Quadratic Equations Chapter Questions

 Joy Baldwin
 4 months ago
 Views:
Transcription
1 Quadratic Equations Chapter Questions 1. Describe the characteristics of a quadratic equation. 2. What are the steps for graphing a quadratic function? 3. How can you determine the number of solutions without graphing? NJ Center for Teaching and Learning ~ 1 ~
2 Quadratic Equations Chapter Questions Standard form and the axis of symmetry Find the axis of symmetry and rewrite in standard form if necessary. 1. y= x 2 +3x x 2 + 5x = 6 3. y= x 24x x 23 =6x 5. y= 3x 24x 2 Homework Find the axis of symmetry and rewrite in standard form if necessary. 6. y= x 2 +2x x 23x = 2 8. y= x 25x x  4 = 2x y= 3x 22x Transforming Quadratic Functions Does the graph of the given equation open up or down? Is the graph wider or narrower than the parent equation of y=x 2? What is the yintercept? 11. y = 2x 2 +3x y = .7x 24x y = 1.2x y = 3x 2 +3x 15. y = 4x 2 Homework Does the graph of the given equation open up or down? Is the graph wider or narrower than the parent equation of y=x 2? What is the yintercept? 16. y =.6x 2 +3x y = 1.7x 24x y = 1.02x y = 1.3x 2 +4x 20. y = 5x 2 NJ Center for Teaching and Learning ~ 2 ~
3 Graphing to Find Zeros Find the zeros of the following quadratics: 21. y x y x y = x 24x y = x 2 +3x y = x 28x y = x 28x y = x 2 +3x y = 2x 2 +4x y = 3x 2 +4x +4 NJ Center for Teaching and Learning ~ 3 ~
4 Homework 30. y x y x y = x 26x y = x 2 +3x y = x 2 +6x y = x 2 +x y = x 2 +2x y = 2x 2 +5x y = 3x 2 +11x +4 Solving by Factoring Solve the following quadratics by factoring. 39. a 2 +4a +3= b 24b 5= c 26c = d 2 +8c = 12 NJ Center for Teaching and Learning ~ 4 ~
5 43. e 2 +9 = f 2 +4f +4 = g 2 +5g = h 2 +7h +6= j 24j = A garden has a length of (x + 2) feet and a width of (2x  1) feet. The garden s total area is 88 square feet. Find the length. Home Work Solve the following quadratics by factoring. 49. a 2 +6a +5= b 2 b 6= c 26c = d 2 +7c = e = f 2 +6f +9 = g 2 +7g = h 2 +8h +6= j 27j = A garden has a length of (x  4)feet and a width of (2x +3)feet. The garden s total area is 76 square feet. Find the length. Solving Using the Square Roots Method Solve the following quadratics using the square roots method 59. m 2 = n 2 = p 2 = q 2 = r 23 =6 64. s 2 +8 = t 26 = u 2 +5 = (v 7) 25 = (w 3) 2 +6 = 56 NJ Center for Teaching and Learning ~ 5 ~
6 69. The square of six less than a number is twentyfive. Write an equation that models this situation. Solve the equation. Homework Solve the following quadratics using the square roots method 70. m 2 = n 2 = p 2 = q 2 = r 23 = s 2 +8 = t 26 = u 2 +5 = (v 2) 2 +4 = (w +4) 24 = Two times the square of five more than a number is seventytwo. Write an equation that models this situation. Solve the equation. Solving by Completing the Square Fill in the blank to complete the square. 81. a 2 + 8a b b c 24c d 26d e 2 + 7e f 25f + Solve the following quadratics by completing the square. 87. h 2 + 6h = j 28j = k = 10k 90. m 213 = 12m n + 20 = n p + p 2 = q 28q = r r = 12 NJ Center for Teaching and Learning ~ 6 ~
7 95. A toy rocket launched into the air has a height (h feet) at any given time (t seconds) as h = 16t t until it hits the ground. At what time(s) is it at a height of 7 feet above the ground? Homework Fill in the blank to complete the square. 96. a a b 2 + b c 214c d 216d e 2 + 9e f 21f + Solve the following quadratics by completing the square h 2 + 4h = j 210j = k = 14k 105. m 221 = 20m n + 80= n p + p 2 = q 212q = r r = A toy rocket launched into the air has a height (h feet) at any given time (t seconds) as h = 16t t until it hits the ground. At what time(s) is it at a height of 9 feet above the ground? Solving Using the Quadratic Formula Solve the following using the quadratic formula. Round answers to the hundredth place x 2 +8x 6 = g 24g +2 = d 2 + 4d 3 = m 2 + 3m = w 28 = 5w z 9z 2 = An employee makes (2x + 3) dollars an hour for x hours. If the employer wants to pay no more than $120 a day, what is the maximum number of hours the employee can work? (Round to the nearest quarter hour) NJ Center for Teaching and Learning ~ 7 ~
8 Homework Solve the following using the quadratic formula. Round answers to the hundredth place x 2 +7x 5 = g 25g +3 = d 2 + 5d 3 = m 2 + 4m = w 22 = 5w z 6z 2 = An employee makes (3x  5) dollars an hour for x hours. If the employer wants to pay no more than $200 a day, what is the maximum number of hours the employee can work? (Round to the nearest quarter hour) Discriminant Find the discriminant for each quadratic equation. State the number of real roots and then find the real solution(s), if any exist x 26x + 5 = x 24x  6 = x + 4x = x 9 = x x 2 = 6x x 29x 2= x (2x 5) = A rock is thrown with a height equation of h = 16t t + 5 (where h is the height of the rock in feet at any given time of t in seconds). Will it reach a height of 30 feet? Explain your answer. Homework Find the discriminant for each quadratic equation. State the number of real roots and then find the real solution(s), if any exist x 29x + 7 = x 24x + 2 = x + 7x = x 6 = 2x x 2 = 7x 6 NJ Center for Teaching and Learning ~ 8 ~
