Lycée des arts Math Grade Algebraic expressions S.S.4
|
|
- Alvin Eaton
- 5 years ago
- Views:
Transcription
1 Lycée des arts Math Grade lgebraic expressions S.S.4 Exercise I: Factorize each of the following algebraic expressions, and then determine its real roots. (x) = 4x (3x 1) (x + ) (3x 1) + 3x 1 B (x) = (x + 1) (4x + 3) 5x (4x + 3) + (x 1) (4x + 3) (x) = (x ) (5x 1) + (x 3) (5x 1) (3x + ) (5x 1) (a) = (3a + 1) (a + 1) + a 1 E (y) = 4y 9 + (y + 3) (y 5) F (x) = (x 3) (x + 7) + (x 6) (3x 1) (9 3x) (x + 1) G (x) = (4x 3) ( x + 5) + (x 1) (x 5) + (x 5) ( x + 5) H (x) = 6(x 16) (3x + 1) (x 4) + (8 x) (x + ) I (x) = (x + 7) (3x + 4) + (9x + 4x + 16) J (x) = 3x 1 + (x 4) ( x) (x 4x + 4) K (x) = (6x 1x + 6) + (3x 3) (x 1) (x + 1) L (x) = 4x 4x + 1 (1 x) (3x + 5) 1x + 3 M (a) = (3a ) (a + 1) (3a ) N (x) = x (x 1) x (x + 1) Exercise II: Factorize each of the following expressions: = a 3 + a + a + 1 ; B = xy 3x y + 6 = b a + ab ; = 10xy + 4x 5y E = x y + a + b + xy ab ; F = 5(3x y) 16(5x + 3y) G = 3(5x 1) 3(x + ) ; H = (a 3) (a 3) + 1 I = (3x + ) + (3x + ) (x 1) + (x 1) ; J = (a + 4) (a + 4) (a + 1) + (a + 1) K = 4x 4xy + y 9x y ; L = 5(x 4) x + 4x 4 + (6 3x) (x + 3) M = 3(x 1) + x (x 1) (x + ) ; N = 5x + (5x 3) (x + 7) 9 O = (3x 5) 4x 4 ; P = (4a + 1) (5a ) Q = a ab b 1 ; R = x 4x + (x 4) x 1 S = 4 3 5x 4 3 x ; T = October - Math S.S-4 lgebraic expressions Grade 9 1/5
2 Exercise III: x x x x B x x x x x. 1º) a) Expand and reduce x and b) Factorize x and B x. B x. º) In the adjacent figure we have: * B is a rectangle such that = 3x cm. * EFG and PMNB are two squares such that: E = x and PM = 1 cm. (x is a real number expressed in cm) a) Show that x 3x. Frame the value of x. b) Express, in terms of x, the area of the rectangle B. x represents the area of the shaded region. c) educe that d) Is there any value of x, for which the area of B is the triple of that of the shaded region? Justify. Exercise IV: (x) = (x 3) (x 1) + 4(3 x) and B (x) = x 3 3x x º) a) Expand and reduce (x). b) alculate ( 3). What can you conclude? c) Solve the equation: B (x) = 3 3x. º) a) Factorize (x), and then show that B (x) = (x 3) (x 1) (x + 1). b) Solve: (x) = B (x). () x 3º) onsider the fractional expression: F () x B () x a) etermine the domain of definition of F (x). b) Simplify F (x), and then calculate F ( ). c) Solve F (x) = 0 and F (x) = 1. Exercise V: Given: (x) = 4x x 4x and B (x) = (5 x) (4x 1). 1º) a) Write (x) and B (x) as products of factors of the first degree. b) For what value of x, the double of (x) is the triple of B (x)? Justify. º) a) etermine the prohibited of values of b) Simplify f (x), and then reduce f. c) Solve : f () x and f () x 0. 3 f () x () x. B () x October - Math S.S-4 lgebraic expressions Grade 9 /5
3 Exercise VI: and P x x a b x a x a x b bx c a Q x x x R x 3m 1 x 5m x m. a, b, c and m are four real numbers m is a parameter. 1º) alculate m knowing that «3» is a root of R x. º) a) Show that: P x 3 b x 3a b x c 3. b) alculate a, b and c so that the polynomials P x and c) alculate a, b and c so that the polynomial P x Exercise VII: Q x are identical. is identically null. Given : P (x) = (6x 3) (x 1) 3(4x 1) + 3(x 1) and Q (x) = P (x) 5x (x -3) 1º) a) Expand and reduce P (x). b) Solve the equation P (x) = 9. º) a) Show that: P (x) = 3(x 3) (x 1), and then solve P (x) = 0. b) Verify that Q (x) is a perfect square. c) educe the solutions of the equation Q (x) = 4. 3º) In this part x represents a real number greater than 1 (x > 1). We designate by S the area of the rectangle B where B = x 1 and B = x 1, and S the area of the triangle IJK right at I where IJ = x 1 and IK = x + 1, and S is that of the square MNPQ of side MN = x 1. a) Show that: 3S 6S + 3S = P (x). b) Find the value of x that verifies the equation: S + S = S. Exercise VIII: Given the following algebraic expressions. f (x) = (x ) + 4(x 5) and g (x) = (x ) 1(x 5). 1º) Expand and reduce f (x) and g(x). º) Verify that: f (x) = x 4. x 4 and g (x) = x 8 3º) Solve: f (x) = 0; g (x) = 0 and g (x) = 5. x - 4º) In what follows, x is expressed in cm such that x > 5. E F The adjacent figure shows a square B of side x - 5 B = x and a rectangle EFG of dimensions of B and EFG a) Express S (x) and S (x) in terms of x. G = 4 and FG = x 5. x - We designate by S (x) and S (x) the respective areas G b) Solve each of the following equations: S (x) = 3S (x) et S (x) + S (x) = 0. x - B October - Math S.S-4 lgebraic expressions Grade 9 3/5
