The problem of transition from school to university mathematics Student Survey E. Krause, F. Wetter, C. Nguyen Phuong (2015)

Honors 213 / Math 300. Second Hour Exam. Name

Honors 213 / Math 300 Second Hour Exam Name Monday, March 6, 2006 95 points (will be adjusted to 100 pts in the gradebook) Page 1 I. Some definitions (5 points each). Give formal definitions of the following:

Lesson 13: Angle Sum of a Triangle

Lesson 13: Angle Sum of a Triangle Classwork Concept Development 1 + 2 + 3 = 4 + 5 + 6 = 7 + 8 + 9 = 180 Note that the sum of angles 7 and 9 must equal 90 because of the known right angle in the right

35 Chapter CHAPTER 4: Mathematical Proof

35 Chapter 4 35 CHAPTER 4: Mathematical Proof Faith is different from proof; the one is human, the other is a gift of God. Justus ex fide vivit. It is this faith that God Himself puts into the heart. 21

lists at least 2 factors from 1, 2, 4, 5, 8, 10, 20, 40 factors/multiples P1 Continues process eg. gives a set of numbers whose sum is greater

1 6.66 B1 cao 2 0.4375 B1 cao 3 27 or 64 B1 cao 4 7.3225 M1 for 5.5225 or 1.8 5 ⅔ B1 oe 6 eg. 1, 2, 18 P1 Starts process eg. Lists at least 2 multiples from 9,18,27,36,45 or lists at least 2 factors from

P1-763.PDF Why Proofs?

P1-763.PDF Why Proofs? During the Iron Age men finally started questioning mathematics which eventually lead to the creating of proofs. People wanted to know how and why is math true, rather than just

Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper.

Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper. 12. What angle has the same measure as its complement? How do you know? 12. What is the

Transversals. What is a proof? A proof is logical argument in which each statement you make is backed up by a statement that is accepted true.

Chapter 2: Angles, Parallel Lines and Transversals Lesson 2.1: Writing a Proof Getting Ready: Your math teacher asked you to solve the equation: 4x 3 = 2x + 25. What is a proof? A proof is logical argument

CMA Geometry Unit 1 Introduction Week 2 Notes

CMA Geometry Unit 1 Introduction Week 2 Notes Assignment: 9. Defined Terms: Definitions betweenness of points collinear points coplanar points space bisector of a segment length of a segment line segment

Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions

Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions Quiz #1. Tuesday, 17 January, 2012. [10 minutes] 1. Given a line segment AB, use (some of) Postulates I V,

Suggested problems - solutions

Suggested problems - solutions Parallel lines Material for this section references College Geometry: A Discovery Approach, 2/e, David C. Kay, Addison Wesley, 2001. In particular, see section 4.1, pp 219-223.

PROOFS IN MATHEMATICS

Appendix 1 PROOFS IN MATHEMATICS Proofs are to Mathematics what calligraphy is to poetry. Mathematical works do consist of proofs just as poems do consist of characters. VLADIMIR ARNOLD A.1.1 Introduction

Math Number 842 Professor R. Roybal MATH History of Mathematics 24th October, Project 1 - Proofs

Math Number 842 Professor R. Roybal MATH 331 - History of Mathematics 24th October, 2017 Project 1 - Proofs Mathematical proofs are an important concept that was integral to the development of modern mathematics.

1. Introduction to commutative rings and fields

1. Introduction to commutative rings and fields Very informally speaking, a commutative ring is a set in which we can add, subtract and multiply elements so that the usual laws hold. A field is a commutative

1. Use what you know about congruent triangles to write a paragraph proof to justify that the opposite sides in the diagram are parallel.