9 138. 3x 27x 8= (x + 3)(2x + 6) = A rock is thrown with a height equation of h = 16t t + 5 (where h is the height of the rock in feet at any given time of t in seconds). Will it reach a height of 50 feet? Explain your answer. Mixed Application Problems Solve the following problems using any method The product of two consecutive positive integers is 272, find the integers The product of two consecutive positive even integers is 528, find the integers The product of two consecutive odd integers is 255, find the integers Two planes leave airport at the same time (from different runways). If three hours later they are 500 miles apart and the plane flying south has traveled 200 miles farther, how far did the one flying west travel? 145. Two cars leave a gas station at the same time, one traveling north and one traveling east. One hour later they are 80 miles apart and the one traveling east went 10 miles farther, how far is it from the gas station? 146. A square has its length increased by 4 feet and its width by 5 feet. If the resulting rectangle has an area of 132 square feet what was the perimeter of the original square? 147. A rectangular parking lot has a width 30 feet more than its length. The owners are able to increase the width by 20 feet and the length by 40. The new lot has an area of 27,200 square feet, what is the area of the original lot? Homework Solve the following problems using any method The product of two consecutive positive integers is 272, find the integers The product of two consecutive positive even integers is 342, find the integers The product of two consecutive odd integers is 483, find the integers Two planes leave airport at the same time (from different runways). If three hours later they are 600 miles apart and the plane flying south has traveled 100 miles farther, how far did the one flying west travel? 152. Two cars leave a gas station at the same time, one traveling north and one traveling east. One hour later they are 90 miles apart and the one traveling east went 15 miles farther, how far is it from the gas station? 153. A square has its length increased by 6 feet and its width by 8 feet. If the resulting rectangle has an area of square feet what was the perimeter of the original square? NJ Center for Teaching and Learning ~ 9 ~
10 154. A rectangular parking lot has a width 20 feet more than its length. The owners are able to increase the width by 20 feet and the length by 40. The new lot has an area of 7225 square feet, what is the area of the original lot? Unit Review Multiple Choice Choose the correct answer for each question. No partial credit will be given. 1. Comparing the graph of y = 5x 2 + 4x  2 to its parent function, it: A) opens down and is wider than the parent function graph. B) opens down and is narrower than the parent function graph. C) opens up and is wider than the parent function graph. D) opens up and is narrower than the parent function graph. 2. What is the equation of the axis of symmetry of y = 3x 212x 5? A) x = 2 B) x = 4 C) x = 4 D) x = 2 3. What are the vertex and axis of symmetry of the parabola y = x 2 + 4x + 3? A) vertex: (2, 1); axis of symmetry: x = 2 B) vertex: (2,1); axis of symmetry: x = 2 C) vertex: ( 2, 1); axis of symmetry: x = 2 D) vertex: ( 2,1); axis of symmetry: x = 2 4.What is the y intercept of y = 2x 2 + 2x 3? A) (0, 5) B) B (3, 0) C) C (0, 3) D) D (3, 0) NJ Center for Teaching and Learning ~ 10 ~
11 5.Which graph(s) has more than one zero? 6.Which of the following is a step in solving y = 2x 2  x  3 by the Factoring Method? A) 2x + 1 = 0 or x + 3 = 0 B) 2x  3 = 0 or x + 1 = 0 C) 2x + 3 = 0 or x  1 = 0 D) 2x  1 = 0 or x  3 = 0 7.The solution to (x + 2) 2 = 16 is A) 14 and 18 B) 14 and 18 C) 6 and 2 D) 2 and 6 8.What value goes in the blank to complete the square: x 26x +? A) 9 B) 36 C) 36 D) 9 NJ Center for Teaching and Learning ~ 11 ~
12 9.What is the discriminant of 2x 2 + 6x + 2 = 0? A) 2 B) 6 C) 20 D) How many real zeros does an equation have if the discriminant is 4? A) 0 B) 1 C) 2 D) Not enough information 11. Solve 3x 2 + 5x + 1 =0 A) B) C) D) ± Simplify 2 A) 8 and 2 B) 3 and 1 C) 3 and 1 D) 3 and 2 NJ Center for Teaching and Learning ~ 12 ~
13 13. Given the height of a rocket as h = 16t t + 896, where t is in seconds. At what time t, does the rocket hit the ground? A)  14 and 4 seconds B) 14 seconds C)  4 seconds D) the rocket will not hit the ground 14. Solve 3x 2 + 7x + 4 = 0 A)  1 and B) 1 and 4 3 C) 7 and  6 D) 7 and 6 Short Constructed Response Write the correct answer for each question. 15. What value goes in the blank to complete the perfect square trinomial: x 2 + x + 36? 16. Solve 6x x + 6 = A square has its length increased by 4 feet and its width decreased by 3 feet; the resulting area is 144 square feet. What was the area of the original square? 18. Solve (3x 7)(x+3)=0 Extended Constructed Response  Solve the problem, showing all work. 19. A rectangle has a length 6 more than its width. If the width is decreased by 2 and the length decreased by 4, the resulting rectangle has an area of 21 square units. What is the length of the original rectangle? What is ratio of the original rectangle s area to the new rectangle s area? What is the perimeter of the new rectangle? NJ Center for Teaching and Learning ~ 13 ~