4 Exercise IX: Given: E(x) = (x + 3) (x + 1) (x + ) and P(x) = (x + 1) (x + 3) (x 3). 1º) Expand and reduce E(x) and P(x). º) a) Use the reduced of E(x) to calculate S = (88889) (88890). b) Use the reduced of P(x) to calculate T = Exercise X: The unit of length is the cm, x is a real number such that x > º) Express, in terms of x, the area of the rectangle B that we denote P(x). º) Express, in terms of x, the area of the rectangle IBJ that we denote Q(x). 3º) Find the value of x for which we have P(x) = x. 4º) etermine the value of x for which the rectangles B and IBJ have two equal areas. x + 3 I B 5º) onsider the expression: F () x P () x x - 1. Q () x a) For what values of x, is F (x) defined? b) Simplify F (x), and then calculate F ( ). c) Solve the equations: F (x) = 0 and F (x) = 3. Exercise XI: In this exercise the unit of length is the cm. Let x be a real number such that x > 6. In the attached figure we have: x - B 1 E 1 * B is a rectangle such that B = x - * BEFG is a square of side 1. G 1 F * G is a point on [B] such that G = x º) Express the area of B in terms of x. º) Show that the area of the polygon EFG is expressed by (x) = (x )(x 4) º) Verify that: (x) = (x 3). 4º) alculate the dimensions of B when the area of EFG is equal to 5 cm. Exercise XII: In the adjacent figure we have two rectangles B and EFG. x is a real number such that x > 7. 1º) Show that the area of the shaded region is: (x) = 3x 1 cm. º) Find the dimensions of the rectangle B when (x) = 180. Exercise XIII: 1º) alculate a when is a root of the polynomial: E (x) = x a + 3( x) (x 1). º) onsider the polynomial: P (x) = x + 3( x) (x 1) 8. Solve the equations: P (x) + 14 = 0 and P (x) = 0. x E 1 x + 1 3x - x + 10 x - 5 F J G B October - Math S.S-4 lgebraic expressions Grade 9 4/5
5 Exercise XIV: Given the expression: E(x) = (x - ) (3x + 1) (x ) (x + 10). 1º) Factorize E(x), and then determine its roots. º) In this question, x is a real number expressed in cm such that x >. onsider a rectangle B such that B = x - and B = 3 + 1, and a triangle MNP right at M, such that MN = (x ) and MP = x We designate by S the area of B and by S that of MNP. a) Express S and S in terms of x, and then show that: S S = E (x). b) alculate x so that that S = S. Exercise XV: Let B be a right triangle at such that : = x + 1 and B = x + 3 P (x) is a polynomial defined by P (x) = B. (x is a real number expressed in cm). 1º) Explain why x must be greater than 0.5 cm. º) Find the expression of P (x). 3º) a) For what value of x B is it isosceles at? b) alculate B for the obtained value. 4º) S(x) designates the area of the triangle B. a) Write the reduce expression of S(x), and then calculate S(x) when x =. b) educe the length of [H], the height-segment relative to [B]. Exercise XVI: EFG is a right triangle at E such that EF = 3x 3 and EG = 3x 1. x is a real number expressed in cm such that x > 1. 1º) I is the midpoint of [EG] and we know that EI = x + 1. Express IG in terms of x. º) Show that the area of the triangle FGI is given by U (x) = (3x 3)(x 1). 3 ) Find the value of x for which EFI and FGI have two equal areas October - Math S.S-4 lgebraic expressions Grade 9 5/5
!"#$%&'(&)*$%&+",#$$-$%&+./#-+ (&)*$%&+%"-$+0!#1%&
!"#$%&'(&)*$%&",#$$-$%&./#- (&)*$%&%"-$0!#1%&23 44444444444444444444444444444444444444444444444444444444444444444444 &53.67689:5;978?58"@A9;8=B!=89C7DE,6=8FG=CD=CF(76F9C7D!)#!/($"%*$H!I"%"&1/%/.!"JK$&3
More information1. 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
More informationIncoming Magnet Precalculus / Functions Summer Review Assignment
Incoming Magnet recalculus / Functions Summer Review ssignment Students, This assignment should serve as a review of the lgebra and Geometry skills necessary for success in recalculus. These skills were
More informationThe WhatPower Function à An Introduction to Logarithms
Classwork Work with your partner or group to solve each of the following equations for x. a. 2 # = 2 % b. 2 # = 2 c. 2 # = 6 d. 2 # 64 = 0 e. 2 # = 0 f. 2 %# = 64 Exploring the WhatPower Function with
