# 04 Mathematics CO-SG-FLD Program for Licensing Assessments for Colorado Educators

Size: px
Start display at page:

Transcription

1 04 Mathematics CO-SG-FLD Program for Licensing Assessments for Colorado Educators

3 TEST FIELD 04: MATHEMATICS PART 1: GENERAL INFORMATION ABOUT THE PLACE AND TEST PREPARATION AN OVERVIEW OF THE PLACE Test Development Process Characteristics of the PLACE Test Administration Score Reports HOW TO PREPARE FOR THE TESTS Study the Test Objectives Identify Resources Develop Study Techniques Answer the Practice Questions Test Directions THE DAY OF THE TEST: HELPFUL HINTS Preparing for the Test Administration Test-Taking Tips PART 2: FIELD-SPECIFIC INFORMATION INTRODUCTION OBJECTIVES PRACTICE QUESTIONS ANSWER KEY

4 Part 1 of this study guide is contained in a separate PDF file. Click the link below to view or print this section: General Information About the PLACE and Test Preparation

6 OBJECTIVES TEST FIELD 04: MATHEMATICS Foundations of Mathematics Functions and Relations Measurement and Geometry Probability and Statistics Calculus and Discrete Mathematics FOUNDATIONS OF MATHEMATICS Understand number relationships and problem-solving strategies. using equivalent forms of a number (e.g., fraction, decimal, percent, scientific notation) to solve problems using ratios and proportions to solve problems analyzing and applying a variety of numerical problem-solving strategies (e.g., invented and standard algorithms, estimation, mental arithmetic) applying technology in problem-solving situations (e.g., graphing calculator) Understand the structure and properties of the real and complex number systems and their subsystems. analyzing similarities and differences among subsets of the real numbers (e.g., the rational numbers versus the real numbers) applying properties of the real numbers to arithmetic and algebraic operations solving problems involving multiple representations of the real numbers (e.g., roots, powers, infinite decimal expansions) using and performing operations on multiple representations of the complex numbers (e.g., algebraic, geometric, trigonometric, exponential) Understand the principles of and connections among number theory and linear and abstract algebra. applying concepts of prime numbers and divisibility (e.g., prime factorization, greatest common factor, least common multiple, modular arithmetic) analyzing and applying the properties and algebra of vectors and matrices to solve problems (e.g., applications to systems of equations, the geometry of matrix transformations, invertibility of matrices) identifying the basic properties of groups, rings, and fields 2-2 Program for Licensing Assessments for Colorado Educators Study Guide

7 Understand concepts of mathematical reasoning, communication, and the history of mathematics. translating among algebraic, geometric, numeric, graphic, and written modes of representing mathematical ideas converting between standard English language and mathematical language (e.g., notation, symbols) demonstrating knowledge of the language of mathematical statements and proof (e.g., contrapositive, proof by contradiction) assessing the validity of a mathematical argument recognizing the development and use of mathematics throughout history and across cultures FUNCTIONS AND RELATIONS Understand the properties of functions. evaluating functions (e.g., f(2), f(x + h)) analyzing the properties of functions (e.g., domain, range, even/odd) determining the effects of transformations (e.g., f(x + k), kf(x)) on the graphs of functions analyzing operations on functions (e.g., inverse, composition) connecting a variety of representations of functions (e.g., algebraic, geometric, graphic, tabular, numeric, verbal) Understand linear functions. analyzing the relationships among algebraic, geometric, graphic, tabular, and verbal representations of linear functions interpreting properties of linear equations in context (e.g., slope, intercepts) solving and analyzing systems of linear equations and inequalities using a variety of methods (e.g., analytical, graphical) applying linear equations and inequalities to model real-world phenomena and solve problems in other disciplines Understand quadratic functions. finding and analyzing real and complex roots of quadratic functions analyzing the relationships among algebraic, geometric, graphic, tabular, and verbal representations of quadratic functions solving and analyzing quadratic equations and systems of equations using a variety of methods (e.g., analytical, graphical) applying quadratic equations and inequalities to model real-world phenomena and solve problems in other disciplines Program for Licensing Assessments for Colorado Educators Study Guide 2-3