14 Quadratic Equations CW HW Answer Key 1. axis of sym. =  3/2 2. axis of sym. =5/2; y = x 25x axis of sym. =2 4. axis of sym. = 3/2; y= 2x 2 + 6x axis of sym = 2/3 6. axis of sym. = axis of sym. = 3/2;y = x 2 +3x axis of sym. =5/2; 9. axis of sym. =  5/4; y = 2x 2 + 5x axis of sym. =1/3 11. Up ;narrower; Down; wider; Down;narrower; Up; narrower; Down; narrower; Down; wider; Up; narrower; Down; narrower; Up; narrower; Up; narrower; Zeros = 1 and Zeros = 1 and Zeros = 1 and Zeros = none 25. Zeros = 3 and Zeros = Zeros = 5 and Zeros = Zeros = 2 and 2/3 30. Zeros = 1 and Zeros = 3 and Zeros = 1 and Zeros = 5 and Zeros = Zeros = 3 and Zeros = none 37. Zeros = 2 and Zeros =  1/3 and and and and and and and /2 and /3 and Length = 8 ft and and and and and and and and 4/3 58. Length = 4 ft. 59. ±4 60. ±5 61. ±2 62. ±4 63. ±3 64. ±3 65. ±1 66. ± and and (x 6) 2 = 25 x = 1 or m=±6 NJ Center for Teaching and Learning ~ 14 ~
15 71. n=±8 72. p=±3 73. q=±2 74. r=±4 75. s=±4 76. t=±3 77. u=±1 78. v=5 or w=0 or (x + 5) 2 = 72 x = 1 or h=2 or j = 1 or k = 9 or m = 13 or n 1.61 or p = 0 or q 6.9 or r.42 or t 5.93 sec h=2 or j=9 or k=1 or m=21 or no solution 107. p=6 or no solution 109. r=1 or t.06 sec. or 9.94 sec or or or m= 1 or 1/ or or hours or or or or or or hrs two solutions; x = 5 or two solutions; x = 3 or no solution 128. one solution; x= no solution 130. two solutions; 2.45 or two solutions; 3.81 or No, the max. ht. is about 11.2 ft no solutions 134. one solution ; x= no solutions 136. two solutions; x = 3/2 or no solutions 138. two solutions; 3.17 or two solutions; .66 or Yes, max ht. is 69 ft & & & 17 NJ Center for Teaching and Learning ~ 15 ~
16 144. About mi About 61.4 mi ft ,000 sq ft & & & About 371 miles 152. About 70.7 miles ft ,925 sq ft. Review Answer Key 1. D 2. A 3. C 4. C 5. B, D 6. B 7. C 8. D 9. C 10. A 11. C 12. B 13. B 14. A and square feet 18. X = 7 and units; 55 ; 20 units 21 NJ Center for Teaching and Learning ~ 16 ~
Final Review. Intermediate Algebra / MAT135 S2014
Final Review Intermediate Algebra / MAT135 S2014 1. Solve for. 2. Solve for. 3. Solve for. 4. Jenny, Abdul, and Frank sent a total of text messages during the weekend. Abdul sent more messages than Jenny.
More information98 Completing the Square
In the previous lesson, you solved quadratic equations by isolating x 2 and then using square roots. This method works if the quadratic equation, when written in standard form, is a perfect square. When
More informationMath 2 1. Lesson 45: Completing the Square. When a=1 in a perfect square trinomial, then. On your own: a. x 2 18x + = b.
Math 1 Lesson 45: Completing the Square Targets: I can identify and complete perfect square trinomials. I can solve quadratic equations by Completing the Square. When a=1 in a perfect square trinomial,
More information3.4 Solving Quadratic Equations by Completing
.4. Solving Quadratic Equations by Completing the Square www.ck1.org.4 Solving Quadratic Equations by Completing the Square Learning objectives Complete the square of a quadratic expression. Solve quadratic
More informationUnit 5: Quadratic Functions
Unit 5: Quadratic Functions LESSON #2: THE PARABOLA APPLICATIONS AND WORD PROBLEMS INVERSE OF A QUADRATIC FUNCTION DO NOW: Review from Lesson #1 (a)using the graph shown to the right, determine the equation
More information1. Graph (on graph paper) the following equations by creating a table and plotting points on a coordinate grid y = 2x 2 4x + 2 x y.
1. Graph (on graph paper) the following equations by creating a table and plotting points on a coordinate grid y = 2x 2 4x + 2 x y y = x 2 + 6x 3 x y domain= range= 43 21 0 1 2 3 4 domain= range=
More information1) Solve the quadratic equation Y=5x*+3 where *=2 A. x = (Y3) B. x = (3+Y) C. x = (3+Y) 2 D. x = (Y3) 2
TEST 13 REVIEW Quadratics 1) Solve the quadratic equation Y=5x*+3 where *=2 A. x = (Y3) B. x = (3+Y) C. x = (3+Y) 2 D. x = (Y3) 2 2) Explain in complete sentences how to solve the following equation
More informationQuadratic Functions and Equations
Quadratic Functions and Equations Quadratic Graphs and Their Properties Objective: To graph quadratic functions of the form y = ax 2 and y = ax 2 + c. Objectives I can identify a vertex. I can grapy y
More informationSection 1.1. Chapter 1. Quadratics. Parabolas. Example. Example. ( ) = ax 2 + bx + c 21
Chapter 1 Quadratic Functions and Factoring Section 1.1 Graph Quadratic Functions in Standard Form Quadratics The polynomial form of a quadratic function is: f x The graph of a quadratic function is a
More informationCC Algebra Quadratic Functions Test Review. 1. The graph of the equation y = x 2 is shown below. 4. Which parabola has an axis of symmetry of x = 1?