More informationSeventeen generic formulas that may generate prime-producing quadratic polynomials
Seventeen generic formulas that may generate prime-producing quadratic polynomials Marius Coman Bucuresti, Romania email: mariuscoman13@gmail.com Abstract. In one of my previous papers I listed forty-two
More informationLINEAR INEQUALITIES. Chapter Overview
LINEAR INEQUALITIES Chapter 6 6.1 Overview 6.1.1 A statement involving the symbols >, 3, x 4, x + y 9. (ii) (iii) (iv) (v) Inequalities which do not involve
More informationSummer Packet for Students Taking Introduction to Calculus in the Fall
Summer Packet for Students Taking Introduction to Calculus in the Fall Algebra 2 Topics Needed for Introduction to Calculus Need to know: à Solve Equations Linear Quadratic Absolute Value Polynomial Rational
More informationInterpolation and Polynomial Approximation I
Interpolation and Polynomial Approximation I If f (n) (x), n are available, Taylor polynomial is an approximation: f (x) = f (x 0 )+f (x 0 )(x x 0 )+ 1 2! f (x 0 )(x x 0 ) 2 + Example: e x = 1 + x 1! +
More informationxvi xxiii xxvi Construction of the Real Line 2 Is Every Real Number Rational? 3 Problems Algebra of the Real Numbers 7
About the Author v Preface to the Instructor xvi WileyPLUS xxii Acknowledgments xxiii Preface to the Student xxvi 1 The Real Numbers 1 1.1 The Real Line 2 Construction of the Real Line 2 Is Every Real
More informationChapter 8. Exploring Polynomial Functions. Jennifer Huss
Chapter 8 Exploring Polynomial Functions Jennifer Huss 8-1 Polynomial Functions The degree of a polynomial is determined by the greatest exponent when there is only one variable (x) in the polynomial Polynomial
More informationMAC 1105-College Algebra LSCC, S. Nunamaker
MAC 1105-College Algebra LSCC, S. Nunamaker Chapter 1-Graphs, Functions, and Models 1.1 Introduction to Graphing I. Reasons for using graphs A. Visual presentations enhance understanding. B. Visual presentations
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 informationSummer Review Packet. for students entering. IB Math SL
Summer Review Packet for students entering IB Math SL The problems in this packet are designed to help you review topics that are important to your success in IB Math SL. Please attempt the problems on
More informationTest 2 Review Math 1111 College Algebra
Test 2 Review Math 1111 College Algebra 1. Begin by graphing the standard quadratic function f(x) = x 2. Then use transformations of this graph to graph the given function. g(x) = x 2 + 2 *a. b. c. d.
More informationMinnesota State High School Mathematics League
011-1 Meet 1, Individual Event Question #1 is intended to be a quickie and is worth 1 point. Each of the next three questions is worth points. Place your answer to each question on the line provided. You
More informationAlgebraic Expressions
Algebraic Expressions 1. Expressions are formed from variables and constants. 2. Terms are added to form expressions. Terms themselves are formed as product of factors. 3. Expressions that contain exactly
More informationTOPIC-1 Rational Numbers
TOPI- Rational Numbers Unit -I : Number System hapter - : Real Numbers Rational Number : number r is called a rational number, if it can be written in the form p/q, where p and q are integers and q 0,
More informationNo books, no notes, no calculators. You must show work, unless the question is a true/false, yes/no, or fill-in-the-blank question.
Math 304 Final Exam (May 8) Spring 206 No books, no notes, no calculators. You must show work, unless the question is a true/false, yes/no, or fill-in-the-blank question. Name: Section: Question Points
More informationFactoring x 2 + bx + c
7.5 Factoring x 2 + bx + c Essential Question How can you use algebra tiles to factor the trinomial x 2 + bx + c into the product of two binomials? Finding Binomial Factors Work with a partner. Use algebra
More informationFor Your Notebook E XAMPLE 1. Factor when b and c are positive KEY CONCEPT. CHECK (x 1 9)(x 1 2) 5 x 2 1 2x 1 9x Factoring x 2 1 bx 1 c
9.5 Factor x2 1 bx 1 c Before You factored out the greatest common monomial factor. Now You will factor trinomials of the form x 2 1 bx 1 c. Why So you can find the dimensions of figures, as in Ex. 61.
