Quadratic Formula, Completing the Square, Systems Review Sheet
|
|
|
- Jordan Crawford
- 5 years ago
- Views:
Transcription
1 Quadratc Formula Completng the Square Systems Revew Sheet 1. Factor the polynomal completely. 6. Use the graph to approxmate the real zeros of the functon. 2. Fnd the real-number solutons of the equaton Fnd all zeros of the polynomal functon. 7. Factor the expresson Factor the expresson Wrte as the product of two factors:
2 no real-number soluton Wrte the expresson as a complex number n standard form Factor completely. Smplfy the expresson Solve for x
3 21. Solve by completng the square and and and and What are the zeros of the polynomal functon graphed below? 22. Use the quadratc formula to solve: Whch equaton(s) represent the graph below? I II III 24. x = x = x = x = Solve by factorng: I only II only I and II II and III Fnd the zeros of the functon. 26.
4 Quadratc Formula Completng the Square Systems Revew Sheet Answer Secton 1. ANS: C PTS: 1 DIF: Level A REF: MAL20784 STA: NY.NYLES.MTH.05.AT2.A2.A.7 TOP: Lesson 5.4 Factor and Solve Polynomal Equatons KEY: factor dfference of squares 2. ANS: C PTS: 1 DIF: Level A REF: MAL20783 STA: NY.NYLES.MTH.05.AT2.A2.A.7 TOP: Lesson 5.4 Factor and Solve Polynomal Equatons KEY: polynomal factor 3. ANS: D PTS: 1 DIF: Level A REF: MAL20797 TOP: Lesson 5.4 Factor and Solve Polynomal Equatons KEY: solve cubc factor zero product BLM: Comprehenson 4. ANS: A PTS: 1 DIF: Level B REF: MAL20835 NAT: NCTM 9-12.ALG.1.c TOP: Lesson 5.7 Apply the Fundamental Theorem of Algebra KEY: rratonal conjugates theorem zeros functons 5. ANS: B PTS: 1 DIF: Level B REF: MAL20833 TOP: Lesson 5.7 Apply the Fundamental Theorem of Algebra KEY: zeros functon complex conjugates 6. ANS: D PTS: 1 DIF: Level A REF: MAL20842 TOP: Lesson 5.7 Apply the Fundamental Theorem of Algebra KEY: estmate root zero functon cubc 7. ANS: C PTS: 1 DIF: Level A REF: MAL20577 TOP: Lesson 4.4 Solve ax2 + bx + c = 0 by Factorng KEY: factor quadratc trnomal 8. ANS: A PTS: 1 DIF: Level B REF: MAL20586 STA: NY.NYLES.MTH.05.AT2.A2.A.7 TOP: Lesson 4.4 Solve ax2 + bx + c = 0 by Factorng KEY: trnomal factor dfference of two squares 9. ANS: B PTS: 1 DIF: Level B REF: MAL20585 STA: NY.NYLES.MTH.05.AT2.A2.A.7 TOP: Lesson 4.4 Solve ax2 + bx + c = 0 by Factorng KEY: factor dfference of squares 10. ANS: C PTS: 1 DIF: Level B REF: MAL20581 TOP: Lesson 4.4 Solve ax2 + bx + c = 0 by Factorng KEY: factor quadratc trnomal 11. ANS: A PTS: 1 DIF: Level B REF: MAL20587 TOP: Lesson 4.4 Solve ax2 + bx + c = 0 by Factorng KEY: factor solve quadratc 12. ANS: D PTS: 1 DIF: Level B REF: MAL20595 TOP: Lesson 4.4 Solve ax2 + bx + c = 0 by Factorng KEY: factor solve quadratc trnomal 13. ANS: A PTS: 1 DIF: Level B REF: MAL20591 STA: NY.NYLES.MTH.05.AT2.A2.A.7 TOP: Lesson 4.4 Solve ax2 + bx + c = 0 by Factorng KEY: polynomal factor 14. ANS: A PTS: 1 DIF: Level B REF: MAL20602 STA: NY.NYLES.MTH.05.AT2.A2.A.16 TOP: Lesson 4.5 Solve Quadratc Equatons by Fndng Square Roots KEY: radcal root property product 15. ANS: D PTS: 1 DIF: Level A REF: MAL20605