Name: CC Algebra Quadratic Functions Test Review Date: 1. The graph of the equation y = x 2 is shown below. 4. Which parabola has an axis of symmetry of x = 1? a. c. c. b. d. Which statement best describes
More informationChapter 2 Polynomial and Rational Functions
SECTION.1 Linear and Quadratic Functions Chapter Polynomial and Rational Functions Section.1: Linear and Quadratic Functions Linear Functions Quadratic Functions Linear Functions Definition of a Linear
More informationName Class Date. Quadratic Functions and Transformations. 4 6 x
 Quadratic Functions and Transformations For Eercises, choose the correct letter.. What is the verte of the function 53()? D (, ) (, ) (, ) (, ). Which is the graph of the function f ()5(3) 5? F 6 6 O
More informationUnit 5 Test: 9.1 Quadratic Graphs and Their Properties
Unit 5 Test: 9.1 Quadratic Graphs and Their Properties Quadratic Equation: (Also called PARABOLAS) 1. of the STANDARD form y = ax 2 + bx + c 2. a, b, c are all real numbers and a 0 3. Always have an x
More informationUsing the Laws of Exponents to Simplify Rational Exponents
6. Explain Radicals and Rational Exponents  Notes Main Ideas/ Questions Essential Question: How do you simplify expressions with rational exponents? Notes/Examples What You Will Learn Evaluate and simplify
More informationUnit four review. Name: Class: Date: Short Answer
Name: Class: Date: ID: A Unit four review Short Answer 1. Graph the quadratic function y = 3x 2 6x + 5. Use the graph to determine the zeros of the function if they exist. 2. For what values of k does
More informationSubtract 16 from both sides. Divide both sides by 9. b. Will the swing touch the ground? Explain how you know.
REVIEW EXAMPLES 1) Solve 9x + 16 = 0 for x. 9x + 16 = 0 9x = 16 Original equation. Subtract 16 from both sides. 16 x 9 Divide both sides by 9. 16 x Take the square root of both sides. 9 4 x i 3 Evaluate.
More informationThe Quadratic Formula VOCABULARY
 The Quadratic Formula TEKS FOCUS TEKS ()(F) Solve quadratic and square root equations. TEKS ()(G) Display, eplain, and justify mathematical ideas and arguments using precise mathematical language in
More informationSolve each equation by completing the square. Round to the nearest tenth if necessary. 5. x 2 + 4x = 6 ANSWER: 5.2, 1.2
Find the value of c that makes each trinomial a perfect square. 1. x 2 18x + c 81 3. x 2 + 9x + c Solve each equation by completing the square. Round to the nearest tenth if necessary. 5. x 2 + 4x = 6
More informationLesson 10.1 Solving Quadratic Equations
Lesson 10.1 Solving Quadratic Equations 1. Sketch the graph of a quadratic equation with each set of conditions. a. One intercept and all nonnegative yvalues b. The verte in the third quadrant and no
More informationMATH College Algebra Review for Test 2
MATH 4  College Algebra Review for Test Sections. and.. For f (x) = x + 4x + 5, give (a) the xintercept(s), (b) the intercept, (c) both coordinates of the vertex, and (d) the equation of the axis of
More informationFinal Exam Review Part 2 #4
Final Eam Review Part # Intermediate Algebra / MAT 135 Fall 01 Master (Prof. Fleischner) Student Name/ID: 1. Solve for, where is a real number. + = 8. Solve for, where is a real number. 9 1 = 3. Solve
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Rationalize the denominator and simplify. 1 1) B) C) 1 D) 1 ) Identify the pair of like
More informationFLC Ch 13 (except 1.4, 3.1, 3.2) Sec 1.2: Graphs of Equations in Two Variables; Intercepts, Symmetry
Math 370 Precalculus [Note to Student: Read/Review Sec 1.1: The Distance and Midpoint Formulas] Sec 1.2: Graphs of Equations in Two Variables; Intercepts, Symmetry Defns A graph is said to be symmetric
More informationCh2 practice test. for the following functions. f (x) = 6x 2 + 2, Find the domain of the function using interval notation:
Ch2 practice test Find for the following functions. f (x) = 6x 2 + 2, Find the domain of the function using interval notation: A hotel chain charges $75 each night for the first two nights and $55 for
More informationChapter 1 Notes: Quadratic Functions
19 Chapter 1 Notes: Quadratic Functions (Textbook Lessons 1.1 1.2) Graphing Quadratic Function A function defined by an equation of the form, The graph is a Ushape called a. Standard Form Vertex Form
More informationQuadratic Function. Parabola. Parent quadratic function. Vertex. Axis of Symmetry
Name: Chapter 10: Quadratic Equations and Functions Section 10.1: Graph = a + c Quadratic Function Parabola Parent quadratic function Verte Ais of Smmetr Parent Function =  1 0 1 1 Eample 1: Make a table,
More informationMath 110 Final Exam Review Revised December 2015
Math 110 Final Exam Review Revised December 2015 Factor out the GCF from each polynomial. 1) 60x  15 2) 7x 8 y + 42x 6 3) x 9 y 5  x 9 y 4 + x 7 y 2  x 6 y 2 Factor each fourterm polynomial by grouping.