More informationCHAPTER TWO. 2.1 Vectors as ordered pairs and triples. The most common set of basic vectors in 3-space is i,j,k. where
40 CHAPTER TWO.1 Vectors as ordered pairs and triples. The most common set of basic vectors in 3-space is i,j,k where i represents a vector of magnitude 1 in the x direction j represents a vector of magnitude
More informationLos Angeles Unified School District Periodic Assessments. Geometry. Assessment 2 ASSESSMENT CODE LA08_G_T2_TST_31241
Los Angeles Unified School District Periodic Assessments Assessment 2 2008 2009 Los Angeles Unified School District Periodic Assessments LA08_G_T2_TST_31241 ASSESSMENT ODE 1100209 The test items contained
More informationAP Exercise 1. This material is created by and is for your personal and non-commercial use only.
1 AP Exercise 1 Question 1 In which of the following situations, does the list of numbers involved make an arithmetic progression, and why? (i) The taxi fare after each km when the fare is Rs 15 for the
More informationChapter 1. Some Basic Theorems. 1.1 The Pythagorean Theorem
hapter 1 Some asic Theorems 1.1 The ythagorean Theorem Theorem 1.1 (ythagoras). The lengths a b < c of the sides of a right triangle satisfy the relation a 2 + b 2 = c 2. roof. b a a 3 2 b 2 b 4 b a b
More informationMath 10 - Unit 5 Final Review - Polynomials
Class: Date: Math 10 - Unit 5 Final Review - Polynomials Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Factor the binomial 44a + 99a 2. a. a(44 + 99a)
More informationGCSE METHODS IN MATHEMATICS
Q Qualifications GCSE METHODS IN MTHEMTICS Linked Pair Pilot Specification (9365) ssessment Guidance Our specification is published on our website (www.aqa.org.uk). We will let centres know in writing
More information(Chapter 10) (Practical Geometry) (Class VII) Question 1: Exercise 10.1 Draw a line, say AB, take a point C outside it. Through C, draw a line parallel to AB using ruler and compasses only. Answer 1: To
More informationAlgebraic Expressions
ALGEBRAIC EXPRESSIONS 229 Algebraic Expressions Chapter 12 12.1 INTRODUCTION We have already come across simple algebraic expressions like x + 3, y 5, 4x + 5, 10y 5 and so on. In Class VI, we have seen
More informationReplacement for a Carpenter s Square
Lesson.1 Skills Practice Name Date Replacement for a arpenter s Square Inscribed and ircumscribed Triangles and Quadrilaterals Vocabulary nswer each question. 1. How are inscribed polygons and circumscribed
More informationSETS. set of natural numbers by N set of integers by Z set of rational numbers by Q set of irrational numbers by T
Chapter SETS. Overview This chapter deals with the concept of a set, operations on sets.concept of sets will be useful in studying the relations and functions... Set and their representations A set is
More informationUNIVERSIDAD CARLOS III DE MADRID Escuela Politécnica Superior Departamento de Matemáticas
UNIVERSIDAD CARLOS III DE MADRID Escuela Politécnica Superior Departamento de Matemáticas a t e a t i c a s PROBLEMS, CALCULUS I, st COURSE 2. DIFFERENTIAL CALCULUS IN ONE VARIABLE BACHELOR IN: Audiovisual
More informationAQA Maths M2. Topic Questions from Papers. Centre of Mass
Q Maths M2 Topic Questions from Papers entre of Mass PhysicsndMathsTutor.com 12 Particles of masses 8 kg, 4 kg, 7 kg and 11 kg are attached to the vertices,, and respectively of a light, rigid, rectangular
More informationEast Penn School District Secondary Curriculum
East Penn School District Secondary Curriculum A Planned Course Statement For Algebra I C.P. Course # 306 Grade(s) 9-12 Department: Mathematics Length of Period (mins.) 41 Total Clock Hours: 123 Periods
More informationLimit Theorems. MATH 464/506, Real Analysis. J. Robert Buchanan. Summer Department of Mathematics. J. Robert Buchanan Limit Theorems
Limit s MATH 464/506, Real Analysis J. Robert Buchanan Department of Mathematics Summer 2007 Bounded Functions Definition Let A R, let f : A R, and let c R be a cluster point of A. We say that f is bounded
More informationName (please print) Mathematics Final Examination December 14, 2005 I. (4)
Mathematics 513-00 Final Examination December 14, 005 I Use a direct argument to prove the following implication: The product of two odd integers is odd Let m and n be two odd integers Since they are odd,
More informationClass IX Chapter 2 Polynomials Maths