5 TOP: Lesson 4.5 Solve Quadratc Equatons by Fndng Square Roots KEY: solve square square root varable dvde 16. ANS: D PTS: 1 DIF: Level B REF: MAL20607 TOP: Lesson 4.5 Solve Quadratc Equatons by Fndng Square Roots KEY: equaton quadratc square root 17. ANS: D PTS: 1 DIF: Level B REF: MAL20626 NAT: NCTM 9-12.NOP.1.b TOP: Lesson 4.6 Perform Operatons wth Complex Numbers KEY: subtract add complex number 18. ANS: C PTS: 1 DIF: Level B REF: MAL20639 NAT: NCTM 9-12.NOP.1.b TOP: Lesson 4.6 Perform Operatons wth Complex Numbers KEY: quotent complex 19. ANS: A PTS: 1 DIF: Level B REF: MAL20657 TOP: Lesson 4.7 Complete the Square KEY: square solve complex quadratc 20. ANS: D PTS: 1 DIF: Level B REF: MAL20661 STA: NY.NYLES.MTH.05.AT2.A2.A.25 TOP: Lesson 4.7 Complete the Square KEY: solve equaton complex quadratc 21. ANS: C PTS: 1 DIF: Level B REF: MAL20674 STA: NY.NYLES.MTH.05.AT2.A2.A.24 TOP: Lesson 4.7 Complete the Square KEY: root completng the square complex quadratc magnary 22. ANS: B PTS: 1 DIF: Level B REF: MAL20684 STA: NY.NYLES.MTH.05.AT2.A2.A.25 TOP: Lesson 4.8 Use the Quadratc Formula and the Dscrmnant KEY: solve quadratc quadratc formula 23. ANS: C PTS: 1 DIF: Level B REF: MAL20690 NAT: NCTM 9-12.NOP.1.b TOP: Lesson 4.8 Use the Quadratc Formula and the Dscrmnant KEY: equaton complex quadratc functon magnary root 24. ANS: C PTS: 1 DIF: Level B REF: MAL20688 TOP: Lesson 4.8 Use the Quadratc Formula and the Dscrmnant KEY: solve equaton quadratc functon dscrmnant one soluton 25. ANS: 9 PTS: 1 DIF: Level B REF: MAL20568 TOP: Lesson 4.3 Solve x2 + bx + c = 0 by Factorng 26. ANS: 9 2 KEY: trnomal factor square bnomal PTS: 1 DIF: Level B REF: MAL20576 NAT: NCTM 9-12.ALG.1.c TOP: Lesson 4.3 Solve x2 + bx + c = 0 by Factorng KEY: solve quadratc factor 27. ANS: A PTS: 2 REF: a2 NAT: A.APR.B.3 STA: A2.A.50 TOP: Zeros of Polynomals
6 28. ANS: B PTS: 2 REF: a NAT: A.APR.B.3 TOP: Zeros of Polynomals
Algebra II: Chapter 5 Review
Name: Class: Date: ID: A Algebra II: Chapter 5 Review Simplify the expression. Give your answer in exponential form. 1. 7 3 8 6 6 ˆ a. 56 54 b. 7 9 8 12 c. 56 15 36 d. 7 18 8 Simplify the expression. 2.
Algebra 1 First Semester Exam Answer Section
Algebra 1 First Semester Exam Answer Section MULTIPLE CHOICE 1. ANS: D PTS: 1 DIF: Level B REF: MALG0086 TOP: Lesson 1.2 Apply Order of Operations KEY: whole variable evaluate substitute rational expression
Complex Numbers. x = B B 2 4AC 2A. or x = x = 2 ± 4 4 (1) (5) 2 (1)
Complex Numbers If you have not yet encountered complex numbers, you wll soon do so n the process of solvng quadratc equatons. The general quadratc equaton Ax + Bx + C 0 has solutons x B + B 4AC A For
UNIT 3 EXPRESSIONS AND EQUATIONS Lesson 4: Fundamental Theorem of Algebra. Instruction. Guided Practice Example 1
Guded Practce 3.4. Example 1 Instructon For each equaton, state the number and type of solutons by frst fndng the dscrmnant. x + 3x =.4x x = 3x = x 9x + 1 = 6x 1. Fnd the dscrmnant of x + 3x =. The equaton
Section 3.6 Complex Zeros
04 Chapter Secton 6 Comple Zeros When fndng the zeros of polynomals, at some pont you're faced wth the problem Whle there are clearly no real numbers that are solutons to ths equaton, leavng thngs there
UNIT 4 EXTENDING THE NUMBER SYSTEM Lesson 3: Operating with Complex Numbers Instruction
Prerequste Sklls Ths lesson requres the use of the followng sklls: understandng that multplyng the numerator and denomnator of a fracton by the same quantty produces an equvalent fracton multplyng complex
8.6 The Complex Number System
8.6 The Complex Number System Earler n the chapter, we mentoned that we cannot have a negatve under a square root, snce the square of any postve or negatve number s always postve. In ths secton we want
Unit 5: Quadratic Equations & Functions
Date Perod Unt 5: Quadratc Equatons & Functons DAY TOPIC 1 Modelng Data wth Quadratc Functons Factorng Quadratc Epressons 3 Solvng Quadratc Equatons 4 Comple Numbers Smplfcaton, Addton/Subtracton & Multplcaton
Algebra 2 Matrices. Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find.