More informationMathematics 2201 Midterm Exam Review
Mathematics 0 Midterm Eam Review Chapter : Radicals Chapter 6: Quadratic Functions Chapter 7: Quadratic Equations. Evaluate: 6 8 (A) (B) (C) (D). Epress as an entire radical. (A) (B) (C) (D). What is the
More information1 of 32 4/24/2018, 11:38 AM
1 of 3 4/4/018, 11:38 AM Student: Date: Instructor: Alfredo Alvarez Course: Math 0410 Spring 018 Assignment: Math 0410 Homework149aleks 1 Insert < or > between the pair of integers to make the statement
More information1) Explain in complete sentences how to solve the following equation using the factoring method. Y=7x
TEST 13 REVIEW Quadratics 1) Explain in complete sentences how to solve the following equation using the factoring method. Y=7x 2 +28. 2) Find the domain and range if the points in the table are discrete
More information2 P a g e. Essential Questions:
NC Math 1 Unit 5 Quadratic Functions Main Concepts Study Guide & Vocabulary Classifying, Adding, & Subtracting Polynomials Multiplying Polynomials Factoring Polynomials Review of Multiplying and Factoring
More informationMAT 1033C  MartinGay Intermediate Algebra Chapter 8 (8.1, 8.2, 8.5, 8.6) Practice for the Exam
MAT 33C  MartinGa Intermediate Algebra Chapter 8 (8.1 8. 8. 8.6) Practice for the Eam Name Date Da/Time: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
More informationMCF3M1 Exam Review. 1. Which relation is not a function? a. c. b. d. 2. What is the range of the function?
MCF3M1 Exam Review 1. Which relation is not a function? 2. What is the range of the function? a. R = {1, 5, 4, 7} c. R = {1, 2, 3, 4, 5, 6, 7} b. R = {1, 2, 3, 6} d. R = {2, 5, 4, 7} 3. Which function
More informationMATH 8 CATALINA FOOTHILLS SCHOOL DISTRICT
MATH 8 CATALINA FOOTHILLS SCHOOL DISTRICT Overarching Understandings for the Course: Students will understand Number Systems, Percents, Expressions, Equations, and Inequalities, Exponent Rules, Functions,
More informationQuadratic Functions. Key Terms. Slide 1 / 200. Slide 2 / 200. Slide 3 / 200. Table of Contents
Slide 1 / 200 Quadratic Functions Table of Contents Key Terms Identify Quadratic Functions Explain Characteristics of Quadratic Functions Solve Quadratic Equations by Graphing Solve Quadratic Equations
More informationQuadratic Functions. Key Terms. Slide 2 / 200. Slide 1 / 200. Slide 3 / 200. Slide 4 / 200. Slide 6 / 200. Slide 5 / 200.
Slide 1 / 200 Quadratic Functions Slide 2 / 200 Table of Contents Key Terms Identify Quadratic Functions Explain Characteristics of Quadratic Functions Solve Quadratic Equations by Graphing Solve Quadratic
More information5. Determine the discriminant for each and describe the nature of the roots.
4. Quadratic Equations Notes Day 1 1. Solve by factoring: a. 3 16 1 b. 3 c. 8 0 d. 9 18 0. Quadratic Formula: The roots of a quadratic equation of the form A + B + C = 0 with a 0 are given by the following
More informationMath Review for Incoming Geometry Honors Students
Solve each equation. 1. 5x + 8 = 3 + 2(3x 4) 2. 5(2n 3) = 7(3 n) Math Review for Incoming Geometry Honors Students 3. Victoria goes to the mall with $60. She purchases a skirt for $12 and perfume for $35.99.
More informationMath 095 Final Exam Review  MLC
Math 095 Final Exam Review  MLC Although this is a comprehensive review, you should also look over your old reviews from previous modules, the readings, and your notes. Round to the thousandth unless
More informationPosition, Velocity, Acceleration
191 CHAPTER 7 Position, Velocity, Acceleration When we talk of acceleration we think of how quickly the velocity is changing. For example, when a stone is dropped its acceleration (due to gravity) is approximately
More informationSolving Quadratic Equations: Algebraically and Graphically Read 3.1 / Examples 1 4
CC Algebra II HW #14 Name Period Row Date Solving Quadratic Equations: Algebraically and Graphically Read 3.1 / Examples 1 4 Section 3.1 In Exercises 3 12, solve the equation by graphing. (See Example
More informationAP Calculus Summer Homework MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
AP Calculus Summer Homework 20152016 Part 2 Name Score MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the distance d(p1, P2) between the points
More information1. Find all relations which are functions. 2. Find all one to one functions.
1 PRACTICE PROBLEMS FOR FINAL (1) Function or not (vertical line test or y = x expression) 1. Find all relations which are functions. (A) x + y = (C) y = x (B) y = x 1 x+ (D) y = x 5 x () One to one function
More informationName: Class: Date: PostAssessment Polynomial Unit. Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: _ lass: _ ate: Postssessment Polynomial Unit Multiple hoice Identify the choice that best completes the statement or answers the question. 1 Write the polynomial in standard form. Then name the polynomial
More informationCHANCE Program. Admissions Mathematics Practice Test. Part One will test your background in basic arithmetic, while Part Two will cover basic algebra.