8 Understand polynomial, rational, absolute-value, and radical functions. finding and analyzing the real and complex roots of polynomial functions analyzing the relationships among algebraic, geometric, graphic, tabular, and verbal representations of polynomial, rational, absolute-value, and radical functions solving and analyzing polynomial, rational, absolute-value, and radical equations using a variety of methods (e.g., analytical, graphical) applying polynomial, rational, absolute-value, and radical functions to model realworld phenomena and solve problems in other disciplines Understand exponential, logarithmic, and trigonometric functions. applying the laws of exponents and logarithms to solve problems recognizing the inverse relationship between exponential and logarithmic functions and converting between the two forms analyzing connections among right triangle trigonometry, the unit circle, and trigonometric functions analyzing the relationships among algebraic, geometric, graphic, tabular, and verbal representations of exponential, logarithmic, and trigonometric functions solving and analyzing exponential, logarithmic, and trigonometric equations using a variety of methods (e.g., analytical, graphical) applying exponential, logarithmic, and trigonometric functions to model real-world phenomena and solve problems in other disciplines MEASUREMENT AND GEOMETRY Understand concepts, systems, and units of measurement. solving problems involving length, area, volume, capacity, time, temperature, angle, weight, and mass analyzing precision and error in measurement (e.g., percentage error, rounding error) converting within and between systems of measurement applying methods of indirect measurement (e.g., similarity, triangulation) Understand trigonometry and Euclidean geometry in two and three dimensions. using properties of points, lines, planes, and geometric figures to solve problems applying the Pythagorean theorem and right triangle trigonometry using similarity and congruence relationships analyzing connections between two- and three-dimensional figures (e.g., nets, projections, cross sections) 2-4 Program for Licensing Assessments for Colorado Educators Study Guide

9 Understand connections between algebra and geometry. representing figures in two- and three-dimensional coordinate systems analyzing translation, rotation, and reflection in the coordinate plane applying slope, distance, and midpoint formulas to investigate figures recognizing connections between algebra and geometry (e.g., conic sections, area representations of algebraic operations) Understand the axiomatic structure of geometry. identifying underlying principles of an axiomatic system recognizing and applying deductive and inductive reasoning making, testing, justifying, and proving conjectures and geometric constructions recognizing properties and examples of non-euclidean geometries PROBABILITY AND STATISTICS Understand the theory of probability. determining empirical probabilities through analysis of data modeling and solving problems using principles (e.g., dependence, independence, conditionality) and techniques (e.g., tree diagrams, combinatorics, area models) of theoretical probability recognizing connections between theoretical and empirical probability applying binomial, uniform, and normal distributions to problem-solving situations Understand descriptive statistics. evaluating real-world situations to determine appropriate data-collection techniques constructing tables, charts, and graphs (e.g., box plots, histograms, scatter plots) to represent statistical data interpreting statistical data represented in tables, charts, and graphs (e.g., box plots, histograms, scatter plots) evaluating arguments and drawing conclusions based on a set of data Understand methods of data analysis. finding and interpreting percentiles, mean, median, mode, range, standard deviation, and variance recognizing the effects of data transformations on measures of central tendency and variability drawing conclusions about distributions of data based on statistical summaries applying technology (e.g., graphing calculator) to analyze a set of data using correlation to analyze the relationship between two sets of data Program for Licensing Assessments for Colorado Educators Study Guide 2-5

10 Understand inferential statistics. analyzing the effect of sampling techniques and sample size on the results of a statistical study (e.g., survey, experiment) interpreting confidence intervals formulating and testing hypotheses CALCULUS AND DISCRETE MATHEMATICS Understand limits, continuity, and average rates of change. investigating the limits of functions, infinite sequences, and series analyzing the asymptotic behavior of functions interpreting continuity and discontinuity geometrically and analytically interpreting average rate of change as the slope of a secant line Understand differentiation and its application to problem-solving situations. recognizing the derivative of a function as the limit of the slope of a secant line (e.g., the difference quotient) interpreting the derivative in context and as an instantaneous rate of change using first and second derivatives to investigate the behavior of a function using differentiation to analyze and solve problems Understand integration and its application to problem-solving situations. using algebraic and geometric techniques to approximate the area under a curve interpreting the definite integral as the area under a curve applying the fundamental theorem of calculus to analyze connections between integration and differentiation using integration to model and solve real-world problems Understand the fundamental principles of discrete mathematics. using recursive formulas and difference equations modeling problems using graph theory solving problems involving permutations and combinations demonstrating an understanding of proof by mathematical induction analyzing sequences and series and using them to model and solve problems 2-6 Program for Licensing Assessments for Colorado Educators Study Guide

11 PRACTICE QUESTIONS: MATHEMATICS SAMPLE MATHEMATICS FORMULAS Formula Description V = 1 3 Bh Volume of a right cone and a pyramid A = 4πr 2 V = 4 3 πr3 Surface area of a sphere Volume of a sphere 2 2 A = πr r + h Lateral surface area of a right circular cone S n = n 2 [2a + (n 1)d] = n a + a n 2 S n = a r n (1 ) 1 r Sum of an arithmetic series Sum of a geometric series n= 0 n ar a = 1, r < 1 Sum of an infinite geometric series r d = ( x x ) + ( y y ) Distance formula x 1 + x 2 2, y 1 + y 2 2 m = Δ y Δ x = y x a sin A = b sin B y x = c sin C c 2 = a 2 + b 2 2ab cos C Midpoint formula Slope Law of sines Law of cosines s 2 = n ( xi i=1 n x) 2 1 Variance s = rθ x = 2 b ± b 4ac 2a Arc length Quadratic formula Program for Licensing Assessments for Colorado Educators Study Guide 2-7