Algebra 2 Matrices Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find. Evaluate the determinant of the matrix. 2. 3. A matrix contains 48 elements.
Algebra 1, Absolute Value Functions Review
Name: Class: Date: ID: A Algebra 1, Absolute Value Functions Review 3.7.1: I can solve absolute value equations. 1. (1 point) x + 10 = 1 2. (1 point) Starting from 1.5 miles away, a car drives towards
Algebra II First Semester Exam
Class: Date: Algebra II First Semester Exam 2013-14 1. Which number line shows the graphs of 10 and 7 3? b. c. d. 2. A string is 0.5 meters long. What is its length in centimeters? 0.5 centimeters b. 0.05
Algebra 2 Summer Math Answer Section
Algebra 2 Summer Math Answer Section 1. ANS: A PTS: 1 DIF: Level B REF: MALG0064 STA: SC.HSCS.MTH.00.AL1.A1.I.C.4 TOP: Lesson 1.1 Evaluate Expressions KEY: word volume cube area solid 2. ANS: C PTS: 1
Section 8.3 Polar Form of Complex Numbers
80 Chapter 8 Secton 8 Polar Form of Complex Numbers From prevous classes, you may have encountered magnary numbers the square roots of negatve numbers and, more generally, complex numbers whch are the
Chapter 1 Review - Challenge Pre-algebra
Name: Class: Date: ID: A Chapter 1 Review - Challenge Pre-algebra Evaluate the expression. 1. 12 8 + 20 8 2 a. 112 b. 102 c. 98 d. 54 2. 14 + 30 13 2 3. ( 6 7) 3 6 + 6 Add parentheses to make the statement
PERT Practice Test #2
Class: Date: PERT Practice Test #2 Multiple Choice Identify the choice that best completes the statement or answers the question. Ê 1. What is the quotient of 6y 6 9y 4 + 12y 2 ˆ Ê 3y 2 ˆ? a. 2y 4 + 3y
AFM Review Test Review
Name: Class: Date: AFM Review Test Review Multiple Choice Identify the choice that best completes the statement or answers the question. What are the solutions of the inequality?. q + (q ) > 0 q < 3 q
Quadratics Unit Review
Name: Class: Date: Quadratics Unit Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. (2 points) Consider the graph of the equation y = ax 2 + bx +
Algebra II: Chapter 6 Test Review
Class: Date: Algebra II: Chapter 6 Test Review 1. Simplify 8 4 /. 1 2 a. c. 2 b. 8 d. 16 2. Which is equivalent to 81 1/4? a. 9 b. c. 1 9 d. 1. The volume of a sphere can be given by the formula V = 4.18879r.