CHANCE Program Admissions Mathematics Practice Test Part One will test your background in basic arithmetic, while Part Two will cover basic algebra. Each part of the test has 30 questions and has been
More information\/ \ i 1. \ I I / 4\ I I1 I. Chapter 7 Review: Quadratics Textbook p Summary: p , p Practice Questions p.398,p.
Chapter 7 Review: Quadratics Textbook p.358444 Summary: p.396397, p.441442 Practice Questions p.398,p.443444 Key Concepts: Quadratic Analysis, Different Forms of Quadratics, Solving Quadratics, Factoring,
More informationAlgebra I EOC Review (Part 3)
1. Some of the steps in Raya s solution to 2.5(6.25x + 0.5) = 11 is shown. Statement Reason 1. 2.5(6.25x + 0.5) = 11 1. Given 2. 2. 3. 3. Subtraction Property of Equality 4. x = 0.624 4.? Select the correct
More informationAlgebra II Chapter 5
Algebra II Chapter 5 5.1 Quadratic Functions The graph of a quadratic function is a parabola, as shown at rig. Standard Form: f ( x) = ax2 + bx + c vertex: (x, y) = b 2a, f b 2a a < 0 graph opens down
More informationAlgebra Notes Quadratic Functions and Equations Unit 08
Note: This Unit contains concepts that are separated for teacher use, but which must be integrated by the completion of the unit so students can make sense of choosing appropriate methods for solving quadratic
More informationLadies and Gentlemen: Please Welcome the Quadratic Formula!
Lesson.1 Skills Practice Name Date Ladies and Gentlemen: Please Welcome the Quadratic Formula! The Quadratic Formula Vocabulary Complete the Quadratic Formula. Then, identify the discriminant and explain
More information1 Linear and Absolute Value Equations
1 Linear and Absolute Value Equations 1. Solve the equation 11x + 6 = 7x + 15. Solution: Use properties of equality to bring the x s to one side and the numbers to the other: 11x (7x) + 6 = 7x (7x) + 15
More informationBasic Fraction and Integer Operations (No calculators please!)
P1 Summer Math Review Packet For Students entering Geometry The problems in this packet are designed to help you review topics from previous mathematics courses that are important to your success in Geometry.
More informationMth 95 Module 4 Chapter 8 Spring Review  Solving quadratic equations using the quadratic formula
Mth 95 Module 4 Chapter 8 Spring 04 Review  Solving quadratic equations using the quadratic formula Write the quadratic formula. The NUMBER of REAL and COMPLEX SOLUTIONS to a quadratic equation ( a b
More informationBonus Homework and Exam Review  Math 141, Frank Thorne Due Friday, December 9 at the start of the final exam.
Bonus Homework and Exam Review  Math 141, Frank Thorne (thornef@mailbox.sc.edu) Due Friday, December 9 at the start of the final exam. It is strongly recommended that you do as many of these problems
More informationLESSON #17  FACTORING COMMON CORE ALGEBRA II FACTOR TWO IMPORTANT MEANINGS
1 LESSON #17  FACTORING COMMON CORE ALGEBRA II In the study of algebra there are certain skills that are called gateway skills because without them a student simply cannot enter into many more comple
More informationAlgebra II 5.3 Solving Quadratic Equations by Finding Square Roots
5.3 Solving Quadratic Equations by Finding Square Roots Today I am solving quadratic equations by finding square roots. I am successful today when solve quadratic functions using square roots. It is important
More informationWelcome to Honors Algebra II Trigonometry at Morton High School!
Welcome to Honors Algebra II Trigonometry at Morton High School! Dear Parents and Students, Mathematics is a discipline that constantly builds on previous knowledge. Students entering Honors Algebra II
More informationChapter 16 Review. 1. What is the solution set of n 2 + 5n 14 = 0? (A) n = {0, 14} (B) n = { 1, 14} (C) n = { 2, 7} (D) n = { 2, 7} (E) n = { 7, 2}
Chapter 16 Review Directions: For each of the questions below, choose the best answer from the five choices given. 1. What is the solution set of n + 5n 14 = 0? (A) n = {0, 14} (B) n = { 1, 14} (C) n =
More information6.4. The Quadratic Formula. LEARN ABOUT the Math. Selecting a strategy to solve a quadratic equation. 2x 2 + 4x  10 = 0
6.4 The Quadratic Formula YOU WILL NEED graphing calculator GOAL Understand the development of the quadratic formula, and use the quadratic formula to solve quadratic equations. LEARN ABOUT the Math Devlin
More informationFull Name. Remember, lots of space, thus lots of pages!
Rising PreCalculus student Summer Packet for 016 (school year 01617) Dear Advanced Algebra: PreCalculus student: To be successful in Advanced Algebra: PreCalculus, you must be proficient at solving
More informationSection 5: Quadratic Equations and Functions Part 1
Section 5: Quadratic Equations and Functions Part 1 Topic 1: RealWorld Examples of Quadratic Functions... 121 Topic 2: Factoring Quadratic Expressions... 125 Topic 3: Solving Quadratic Equations by Factoring...