12 Calculators for the Mathematics Test (Test Field 04) You must bring your own graphing calculator to the administration. Only the brands and models listed in the current PLACE Registration Bulletin may be used. The approved calculator brands and models are subject to change. If there is a change, examinees will be notified. Administration staff will clear the memory of your calculator both before and after the test. Be sure you back up the memory on your calculator, including applications, to an external device before arriving at the test site. 1. Use the expression below to answer the question that follows. 1 a + bi + 1 a bi Which of the following is equivalent to the expression above where i is the imaginary unit? A. B. C. D. 2a a 2 + b 2 2a a 2 b 2 1 a 2 + b 2 1 a 2. If today is Thursday, what day of the week will it be 1000 days from today? A. Sunday B. Monday C. Tuesday D. Wednesday 2-8 Program for Licensing Assessments for Colorado Educators Study Guide

13 3. Use the formula below to answer the question that follows. F = G m 1 m 2 r 2 The formula above states Newton's law of gravitation where F represents the gravitational force, G is a universal constant, m 1 and m 2 represent the masses of 2 objects, and r represents the distance between the 2 objects. Which of the following statements describes this law? A. The gravitational force is directly proportional to the product of the masses of the 2 objects and inversely proportional to the square of the distance between the 2 objects. B. The gravitational force varies linearly with the masses of the 2 objects and quadratically with the distance between the 2 objects. C. The gravitational force is inversely proportional to the product of the masses of the 2 objects and directly proportional to the square of the distance between the 2 objects. D. The gravitational force varies linearly with the masses of the 2 objects and exponentially with the distance between the 2 objects. 4. Given that f(x) = 1 x, which of the following is equivalent to 2f(3x + 1)? A. 8 6x B. 6x C. 4 6x D x 6x 2 Program for Licensing Assessments for Colorado Educators Study Guide 2-9

14 5. Use the table below to answer the question that follows. x f(x) 0 K If f(x) is a function of the form f(x) = ax 2 + bx + c, then which of the following expressions represents the coefficient a? A. B. C. D. 10 K K K K Program for Licensing Assessments for Colorado Educators Study Guide

15 6. Use the diagram below to answer the question that follows. q c A chord of length c subtends central angle θ on a unit circle. Which of the following equations represents the relationship between θ and c? A. c = sin θ B. c = sec θ C. c = 2 sin θ 2 D. c = 2 sec θ 2 Program for Licensing Assessments for Colorado Educators Study Guide 2-11

16 7. Use the diagram below to answer the question that follows. A carpenter uses a large metal square that forms a right angle as shown above to find and mark a diameter line on a circular tabletop. Which of the following theorems justifies this measurement technique? A. The measure of an inscribed angle is equal to half the measure of the inscribed arc. B. The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc. C. A diameter that is perpendicular to a chord bisects the chord and its arc. D. In the same circle or in congruent circles, 2 minor arcs are congruent if and only if their central angles are congruent. 8. PQR has coordinates P(0,0), Q(2a,0), and R(2a,4a). If PQR is rotated 90 counterclockwise about the origin to form P'Q'R', what are the coordinates of point R? A. ( 2a, 4a) B. ( 2a, 4a) C. ( 4a, 2a) D. ( 4a, 2a) 2-12 Program for Licensing Assessments for Colorado Educators Study Guide

17 9. A coin is tossed 10 times, yielding 4 heads. The same coin is tossed 1000 times, yielding 492 heads. Which of the following statements best explains these results? A. The theoretical probability is an upper bound for the empirical probability. B. The longer the coin is tossed, the more reliable the theoretical probability becomes at predicting the next outcome. C. As the number of trials increases, the empirical probability becomes arbitrarily close to the theoretical probability. D. Theoretical probability is based on mathematical models, and hence it can never be as exact as empirical probability. 10. A national restaurant chain provides self-addressed comment cards on the tables of their restaurants in a sampling of major cities. Which of the following changes would most effectively make the information gained from this survey more representative of all customers' experiences? A. Discard data from the smaller cities involved in the survey. B. Administer the survey over the Internet instead of on paper. C. Provide an incentive for customers to fill out the cards. D. Provide comment cards only to customers who request them. Program for Licensing Assessments for Colorado Educators Study Guide 2-13

18 11. What is the average rate of change of the function F(x) = 2x over the interval x = 1 to x = 2? A. 4 B. 2 C. 2 D Use the diagram below to answer the question that follows. x 100 4x x The diagram shows the dimensional restrictions for a shipping box. Which of the following equations should be solved to find the value of x that maximizes the volume of the box? A x = 0 B. 200x 12x 2 = 0 C. 100x 2 4x 3 = 0 D. 33.3x 3 x 4 = Program for Licensing Assessments for Colorado Educators Study Guide