NCRTSOLUTIONS.BLOGSPOT.COM Class IX Chapter 2 Polynomials Maths Exercise 2.1 Question 1: Which of the following expressions are polynomials in one variable and which are No. It can be observed that the
More informationA Partial List of Topics: Math Spring 2009
A Partial List of Topics: Math 112 - Spring 2009 This is a partial compilation of a majority of the topics covered this semester and may not include everything which might appear on the exam. The purpose
More informationImmaculate Heart Academy Summer Math Assignment for Algebra II Honors and Algebra II/Pre- Calculus- STEM COURSE CODES (5330 and STEM)
Immaculate Heart Academy Summer Math Assignment for Algebra II Honors and Algebra II/Pre- Calculus- STEM COURSE CODES (50 and 551- STEM) LEARN PRACTICE EXCEL You are taking Algebra II Honors or Algebra
More informationSouthington High School 720 Pleasant Street Southington, CT 06489
BLUE KNIGHTS Southington High School 720 Pleasant Street Southington, CT 06489 Phone: (860) 628-3229 Fax: (860) 628-3397 Home Page: www.southingtonschools.org Principal Brian Stranieri Assistant Principals
More information5. Introduction to Euclid s Geometry
5. Introduction to Euclid s Geometry Multiple Choice Questions CBSE TREND SETTER PAPER _ 0 EXERCISE 5.. If the point P lies in between M and N and C is mid-point of MP, then : (A) MC + PN = MN (B) MP +
More informationAlgebra I. Course Outline
Algebra I Course Outline I. The Language of Algebra A. Variables and Expressions B. Order of Operations C. Open Sentences D. Identity and Equality Properties E. The Distributive Property F. Commutative
More informationExercise 6.2. Q. 1. x = 3. Q. 2. y = 2. Q. 3. 2x = 8 x = 4. Q. 4. 3a = 27 a = 9. Q. 5. 3x = 3 x = 1. Q. 6. 4x = 20 x = 5. Q. 7.
Chapter Exercise. Q.. (i) (vi) 9 (ii) 7 (vii) 9 (iii) (viii) (iv) (ix) (v) (x) Q.. (i) () + ( ) = = = False (, ) is not solution (ii) + = = () + () = + = = (,) is solution (iii) ( ) () = = = False (,)
More informationPolynomial Functions
Polynomial Functions NOTE: Some problems in this file are used with permission from the engageny.org website of the New York State Department of Education. Various files. Internet. Available from https://www.engageny.org/ccss-library.
More informationSummer Review Packet. for students entering. AP Calculus BC
Summer Review Packet for students entering AP Calculus BC The problems in this packet are designed to help you review topics that are important to your success in AP Calculus. Please attempt the problems
More informationCALCULUS AB/BC SUMMER REVIEW PACKET (Answers)
Name CALCULUS AB/BC SUMMER REVIEW PACKET (Answers) I. Simplify. Identify the zeros, vertical asymptotes, horizontal asymptotes, holes and sketch each rational function. Show the work that leads to your
More informationMR. YATES. Vocabulary. Quadratic Cubic Monomial Binomial Trinomial Term Leading Term Leading Coefficient
ALGEBRA II WITH TRIGONOMETRY COURSE OUTLINE SPRING 2009. MR. YATES Vocabulary Unit 1: Polynomials Scientific Notation Exponent Base Polynomial Degree (of a polynomial) Constant Linear Quadratic Cubic Monomial
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 informationAP Calculus AB Summer Math Packet
Name Date Section AP Calculus AB Summer Math Packet This assignment is to be done at you leisure during the summer. It is meant to help you practice mathematical skills necessary to be successful in Calculus
More informationGrade 7/8 Math Circles Fall Nov. 4/5 Solution Set - The Pythagorean Theorem
1 Faculty of Mathematics Waterloo, Ontario Centre for Education in Mathematics and Computing Grade 7/8 Math Circles Fall 014 - Nov. 4/5 Solution Set - The Pythagorean Theorem 1. Let a and b be the lengths
More informationRequisite Approval must be attached
Requisite Approval must be attached CITRUS COMMUNITY COLLEGE DISTRICT DEPARTMENT Mathematics COURSE NUMBER MATH 150 TITLE Intermediate Algebra THIS COURSE IS CLASSIFIED AS: DEGREE APPLICABLE UNIT VALUE
More informationCLASS IX : CHAPTER - 1 NUMBER SYSTEM
MCQ WORKSHEET-I CLASS IX : CHAPTER - 1 NUMBER SYSTEM 1. Rational number 3 40 is equal to: (a) 0.75 (b) 0.1 (c) 0.01 (d) 0.075. A rational number between 3 and 4 is: (a) 3 (b) 4 3 (c) 7 (d) 7 4 3. A rational
More informationANSWERS. CLASS: VIII TERM - 1 SUBJECT: Mathematics. Exercise: 1(A) Exercise: 1(B)
ANSWERS CLASS: VIII TERM - 1 SUBJECT: Mathematics TOPIC: 1. Rational Numbers Exercise: 1(A) 1. Fill in the blanks: (i) -21/24 (ii) -4/7 < -4/11 (iii)16/19 (iv)11/13 and -11/13 (v) 0 2. Answer True or False:
