MATH 150 Pre-Calculus
|
|
- Beverly Wood
- 5 years ago
- Views:
Transcription
1 MATH 150 Pre-Calculus Fall, 2014, WEEK 3 JoungDong Kim Week 3: 2B, 3A Chapter 2B. Solving Inequalities a < b a is less than b a b a is less than or equal to b a > b a is greater than b a b a is greater than or equal to b Notation 1. (a,b) represents the set of all real numbers x such that a < x < b. (All numbers between a and b) 2. [a,b] represents the set of all real numbers x such that a x b. (including two endpoints of interval) 3. The set (, ) is used to represent all real numbers. In summary open parentheses mean exclude the endpoint and square brackets mean include the endpoint. Ex1) Which of the following numbers ( 7, 5, 3, 1,0) are in the interval [ 5, 1), 1
2 Linear Inequalities To solve a linear inequality, isolate the variable in the same fashion as solving a linear equation. However, there is one major difference: Whenever you multiply or divide an inequality by a negative number, you must switch the inequality symbol (or direction). Rules for Inequalities (A,B and C: real numbers) 1. A B A+C B +C 2. A B A C B C 3. If C > 0, then A B CA CB 4. If C < 0, then A B CA CB 5. If A > 0, and B > 0 then A B 1 A 1 B 6. If A B and C D, then A+C B +D 2
3 Ex2) Solve the inequality 3x < 9x+4 Ex3) Solve for y: y 1 3 3y 5 > 1 3
4 Pair of Simultaneous Inequalities a < x < b means the number x is between a and b. More formally, we say that a < x and x < b. Ex4) Solve the inequalities 4 3x 2 < 13. 4
5 Ex5) Solve for x: x+4 < 2x 7 < 3 3x. 5
6 Absolute Value Inequalities We use the following properties to solve inequalities that involve absolute value. Properties of Absolute Value Inequalities 1. x < c c < x < c 2. x c c x c 3. x > c x < c or x > c 4. x c x c or x c Ex6) Solve the inequality x 5 < 2 6
7 Ex7) Solve the inequality 3x Ex8) Solve the inequality 3x
8 Nonlinear Inequalities If an inequality is not linear, 1. Move all terms to one side. If necessary, rewrite the inequality so that all nonzero terms appear on one side of the inequality sign. If the nonzero side of the inequality involves quotients, bring them to a common denominator. 2. Factor. Factor the nonzero side of the inequality. 3. Find the intervals. Determine the values for which each factor is zero. These numbers will divide the real line into intervals. List the intervals determined by these numbers. 4. Solve. To determine which, test a number in the interval by substituting it into the inequality. If the chosen number satisfies the inequality, then so does every other number in the interval, and if the number does not satisfy the inequality, then no other number from that interval will satisfy the inequality. Ex9) Solver the inequality x 2 5x+6 0 8
9 Ex10) Solve for x: x 2 4x > 12 Ex11) Solve for x: x 4 +3x 3 4x 2 0 9
10 Ex12) Solve: 1+x 1 x 1 Ex13) Solve for x: x < 2 x 1 10
11 Ex14) Solve: x+4 x 14 < 2 x 6 11
12 Chapter 3. Graphing Chapter 3A. Rectangular Coordinate System Rectangular Coordinate System (or Cartesian Coordinate System) (x,y) is called the coordinates of the point, which gives the horizontal and vertical distance of the point from the origin respectively. The point of intersection of the x-axis and the y-axis is the origin, (0,0), and the two axes divide the plane into four Quadrants, labeled I, II, III, and IV. Ex15) Plot the following points on a rectangular coordinate system. A(2, 3), B(0, 5), C( 4, 1), D(3, 0), E( 2, 4) 12
13 Ex16) Shade the regions given by each set a) { (x,y) x 0 } b) { (x,y) x > 1 } c) { (x,y) x > 1, 1 y 2 } 13
14 Definition Any set of ordered pairs is called a relation. The plot of every point associated with an ordered pair in the relation is called the graph of the relation. The set of all first elements in the ordered pairs is called the domain of the relation. The set of al second elements in the ordered pairs is called the range of the relation. In Ex15) In Ex16-a) In Ex16-c) 14