More informationr r 30 y 20y 8 7y x 6x x 5x x 8x m m t 9t 12 n 4n r 17r x 9x m 7m x 7x t t 18 x 2x U3L1  Review of Distributive Law and Factoring
UL  Review of Distributive Law and Factoring. Expand and simplify. a) (6mn )(5m 4 n 6 ) b) 6x 4 y 5 z 7 (x 7 y 4 z) c) (x 4)  (x 5) d) (y 9y + 5) 5(y 4) e) 5(x 4y) (x 5y) + 7 f) 4(a b c) 6(4a + b
More informationAcquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A4b & MM2A4c Time allotted for this Lesson: 9 hours
Acquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A4b & MM2A4c Time allotted for this Lesson: 9 hours Essential Question: LESSON 3 Solving Quadratic Equations and Inequalities
More informationUnit: Solving Quadratic Equations
Unit: Solving Quadratic Equations Name Dates Taught Outcome 11P.R.1. Factor polynomial expressions of the of the form o ax 2  bx +c = 0, a 0 o a 2 x 2 b 2 y 2  c = 0, a 0 b 0 o a(f(x)) 2 b(f(x))x +c
More informationHonors Algebra 2 ~ Spring 2014 Name 1 Unit 3: Quadratic Functions and Equations
Honors Algebra ~ Spring Name Unit : Quadratic Functions and Equations NC Objectives Covered:. Define and compute with comple numbers. Operate with algebraic epressions (polnomial, rational, comple fractions)
More informationSolve Quadratic Equations
Skill: solve quadratic equations by factoring. Solve Quadratic Equations A.SSE.A. Interpret the structure of epressions. Use the structure of an epression to identify ways to rewrite it. For eample, see
More informationMath 1050 REVIEW for Exam 1. Use synthetic division to find the quotient and the remainder. 1) x3  x2 + 6 is divided by x + 2
Math 0 REVIEW for Eam 1 Use snthetic division to find the quotient and the remainder. 1) 32 + 6 is divided b + 2 Use snthetic division to determine whether  c is a factor of the given polnomial. 2) 332
More informationMath 1720 Final Exam REVIEW Show All work!
Math 1720 Final Exam REVIEW Show All work! The Final Exam will contain problems/questions that fit into these Course Outcomes (stated on the course syllabus): Upon completion of this course, students will:
More informationChapters 8 & 9 Review for Final
Math 203  Intermediate Algebra Professor Valdez Chapters 8 & 9 Review for Final SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the formula for
More informationAlgebra I. Polynomials.
1 Algebra I Polynomials 2015 11 02 www.njctl.org 2 Table of Contents Definitions of Monomials, Polynomials and Degrees Adding and Subtracting Polynomials Multiplying a Polynomial by a Monomial Multiplying
More informationCHAPTER 4: APPLICATIONS OF DERIVATIVES
(Exercises for Section 4.1: Extrema) E.4.1 CHAPTER 4: APPLICATIONS OF DERIVATIVES SECTION 4.1: EXTREMA 1) For each part below, find the absolute maximum and minimum values of f on the given interval. Also
More informationMTH 65 Supplemental Problem Sets SUPPLEMENT TO 4.1
SUPPLEMENT TO 4.1 1. Solve the following systems of equations by graphing. You will need to set up different scales on the different coordinate planes to get the graphs to fit nicely. Remember you may
More informationLesson 17 Quadratic Word Problems. The equation to model Vertical Motion is
W8D1 Quadratic Word Problems Warm Up 1. A rectangle has dimensions of x+2 and x+3. What is the area of the rectangle? 2. What is the Perimeter of the rectangle? 3. If the area of the rectangle is 30 m
More informationSection 2.1 Intercepts and symmetry. #1 4: Find the x and yintercepts
Section 2.1 Intercepts and symmetry #1 4: Find the x and yintercepts 1) 2) 3) Section 2.1 Intercepts and symmetry 4) #518: Find the x and yintercepts. 5) 3x  6y = 24 6) 2x + 4y = 12 7) y 2 = x + 9
More informationMATH98 Intermediate Algebra Practice Test Form A
MATH98 Intermediate Algebra Practice Test Form A MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) (y  4)  (y + ) = 3y 1) A)
More informationYou analyzed parent functions and their families of graphs. (Lesson 15)
You analyzed parent functions and their families of graphs. (Lesson 15) Graph and analyze power functions. Graph and analyze radical functions, and solve radical equations. power function monomial function
More information1 Which expression represents 5 less than twice x? 1) 2) 3) 4)
1 Which expression represents 5 less than twice x? 2 Gabriella has 20 quarters, 15 dimes, 7 nickels, and 8 pennies in a jar. After taking 6 quarters out of the jar, what will be the probability of Gabriella
More informationRemember, you may not use a calculator when you take the assessment test.
Elementary Algebra problems you can use for practice. Remember, you may not use a calculator when you take the assessment test. Use these problems to help you get up to speed. Perform the indicated operation.
More informationMAT 210 TEST 2 REVIEW (Ch 12 and 13)
Class: Date: MAT 0 TEST REVIEW (Ch and ) Multiple Choice Identify the choice that best completes the statement or answers the question.. The population P is currently 0,000 and growing at a rate of 7,000
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 informationLast modified Spring 2016
Math 00 Final Review Questions In problems 6, perform the indicated operations and simplif if necessar.. 8 6 8. 7 6. ( i) ( 4 i) 4. (8 i). ( 9 i)( 7 i) 6. ( i)( i) In problems 7, solve the following applications.
More informationState whether the following statements are true or false: 27.