19 ANSWER KEY: MATHEMATICS Question Number Correct Response Objective 1. A Understand the structure and properties of the real and complex number systems and their subsystems. 2. D Understand the principles of and connections among number theory and linear and abstract algebra. 3. A Understand concepts of mathematical reasoning, communication, and the history of mathematics. 4. B Understand the properties of functions. 5. D Understand quadratic functions. 6. C Understand exponential, logarithmic, and trigonometric functions. 7. A Understand concepts, systems, and units of measurement. 8. D Understand connections between algebra and geometry. 9. C Understand the theory of probability. 10. C Understand inferential statistics. 11. C Understand limits, continuity, and average rates of change. 12. B Understand differentiation and its application to problem-solving situations. Program for Licensing Assessments for Colorado Educators Study Guide 2-15

### NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS

NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS TEST DESIGN AND FRAMEWORK September 2014 Authorized for Distribution by the New York State Education Department This test design and framework document

### Prentice Hall Algebra 2 2011 Correlated to: Colorado P-12 Academic Standards for High School Mathematics, Adopted 12/2009

Content Area: Mathematics Grade Level Expectations: High School Standard: Number Sense, Properties, and Operations Understand the structure and properties of our number system. At their most basic level

### MATH BOOK OF PROBLEMS SERIES. New from Pearson Custom Publishing!

MATH BOOK OF PROBLEMS SERIES New from Pearson Custom Publishing! The Math Book of Problems Series is a database of math problems for the following courses: Pre-algebra Algebra Pre-calculus Calculus Statistics

### South Carolina College- and Career-Ready (SCCCR) Pre-Calculus

South Carolina College- and Career-Ready (SCCCR) Pre-Calculus Key Concepts Arithmetic with Polynomials and Rational Expressions PC.AAPR.2 PC.AAPR.3 PC.AAPR.4 PC.AAPR.5 PC.AAPR.6 PC.AAPR.7 Standards Know

### Curriculum Map by Block Geometry Mapping for Math Block Testing 2007-2008. August 20 to August 24 Review concepts from previous grades.

Curriculum Map by Geometry Mapping for Math Testing 2007-2008 Pre- s 1 August 20 to August 24 Review concepts from previous grades. August 27 to September 28 (Assessment to be completed by September 28)

### Algebra and Geometry Review (61 topics, no due date)

Course Name: Math 112 Credit Exam LA Tech University Course Code: ALEKS Course: Trigonometry Instructor: Course Dates: Course Content: 159 topics Algebra and Geometry Review (61 topics, no due date) Properties

### Current Standard: Mathematical Concepts and Applications Shape, Space, and Measurement- Primary

Shape, Space, and Measurement- Primary A student shall apply concepts of shape, space, and measurement to solve problems involving two- and three-dimensional shapes by demonstrating an understanding of:

### KEANSBURG SCHOOL DISTRICT KEANSBURG HIGH SCHOOL Mathematics Department. HSPA 10 Curriculum. September 2007

KEANSBURG HIGH SCHOOL Mathematics Department HSPA 10 Curriculum September 2007 Written by: Karen Egan Mathematics Supervisor: Ann Gagliardi 7 days Sample and Display Data (Chapter 1 pp. 4-47) Surveys and

### DELAWARE MATHEMATICS CONTENT STANDARDS GRADES 9-10. PAGE(S) WHERE TAUGHT (If submission is not a book, cite appropriate location(s))

Prentice Hall University of Chicago School Mathematics Project: Advanced Algebra 2002 Delaware Mathematics Content Standards (Grades 9-10) STANDARD #1 Students will develop their ability to SOLVE PROBLEMS

### MATH. ALGEBRA I HONORS 9 th Grade 12003200 ALGEBRA I HONORS

* Students who scored a Level 3 or above on the Florida Assessment Test Math Florida Standards (FSA-MAFS) are strongly encouraged to make Advanced Placement and/or dual enrollment courses their first choices

### 089 Mathematics (Elementary)

089 Mathematics (Elementary) MI-SG-FLD089-07 TABLE OF CONTENTS PART 1: General Information About the MTTC Program and Test Preparation OVERVIEW OF THE TESTING PROGRAM... 1-1 Contact Information Test Development

### Higher Education Math Placement

Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication

### Big Ideas in Mathematics

Big Ideas in Mathematics which are important to all mathematics learning. (Adapted from the NCTM Curriculum Focal Points, 2006) The Mathematics Big Ideas are organized using the PA Mathematics Standards

### PCHS ALGEBRA PLACEMENT TEST

MATHEMATICS Students must pass all math courses with a C or better to advance to the next math level. Only classes passed with a C or better will count towards meeting college entrance requirements. If

### Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks

Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks Welcome to Thinkwell s Homeschool Precalculus! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson

### TExMaT I Texas Examinations for Master Teachers. Preparation Manual. 089 Master Mathematics Teacher 8 12

TExMaT I Texas Examinations for Master Teachers Preparation Manual 089 Master Mathematics Teacher 8 12 Copyright 2006 by the Texas Education Agency (TEA). All rights reserved. The Texas Education Agency

### Precalculus REVERSE CORRELATION. Content Expectations for. Precalculus. Michigan CONTENT EXPECTATIONS FOR PRECALCULUS CHAPTER/LESSON TITLES

Content Expectations for Precalculus Michigan Precalculus 2011 REVERSE CORRELATION CHAPTER/LESSON TITLES Chapter 0 Preparing for Precalculus 0-1 Sets There are no state-mandated Precalculus 0-2 Operations

### Math Course Descriptions & Student Learning Outcomes

Math Course Descriptions & Student Learning Outcomes Table of Contents MAC 100: Business Math... 1 MAC 101: Technical Math... 3 MA 090: Basic Math... 4 MA 095: Introductory Algebra... 5 MA 098: Intermediate

PRE-CALCULUS GRADE 12 [C] Communication Trigonometry General Outcome: Develop trigonometric reasoning. A1. Demonstrate an understanding of angles in standard position, expressed in degrees and radians.

Accelerated Mathematics 3 This is a course in precalculus and statistics, designed to prepare students to take AB or BC Advanced Placement Calculus. It includes rational, circular trigonometric, and inverse

### MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education)

MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,

### TExES Texas Examinations of Educator Standards. Preparation Manual. 135 Mathematics 8 12

TExES Texas Examinations of Educator Standards Preparation Manual 135 Mathematics 8 1 Copyright 010 by Texas Education Agency (TEA). All rights reserved. The Texas Education Agency logo and TEA are registered

### MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab

MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab MATH 0110 is established to accommodate students desiring non-course based remediation in developmental mathematics. This structure will

### Prentice Hall Mathematics: Algebra 2 2007 Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary)

Core Standards of the Course Standard 1 Students will acquire number sense and perform operations with real and complex numbers. Objective 1.1 Compute fluently and make reasonable estimates. 1. Simplify

### Pre-Calculus Semester 1 Course Syllabus

Pre-Calculus Semester 1 Course Syllabus The Plano ISD eschool Mission is to create a borderless classroom based on a positive student-teacher relationship that fosters independent, innovative critical

Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express

### Mathematics Georgia Performance Standards

Mathematics Georgia Performance Standards K-12 Mathematics Introduction The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by

### TExMaT I Texas Examinations for Master Teachers. Preparation Manual. 088 Master Mathematics Teacher 4 8

TExMaT I Texas Examinations for Master Teachers Preparation Manual 088 Master Mathematics Teacher 4 8 Copyright 2006 by the Texas Education Agency (TEA). All rights reserved. The Texas Education Agency

### Mathematics (MAT) MAT 061 Basic Euclidean Geometry 3 Hours. MAT 051 Pre-Algebra 4 Hours

MAT 051 Pre-Algebra Mathematics (MAT) MAT 051 is designed as a review of the basic operations of arithmetic and an introduction to algebra. The student must earn a grade of C or in order to enroll in MAT

### Glencoe. correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 3-3, 5-8 8-4, 8-7 1-6, 4-9

Glencoe correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 STANDARDS 6-8 Number and Operations (NO) Standard I. Understand numbers, ways of representing numbers, relationships among numbers,

### Algebra I Credit Recovery

Algebra I Credit Recovery COURSE DESCRIPTION: The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics,

### Algebra 1 Course Title

Algebra 1 Course Title Course- wide 1. What patterns and methods are being used? Course- wide 1. Students will be adept at solving and graphing linear and quadratic equations 2. Students will be adept

### Prentice Hall: Middle School Math, Course 1 2002 Correlated to: New York Mathematics Learning Standards (Intermediate)

New York Mathematics Learning Standards (Intermediate) Mathematical Reasoning Key Idea: Students use MATHEMATICAL REASONING to analyze mathematical situations, make conjectures, gather evidence, and construct

### In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data.

MATHEMATICS: THE LEVEL DESCRIPTIONS In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. Attainment target

### GRADES 7, 8, AND 9 BIG IDEAS

Table 1: Strand A: BIG IDEAS: MATH: NUMBER Introduce perfect squares, square roots, and all applications Introduce rational numbers (positive and negative) Introduce the meaning of negative exponents for

### X On record with the USOE.

Textbook Alignment to the Utah Core Algebra 2 Name of Company and Individual Conducting Alignment: Chris McHugh, McHugh Inc. A Credential Sheet has been completed on the above company/evaluator and is