15 Distance Formula The distance between the points A(x 1,y 1 ) and B(x 2,y 2 ) in the plane is d(a,b) = (x 2 x 1 ) 2 +(y 2 y 1 ) 2 15
16 Ex17) Determine whether the points A( 2,1), B(5,1) and C(0,3) are the vertices of a right triangle 16
17 Midpoint Formula The midpoint of the line segment that connects points A(x 1,y 1 ) and B(x 2,y 2 ) is the point M(x,y) with coordinates ( x2 +x 1, y ) 2 +y Ex18) Find the midpoint of the line segment that connects the points ( 2,9) and (7, 3). 17
18 Ex19) If ( 5,8) is the midpoint of the line segment connecting A(3, 2) and B, find the coordinates of the other endpoint B. 18
19 Circles The set of all points P(x,y) that are a given fixed distance from a given fixed point is called a circle. The fixed distance, r, is called the radius and the fixed point C(h,k) is called thecenter. Equation of a circle with center (h,k) and the radius r is (Standard form) (x h) 2 +(y k) 2 = r 2 If center is (0,0) x 2 +y 2 = r 2 19
20 Ex20) Find the center and radius, and graph each equation a) x 2 +y 2 = 25 b) (x 2) 2 +(y +1) 2 = 25 Ex21) Write an equation for the circle with C(3, 5) and radius 2. 20
21 General form of an Equation of a Circle x 2 +y 2 +cx+dy +e = 0 Note. To find the center and radius of a circle that is in general form, we must write the equation in standard form. (by Completing the Square) 21
22 Ex22) Find the center and radius of the circle x 2 + y 2 + 2x 6y + 6 = 0. Graph the circle. Find domain and range. Ex23) Find the center and radius of the circle 3x 2 +3y 2 6x+12y+2 = 0. 22
23 Ex24) If A( 7,2) and B(5,8) are coordinates of a diameter of a circle. Write the equation for the circle. 23
Section 1.4 Circles. Objective #1: Writing the Equation of a Circle in Standard Form.
1 Section 1. Circles Objective #1: Writing the Equation of a Circle in Standard Form. We begin by giving a definition of a circle: Definition: A Circle is the set of all points that are equidistant from
More information1.3 Distance and Midpoint Formulas
Graduate Teacher Department of Mathematics San Diego State University Dynamical Systems Program August 29, 2011 In mathematics, a theorem is a statement that has been proven on the basis of previously
More informationMath ~ Exam #1 Review Guide* *This is only a guide, for your benefit, and it in no way replaces class notes, homework, or studying
Math 1050 2 ~ Exam #1 Review Guide* *This is only a guide, for your benefit, and it in no way replaces class notes, homework, or studying General Tips for Studying: 1. Review this guide, class notes, the
More informationSolve by factoring and applying the Zero Product Property. Review Solving Quadratic Equations. Three methods to solve equations of the
Topic 0: Review Solving Quadratic Equations Three methods to solve equations of the form ax 2 bx c 0. 1. Factoring the expression and applying the Zero Product Property 2. Completing the square and applying
More informationReview Solving Quadratic Equations. Solve by factoring and applying the Zero Product Property. Three methods to solve equations of the
Topic 0: Review Solving Quadratic Equations Three methods to solve equations of the form ax bx c 0. 1. Factoring the expression and applying the Zero Product Property. Completing the square and applying
More information9.7 Extension: Writing and Graphing the Equations
www.ck12.org Chapter 9. Circles 9.7 Extension: Writing and Graphing the Equations of Circles Learning Objectives Graph a circle. Find the equation of a circle in the coordinate plane. Find the radius and
More informationChapter 3. September 11, ax + b = 0.