The Fundamental Theorem of Algebra. Objective To use the Fundamental Theorem of Algebra to solve polynomial equations with complex solutions
5-6 The Fundamental Theorem of Algebra Content Standards N.CN.7 Solve quadratc equatons wth real coeffcents that have comple solutons. N.CN.8 Etend polnomal denttes to the comple numbers. Also N.CN.9,
Chapters 1 and 2 Test
Class: Date: Chapters 1 and 2 Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. 2r 9 6 Solve the inequality. Graph the solution set. a. r 1 1 2 c. r
Pre-Calculus Summer Assignment
Pre-Calculus Summer Assgnment Dear Future Pre-Calculus Student, Congratulatons on our successful completon of Algebra! Below ou wll fnd the summer assgnment questons. It s assumed that these concepts,
Distributive Property, Expressions, and Equations Study Guide
Distributive Property, Expressions, and Equations Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which word phrase could represent the variable
Review Algebra Test
Name: Class: Date: Review Algebra Test.4-2.3 Multiple Choice Identify the choice that best completes the statement or answers the question. Solve the equation.. 5y 9 (y ) a. 2 b. 2 2 c. 2 d. 2 5 Use an
332600_08_1.qxp 4/17/08 11:29 AM Page 481
336_8_.qxp 4/7/8 :9 AM Page 48 8 Complex Vector Spaces 8. Complex Numbers 8. Conjugates and Dvson of Complex Numbers 8.3 Polar Form and DeMovre s Theorem 8.4 Complex Vector Spaces and Inner Products 8.5
COMPLEX NUMBERS AND QUADRATIC EQUATIONS
COMPLEX NUMBERS AND QUADRATIC EQUATIONS INTRODUCTION We know that x 0 for all x R e the square of a real number (whether postve, negatve or ero) s non-negatve Hence the equatons x, x, x + 7 0 etc are not
Algebra 2 Spring 2015 Test 1
Name: Class: Date: Algebra 2 Spring 2015 Test 1 Multiple Choice (23 questions) Identify the choice that best completes the statement or answers the question on your scantron sheet. Do any scratch work
Honors Algebra 2 Quarterly #3 Review
Name: Class: Date: ID: A Honors Algebra Quarterly #3 Review Mr. Barr Multiple Choice Identify the choice that best completes the statement or answers the question. Simplify the expression. 1. (3 + i) +
Chapter 12 Final Review
Chapter 12 Final Review Simplify the rational expression. 1. 2. 3. 4. 5. 6. 7. Multiply. 8. 9. 10. 11. 12. Divide. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. Add or subtract. 24. 25. 26. 27. 28. 29. Find
Algebra 1 Chapter 3 Practice Test
Name: Class: Date: ID: A Algebra 1 Chapter 3 Practice Test Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. Which number is a solution of the
Algebra II - Chapter 2 Practice Test Answer Section
Algebra II - Chapter Practice Test Answer Section SHORT ANSWER 1. ANS: g(x) is f(x) translated 3 units left and units up. Because h = + 3, the graph is translated 3 units left. Because k = +, the graph
Solving Quadratic Equations by Formula
Algebra Unit: 05 Lesson: 0 Complex Numbers All the quadratic equations solved to this point have had two real solutions or roots. In some cases, solutions involved a double root, but there were always
Review Unit Multiple Choice Identify the choice that best completes the statement or answers the question.
Review Unit 3 1201 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following numbers is not both a perfect square and a perfect cube? a. 531
Complex Numbers Alpha, Round 1 Test #123
Complex Numbers Alpha, Round Test #3. Wrte your 6-dgt ID# n the I.D. NUMBER grd, left-justfed, and bubble. Check that each column has only one number darkened.. In the EXAM NO. grd, wrte the 3-dgt Test
Algebra I: Chapter 8 Test
Name: Class: Date: Algebra I: Chapter 8 Test. 8 8 6 Simplify. Leave your answer in exponential form. a. 8 6 b. 64 7 c. 8 5 d. 8 7 Simplify: 2. r 4 r 5 r 6 a. r 20 b. 3r 20 c. r 5 d. 3r 5 3. w c 7 8w 3
Chapter 1 Test Review
Name Per ID: A Chapter 1 Test Review Short Answer Insert , or = to make the sentence true. 1. 7 12 2. 5 9 1 8 3. 16 + 6 8 + 7 Name the property of real numbers illustrated by the equation. 4. 2(x +
Linear Approximation with Regularization and Moving Least Squares
Lnear Approxmaton wth Regularzaton and Movng Least Squares Igor Grešovn May 007 Revson 4.6 (Revson : March 004). 5 4 3 0.5 3 3.5 4 Contents: Lnear Fttng...4. Weghted Least Squares n Functon Approxmaton...
Polynomials Practice Test
Name: Class: Date: Polynomials Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. From the list, which terms are like 7x? 7x 2, 6x, 5, 8x, 7x,
Alg 1 Systems. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Class: Date: Alg 1 Systems Multiple Choice Identify the choice that best completes the statement or answers the question. What is the solution of the system? Use a graph. 1. y = x + 2 y = 3x 1 a. c. b.
Alg 1B Chapter 7 Final Exam Review
Name: Class: Date: ID: A Alg B Chapter 7 Final Exam Review Please answer all questions and show your work. Simplify ( 2) 4. 2. Simplify ( 4) 4. 3. Simplify 5 2. 4. Simplify 9x0 y 3 z 8. 5. Simplify 7w0
Exponents Unit Assessment Review
Name: Class: Date: ID: A Exponents Unit Assessment Review Multiple Choice Identify the choice that best completes the statement or answers the question. Simplify the expression.. 7x 8 6x 3 a. 42 x 5 b.