More informationGaithersburg High School Summer 2018 Math Packet For Rising Algebra 2/Honors Algebra 2 Students
Gaithersburg High School Math Packet For Rising Algebra 2/Honors Algebra 2 Students 1 This packet is an optional review of the skills that will help you be successful in Algebra 2 in the fall. By completing
More informationSkills Practice Skills Practice for Lesson 11.1
Skills Practice Skills Practice for Lesson.1 Name ate Riding a Ferris Wheel Introduction to ircles Vocabulary Identify an instance of each term in the diagram. 1. circle X T 2. center of the circle H I
More information27 th ARYABHATTA INTER-SCHOOL MATHEMATICS COMPETITION 2010 CLASS = VIII
7 th ARYABHATTA INTER-SCHOOL MATHEMATICS COMPETITION 00 CLASS = VIII Time Allowed: Hours Max. Marks: 00 Roll No. of the Participant: GENERAL INSTRUCTIONS :. Participant should not write his/her name on
More informationCALCULUS ASSESSMENT REVIEW
CALCULUS ASSESSMENT REVIEW DEPARTMENT OF MATHEMATICS CHRISTOPHER NEWPORT UNIVERSITY 1. Introduction and Topics The purpose of these notes is to give an idea of what to expect on the Calculus Readiness
More informationAlg. Exercise (1) Department : Math Form : 1 st prep. Sheet. [1] Complete : 1) Rational number is 2) The set of integer is.. 3) If. is rational if x.
airo Governorate Nozha irectorate of Education Nozha Language Schools Ismailia Road epartment : Math Form : 1 st prep. Sheet [1] omplete : lg. Exercise (1) 1) Rational number is ) The set of integer is..
More informationcos t 2 sin 2t (vi) y = cosh t sinh t (vii) y sin x 2 = x sin y 2 (viii) xy = cot(xy) (ix) 1 + x = sin(xy 2 ) (v) g(t) =
MATH1003 REVISION 1. Differentiate the following functions, simplifying your answers when appropriate: (i) f(x) = (x 3 2) tan x (ii) y = (3x 5 1) 6 (iii) y 2 = x 2 3 (iv) y = ln(ln(7 + x)) e 5x3 (v) g(t)
More information2.5 Justify a Number Trick
Investigating g Geometry ACTIVITY Use before Lesson 2.5 2.5 Justify a Number Trick MATERIALS paper pencil QUESTION How can you use algebra to justify a number trick? Number tricks can allow you to guess
More informationUMUC MATH-107 Final Exam Information
UMUC MATH-07 Final Exam Information What should you know for the final exam? Here are some highlights of textbook material you should study in preparation for the final exam. Review this material from
More informationUnit 2 Review. Determine the scale factor of the dilation below.
Unit 2 Review 1. oes the graph below represent a dilation? Why or why not? y 10 9 8 7 (0, 7) 6 5 4 3 (0, 3.5) 2 1 (5, 7) (5, 3.5) -10-9 -8-7 -6-5 -4-3 -2-1 0 1 2 3 4 5 6 7 8 9 10-1 F -2 (5, 0) -3-4 -5-6
More informationSkills Practice Skills Practice for Lesson 9.1
Skills Practice Skills Practice for Lesson.1 Name Date Meeting Friends The Distance Formula Vocabular Define the term in our own words. 1. Distance Formula Problem Set Archaeologists map the location of
More information3.9 My Irrational and Imaginary Friends A Solidify Understanding Task
3.9 My Irrational and Imaginary Friends A Solidify Understanding Task Part 1: Irrational numbers Find the perimeter of each of the following figures. Express your answer as simply as possible. 2013 www.flickr.com/photos/lel4nd
More informationMath Day at the Beach 2017
Math Day at the Beach 017 Multiple Choice Write your name and school and mark your answers on the answer sheet. You have 0 minutes to work on these problems. No calculator is allowed. 1. How many integers
More informationI) Simplifying fractions: x x. 1) 1 1 y x. 1 1 x 1. 4 x. 13x. x y xy. x 2. Factoring: 10) 13) 12) III) Solving: x 9 Prime (using only) 11)
AP Calculus Summer Packet Answer Key Reminders:. This is not an assignment.. This will not be collected.. You WILL be assessed on these skills at various times throughout the course.. You are epected to
More informationBrilliant Public School, Sitamarhi. Class -VII. Maths Worksheets. Session :
Brilliant Public School, Sitamarhi Class -VII Maths Worksheets Session : 2012-13 Rajopatti,Dumra Road,Sitamarhi(Bihar),Pin-843301 Ph.06226-252314,Mobile:9431636758 1. SIMPLE EQUATIONS I. SOLVE (i) 7y +
More informationStatistics 349(02) Review Questions
Statistics 349(0) Review Questions I. Suppose that for N = 80 observations on the time series { : t T} the following statistics were calculated: _ x = 10.54 C(0) = 4.99 In addition the sample autocorrelation
More informationSummer Review Packet AP Calculus