Chapter 3 September 11, 2017 3.1 Solving equations Solving Linear Equations: These are equations that can be written as ax + b = 0. Move all the variables to one side of the equation and all the constants
More informationCoach Stones Expanded Standard Pre-Calculus Algorithm Packet Page 1 Section: P.1 Algebraic Expressions, Mathematical Models and Real Numbers
Coach Stones Expanded Standard Pre-Calculus Algorithm Packet Page 1 Section: P.1 Algebraic Expressions, Mathematical Models and Real Numbers CLASSIFICATIONS OF NUMBERS NATURAL NUMBERS = N = {1,2,3,4,...}
More informationWhen using interval notation use instead of open circles, and use instead of solid dots.
P.1 Real Numbers PreCalculus P.1 REAL NUMBERS Learning Targets for P1 1. Describe an interval on the number line using inequalities. Describe an interval on the number line using interval notation (closed
More informationThe Coordinate Plane; Graphs of Equations of Two Variables. A graph of an equation is the set of all points which are solutions to the equation.
Hartfield College Algebra (Version 2015b - Thomas Hartfield) Unit TWO Page 1 of 30 Topic 9: The Coordinate Plane; Graphs of Equations of Two Variables A graph of an equation is the set of all points which
More informationCONTENTS COLLEGE ALGEBRA: DR.YOU
1 CONTENTS CONTENTS Textbook UNIT 1 LECTURE 1-1 REVIEW A. p. LECTURE 1- RADICALS A.10 p.9 LECTURE 1- COMPLEX NUMBERS A.7 p.17 LECTURE 1-4 BASIC FACTORS A. p.4 LECTURE 1-5. SOLVING THE EQUATIONS A.6 p.
More informationChapter 1 Linear Equations and Graphs
Chapter 1 Linear Equations and Graphs Section R Linear Equations and Inequalities Important Terms, Symbols, Concepts 1.1. Linear Equations and Inequalities A first degree, or linear, equation in one variable
More informationSolve by factoring and applying the Zero Product Property. Review Solving Quadratic Equations. Three methods to solve equations of the
Hartfield College Algebra (Version 2015b - Thomas Hartfield) Unit ONE Page - 1 - of 26 Topic 0: Review Solving Quadratic Equations Three methods to solve equations of the form ax 2 bx c 0. 1. Factoring
More informationKing Fahd University of Petroleum and Minerals Prep-Year Math Program Math (001) - Term 181 Recitation (1.1)
Recitation (1.1) Question 1: Find a point on the y-axis that is equidistant from the points (5, 5) and (1, 1) Question 2: Find the distance between the points P(2 x, 7 x) and Q( 2 x, 4 x) where x 0. Question
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 informationChapter P. Prerequisites. Slide P- 1. Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide P- 1 Chapter P Prerequisites 1 P.1 Real Numbers Quick Review 1. List the positive integers between -4 and 4.. List all negative integers greater than -4. 3. Use a calculator to evaluate the expression
More informationChapter 0 Preliminaries
Chapter 0 Preliminaries MA1101 Mathematics 1A Semester I Year 2017/2018 FTMD & FTI International Class Odd NIM (K-46) Lecturer: Dr. Rinovia Simanjuntak 0.1 Real Numbers and Logic Real Numbers Repeating
More informationChapter 1A -- Real Numbers. iff. Math Symbols: Sets of Numbers
Fry Texas A&M University! Fall 2016! Math 150 Notes! Section 1A! Page 1 Chapter 1A -- Real Numbers Math Symbols: iff or Example: Let A = {2, 4, 6, 8, 10, 12, 14, 16,...} and let B = {3, 6, 9, 12, 15, 18,
More informationMATH 150 Pre-Calculus
MATH 150 Pre-Calculus Fall, 2014, WEEK 2 JoungDong Kim Week 2: 1D, 1E, 2A Chapter 1D. Rational Expression. Definition of a Rational Expression A rational expression is an expression of the form p, where
More information9.5. Polynomial and Rational Inequalities. Objectives. Solve quadratic inequalities. Solve polynomial inequalities of degree 3 or greater.
Chapter 9 Section 5 9.5 Polynomial and Rational Inequalities Objectives 1 3 Solve quadratic inequalities. Solve polynomial inequalities of degree 3 or greater. Solve rational inequalities. Objective 1
More informationMTH103 Section 065 Exam 2. x 2 + 6x + 7 = 2. x 2 + 6x + 5 = 0 (x + 1)(x + 5) = 0
Absolute Value 1. (10 points) Find all solutions to the following equation: x 2 + 6x + 7 = 2 Solution: You first split this into two equations: x 2 + 6x + 7 = 2 and x 2 + 6x + 7 = 2, and solve each separately.