Flow Chart and Paragraph Proofs SUGGESTED LEARNING STRATEGIES: Marking the Text, Prewriting, Self/Peer Revision, You know how to write two-column and paragraph proofs. In this activity you will use your

October 16, Geometry, the Common Core, and Proof. John T. Baldwin, Andreas Mueller. The motivating problem. Euclidean Axioms and Diagrams

October 16, 2012 Outline 1 2 3 4 5 Agenda 1 G-C0-1 Context. 2 Activity: Divide a line into n pieces -with string; via construction 3 Reflection activity (geometry/ proof/definition/ common core) 4 mini-lecture

Chapter. Triangles. Copyright Cengage Learning. All rights reserved.

Chapter 3 Triangles Copyright Cengage Learning. All rights reserved. 3.5 Inequalities in a Triangle Copyright Cengage Learning. All rights reserved. Inequalities in a Triangle Important inequality relationships

Neutral Geometry. October 25, c 2009 Charles Delman

Neutral Geometry October 25, 2009 c 2009 Charles Delman Taking Stock: where we have been; where we are going Set Theory & Logic Terms of Geometry: points, lines, incidence, betweenness, congruence. Incidence

7 th Grade Math Scope and Sequence Student Outcomes (Objectives Skills/Verbs)

own discovery of the Big BIG IDEA: How are different types of numbers used to represent real life situations? Why is it necessary to have different types of numbers for different situations? Pg 762 1-4(no

1 FUNDAMENTALS OF LOGIC NO.1 WHAT IS LOGIC Tatsuya Hagino hagino@sfc.keio.ac.jp lecture URL https://vu5.sfc.keio.ac.jp/slide/ 2 Course Summary What is the correct deduction? Since A, therefore B. It is

GCSE: Congruent Triangles Dr J Frost

GCSE: Congruent Triangles Dr J Frost (jfrost@tiffin.kingston.sch.uk) www.drfrostmaths.com GCSE Revision Pack Refs: 169, 170 Understand and use SSS, SAS, and conditions to prove the congruence of triangles

Hawai`i Post-Secondary Math Survey -- Content Items

Hawai`i Post-Secondary Math Survey -- Content Items Section I: Number sense and numerical operations -- Several numerical operations skills are listed below. Please rank each on a scale from 1 (not essential)

ACTIVITY 15 Continued Lesson 15-2

Continued PLAN Pacing: 1 class period Chunking the Lesson Examples A, B Try These A B #1 2 Example C Lesson Practice TEACH Bell-Ringer Activity Read the introduction with students and remind them of the

The Pythagorean Theorem & Special Right Triangles

Theorem 7.1 Chapter 7: Right Triangles & Trigonometry Sections 1 4 Name Geometry Notes The Pythagorean Theorem & Special Right Triangles We are all familiar with the Pythagorean Theorem and now we ve explored

Foundation Unit 6 topic test

Name: Foundation Unit 6 topic test Date: Time: 45 minutes Total marks available: 39 Total marks achieved: Questions Q1. The diagram shows a rectangle, a parallelogram and a triangle. (a) Mark with arrows

that if a b (mod m) and c d (mod m), then ac bd (mod m) soyou aren't allowed to use this fact!) A5. (a) Show that a perfect square must leave a remain

PUTNAM PROBLEM SOLVING SEMINAR WEEK 2 The Rules. You are not allowed to try a problem that you already know how to solve. These are way too many problems to consider. Just pick a few problems in one of

1. Introduction to commutative rings and fields

1. Introduction to commutative rings and fields Very informally speaking, a commutative ring is a set in which we can add, subtract and multiply elements so that the usual laws hold. A field is a commutative

Essential Question How can you cube a binomial? Work with a partner. Find each product. Show your steps. = (x + 1) Multiply second power.

4.2 Adding, Subtracting, and Multiplying Polynomials COMMON CORE Learning Standards HSA-APR.A.1 HSA-APR.C.4 HSA-APR.C.5 Essential Question How can you cube a binomial? Cubing Binomials Work with a partner.

Definitions, Axioms, Postulates, Propositions, and Theorems from Euclidean and Non-Euclidean Geometries by Marvin Jay Greenberg ( )

Definitions, Axioms, Postulates, Propositions, and Theorems from Euclidean and Non-Euclidean Geometries by Marvin Jay Greenberg (2005-02-16) Logic Rules (Greenberg): Logic Rule 1 Allowable justifications.