Summer Review Packet AP Calculus ************************************************************************ Directions for this packet: On a separate sheet of paper, show your work for each problem in this
More informationSolving 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
More information1. Town A is 48 km from town B and 32 km from town C as shown in the diagram. A 48km
1. Town is 48 km from town and 32 km from town as shown in the diagram. 32km 48km Given that town is 56 km from town, find the size of angle (Total 4 marks) Â to the nearest degree. 2. The diagram shows
More informationAlgebra I Lesson 6 Monomials and Polynomials (Grades 9-12) Instruction 6-1 Multiplying Polynomials
In algebra, we deal with different types of expressions. Grouping them helps us to learn rules and concepts easily. One group of expressions is called polynomials. In a polynomial, the powers are whole
More informationTheorem 1.2 (Converse of Pythagoras theorem). If the lengths of the sides of ABC satisfy a 2 + b 2 = c 2, then the triangle has a right angle at C.
hapter 1 Some asic Theorems 1.1 The ythagorean Theorem Theorem 1.1 (ythagoras). The lengths a b < c of the sides of a right triangle satisfy the relation a + b = c. roof. b a a 3 b b 4 b a b 4 1 a a 3
More informationCALCULUS AB/BC SUMMER REVIEW PACKET
Name CALCULUS AB/BC SUMMER REVIEW PACKET Welcome to AP Calculus! Calculus is a branch of advanced mathematics that deals with problems that cannot be solved with ordinary algebra such as rate problems
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 informationSpring Nikos Apostolakis
Spring 07 Nikos Apostolakis Review of fractions Rational expressions are fractions with numerator and denominator polynomials. We need to remember how we work with fractions (a.k.a. rational numbers) before
More informationGeometry. Class Examples (July 8) Paul Yiu. Department of Mathematics Florida Atlantic University. Summer 2014
Geometry lass Examples (July 8) Paul Yiu Department of Mathematics Florida tlantic University c b a Summer 2014 1 The incircle The internal angle bisectors of a triangle are concurrent at the incenter
More informationALGEBRA I FORM I. Textbook: Algebra, Second Edition;Prentice Hall,2002
ALGEBRA I FORM I Textbook: Algebra, Second Edition;Prentice Hall,00 Prerequisites: Students are expected to have a knowledge of Pre Algebra and proficiency of basic math skills including: positive and
More informationDefinitions. (V.1). A magnitude is a part of a magnitude, the less of the greater, when it measures
hapter 8 Euclid s Elements ooks V 8.1 V.1-3 efinitions. (V.1). magnitude is a part of a magnitude, the less of the greater, when it measures the greater. (V.2). The greater is a multiple of the less when
More informationALLEN PARK HIGH SCHOOL Second Semester Review
Algebra Semester Review Spring 0 ALLEN PARK HIGH SCHOOL Second Semester Review Algebra Spring 0 Algebra Semester Review Spring 0 Select the best answer for all questions. For questions through use the
More informationIntermediate Math Circles for Wednesday 13 October 2010
University of Waterloo Faculty of Mathematics entre for ducation in Mathematics and omputing Intermediate Math ircles for Wednesday 13 October 2010 2. Intermediate Week 1 roblem Set 1: Solving More roblems
More informationMath 0095: Developmental Mathematics Emporium
Math 0095: Developmental Mathematics Emporium Course Titles: Credit hours: Prerequisites: Math 0099: Early Foundations of College Mathematics Math 0100: Foundations of College Mathematics Math 0101: Foundations
More informationUnit 8. ANALYTIC GEOMETRY.
Unit 8. ANALYTIC GEOMETRY. 1. VECTORS IN THE PLANE A vector is a line segment running from point A (tail) to point B (head). 1.1 DIRECTION OF A VECTOR The direction of a vector is the direction of the
More informationACT Math Homework Math 1 60 Minutes 60 Questions
DIRECTIONS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document. ACT Math Homework Math 1 60 Minutes 60 Questions Note: Unless otherwise stated,
More informationMath 4310 Solutions to homework 7 Due 10/27/16
Math 4310 Solutions to homework 7 Due 10/27/16 1. Find the gcd of x 3 + x 2 + x + 1 and x 5 + 2x 3 + x 2 + x + 1 in Rx. Use the Euclidean algorithm: x 5 + 2x 3 + x 2 + x + 1 = (x 3 + x 2 + x + 1)(x 2 x
More informationCongratulations on being placed in the GSE Accelerated Analytic Geometry B/Advanced Algebra class for the school year!