More informationUniversity of North Georgia Department of Mathematics
University of North Georgia Department of Mathematics Instructor: Berhanu Kidane Course: College Algebra Math 1111 Text Book: For this course we use the free e book by Stitz and Zeager with link: http://www.stitz-zeager.com/szca07042013.pdf
More informationPrep for College Algebra
Prep for College Algebra This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (219 topics + 85 additional topics)
More informationAn equation is a statement that states that two expressions are equal. For example:
Section 0.1: Linear Equations Solving linear equation in one variable: An equation is a statement that states that two expressions are equal. For example: (1) 513 (2) 16 (3) 4252 (4) 64153 To solve the
More informationPrep for College Algebra with Trigonometry
Prep for College Algebra with Trigonometry This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (246 topics +
More informationR1: Sets A set is a collection of objects sets are written using set brackets each object in onset is called an element or member
Chapter R Review of basic concepts * R1: Sets A set is a collection of objects sets are written using set brackets each object in onset is called an element or member Ex: Write the set of counting numbers
More informationMath Precalculus I University of Hawai i at Mānoa Spring
Math 135 - Precalculus I University of Hawai i at Mānoa Spring - 2013 Created for Math 135, Spring 2008 by Lukasz Grabarek and Michael Joyce Send comments and corrections to lukasz@math.hawaii.edu Contents
More information1 Solving Algebraic Equations
Arkansas Tech University MATH 1203: Trigonometry Dr. Marcel B. Finan 1 Solving Algebraic Equations This section illustrates the processes of solving linear and quadratic equations. The Geometry of Real
More informationBasic Equations and Inequalities
Hartfield College Algebra (Version 2017a - Thomas Hartfield) Unit ONE Page - 1 - of 45 Topic 0: Definition: Ex. 1 Basic Equations and Inequalities An equation is a statement that the values of two expressions
More informationA2 HW Imaginary Numbers
Name: A2 HW Imaginary Numbers Rewrite the following in terms of i and in simplest form: 1) 100 2) 289 3) 15 4) 4 81 5) 5 12 6) -8 72 Rewrite the following as a radical: 7) 12i 8) 20i Solve for x in simplest
More informationChapter 1: Precalculus Review
: Precalculus Review Math 115 17 January 2018 Overview 1 Important Notation 2 Exponents 3 Polynomials 4 Rational Functions 5 Cartesian Coordinates 6 Lines Notation Intervals: Interval Notation (a, b) (a,
More informationTable of contents. Jakayla Robbins & Beth Kelly (UK) Precalculus Notes Fall / 53
Table of contents The Cartesian Coordinate System - Pictures of Equations Your Personal Review Graphs of Equations with Two Variables Distance Equations of Circles Midpoints Quantifying the Steepness of
More informationOBJECTIVES UNIT 1. Lesson 1.0
OBJECTIVES UNIT 1 Lesson 1.0 1. Define "set," "element," "finite set," and "infinite set," "empty set," and "null set" and give two examples of each term. 2. Define "subset," "universal set," and "disjoint
More informationEquations and Inequalities. College Algebra
Equations and Inequalities College Algebra Radical Equations Radical Equations: are equations that contain variables in the radicand How to Solve a Radical Equation: 1. Isolate the radical expression on
More informationTopic Review Precalculus Handout 1.2 Inequalities and Absolute Value. by Kevin M. Chevalier
Topic Review Precalculus Handout 1.2 Inequalities and Absolute Value by Kevin M. Chevalier Real numbers are ordered where given the real numbers a, b, and c: a < b a is less than b Ex: 1 < 2 c > b c is
More informationMath Analysis Notes Mrs. Atkinson 1
Name: Math Analysis Chapter 7 Notes Day 6: Section 7-1 Solving Systems of Equations with Two Variables; Sections 7-1: Solving Systems of Equations with Two Variables Solving Systems of equations with two
More information1. Find the domain of the following functions. Write your answer using interval notation. (9 pts.)
MATH- Sample Eam Spring 7. Find the domain of the following functions. Write your answer using interval notation. (9 pts.) a. 9 f ( ) b. g ( ) 9 8 8. Write the equation of the circle in standard form given
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 informationThe Circle. 1 The equation of a circle. Nikos Apostolakis. Spring 2017
The Circle Nikos Apostolakis Spring 017 1 The equation of a circle Definition 1. Given a point C in the plane and a positive number r, the circle with center C and radius r, is the locus of points that
More informationMath Analysis/Honors Math Analysis Summer Assignment
Math Analysis/Honors Math Analysis Summer Assignment To be successful in Math Analysis or Honors Math Analysis, a full understanding of the topics listed below is required prior to the school year. To
More informationAlgebra II Vocabulary Alphabetical Listing. Absolute Maximum: The highest point over the entire domain of a function or relation.
Algebra II Vocabulary Alphabetical Listing Absolute Maximum: The highest point over the entire domain of a function or relation. Absolute Minimum: The lowest point over the entire domain of a function
More informationSummer Packet Pre-AP Algebra
Name: (5/11/17) Summer Packet Pre-AP Algebra 1-2018-19 To receive credit all work must be shown. There will be a test the first week back from summer on this packet. Any work done on additional paper must
More information2-7 Solving Quadratic Inequalities. ax 2 + bx + c > 0 (a 0)
Quadratic Inequalities In One Variable LOOKS LIKE a quadratic equation but Doesn t have an equal sign (=) Has an inequality sign (>,
More informationRev Name Date. . For example: 5x 3x
Name Date TI-84+ GC 7 Testing Polynomial Inequalities in One Variable Objectives: Review algebraic method for solving polynomial inequalities Review the signs of y-coordinates of points in each quadrant
More informationSUMMER MATH PACKET students. Entering Geometry-2B
SUMMER MATH PACKET students Entering Geometry-2B The problems in this packet have been selected to help you to review concepts in preparation for your next math class. Please complete the odd problems
More informationCHAPTERS 5-7 TRIG. FORMULAS PACKET
CHAPTERS 5-7 TRIG. FORMULAS PACKET PRE-CALCULUS SECTION 5-2 IDENTITIES Reciprocal Identities sin x = ( 1 / csc x ) csc x = ( 1 / sin x ) cos x = ( 1 / sec x ) sec x = ( 1 / cos x ) tan x = ( 1 / cot x
More informationMath Review for AP Calculus
Math Review for AP Calculus This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet
More information4 The Cartesian Coordinate System- Pictures of Equations
4 The Cartesian Coordinate System- Pictures of Equations Concepts: The Cartesian Coordinate System Graphs of Equations in Two Variables x-intercepts and y-intercepts Distance in Two Dimensions and the
More informationCheck boxes of Edited Copy of Sp Topics (was 261-pilot)
Check boxes of Edited Copy of 10023 Sp 11 253 Topics (was 261-pilot) Intermediate Algebra (2011), 3rd Ed. [open all close all] R-Review of Basic Algebraic Concepts Section R.2 Ordering integers Plotting
More informationBasic Equations and Inequalities. An equation is a statement that the values of two expressions are equal.
Hartfield College Algebra (Version 2018 - Thomas Hartfield) Unit ZERO Page - 1 - of 7 Topic 0: Definition: Ex. 1 Basic Equations and Inequalities An equation is a statement that the values of two expressions
More informationAlgebra I. abscissa the distance along the horizontal axis in a coordinate graph; graphs the domain.
Algebra I abscissa the distance along the horizontal axis in a coordinate graph; graphs the domain. absolute value the numerical [value] when direction or sign is not considered. (two words) additive inverse
More informationKing s Year 12 Medium Term Plan for LC1- A-Level Mathematics
King s Year 12 Medium Term Plan for LC1- A-Level Mathematics Modules Algebra, Geometry and Calculus. Materials Text book: Mathematics for A-Level Hodder Education. needed Calculator. Progress objectives
More informationBonus Section II: Solving Trigonometric Equations
Fry Texas A&M University Math 150 Spring 2017 Bonus Section II 260 Bonus Section II: Solving Trigonometric Equations (In your text this section is found hiding at the end of 9.6) For what values of x does
More informationCHAPTER 1: Review (See also the Precalculus notes at
CHAPTER 1: Review (See also the Precalculus notes at http://www.kkuniyuk.com) TOPIC 1: FUNCTIONS (Chapter 1: Review) 1.01 PART A: AN EXAMPLE OF A FUNCTION Consider a function f whose rule is given by f
More informationEvaluate algebraic expressions for given values of the variables.
Algebra I Unit Lesson Title Lesson Objectives 1 FOUNDATIONS OF ALGEBRA Variables and Expressions Exponents and Order of Operations Identify a variable expression and its components: variable, coefficient,
More informationCopyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 2/10
Prep for Calculus This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (281 topics + 125 additional topics) Real
More informationStudy Guide for Math 095
Study Guide for Math 095 David G. Radcliffe November 7, 1994 1 The Real Number System Writing a fraction in lowest terms. 1. Find the largest number that will divide into both the numerator and the denominator.
More informationIntermediate Algebra with Applications
Lakeshore Technical College 10-804-118 Intermediate Algebra with Applications Course Outcome Summary Course Information Alternate Title Description Total Credits 4 Total Hours 72 Pre/Corequisites Prerequisite
More informationMath 8 Honors Coordinate Geometry part 1 Unit Updated July 29, 2016
Reviewing the basics The number line A number line is a visual representation of all real numbers. Each of the images below are examples of number lines. The top left one includes only positive whole numbers,
More informationThe Distance Formula. The Midpoint Formula
Math 120 Intermediate Algebra Sec 9.1: Distance Midpoint Formulas The Distance Formula The distance between two points P 1 = (x 1, y 1 ) P 2 = (x 1, y 1 ), denoted by d(p 1, P 2 ), is d(p 1, P 2 ) = (x
More informationSolving and Graphing Inequalities
Solving and Graphing Inequalities Graphing Simple Inequalities: x > 3 When finding the solution for an equation we get one answer for x. (There is only one number that satisfies the equation.) For 3x 5
More informationCollege Algebra with Trigonometry
College Algebra with Trigonometry This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (556 topics + 614 additional
More informationCHAPTER 0: Preliminary Topics
(Exercises for Chapter 0: Preliminary Topics) E.0.1 CHAPTER 0: Preliminary Topics (A) means refer to Part A, (B) means refer to Part B, etc. (Calculator) means use a calculator. Otherwise, do not use a
More informationGlossary. Glossary 981. Hawkes Learning Systems. All rights reserved.
A Glossary Absolute value The distance a number is from 0 on a number line Acute angle An angle whose measure is between 0 and 90 Addends The numbers being added in an addition problem Addition principle
More information10.1. Square Roots and Square- Root Functions 2/20/2018. Exponents and Radicals. Radical Expressions and Functions
10 Exponents and Radicals 10.1 Radical Expressions and Functions 10.2 Rational Numbers as Exponents 10.3 Multiplying Radical Expressions 10.4 Dividing Radical Expressions 10.5 Expressions Containing Several
More informationP.1: Algebraic Expressions, Mathematical Models, and Real Numbers
Chapter P Prerequisites: Fundamental Concepts of Algebra Pre-calculus notes Date: P.1: Algebraic Expressions, Mathematical Models, and Real Numbers Algebraic expression: a combination of variables and
More informationGeneral Form: y = a n x n + a n 1 x n a 2 x 2 + a 1 x + a 0
Families of Functions Prepared by: Sa diyya Hendrickson Name: Date: Definition: function A function f is a rule that relates two sets by assigning to some element (e.g. x) in a set A exactly one element
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 informationMath Prep for Statics
Math Prep for Statics This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular
More informationCircles. Example 2: Write an equation for a circle if the enpoints of a diameter are at ( 4,5) and (6, 3).
Conics Unit Ch. 8 Circles Equations of Circles The equation of a circle with center ( hk, ) and radius r units is ( x h) ( y k) r. Example 1: Write an equation of circle with center (8, 3) and radius 6.
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 informationCOURSE SYLLABUS Part I Course Title: MATH College Algebra Credit Hours: 4, (4 Lecture 0 Lab G) OTM-TMM001
COURSE SYLLABUS Part I Course Title: MATH 1340 - College Algebra Credit Hours: 4, (4 Lecture 0 Lab G) OTM-TMM001 Course Description: College Algebra in conjunction with MATH 1350, Pre-Calculus, provides
More informationMath 1 packet for Coordinate Geometry part 1. Reviewing the basics. The coordinate plane
Math 1 packet for Coordinate Geometry part 1 Reviewing the basics The coordinate plane The coordinate plane (also called the Cartesian plane named after French mathematician Rene Descartes, who formalized
More informationMathematics 1 Lecture Notes Chapter 1 Algebra Review
Mathematics 1 Lecture Notes Chapter 1 Algebra Review c Trinity College 1 A note to the students from the lecturer: This course will be moving rather quickly, and it will be in your own best interests to
More informationSECTION 1.4: FUNCTIONS. (See p.40 for definitions of relations and functions and the Technical Note in Notes 1.24.) ( ) = x 2.
SECTION 1.4: FUNCTIONS (Section 1.4: Functions) 1.18 (See p.40 for definitions of relations and functions and the Technical Note in Notes 1.24.) Warning: The word function has different meanings in mathematics
More informationFoundations of Algebra/Algebra/Math I Curriculum Map
*Standards N-Q.1, N-Q.2, N-Q.3 are not listed. These standards represent number sense and should be integrated throughout the units. *For each specific unit, learning targets are coded as F for Foundations
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 informationDATE: MATH ANALYSIS 2 CHAPTER 12: VECTORS & DETERMINANTS
NAME: PERIOD: DATE: MATH ANALYSIS 2 MR. MELLINA CHAPTER 12: VECTORS & DETERMINANTS Sections: v 12.1 Geometric Representation of Vectors v 12.2 Algebraic Representation of Vectors v 12.3 Vector and Parametric
More informationMath Precalculus I University of Hawai i at Mānoa Spring
Math 135 - Precalculus I University of Hawai i at Mānoa Spring - 2014 Created for Math 135, Spring 2008 by Lukasz Grabarek and Michael Joyce Send comments and corrections to lukasz@math.hawaii.edu Contents
More informationChapter 2A - Solving Equations
- Chapter A Chapter A - Solving Equations Introduction and Review of Linear Equations An equation is a statement which relates two or more numbers or algebraic expressions. For example, the equation 6
More informationCLEP Precalculus - Problem Drill 02: Prerequisite Review
CLEP Precalculus - Problem Drill 02: Prerequisite Review No. 1 of 10 1. Given a right triangle with leg lengths 5 and 12, find the length of the hypotenuse. (A) 14 (B) 10 (C) 8 (D) 13 (E) 17 This is incorrect
More informationRegents Review Session #3 Functions
Regents Review Session #3 Functions A relation is a set of ordered pairs. A function is a relation in which each element of the domain corresponds t exactly one element in the range. (Each x value is paired
More informationExample. 171S Introduction to Graphing. January 06, Introduction to Graphing. Cartesian Coordinate System
MAT 171 Dr. Claude Moore, CFCC CHAPTER 1: Graphs, Functions, and Models 1.1 Introduction to Graphing 1.2 Functions and Graphs 1.3 Linear Functions, Slope, and Applications 1.4 Equations of Lines and Modeling
More informationSUMMER MATH PACKET. Geometry A COURSE 227
SUMMER MATH PACKET Geometry A COURSE 7 MATH SUMMER PACKET INSTRUCTIONS Attached you will find a packet of exciting math problems for your enjoyment over the summer. The purpose of the summer packet is
More informationAdvanced Math. ABSOLUTE VALUE - The distance of a number from zero; the positive value of a number. < 2 indexes draw 2 lines down like the symbol>
Advanced Math ABSOLUTE VALUE - The distance of a number from zero; the positive value of a number. < 2 indexes draw 2 lines down like the symbol> ALGEBRA - A branch of mathematics in which symbols, usually
More informationMATH 190 KHAN ACADEMY VIDEOS
MATH 10 KHAN ACADEMY VIDEOS MATTHEW AUTH 11 Order of operations 1 The Real Numbers (11) Example 11 Worked example: Order of operations (PEMDAS) 7 2 + (7 + 3 (5 2)) 4 2 12 Rational + Irrational Example
More informationMaths Higher Prelim Content
Maths Higher Prelim Content Straight Line Gradient of a line A(x 1, y 1 ), B(x 2, y 2 ), Gradient of AB m AB = y 2 y1 x 2 x 1 m = tanθ where θ is the angle the line makes with the positive direction of
More informationCheck boxes of Edited Copy of Sp Topics (was 217-pilot)
Check boxes of Edited Copy of 10024 Sp 11 213 Topics (was 217-pilot) College Algebra, 9th Ed. [open all close all] R-Basic Algebra Operations Section R.1 Integers and rational numbers Rational and irrational
More informationRising 8th Grade Math. Algebra 1 Summer Review Packet
Rising 8th Grade Math Algebra 1 Summer Review Packet 1. Clear parentheses using the distributive property. 2. Combine like terms within each side of the equal sign. Solving Multi-Step Equations 3. Add/subtract
More informationMATH 151 Engineering Mathematics I
MATH 151 Engineering Mathematics I Spring 2018, WEEK 1 JoungDong Kim Week 1 Vectors, The Dot Product, Vector Functions and Parametric Curves. Section 1.1 Vectors Definition. A Vector is a quantity that
More informationCourse Number 420 Title Algebra I Honors Grade 9 # of Days 60
Whitman-Hanson Regional High School provides all students with a high- quality education in order to develop reflective, concerned citizens and contributing members of the global community. Course Number
More informationWords to Review. Give an example of the vocabulary word. Numerical expression. Variable. Evaluate a variable expression. Variable expression
1 Words to Review Give an example of the vocabulary word. Numerical expression 5 12 Variable x Variable expression 3x 1 Verbal model Distance Rate p Time Evaluate a variable expression Evaluate the expression
More informationBishop Kelley High School Summer Math Program Course: Algebra II B
016 017 Summer Math Program Course: NAME: DIRECTIONS: Show all work in the packet. You may not use a calculator. No matter when you have math, this packet is due on the first day of class This material
More information8th Grade Math Definitions
8th Grade Math Definitions Absolute Value: 1. A number s distance from zero. 2. For any x, is defined as follows: x = x, if x < 0; x, if x 0. Acute Angle: An angle whose measure is greater than 0 and less
More informationChapter 8B - Trigonometric Functions (the first part)
Fry Texas A&M University! Spring 2016! Math 150 Notes! Section 8B-I! Page 79 Chapter 8B - Trigonometric Functions (the first part) Recall from geometry that if 2 corresponding triangles have 2 angles of
More informationOCR Maths FP1. Topic Questions from Papers. Complex Numbers. Answers
OCR Maths FP1 Topic Questions from Papers Complex Numbers Answers PhysicsAndMathsTutor.com . 1 (i) i Correct real and imaginary parts z* = i 1i Correct conjugate seen or implied Correct real and imaginary
More informationChapter 3 Differentiation Rules
Chapter 3 Differentiation Rules Derivative constant function if c is any real number, then Example: The Power Rule: If n is a positive integer, then Example: Extended Power Rule: If r is any real number,
More informationx and y, called the coordinates of the point.
P.1 The Cartesian Plane The Cartesian Plane The Cartesian Plane (also called the rectangular coordinate system) is the plane that allows you to represent ordered pairs of real numbers by points. It is
More informationInequalities. Some problems in algebra lead to inequalities instead of equations.
1.6 Inequalities Inequalities Some problems in algebra lead to inequalities instead of equations. An inequality looks just like an equation except that, in the place of the equal sign is one of these symbols:
More information