DISCOVERING GEOMETRY Over 6000 years ago, geometry consisted primarily of practical rules for measuring land and for

Name Period GEOMETRY Chapter One BASICS OF GEOMETRY Geometry, like much of mathematics and science, developed when people began recognizing and describing patterns. In this course, you will study many

Math 103 Finite Math with a Special Emphasis on Math & Art by Lun-Yi Tsai, Spring 2010, University of Miami

Math 103 Finite Math with a Special Emphasis on Math & rt by Lun-Yi Tsai, Spring 2010, University of Miami 1 Geometry notes 1.1 ngles and Parallel Lines efinition 1.1. We defined the complement of an acute

Maths home based learning

Maths home based learning Name: Maths Group: Date Given: HAND IN DATE: No excuses as a copy is available on the school s website http://ripleyacademy.org/index.php/curriculum/25-curriculum/69-mathsks4

End of Course Review

End of Course Review Geometry AIR Test Mar 14 3:07 PM Test blueprint with important areas: Congruence and Proof 33 39% Transformations, triangles (including ASA, SAS, SSS and CPCTC), proofs, coordinate/algebraic

triangles in neutral geometry three theorems of measurement

lesson 10 triangles in neutral geometry three theorems of measurement 112 lesson 10 in this lesson we are going to take our newly created measurement systems, our rulers and our protractors, and see what

3.2. Parallel Lines and Transversals

. Parallel Lines and Transversals Essential Question When two parallel lines are cut by a transversal, which of the resulting pairs of angles are congruent? Exploring Parallel Lines Work with a partner.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE II. Wednesday, August 16, :30 to 11:30 a.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II Wednesday, August 16, 000 8:30 to 11:30 a.m., only Notice... Scientific

3.2. Parallel Lines and Transversals

. Parallel Lines and Transversals COMMON CORE Learning Standard HSG-CO.C.9 Essential Question When two parallel lines are cut by a transversal, which of the resulting pairs of angles are congruent? Work

Parallel Lines, Transversals, and Angle Relationships

Module 2: Part 2 Congruence Parallel Lines, Transversals, and Angle Relationships parallel lines tranversal line vertical angles alternate interior angles alternate exterior angles consecutive interior

11. Prove that the Missing Strip Plane is an. 12. Prove the above proposition.

10 Pasch Geometries Definition (Pasch s Postulate (PP)) A metric geometry satisfies Pasch s Postulate (PP) if for any line l, any triangle ABC, and any point D l such that A D B, then either l AC or l

MAC-CPTM Situations Project

Prompt MAC-CPTM Situations Project Situation 51: Proof by Mathematical Induction Prepared at the University of Georgia Center for Proficiency in Teaching Mathematics 13 October 2006-Erik Tillema 22 February

NAME: Mathematics 133, Fall 2013, Examination 3

NAME: Mathematics 133, Fall 2013, Examination 3 INSTRUCTIONS: Work all questions, and unless indicated otherwise give reasons for your answers. If the problem does not explicitly state that the underlying

Euclid Geometry And Non-Euclid Geometry. Have you ever asked yourself why is it that if you walk to a specific place from

Hu1 Haotian Hu Dr. Boman Math 475W 9 November 2016 Euclid Geometry And Non-Euclid Geometry Have you ever asked yourself why is it that if you walk to a specific place from somewhere, you will always find

Dr Prya Mathew SJCE Mysore

1 2 3 The word Mathematics derived from two Greek words Manthanein means learning Techne means an art or technique So Mathematics means the art of learning related to disciplines or faculties disciplines

Example ( x.(p(x) Q(x))) ( x.p(x) x.q(x)) premise. 2. ( x.(p(x) Q(x))) -elim, 1 3. ( x.p(x) x.q(x)) -elim, x. P(x) x.