Dear Student: Congratulations on being placed in the GSE Accelerated Analytic Geometry B/Advanced Algebra class for the 0-09 school year! This is a fast-paced and rigorous college-preparatory math course
More information0.1 Rational Canonical Forms
We have already seen that it is useful and simpler to study linear systems using matrices. But matrices are themselves cumbersome, as they are stuffed with many entries, and it turns out that it s best
More informationReid State Technical College
Reid State Technical College I. COURSE PREFIX, NUMBER, TITLE MTH 098 D - Elementary Algebra II. COURSE HOURS 3 Theory credit hours 0 Lab credit hours 0 Clinical credit hours 3 Contact hours III. CLASS
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE II. Wednesday, June 21, :15 to 4:15 p.m.
The University of the State of New York REGENTS HIGH SHOOL EXMINTION THREE-YER SEQUENE FOR HIGH SHOOL MTHEMTIS OURSE II Wednesday, June, 000 :5 to 4:5 p.m., only Notice... Scientific calculators must be
More informationAlgebra. Practice Pack
Algebra Practice Pack WALCH PUBLISHING Table of Contents Unit 1: Algebra Basics Practice 1 What Are Negative and Positive Numbers?... 1 Practice 2 Larger and Smaller Numbers................ 2 Practice
More informationChapter 4 Review Formal Geometry Name: Period: Due on the day of your test:
Multiple Choice Identif the choice that best completes the statement or answers the question. 1. In the figure, what is the m 3?. 97 B. 62 97 2 C. 48. 35 35 1 3 2. In the figure, PR SU and QT QU. What
More informationPrecalculus Summer Assignment 2015
Precalculus Summer Assignment 2015 The following packet contains topics and definitions that you will be required to know in order to succeed in CP Pre-calculus this year. You are advised to be familiar
More information5.1 Modelling Polynomials
5.1 Modelling Polynomials FOCUS Model, write, and classify polynomials. In arithmetic, we use Base Ten Blocks to model whole numbers. How would you model the number 234? In algebra, we use algebra tiles
More informationAlgebraic Expressions and Identities
ALGEBRAIC EXPRESSIONS AND IDENTITIES 137 Algebraic Expressions and Identities CHAPTER 9 9.1 What are Expressions? In earlier classes, we have already become familiar with what algebraic expressions (or
More informationReview for Geometry Midterm 2015: Chapters 1-5
Name Period Review for Geometry Midterm 2015: Chapters 1-5 Short Answer 1. What is the length of AC? 2. Tell whether a triangle can have sides with lengths 1, 2, and 3. 3. Danny and Dana start hiking from
More informationContents. List of Applications. Basic Concepts 1. iii
46891_01_FM_pi_pxviii.QXD 10/1/09 3:25 PM Page iii 1 List of Applications ix Preface xiii Basic Concepts 1 Unit 1A REVIEW OF OPERATIONS WITH WHOLE NUMBERS 2 1.1 Review of Basic Operations 2 1.2 Order of
More informationLyman Memorial High School. CP Pre-Calculus Prerequisite Packet. Name:
Lyman Memorial High School CP Pre-Calculus Prerequisite Packet 018 Name: Dear Pre-Calculus Student, Within this packet you will find mathematical concepts and skills covered in Algebra I, II and Geometry.
More information3.0 INTRODUCTION 3.1 OBJECTIVES 3.2 SOLUTION OF QUADRATIC EQUATIONS. Structure
UNIT 3 EQUATIONS Equations Structure 3.0 Introduction 3.1 Objectives 3.2 Solution of Quadratic Equations 3.3 Quadratic Formula 3.4 Cubic and Bioquadratic Equations 3.5 Answers to Check Your Progress 3.6
More informationMath 0095: Developmental Emporium Mathematics
Math 0095: Developmental Emporium Mathematics Course Titles: Credit hours: Prerequisites: Math 0099: Early Foundations of College Mathematics Math 0100: Foundations of College Mathematics Math 0101: Foundations
More informationVIII - Geometric Vectors
MTHEMTIS 0-NY-05 Vectors and Matrices Martin Huard Fall 07 VIII - Geometric Vectors. Find all ectors in the following parallelepiped that are equialent to the gien ectors. E F H G a) b) c) d) E e) f) F
More information8 th Grade Essential Learnings
8 th Grade Essential Learnings Subject: Math Grade/Course: 8 th Grade AG1 EL # Ex 1 Essential Learning Benchmark (framed by Standard) Learning Goal Topic (Report Card) NCTM Focal Points (Grade Level and/or
More information