Cumulative MTE 9 Review This packet includes major developmental math concepts that students ma use to prepare for the VPT Math (Virginia Placement Test for Math or for students to use to review essential
More informationState whether the following statements are true or false: 30. 1
Cumulative MTE 9 Review This packet includes major developmental math concepts that students ma use to prepare for the VPT Math (Virginia Placement Test for Math or for students to use to review essential
More informationChapter 8 RADICAL EXPRESSIONS AND EQUATIONS
Name: Instructor: Date: Section: Chapter 8 RADICAL EXPRESSIONS AND EQUATIONS 8.1 Introduction to Radical Expressions Learning Objectives a Find the principal square roots and their opposites of the whole
More information43 Solving Quadratic Equations by Factoring. Write a quadratic equation in standard form with the given root(s). 1. 8, 5 ANSWER: ANSWER: ANSWER:
Write a quadratic equation in standard form with the given root(s). 1. 8, 5 8. 9. (2x 5)(x + 6) 2. (4x 3)(4x 1) Solve each equation. 3. 10. 6, 6 4. Factor each polynomial. 5x(7x 3) 11. 12. 5. 6. (6x 1)(3x
More informationhttps://www.webassign.net/v4cgi/assignments/pre...
Practice Test 2 Part A Chap 1 Sections 5,6,7,8 (11514149) Question 12345678910111213141516171819202122232425262728293031323334353 Description This is one of two practice tests to help you prepare for Test
More informationWhen factoring, we ALWAYS start with the (unless it s 1).
Math 100 Elementary Algebra Sec 5.1: The Greatest Common Factor and Factor By Grouping (FBG) Recall: In the product XY, X and Y are factors. Defn In an expression, any factor that is common to each term
More information26 Analyzing Functions with Successive Differences
Graph each set of ordered pairs. Determine whether the ordered pairs represent a linear function, a quadratic function, or an exponential function. 1. ( 2, 8), ( 1, 5), (0, 2), (1, 1) linear 3. ( 3, 8),
More informationName: Period: Unit 3 Modeling with Radical and Rational Functions
Name: Period: Unit Modeling with Radical and Rational Functions 1 Equivalent Forms of Exponential Expressions Before we begin today s lesson, how much do you remember about exponents? Use expanded form
More informationPRACTICE FINAL EXAM. 3. Solve: 3x 8 < 7. Write your answer using interval notation. Graph your solution on the number line.
MAC 1105 PRACTICE FINAL EXAM College Algebra *Note: this eam is provided as practice onl. It was based on a book previousl used for this course. You should not onl stud these problems in preparing for
More informationAssignment: Summer Assignment Part 1 of 8 Real Numbers and Their Properties. Student: Date:
Student: Date: Assignment: Summer Assignment Part of 8 Real Numbers and Their Properties. Identify to which number groups (natural numbers, whole numbers, integers, rational numbers, real numbers, and
More information9 (0, 3) and solve equations to earn full credit.
Math 0 Intermediate Algebra II Final Eam Review Page of Instructions: (6, ) Use our own paper for the review questions. For the final eam, show all work on the eam. (6, ) This is an algebra class do not
More informationWelcome to IB MATH SL1!
Welcome to IB MATH SL1! Congratulations! You are currently enrolled in IB Math SL1 for the Fall of 017. This is a twosemester course, which prepares you for the IB Math SL you will take in 018019 school
More informationIntermediate Algebra 100A Final Exam Review Fall 2007
1 Basic Concepts 1. Sets and Other Basic Concepts Words/Concepts to Know: roster form, set builder notation, union, intersection, real numbers, natural numbers, whole numbers, integers, rational numbers,
More informationQuadratic Equations. Math 201 Chapter 4. General Outcome: Develop algebraic and graphical reasoning through the study of relations.
Math 201 Chapter 4 Quadratic Equations General Outcome: Develop algebraic and graphical reasoning through the study of relations. Specific Outcomes: RF1. Factor polynomial expressions of the form: ax
More information8.2 Solving Quadratic Equations by the Quadratic Formula
Section 8. Solving Quadratic Equations by the Quadratic Formula 85 8. Solving Quadratic Equations by the Quadratic Formula S Solve Quadratic Equations by Using the Quadratic Formula. Determine the Number
More informationPreCalc Chapter 1 Sample Test. D) slope: 3 4
PreCalc Chapter 1 Sample Test 1. Use the graphs of f and g to evaluate the function. f( x) gx ( ) (f o g)(0.5) 1 1 0 4. Plot the points and find the slope of the line passing through the pair of points.
More informationName Teacher: Period: Date: ALGEBRA I FINAL REVIEW SPRING 2016
Name Teacher: Period: Date: ALGEBRA I FINAL REVIEW SPRING 016 Solve each system of inequalities by graphing. (Book sections 45and 46) y x4 1.).) y x1 y x 4 4yx.) x y 14 x y0 4.) x y 4x y 10 5.) x y 1
More information6.1 Solving Quadratic Equations by Factoring
6.1 Solving Quadratic Equations by Factoring A function of degree 2 (meaning the highest exponent on the variable is 2), is called a Quadratic Function. Quadratic functions are written as, for example,
More informationChapter 1. WorkedOut Solutions. Chapter 1 Maintaining Mathematical Proficiency (p. 1)
Chapter Maintaining Mathematical Proficiency (p. ). + ( ) = 7. 0 + ( ) =. 6 + = 8. 9 ( ) = 9 + =. 6 = + ( 6) = 7 6. ( 7) = + 7 = 7. 7 + = 8. 8 + ( ) = 9. = + ( ) = 0. (8) =. 7 ( 9) = 6. ( 7) = 8. ( 6)
More information