Announcements CS311H: Discrete Mathematics More Logic Intro to Proof Techniques Homework due next lecture Instructor: Işıl Dillig Instructor: Işıl Dillig, CS311H: Discrete Mathematics More Logic Intro

Grade 8 Mathematics Performance Level Descriptors

Limited A student performing at the Limited Level demonstrates a minimal command of Ohio s Learning Standards for Grade 8 Mathematics. A student at this level has an emerging ability to formulate and reason

Chapter 2 Preliminaries

Chapter 2 Preliminaries Where there is matter, there is geometry. Johannes Kepler (1571 1630) 2.1 Logic 2.1.1 Basic Concepts of Logic Let us consider A to be a non-empty set of mathematical objects. One

Lecture 3: Probability

Lecture 3: Probability 28th of October 2015 Lecture 3: Probability 28th of October 2015 1 / 36 Summary of previous lecture Define chance experiment, sample space and event Introduce the concept of the

Lesson 13: Angle Sum of a Triangle

Student Outcomes Students know the angle sum theorem for triangles; the sum of the interior angles of a triangle is always 180. Students present informal arguments to draw conclusions about the angle sum

MATHE 4800C FOUNDATIONS OF ALGEBRA AND GEOMETRY CLASS NOTES FALL 2011

MATHE 4800C FOUNDATIONS OF ALGEBRA AND GEOMETRY CLASS NOTES FALL 2011 MATTHEW AUTH, LECTURER OF MATHEMATICS 1. Foundations of Euclidean Geometry (Week 1) During the first weeks of the semester we will

5.5 Special Rights. A Solidify Understanding Task

SECONDARY MATH III // MODULE 5 MODELING WITH GEOMETRY 5.5 In previous courses you have studied the Pythagorean theorem and right triangle trigonometry. Both of these mathematical tools are useful when

of Nebraska - Lincoln

University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln MAT Exam Expository Papers Math in the Middle Institute Partnership 7-007 Pythagorean Triples Diane Swartzlander University

2. If two isosceles triangles have congruent vertex angles, then the triangles must be A. congruent B. right C. equilateral D.

1. If two angles of a triangle measure 56 and 68, the triangle is A. scalene B. isosceles C. obtuse D. right 2. If two isosceles triangles have congruent vertex angles, then the triangles must be A. congruent

Part 1: You are given the following system of two equations: x + 2y = 16 3x 4y = 2

Solving Systems of Equations Algebraically Teacher Notes Comment: As students solve equations throughout this task, have them continue to explain each step using properties of operations or properties

Geometry Problem Solving Drill 08: Congruent Triangles

Geometry Problem Solving Drill 08: Congruent Triangles Question No. 1 of 10 Question 1. The following triangles are congruent. What is the value of x? Question #01 (A) 13.33 (B) 10 (C) 31 (D) 18 You set

Foundations of Neutral Geometry

C H A P T E R 12 Foundations of Neutral Geometry The play is independent of the pages on which it is printed, and pure geometries are independent of lecture rooms, or of any other detail of the physical

Section 2-1. Chapter 2. Make Conjectures. Example 1. Reasoning and Proof. Inductive Reasoning and Conjecture

Chapter 2 Reasoning and Proof Section 2-1 Inductive Reasoning and Conjecture Make Conjectures Inductive reasoning - reasoning that uses a number of specific examples to arrive at a conclusion Conjecture

Q1: Lesson 6 Parallel Lines Handouts Page 1

6.1 Warmup Per ate Instructions: Justify each statement using your Vocab/Theorems ook. If!! =!! and!! = 50, then!! = 50. P F S If!" is rotated 180 around point F, then!"!" If!!"# +!!"# = 180, then!"# is

2-1. Inductive Reasoning and Conjecture. Lesson 2-1. What You ll Learn. Active Vocabulary

2-1 Inductive Reasoning and Conjecture What You ll Learn Scan Lesson 2-1. List two headings you would use to make an outline of this lesson. 1. Active Vocabulary 2. New Vocabulary Fill in each blank with

