complex numbers. N.CN.1 N.CN.2 There is a complex number i such that i 2 = -1, and every
More informationAssessment Exemplars: Polynomials, Radical and Rational Functions & Equations
Class: Date: Assessment Exemplars: Polynomials, Radical and Rational Functions & Equations 1 Express the following polynomial function in factored form: P( x) = 10x 3 + x 2 52x + 20 2 SE: Express the following
More informationLee County Schools Curriculum Road Map Algebra 2
Quarter 1 1 Equations, Inequalities, & Introduction to AL 16 A.CED.1 AL 17, 19, 28, 28a, 30 A.CED.2 A.CED.4 F.BF.1 F.BF.1b F.BF.4a AL 18 A.CED.3; AL 25, 23, 24, 30 F.IF.7a; F.IF.5, F.IF.6, F.BF.4a; ALCOS
More informationAlgebra 2 (3 rd Quad Expectations) CCSS covered Key Vocabulary Vertical
Algebra 2 (3 rd Quad Expectations) CCSS covered Key Vocabulary Vertical Chapter (McGraw-Hill Algebra 2) Chapter 7 (Suggested Pacing 14 Days) Lesson 7-1: Graphing Exponential Functions Lesson 7-2: Solving
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 informationMath Analysis Notes Mrs. Atkinson 1
Name: Math Analysis Chapter 7 Notes Day 6: Section 7-1 Solving Systems of Equations with Two Variables; Sections 7-1: Solving Systems of Equations with Two Variables Solving Systems of equations with two
More informationAdditional Practice Lessons 2.02 and 2.03
Additional Practice Lessons 2.02 and 2.03 1. There are two numbers n that satisfy the following equations. Find both numbers. a. n(n 1) 306 b. n(n 1) 462 c. (n 1)(n) 182 2. The following function is defined
More informationGiven a polynomial and one of its factors, find the remaining factors of the polynomial. 4. x 3 6x x 6; x 1 SOLUTION: Divide by x 1.
Use synthetic substitution to find f (4) and f ( 2) for each function. 2. f (x) = x 4 + 8x 3 + x 2 4x 10 Divide the function by x 4. The remainder is 758. Therefore, f (4) = 758. Divide the function by
More informationCHAPTER 2 POLYNOMIALS KEY POINTS
CHAPTER POLYNOMIALS KEY POINTS 1. Polynomials of degrees 1, and 3 are called linear, quadratic and cubic polynomials respectively.. A quadratic polynomial in x with real coefficient is of the form a x
More informationBeal City High School Algebra 2A Curriculum and Alignment
Beal City High School Algebra 2A Curriculum and Alignment UNIT 1 Linear Functions (Chapters 1-3) 1. Combine like terms, solve equations, solve inequalities, evaluate expressions(1-2,3,4) 2. Solve an equation
More information1.3 Algebraic Expressions. Copyright Cengage Learning. All rights reserved.
1.3 Algebraic Expressions Copyright Cengage Learning. All rights reserved. Objectives Adding and Subtracting Polynomials Multiplying Algebraic Expressions Special Product Formulas Factoring Common Factors
More informationElectrostatics Review A. A B. B C. C D. D
Name: ate: 1. Which sketch best represents the charge distribution around a neutral electroscope when a positively charged strip is brought near, but does not touch, the electroscope? 4. In the diagram
More informationStandards-Based Learning Power Standards. High School- Algebra
Standards-Based Learning Power Standards Mathematics Algebra 3,4 The high school standards specify the mathematics that all students should study in order to be college and career ready. High School Number
More information, a 1. , a 2. ,..., a n
CHAPTER Points to Remember :. Let x be a variable, n be a positive integer and a 0, a, a,..., a n be constants. Then n f ( x) a x a x... a x a, is called a polynomial in variable x. n n n 0 POLNOMIALS.
More informationUnit 1 Vocabulary. A function that contains 1 or more or terms. The variables may be to any non-negative power.
MODULE 1 1 Polynomial A function that contains 1 or more or terms. The variables may be to any non-negative power. 1 Modeling Mathematical modeling is the process of using, and to represent real world
More informationTrimester 2 Expectations. Chapter (McGraw-Hill. CCSS covered Key Vocabulary Vertical. Alignment
Algebra 2 Trimester 2 Expectations Chapter (McGraw-Hill Algebra 2) Chapter 5 (Suggested Pacing 14 Days) Polynomials and Polynomial Functions Lesson 5-1: Operations with Polynomials Lesson 5-2: Dividing
More informationA monomial or sum of monomials
Polynomial: A monomial or sum of monomials Polynomial in x is an expression of the form a n x n + a n 1 x n 1 + a n 2 x n 2 +. a 1 x 1 + a 0 where n is a positive integer and a n 0 Example: 6x 3 + 2x 8x
More informationThe Real Number System The Complex Number System Extend the properties of exponents to rational exponents. o Know there is a complex number such that
SUBJECT: MATH 2012 2013 SCOPE AND SEQUENCE ST 1 Semester The Real Number System The Complex Number System Seeing Structure in Expressions Interpret the structure of expressions o Interpret expressions
More informationKEY CONCEPTS. Factoring is the opposite of expanding.
KEY CONCEPTS Factoring is the opposite of expanding. To factor simple trinomials in the form x 2 + bx + c, find two numbers such that When you multiply them, their product (P) is equal to c When you add
More informationPartial Fractions. Calculus 2 Lia Vas
Calculus Lia Vas Partial Fractions rational function is a quotient of two polynomial functions The method of partial fractions is a general method for evaluating integrals of rational function The idea
More informationAnswers to Sample Exam Problems
Math Answers to Sample Exam Problems () Find the absolute value, reciprocal, opposite of a if a = 9; a = ; Absolute value: 9 = 9; = ; Reciprocal: 9 ; ; Opposite: 9; () Commutative law; Associative law;
More informationA2 HW Imaginary Numbers
Name: A2 HW Imaginary Numbers Rewrite the following in terms of i and in simplest form: 1) 100 2) 289 3) 15 4) 4 81 5) 5 12 6) -8 72 Rewrite the following as a radical: 7) 12i 8) 20i Solve for x in simplest
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 informationThe absolute value (modulus) of a number
The absolute value (modulus) of a number Given a real number x, its absolute value or modulus is dened as x if x is positive x = 0 if x = 0 x if x is negative For example, 6 = 6, 10 = ( 10) = 10. The absolute
More information9.5. Polynomial and Rational Inequalities. Objectives. Solve quadratic inequalities. Solve polynomial inequalities of degree 3 or greater.
Chapter 9 Section 5 9.5 Polynomial and Rational Inequalities Objectives 1 3 Solve quadratic inequalities. Solve polynomial inequalities of degree 3 or greater. Solve rational inequalities. Objective 1
More informationTenth Bit Bank Mathematics Real Numbers
Tenth Bit Bank Mathematics Real Numbers 1. The rational number among the following is... i) 4.28 ii) 4.282828... iii) 4.288888... A) i) & ii) B) ii) & iii) C) i) & iii) D) All the above 2. A rational number
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 information(x + 1)(x 2) = 4. x
dvanced Integration Techniques: Partial Fractions The method of partial fractions can occasionally make it possible to find the integral of a quotient of rational functions. Partial fractions gives us
More informationAlgebra II Pacing Guide Last Updated: August, Guiding Question & Key Topics
1-14 Unit 1 Investigations & AS I investigate functions, am I analyzing the function thoroughly and clearly communicating my reasoning to others? Solving puzzles in Teams Using a Graphing Calculator to
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 informationConcept Category 4. Polynomial Functions
Concept Category 4 Polynomial Functions (CC1) A Piecewise Equation 2 ( x 4) x 2 f ( x) ( x 3) 2 x 1 The graph for the piecewise Polynomial Graph (preview) Still the same transformations CC4 Learning Targets
More informationChapter 2: Polynomial and Rational Functions
Chapter 2: Polynomial and Rational Functions Section 2.1 Quadratic Functions Date: Example 1: Sketching the Graph of a Quadratic Function a) Graph f(x) = 3 1 x 2 and g(x) = x 2 on the same coordinate plane.
More informationINSIDE ALGEBRA CORRELATED WITH CALIFORNIA S COMMON CORE STANDARDS HIGH SCHOOL ALGEBRA
We CA Can COMMON Early Learning CORE STANDARDS Curriculum PreK Grades 8 12 INSIDE ALGEBRA CORRELATED WITH CALIFORNIA S COMMON CORE STANDARDS HIGH SCHOOL ALGEBRA May 2011 www.voyagersopris.com/insidealgebra
More informationAlgebra I Unit Report Summary
Algebra I Unit Report Summary No. Objective Code NCTM Standards Objective Title Real Numbers and Variables Unit - ( Ascend Default unit) 1. A01_01_01 H-A-B.1 Word Phrases As Algebraic Expressions 2. A01_01_02
More informationSection 3.2 Polynomial Functions and Their Graphs
Section 3.2 Polynomial Functions and Their Graphs EXAMPLES: P (x) = 3, Q(x) = 4x 7, R(x) = x 2 + x, S(x) = 2x 3 6x 2 10 QUESTION: Which of the following are polynomial functions? (a) f(x) = x 3 + 2x +
More informationSummer Packet A Math Refresher For Students Entering IB Mathematics SL
Summer Packet A Math Refresher For Students Entering IB Mathematics SL Name: PRECALCULUS SUMMER PACKET Directions: This packet is required if you are registered for Precalculus for the upcoming school
More informationNotes Chapter 5 Systems of Linear Equations. Section Number and Topic 5.1 Solve Systems by Graphing
Notes Chapter 5 Systems of Linear Equations Section Number and Topic 5.1 Solve Systems by Graphing Standards REI.3.6 REI.4.11 CED.1.2 MAFS.912.N-Q.1.2 MAFS. 912.A- SSE.1.1 MAFS. 912.A- CED.1.2 CED.1.3
More informationAlgebra 2 (4 th Quad Expectations) Chapter (McGraw-Hill Algebra 2) Chapter 10 (Suggested Pacing 13 Days)
Algebra 2 (4 th Quad Expectations) Chapter (McGraw-Hill Algebra 2) Chapter 10 (Suggested Pacing 13 Days) Lesson 10-1: Sequences as Lesson 10-2: Arithmetic Sequences and Series Lesson 10-3: Geometric Sequences
More information