### AMSCO S Ann Xavier Gantert

AMSCO S Integrated ALGEBRA 1 Ann Xavier Gantert AMSCO SCHOOL PUBLICATIONS, INC. 315 HUDSON STREET, NEW YORK, N.Y. 10013 Dedication This book is dedicated to Edward Keenan who left a profound influence

### Sequence of Mathematics Courses

Sequence of ematics Courses Where do I begin? Associates Degree and Non-transferable Courses (For math course below pre-algebra, see the Learning Skills section of the catalog) MATH M09 PRE-ALGEBRA 3 UNITS

### HIGH SCHOOL: GEOMETRY (Page 1 of 4)

HIGH SCHOOL: GEOMETRY (Page 1 of 4) Geometry is a complete college preparatory course of plane and solid geometry. It is recommended that there be a strand of algebra review woven throughout the course

### Estimated Pre Calculus Pacing Timeline

Estimated Pre Calculus Pacing Timeline 2010-2011 School Year The timeframes listed on this calendar are estimates based on a fifty-minute class period. You may need to adjust some of them from time to

### Florida Math for College Readiness

Core Florida Math for College Readiness Florida Math for College Readiness provides a fourth-year math curriculum focused on developing the mastery of skills identified as critical to postsecondary readiness

### Credit Number Lecture Lab / Shop Clinic / Co-op Hours. MAC 224 Advanced CNC Milling 1 3 0 2. MAC 229 CNC Programming 2 0 0 2

MAC 224 Advanced CNC Milling 1 3 0 2 This course covers advanced methods in setup and operation of CNC machining centers. Emphasis is placed on programming and production of complex parts. Upon completion,

### Chapter 111. Texas Essential Knowledge and Skills for Mathematics. Subchapter B. Middle School

Middle School 111.B. Chapter 111. Texas Essential Knowledge and Skills for Mathematics Subchapter B. Middle School Statutory Authority: The provisions of this Subchapter B issued under the Texas Education

### Geometry Course Summary Department: Math. Semester 1

Geometry Course Summary Department: Math Semester 1 Learning Objective #1 Geometry Basics Targets to Meet Learning Objective #1 Use inductive reasoning to make conclusions about mathematical patterns Give

### The Australian Curriculum Mathematics

The Australian Curriculum Mathematics Mathematics ACARA The Australian Curriculum Number Algebra Number place value Fractions decimals Real numbers Foundation Year Year 1 Year 2 Year 3 Year 4 Year 5 Year

### Math Placement Test Study Guide. 2. The test consists entirely of multiple choice questions, each with five choices.

Math Placement Test Study Guide General Characteristics of the Test 1. All items are to be completed by all students. The items are roughly ordered from elementary to advanced. The expectation is that

COURSE SYLLABUS Pre-Calculus A/B Last Modified: April 2015 Course Description: In this year-long Pre-Calculus course, students will cover topics over a two semester period (as designated by A and B sections).

### Pre-Algebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems

Academic Content Standards Grade Eight Ohio Pre-Algebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small

### Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.

Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used

### Prentice Hall Connected Mathematics 2, 7th Grade Units 2009

Prentice Hall Connected Mathematics 2, 7th Grade Units 2009 Grade 7 C O R R E L A T E D T O from March 2009 Grade 7 Problem Solving Build new mathematical knowledge through problem solving. Solve problems

### Week 1 Chapter 1: Fundamentals of Geometry. Week 2 Chapter 1: Fundamentals of Geometry. Week 3 Chapter 1: Fundamentals of Geometry Chapter 1 Test

Thinkwell s Homeschool Geometry Course Lesson Plan: 34 weeks Welcome to Thinkwell s Homeschool Geometry! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson plan

### DRAFT. Algebra 1 EOC Item Specifications

DRAFT Algebra 1 EOC Item Specifications The draft Florida Standards Assessment (FSA) Test Item Specifications (Specifications) are based upon the Florida Standards and the Florida Course Descriptions as

### 10 th Grade Math Special Education Course of Study

10 th Grade Math Special Education Course of Study Findlay City Schools 2006 Table of Contents 1. Findlay City Schools Mission Statement 2. 10 th Grade Math Curriculum Map 3. 10 th Grade Math Indicators

### South Carolina College- and Career-Ready (SCCCR) Algebra 1

South Carolina College- and Career-Ready (SCCCR) Algebra 1 South Carolina College- and Career-Ready Mathematical Process Standards The South Carolina College- and Career-Ready (SCCCR) Mathematical Process

### TExMaT I Texas Examinations for Master Teachers. Preparation Manual. 087 Master Mathematics Teacher EC 4

TExMaT I Texas Examinations for Master Teachers Preparation Manual 087 Master Mathematics Teacher EC 4 Copyright 2006 by the Texas Education Agency (TEA). All rights reserved. The Texas Education Agency

### Diablo Valley College Catalog 2014-2015

Mathematics MATH Michael Norris, Interim Dean Math and Computer Science Division Math Building, Room 267 Possible career opportunities Mathematicians work in a variety of fields, among them statistics,

### CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREER-READY FOUNDATIONS IN ALGEBRA

We Can Early Learning Curriculum PreK Grades 8 12 INSIDE ALGEBRA, GRADES 8 12 CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREER-READY FOUNDATIONS IN ALGEBRA April 2016 www.voyagersopris.com Mathematical

### The program also provides supplemental modules on topics in geometry and probability and statistics.

Algebra 1 Course Overview Students develop algebraic fluency by learning the skills needed to solve equations and perform important manipulations with numbers, variables, equations, and inequalities. Students

### Mathematics. GCSE subject content and assessment objectives

Mathematics GCSE subject content and assessment objectives June 2013 Contents Introduction 3 Subject content 4 Assessment objectives 11 Appendix: Mathematical formulae 12 2 Introduction GCSE subject criteria

### PHILOSOPHY OF THE MATHEMATICS DEPARTMENT

PHILOSOPHY OF THE MATHEMATICS DEPARTMENT The Lemont High School Mathematics Department believes that students should develop the following characteristics: Understanding of concepts and procedures Building

### Dear Accelerated Pre-Calculus Student:

Dear Accelerated Pre-Calculus Student: I am very excited that you have decided to take this course in the upcoming school year! This is a fastpaced, college-preparatory mathematics course that will also

### Geometry. Higher Mathematics Courses 69. Geometry

The fundamental purpose of the course is to formalize and extend students geometric experiences from the middle grades. This course includes standards from the conceptual categories of and Statistics and

### North Carolina Math 2

Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4.

### Algebra 2 Chapter 1 Vocabulary. identity - A statement that equates two equivalent expressions.

Chapter 1 Vocabulary identity - A statement that equates two equivalent expressions. verbal model- A word equation that represents a real-life problem. algebraic expression - An expression with variables.

### Birmingham City Schools

Activity 1 Classroom Rules & Regulations Policies & Procedures Course Curriculum / Syllabus LTF Activity: Interval Notation (Precal) 2 Pre-Assessment 3 & 4 1.2 Functions and Their Properties 5 LTF Activity:

### Mathematics programmes of study: key stage 4. National curriculum in England

Mathematics programmes of study: key stage 4 National curriculum in England July 2014 Contents Purpose of study 3 Aims 3 Information and communication technology (ICT) 4 Spoken language 4 Working mathematically

### Appendix 3 IB Diploma Programme Course Outlines

Appendix 3 IB Diploma Programme Course Outlines The following points should be addressed when preparing course outlines for each IB Diploma Programme subject to be taught. Please be sure to use IBO nomenclature

### GEOMETRY CONCEPT MAP. Suggested Sequence:

CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons

### Mathematics: Content Knowledge

The Praxis Study Companion Mathematics: Content Knowledge 5161 www.ets.org/praxis Welcome to the Praxis Study Companion Welcome to the Praxis Study Companion Prepare to Show What You Know You have been

### Algebra Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the 2012-13 school year.

This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continually updating and improving these tools to better serve teachers. Algebra

### Functional Math II. Information CourseTitle. Types of Instruction

Functional Math II Course Outcome Summary Riverdale School District Information CourseTitle Functional Math II Credits 0 Contact Hours 135 Instructional Area Middle School Instructional Level 8th Grade

### http://www.aleks.com Access Code: RVAE4-EGKVN Financial Aid Code: 6A9DB-DEE3B-74F51-57304

MATH 1340.04 College Algebra Location: MAGC 2.202 Meeting day(s): TR 7:45a 9:00a, Instructor Information Name: Virgil Pierce Email: piercevu@utpa.edu Phone: 665.3535 Teaching Assistant Name: Indalecio

### School of Mathematics, Computer Science and Engineering. Mathematics* Associate in Arts Degree COURSES, PROGRAMS AND MAJORS

Mathematics School of Mathematics, Computer Science and Engineering Dean: Lianna Zhao, MD Academic Chair: Miriam Castroconde Faculty: Miriam Castroconde; Terry Cheng; Howard Dachslager, PhD; Ilknur Erbas

### Algebra 1 Course Information

Course Information Course Description: Students will study patterns, relations, and functions, and focus on the use of mathematical models to understand and analyze quantitative relationships. Through

### Grade 6 Mathematics Assessment. Eligible Texas Essential Knowledge and Skills

Grade 6 Mathematics Assessment Eligible Texas Essential Knowledge and Skills STAAR Grade 6 Mathematics Assessment Mathematical Process Standards These student expectations will not be listed under a separate