Objectives. Cabri Jr. Tools

^Åíáîáíó=R püçêíéëí=aáëí~ååé _ÉíïÉÉå=mçáåíë ~åç=iáåéë Objectives To investigate the shortest distance between two points To investigate the shortest distance between a line and a point To investigate the

Direct Proof and Counterexample I:Introduction

Direct Proof and Counterexample I:Introduction Copyright Cengage Learning. All rights reserved. Goal Importance of proof Building up logic thinking and reasoning reading/using definition interpreting :

Euclidean Geometry Proofs

Euclidean Geometry Proofs History Thales (600 BC) First to turn geometry into a logical discipline. Described as the first Greek philosopher and the father of geometry as a deductive study. Relied on rational

Distance in the Plane

Distance in the Plane The absolute value function is defined as { x if x 0; and x = x if x < 0. If the number a is positive or zero, then a = a. If a is negative, then a is the number you d get by erasing

example can be used to refute a conjecture, it cannot be used to prove one is always true.] propositions or conjectures

Task Model 1 Task Expectations: The student is asked to give an example that refutes a proposition or conjecture; or DOK Level 2 The student is asked to give an example that supports a proposition or conjecture.

Direct Proof and Counterexample I:Introduction. Copyright Cengage Learning. All rights reserved.

Direct Proof and Counterexample I:Introduction Copyright Cengage Learning. All rights reserved. Goal Importance of proof Building up logic thinking and reasoning reading/using definition interpreting statement:

JANE LONG ACADEMY HIGH SCHOOL MATH SUMMER PREVIEW PACKET SCHOOL YEAR. Geometry

JANE LONG ACADEMY HIGH SCHOOL MATH SUMMER PREVIEW PACKET 2015-2016 SCHOOL YEAR Geometry STUDENT NAME: THE PARTS BELOW WILL BE COMPLETED ON THE FIRST DAY OF SCHOOL: DUE DATE: MATH TEACHER: PERIOD: Algebra

Definitions, Axioms, Postulates, Propositions, and Theorems from Euclidean and Non-Euclidean Geometries by Marvin Jay Greenberg

Definitions, Axioms, Postulates, Propositions, and Theorems from Euclidean and Non-Euclidean Geometries by Marvin Jay Greenberg Undefined Terms: Point, Line, Incident, Between, Congruent. Incidence Axioms:

MATH GRADE 8 PLD Standard Below Proficient Approaching Proficient Proficient Highly Proficient

MATH GRADE 8 PLD Standard Below Proficient Approaching Proficient Proficient Highly Proficient The Level 1 student is below proficient The Level 2 student is approaching The Level 3 student is proficient

THE FIVE GROUPS OF AXIOMS.

2 THE FIVE GROUPS OF AXIOMS. 1. THE ELEMENTS OF GEOMETRY AND THE FIVE GROUPS OF AXIOMS. Let us consider three distinct systems of things. The things composing the first system, we will call points and

If you are given: 12 = 3(x 9)

Name [PACKET 2.2: INTRO TO PROOFS] 1 A, is a convincing argument that uses deductive reasoning. Every statement you make must be justified with a valid property. The following properties will be super

What can you prove by induction?

MEI CONFERENCE 013 What can you prove by induction? Martyn Parker M.J.Parker@keele.ac.uk Contents Contents iii 1 Splitting Coins.................................................. 1 Convex Polygons................................................

Unit 1: Introduction to Proof

Unit 1: Introduction to Proof Prove geometric theorems both formally and informally using a variety of methods. G.CO.9 Prove and apply theorems about lines and angles. Theorems include but are not restricted

Math Project 1 We haven t always been a world where proof based mathematics existed and in fact, the

336 Math Project 1 We haven t always been a world where proof based mathematics existed and in fact, the 1 use of proofs emerged in ancient Greek mathematics sometime around 300 BC. It was essentially

0609ge. Geometry Regents Exam AB DE, A D, and B E.