(2mn, m 2 n 2, m 2 + n 2 )
MATH 16T Homewk Solutons 1. Recall that a natural number n N s a perfect square f n = m f some m N. a) Let n = p α even f = 1,,..., k. be the prme factzaton of some n. Prove that n s a perfect square f
Abs.Value Equations/Inequalities, Direct Variation, and Parallel/Perpendicular Lines - QUIZ
Abs.Value Equations/Inequalities, Direct Variation, and Parallel/Perpendicular Lines - QUIZ Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which equation
Name: Class: Date: 6. What is the y intercept of the function h(x) = 3 x 3 a. (0, -2) b. (-2, 0) c. (-3, 0) d. (0, -3)
Name: Class: Date: ID: A Exponential Study Guide 1. Identify each of the following for the function f(x) = 4 2 x. Then graph the function. a. x-intercept(s) b.y-intercept c. asymptote d. domain e. range
Chapter 3 Algebra (pearson)
Class: Date: Chapter 3 Algebra (pearson) What inequality represents the verbal expression? 1. 8 less than a number n is less than 13 a. 8 n < 13 c. n 8 < 13 b. 13 8 < n d. 13 < 8 n Which number is a solution
Pre-Algebra Unit 8 Practice Test: Ratios, Rates, & Proportions Answer Section
Pre-Algebra Unit 8 Practice Test: Ratios, Rates, & Proportions Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: L2 REF: -1 Ratios and Unit Rates STA: CA 7.MG.1.1 CA 7.MG.1.3 CA 7.AF.4.2 TOP: -1 Example
9. Complex Numbers. 1. Numbers revisited. 2. Imaginary number i: General form of complex numbers. 3. Manipulation of complex numbers
9. Comple Numbers. Numbers revsted. Imagnar number : General form of comple numbers 3. Manpulaton of comple numbers 4. The Argand dagram 5. The polar form for comple numbers 9.. Numbers revsted We saw
CALCULUS CLASSROOM CAPSULES
CALCULUS CLASSROOM CAPSULES SESSION S86 Dr. Sham Alfred Rartan Valley Communty College salfred@rartanval.edu 38th AMATYC Annual Conference Jacksonvlle, Florda November 8-, 202 2 Calculus Classroom Capsules
Be true to your work, your word, and your friend.
Chemstry 13 NT Be true to your work, your word, and your frend. Henry Davd Thoreau 1 Chem 13 NT Chemcal Equlbrum Module Usng the Equlbrum Constant Interpretng the Equlbrum Constant Predctng the Drecton
Lectures - Week 4 Matrix norms, Conditioning, Vector Spaces, Linear Independence, Spanning sets and Basis, Null space and Range of a Matrix
Lectures - Week 4 Matrx norms, Condtonng, Vector Spaces, Lnear Independence, Spannng sets and Bass, Null space and Range of a Matrx Matrx Norms Now we turn to assocatng a number to each matrx. We could
Curve Fitting with the Least Square Method
WIKI Document Number 5 Interpolaton wth Least Squares Curve Fttng wth the Least Square Method Mattheu Bultelle Department of Bo-Engneerng Imperal College, London Context We wsh to model the postve feedback
Accentuate the Negative - Unit Test Review Sheet
Name: Class: _ Date: _ Accentuate the Negative - Unit Test Review Sheet Short Answer 1. A football team loses an average of 3 yards per play. How many yards have they lost after 4 plays? Write a number
Midterm Review. Name: Class: Date: ID: A. Short Answer. 1. For each graph, write the equation of a radical function of the form y = a b(x h) + k.
Name: Class: Date: ID: A Midterm Review Short Answer 1. For each graph, write the equation of a radical function of the form y = a b(x h) + k. a) b) c) 2. Determine the domain and range of each function.
Seminar Alg Basics. Name: Class: Date: ID: A. Multiple Choice Identify the choice that best completes the statement or answers the question.