### NEW MEXICO Grade 6 MATHEMATICS STANDARDS

PROCESS STANDARDS To help New Mexico students achieve the Content Standards enumerated below, teachers are encouraged to base instruction on the following Process Standards: Problem Solving Build new mathematical

### Biggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress

Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation

### Common Core Unit Summary Grades 6 to 8

Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity- 8G1-8G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations

### Algebra II. Weeks 1-3 TEKS

Algebra II Pacing Guide Weeks 1-3: Equations and Inequalities: Solve Linear Equations, Solve Linear Inequalities, Solve Absolute Value Equations and Inequalities. Weeks 4-6: Linear Equations and Functions:

### Number Sense and Operations

Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents

### Mathematics. Mathematics MATHEMATICS. 298 2015-16 Sacramento City College Catalog. Degree: A.S. Mathematics AS-T Mathematics for Transfer

MATH Degree: A.S. AS-T for Transfer Division of /Statistics & Engineering Anne E. Licciardi, Dean South Gym 220 916-558-2202 Associate in Science Degree Program Information The mathematics program provides

### Expression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds

Isosceles Triangle Congruent Leg Side Expression Equation Polynomial Monomial Radical Square Root Check Times Itself Function Relation One Domain Range Area Volume Surface Space Length Width Quantitative

### Algebra I. In this technological age, mathematics is more important than ever. When students

In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,

### New York State Student Learning Objective: Regents Geometry

New York State Student Learning Objective: Regents Geometry All SLOs MUST include the following basic components: Population These are the students assigned to the course section(s) in this SLO all students

### Algebra 2 Year-at-a-Glance Leander ISD 2007-08. 1st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks

Algebra 2 Year-at-a-Glance Leander ISD 2007-08 1st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks Essential Unit of Study 6 weeks 3 weeks 3 weeks 6 weeks 3 weeks 3 weeks

### Prentice Hall Mathematics Courses 1-3 Common Core Edition 2013

A Correlation of Prentice Hall Mathematics Courses 1-3 Common Core Edition 2013 to the Topics & Lessons of Pearson A Correlation of Courses 1, 2 and 3, Common Core Introduction This document demonstrates

### CURRICULUM FOR THE COMMON CORE SUBJECT OF MATHEMATICS

CURRICULUM FOR THE COMMON CORE SUBJECT OF Dette er ei omsetjing av den fastsette læreplanteksten. Læreplanen er fastsett på Nynorsk Established as a Regulation by the Ministry of Education and Research

### Algebra I Vocabulary Cards

Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression

### CRLS Mathematics Department Algebra I Curriculum Map/Pacing Guide

Curriculum Map/Pacing Guide page 1 of 14 Quarter I start (CP & HN) 170 96 Unit 1: Number Sense and Operations 24 11 Totals Always Include 2 blocks for Review & Test Operating with Real Numbers: How are

### Mathematics Pre-Test Sample Questions A. { 11, 7} B. { 7,0,7} C. { 7, 7} D. { 11, 11}

Mathematics Pre-Test Sample Questions 1. Which of the following sets is closed under division? I. {½, 1,, 4} II. {-1, 1} III. {-1, 0, 1} A. I only B. II only C. III only D. I and II. Which of the following

Academic Standards for Grades Pre K High School Pennsylvania Department of Education INTRODUCTION The Pennsylvania Core Standards in in grades PreK 5 lay a solid foundation in whole numbers, addition,

### MATHEMATICS Department Chair: Michael Cordova - mccordova@dcsdk12.org

MATHEMATICS Department Chair: Michael Cordova - mccordova@dcsdk12.org Course Offerings Grade 9 Algebra I Algebra II/Trig Honors Geometry Honors Geometry Grade 10 Integrated Math II (2014-2015 only) Algebra

### About Tutorials... 1 Algebra I... 2 Geometry... 3 Algebra II... 4 English I... 5 English II... 6 English III... 7

Outlines Texas Tutorials Apex Learning Texas Tutorials provide teachers with a solution to support all students in rising to the expectations established by the Texas state standards. With content developed

### Creating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities

Algebra 1, Quarter 2, Unit 2.1 Creating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned

### Prentice Hall MyMathLab Algebra 1, 2011

Prentice Hall MyMathLab Algebra 1, 2011 C O R R E L A T E D T O Tennessee Mathematics Standards, 2009-2010 Implementation, Algebra I Tennessee Mathematics Standards 2009-2010 Implementation Algebra I 3102

### A Correlation of Pearson Texas Geometry Digital, 2015

A Correlation of Pearson Texas Geometry Digital, 2015 To the Texas Essential Knowledge and Skills (TEKS) for Geometry, High School, and the Texas English Language Proficiency Standards (ELPS) Correlations

### of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property