0609ge 1 Juliann plans on drawing ABC, where the measure of A can range from 50 to 60 and the measure of B can range from 90 to 100. Given these conditions, what is the correct range of measures possible

Logic, Proof, Axiom Systems

Logic, Proof, Axiom Systems MA 341 Topics in Geometry Lecture 03 29-Aug-2011 MA 341 001 2 Rules of Reasoning A tautology is a sentence which is true no matter what the truth value of its constituent parts.

Geometry/Trigonometry Unit 2: Parallel Lines Notes Period:

Geometry/Trigonometry Unit 2: Parallel Lines Notes Name: Date: Period: # (1) Pg 108 109 #1-10 all (2) Pg 108 109 #12-22 Even and 30, 32 (3) Pg 114 #1-6; 9-13 (4) Pg 114-115 #15-18; 20; 22; 24; 26; 29 and

Prompt. Commentary. Mathematical Foci

Situation 51: Proof by Mathematical Induction Prepared at the University of Georgia Center for Proficiency in Teaching Mathematics 9/15/06-Erik Tillema 2/22/07-Jeremy Kilpatrick Prompt A teacher of a calculus

FORMAL PROOFS DONU ARAPURA

FORMAL PROOFS DONU ARAPURA This is a supplement for M385 on formal proofs in propositional logic. Rather than following the presentation of Rubin, I want to use a slightly different set of rules which

22m:033 Notes: 6.1 Inner Product, Length and Orthogonality

m:033 Notes: 6. Inner Product, Length and Orthogonality Dennis Roseman University of Iowa Iowa City, IA http://www.math.uiowa.edu/ roseman April, 00 The inner product Arithmetic is based on addition and

7.5 Proportionality Relationships

www.ck12.org Chapter 7. Similarity 7.5 Proportionality Relationships Learning Objectives Identify proportional segments when two sides of a triangle are cut by a segment parallel to the third side. Extend

Math 300 Introduction to Mathematical Reasoning Autumn 2017 Axioms for the Real Numbers

Math 300 Introduction to Mathematical Reasoning Autumn 2017 Axioms for the Real Numbers PRIMITIVE TERMS To avoid circularity, we cannot give every term a rigorous mathematical definition; we have to accept

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 27, 2011 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name

Draft Version 1 Mark scheme Further Maths Core Pure (AS/Year 1) Unit Test 1: Complex numbers 1

1 w z k k States or implies that 4 i TBC Uses the definition of argument to write 4 k π tan 1 k 4 Makes an attempt to solve for k, for example 4 + k = k is seen. M1.a Finds k = 6 (4 marks) Pearson Education

2. Two binary operations (addition, denoted + and multiplication, denoted

Chapter 2 The Structure of R The purpose of this chapter is to explain to the reader why the set of real numbers is so special. By the end of this chapter, the reader should understand the difference between

Triangle Congruence and Similarity Review. Show all work for full credit. 5. In the drawing, what is the measure of angle y?

Triangle Congruence and Similarity Review Score Name: Date: Show all work for full credit. 1. In a plane, lines that never meet are called. 5. In the drawing, what is the measure of angle y? A. parallel

Reasoning and Proof Unit

Reasoning and Proof Unit 1 2 2 Conditional Statements Conditional Statement if, then statement the if part is hypothesis the then part is conclusion Conditional Statement How? if, then Example If an angle

Introducing Proof 1. hsn.uk.net. Contents

Contents 1 1 Introduction 1 What is proof? 1 Statements, Definitions and Euler Diagrams 1 Statements 1 Definitions Our first proof Euler diagrams 4 3 Logical Connectives 5 Negation 6 Conjunction 7 Disjunction

SOLUTION. Taken together, the preceding equations imply that ABC DEF by the SSS criterion for triangle congruence.