Class: Date: Seminar Alg Basics Multiple Choice Identify the choice that best completes the statement or answers the question. Use a pattern to answer each question. 1. How many line segments are in figure
Algebra 1 - Chapter 5 Test Review
Name: Period: Date: Algebra 1 - Chapter 5 Test Review Tell whether the ordered pair is a solution of the system of linear equations. 1. x y = 5 3x y = 11 Ê 2, 3 ˆ a. Yes b. No 2. y = 6x 8 y = 8x 12 Ê 1,
PreCalc 11 Chapter 5 Review Pack v1 Answer Section
PreCalc 11 Chapter 5 Review Pack v1 Answer Section MULTIPLE CHOICE 1. ANS: A PTS: 0 DIF: Easy REF: 5.1 Solving Quadratic Inequalities in One Variable LOC: 11.RF8. ANS: D PTS: 0 DIF: Easy REF: 5.1 Solving
Moving Straight Ahead - Unit Test Review Sheet
Name: Class: Date: ID: A Moving Straight Ahead - Unit Test Review Sheet Short Answer 1. Use the graph at the right. a. Find the slope of the line. b. Find the equation of the line. 2. Does the table below
= z 20 z n. (k 20) + 4 z k = 4
Problem Set #7 solutons 7.2.. (a Fnd the coeffcent of z k n (z + z 5 + z 6 + z 7 + 5, k 20. We use the known seres expanson ( n+l ( z l l z n below: (z + z 5 + z 6 + z 7 + 5 (z 5 ( + z + z 2 + z + 5 5
18.781: Solution to Practice Questions for Final Exam
18.781: Soluton to Practce Questons for Fnal Exam 1. Fnd three solutons n postve ntegers of x 6y = 1 by frst calculatng the contnued fracton expanson of 6. Soluton: We have 1 6=[, ] 6 6+ =[, ] 1 =[,, ]=[,,
Review of Taylor Series. Read Section 1.2
Revew of Taylor Seres Read Secton 1.2 1 Power Seres A power seres about c s an nfnte seres of the form k = 0 k a ( x c) = a + a ( x c) + a ( x c) + a ( x c) k 2 3 0 1 2 3 + In many cases, c = 0, and the
REDUCTION MODULO p. We will prove the reduction modulo p theorem in the general form as given by exercise 4.12, p. 143, of [1].
![REDUCTION MODULO p. We will prove the reduction modulo p theorem in the general form as given by exercise 4.12, p. 143, of [1].](/thumbs/73/68500980.jpg "REDUCTION MODULO p. We will prove the reduction modulo p theorem in the general form as given by exercise 4.12, p. 143, of [1].")
REDUCTION MODULO p. IAN KIMING We wll prove the reducton modulo p theorem n the general form as gven by exercse 4.12, p. 143, of [1]. We consder an ellptc curve E defned over Q and gven by a Weerstraß
ALGEBRA 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.
Kernel Methods and SVMs Extension
Kernel Methods and SVMs Extenson The purpose of ths document s to revew materal covered n Machne Learnng 1 Supervsed Learnng regardng support vector machnes (SVMs). Ths document also provdes a general
POlynomials. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Class: Date: POlynomials Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Write 4x 2 ( 2x 2 + 5x 3 ) in standard form. Then classify it by degree
Math1110 (Spring 2009) Prelim 3 - Solutions
Math 1110 (Sprng 2009) Solutons to Prelm 3 (04/21/2009) 1 Queston 1. (16 ponts) Short answer. Math1110 (Sprng 2009) Prelm 3 - Solutons x a 1 (a) (4 ponts) Please evaluate lm, where a and b are postve numbers.
Formulas for the Determinant
page 224 224 CHAPTER 3 Determnants e t te t e 2t 38 A = e t 2te t e 2t e t te t 2e 2t 39 If 123 A = 345, 456 compute the matrx product A adj(a) What can you conclude about det(a)? For Problems 40 43, use
Moving Straight Ahead - Unit Test Review Sheet
Name: Class: Date: ID: A Moving Straight Ahead - Unit Test Review Sheet Short Answer 1. Brent's Video Shack charges $1.50 to rent a video game for a night. Mr. Buck's Entertainments opens a new store in
Formal solvers of the RT equation
Formal solvers of the RT equaton Formal RT solvers Runge- Kutta (reference solver) Pskunov N.: 979, Master Thess Long characterstcs (Feautrer scheme) Cannon C.J.: 970, ApJ 6, 55 Short characterstcs (Hermtan
ACTM State Calculus Competition Saturday April 30, 2011
ACTM State Calculus Competton Saturday Aprl 30, 2011 ACTM State Calculus Competton Sprng 2011 Page 1 Instructons: For questons 1 through 25, mark the best answer choce on the answer sheet provde Afterward
= = = (a) Use the MATLAB command rref to solve the system. (b) Let A be the coefficient matrix and B be the right-hand side of the system.
Chapter Matlab Exercses Chapter Matlab Exercses. Consder the lnear system of Example n Secton.. x x x y z y y z (a) Use the MATLAB command rref to solve the system. (b) Let A be the coeffcent matrx and
ID: A MATCHING MULTIPLE CHOICE
Chemistry-575 Semester-1 Review Practice Test (General review with an emphasis on the types of questions missed most frequently by students.) Answer Section MATCHING 1. ANS: B PTS: 1 DIF: L1 REF: p. 808
Algebra 2 Chapter 6 and 7 Test Review (part 1)
Name: Class: Date: Algebra 2 Chapter 6 and 7 Test Review (part ). Find the annual percent increase or decrease that y = 0.35(2.3) x models. a. 230% increase c. 35% decrease b. 35% increase d. 65% decrease
of Nebraska - Lincoln
Unversty of Nebraska - Lncoln DgtalCommons@Unversty of Nebraska - Lncoln MAT Exam Expostory Papers Math n the Mddle Insttute Partnershp 008 The Square Root of Tffany Lothrop Unversty of Nebraska-Lncoln
% & 5.3 PRACTICAL APPLICATIONS. Given system, (49) , determine the Boolean Function, , in such a way that we always have expression: " Y1 = Y2
5.3 PRACTICAL APPLICATIONS st EXAMPLE: Gven system, (49) & K K Y XvX 3 ( 2 & X ), determne the Boolean Functon, Y2 X2 & X 3 v X " X3 (X2,X)", n such a way that we always have expresson: " Y Y2 " (50).
1. Definition of a Polynomial
1. Definition of a Polynomial What is a polynomial? A polynomial P(x) is an algebraic expression of the form Degree P(x) = a n x n + a n 1 x n 1 + a n 2 x n 2 + + a 3 x 3 + a 2 x 2 + a 1 x + a 0 Leading
Algebra 2 Midterm Review
Name: Class: Date: Algebra 2 Midterm Review Short Answer 1. Find the product (2x 3y) 3. 2. Find the zeros of f(x) = x 2 + 7x + 9 by using the Quadratic Formula. 3. Solve the polynomial equation 2x 5 +
EEE 241: Linear Systems
EEE : Lnear Systems Summary #: Backpropagaton BACKPROPAGATION The perceptron rule as well as the Wdrow Hoff learnng were desgned to tran sngle layer networks. They suffer from the same dsadvantage: they
Rao IIT Academy/ SSC - Board Exam 2018 / Mathematics Code-A / QP + Solutions JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS SSC - BOARD
Rao IIT Academy/ SSC - Board Exam 08 / Mathematcs Code-A / QP + Solutons JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS SSC - BOARD - 08 Date: 0.03.08 MATHEMATICS - PAPER- - SOLUTIONS Q. Attempt any FIVE of
Chapter 4: Root Finding
Chapter 4: Root Fndng Startng values Closed nterval methods (roots are search wthn an nterval o Bsecton Open methods (no nterval o Fxed Pont o Newton-Raphson o Secant Method Repeated roots Zeros of Hgher-Dmensonal
Solutions to Problem Set 6
Solutons to Problem Set 6 Problem 6. (Resdue theory) a) Problem 4.7.7 Boas. n ths problem we wll solve ths ntegral: x sn x x + 4x + 5 dx: To solve ths usng the resdue theorem, we study ths complex ntegral:
1 Matrix representations of canonical matrices
1 Matrx representatons of canoncal matrces 2-d rotaton around the orgn: ( ) cos θ sn θ R 0 = sn θ cos θ 3-d rotaton around the x-axs: R x = 1 0 0 0 cos θ sn θ 0 sn θ cos θ 3-d rotaton around the y-axs:
NUMERICAL DIFFERENTIATION
NUMERICAL DIFFERENTIATION 1 Introducton Dfferentaton s a method to compute the rate at whch a dependent output y changes wth respect to the change n the ndependent nput x. Ths rate of change s called the
Digital Signal Processing
Dgtal Sgnal Processng Dscrete-tme System Analyss Manar Mohasen Offce: F8 Emal: manar.subh@ut.ac.r School of IT Engneerng Revew of Precedent Class Contnuous Sgnal The value of the sgnal s avalable over
Recursion and growth estimates in quantum field theory
Recurson and growth estmates n quantum feld theory Karen Yeats Boston Unversty Aprl 9, 2007 Johns Hopns Unversty Some recursve equatons Start n the mddle γ (x) = γ (x)( rx x )γ (x) γ,n = p(n) ( rj )γ,j
AFM Unit 2A Review Sheet
AFM Unit A Review Sheet Multiple Choice Identif the choice that best completes the statement or answers the question. 1. Write the ordered pairs for the relation. Find the domain and range. O x {(, 5),
: Numerical Analysis Topic 2: Solution of Nonlinear Equations Lectures 5-11:
764: Numercal Analyss Topc : Soluton o Nonlnear Equatons Lectures 5-: UIN Malang Read Chapters 5 and 6 o the tetbook 764_Topc Lecture 5 Soluton o Nonlnear Equatons Root Fndng Problems Dentons Classcaton
Bezier curves. Michael S. Floater. August 25, These notes provide an introduction to Bezier curves. i=0
Bezer curves Mchael S. Floater August 25, 211 These notes provde an ntroducton to Bezer curves. 1 Bernsten polynomals Recall that a real polynomal of a real varable x R, wth degree n, s a functon of the
DISCRIMINANTS AND RAMIFIED PRIMES. 1. Introduction A prime number p is said to be ramified in a number field K if the prime ideal factorization
DISCRIMINANTS AND RAMIFIED PRIMES KEITH CONRAD 1. Introducton A prme number p s sad to be ramfed n a number feld K f the prme deal factorzaton (1.1) (p) = po K = p e 1 1 peg g has some e greater than 1.
ALGEBRA MID-TERM. 1 Suppose I is a principal ideal of the integral domain R. Prove that the R-module I R I has no non-zero torsion elements.
ALGEBRA MID-TERM CLAY SHONKWILER 1 Suppose I s a prncpal deal of the ntegral doman R. Prove that the R-module I R I has no non-zero torson elements. Proof. Note, frst, that f I R I has no non-zero torson
A.APR.B.3: Find Zeros of Polynomials B. Understand the relationship between zeros and factors of polynomials.
A.APR.B.3: Find Zeros of Polynomials POLYNOMIALS AND QUADRATICS A.APR.B.3: Find Zeros of Polynomials B. Understand the relationship between zeros and factors of polynomials. 3. Identify zeros of polynomials
Geometry CP - Ch. 4 Review
Geometry CP - Ch. 4 Review 1. If, which of the following can you NOT conclude as being true? A. B. C. D. 2. A. B. C. D. 3. Given and, find the length of QS and TV. A. 7 B. 25 C. 8 D. 2 4. The two triangles
Newton s Method for One - Dimensional Optimization - Theory
Numercal Methods Newton s Method for One - Dmensonal Optmzaton - Theory For more detals on ths topc Go to Clck on Keyword Clck on Newton s Method for One- Dmensonal Optmzaton You are free to Share to copy,
Difference Equations
Dfference Equatons c Jan Vrbk 1 Bascs Suppose a sequence of numbers, say a 0,a 1,a,a 3,... s defned by a certan general relatonshp between, say, three consecutve values of the sequence, e.g. a + +3a +1
Module 5 Study Guide--Linear Functions
Module Stud Guide--Linear Functions The rate of change is constant in the table. Find the rate of change. Explain what the rate of change means for the situation.. The table shows the cost of a ski rental
ACCURACY AND PRECISION
Science, Measurement, and Uncertainty: Accuracy and Precision Name Period Date ACCURACY AND PRECISION Definitions: Accuracy how close a measurement is to Precision how close a measurement is to Precision
Lecture 2 Solution of Nonlinear Equations ( Root Finding Problems )
Lecture Soluton o Nonlnear Equatons Root Fndng Problems Dentons Classcaton o Methods Analytcal Solutons Graphcal Methods Numercal Methods Bracketng Methods Open Methods Convergence Notatons Root Fndng
Solving Quadratic Equations
Solving Quadratic Equations MATH 101 College Algebra J. Robert Buchanan Department of Mathematics Summer 2012 Objectives In this lesson we will learn to: solve quadratic equations by factoring, solve quadratic
Say it with Symbols - Unit Test Review Shet
Name: Class: Date: ID: A Say it with Symbols - Unit Test Review Shet Short Answer 1. What does it mean to say that two algebraic expressions are equivalent? Evaluate the expression for the given value
Algebra 1B Final Review
Name: Class: Date: ID: A Algebra 1B Final Review Short Answer 1. Originally a rectangle was twice as long as it was wide. When 5 m was subtracted from its length and 3 m subtracted from its width, the
North Caroline Math 2 Transition Edition Unit 3 Assessment: Radical and Rational Functions
Class: Date: North Caroline Math 2 Transition Edition Unit 3 Assessment: Radical and Rational Functions Multiple Choice Identify the choice that best completes the statement or answers the question.. Evalue
Solutions HW #2. minimize. Ax = b. Give the dual problem, and make the implicit equality constraints explicit. Solution.
Solutons HW #2 Dual of general LP. Fnd the dual functon of the LP mnmze subject to c T x Gx h Ax = b. Gve the dual problem, and make the mplct equalty constrants explct. Soluton. 1. The Lagrangan s L(x,