1. [20 points] Suppose that we have ABC and DEF in the Euclidean plane and points G and H on (BC) and (EF) respectively such that ABG DEH and AGC DHF. Prove that ABC DEF. The first congruence assumption

UNIT 3 CIRCLES AND VOLUME Lesson 1: Introducing Circles Instruction

Prerequisite Skills This lesson requires the use of the following skills: performing operations with fractions understanding slope, both algebraically and graphically understanding the relationship of

WORKSHEET MATH 215, FALL 15, WHYTE. We begin our course with the natural numbers:

WORKSHEET MATH 215, FALL 15, WHYTE We begin our course with the natural numbers: N = {1, 2, 3,...} which are a subset of the integers: Z = {..., 2, 1, 0, 1, 2, 3,... } We will assume familiarity with their

, p 1 < p 2 < < p l primes.

Solutions Math 347 Homework 1 9/6/17 Exercise 1. When we take a composite number n and factor it into primes, that means we write it as a product of prime numbers, usually in increasing order, using exponents

Factoring Polynomials. Review and extend factoring skills. LEARN ABOUT the Math. Mai claims that, for any natural number n, the function

Factoring Polynomials GOAL Review and extend factoring skills. LEARN ABOUT the Math Mai claims that, for any natural number n, the function f (n) 5 n 3 1 3n 2 1 2n 1 6 always generates values that are

Unit 5, Lesson 4.3 Proving the Pythagorean Theorem using Similarity

Unit 5, Lesson 4.3 Proving the Pythagorean Theorem using Similarity Geometry includes many definitions and statements. Once a statement has been shown to be true, it is called a theorem. Theorems, like

UCLA Curtis Center: March 5, 2016

Transformations in High-School Geometry: A Workable Interpretation of Common Core UCLA Curtis Center: March 5, 2016 John Sarli, Professor Emeritus of Mathematics, CSUSB MDTP Workgroup Chair Abstract. Previous

MTH 250 Graded Assignment 4

MTH 250 Graded Assignment 4 Measurement Material from Kay, sections 2.4, 3.2, 2.5, 2.6 Q1: Suppose that in a certain metric geometry* satisfying axioms D1 through D3 [Kay, p78], points A, B, C and D are

4-2 Angles of Triangles. Find the measures of each numbered angle. 1. ANSWER: ANSWER: m 1 = 42, m 2 = 39, m 3 = 51. Find each measure. 3.

Find the measures of each numbered angle. DECK CHAIRS The brace of this deck chair forms a triangle with the rest of the chair s frame as shown. If m 1 = 95 and m 3 = 55, find each measure. Refer to the

Definitions, Axioms, Postulates, Propositions, and Theorems from Euclidean and Non-Euclidean Geometries by Marvin Jay Greenberg ( )

Definitions, Axioms, Postulates, Propositions, and Theorems from Euclidean and Non-Euclidean Geometries by Marvin Jay Greenberg (2009-03-26) Logic Rule 0 No unstated assumptions may be used in a proof.

The Nature and Role of Reasoning and Proof

The Nature and Role of Reasoning and Proof Reasoning and proof are fundamental to mathematics and are deeply embedded in different fields of mathematics. Understanding of both is needed for all. Across

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II Tuesday, August 13, 2002 8:30 to 11:30 a.m., only Notice... Scientific

. Do the assigned problems on separate paper and show your work

Dear future AP Physics students, Here s the short story: Physics is NOT a math class. But you can t do collegelevel physics without math. So I need you to be solid in the basic math techniques that we

Unit 1 Packet Honors Math 2 1

Unit 1 Packet Honors Math 2 1 Day 1 Homework Part 1 Graph the image of the figure using the transformation given and write the algebraic rule. translation: < 1, -2 > translation: < 0, 3 > Unit 1 Packet

Special Relativity - Math Circle

Special Relativity - Math Circle Jared Claypoole Julio Parra Andrew Yuan January 24, 2016 Introduction: The Axioms of Special Relativity The principle of relativity existed long before Einstein. It states: