Instructions for SA Completion


 Tobias Warner
 1 years ago
 Views:
Transcription
1 Instructions for SA Completion 1 Take notes on these Pythagorean Theorem Course Materials then do and check the associated practice questions for an explanation on how to do the Pythagorean Theorem Substantive Assignment questions correctly. 2 Go to the Online Unit 1 Course Materials website (below) for an explanation on how to do the Trigonometry Ratio Substantive Assignment questions correctly Take notes on the video Lessons 1&2 using the note taking supplements. 4 Complete the practice assignments from Lessons 1&2. 5 Check the practice assignment with the answers provided. 6 Check the video solutions to the questions you did not do correctly. 7 Seek help with questions the video solutions do not fully explain to you. 8 Complete the Substantive Assignment questions showing all work to earn full marks for each question. 9 Seek help if you are confused with any questions. 10 When you are happy with your final product please scan and submit your Substantive Assignment with your registration package. 11While you are waiting for your registration to be processed, please complete all the Online Unit 1 Course Materials Lessons in preparation for your Unit 1 Exam. Page 1 of 20
2 Pythagorean Theorem Course Materials In mathematics, the Pythagorean Theorem is a relation among the three sides of a right triangle (rightangled triangle). The theorem can be written as an equation (or formula) relating the lengths of the sides a, b and c, often called the Pythagorean equation: The longest side of a rightangled triangle is found across from the right angle and is called the hypotenuse. The hypotenuse is represented by the letter c in the Pythagorean formula. The legs of the triangle are the two shorter sides. The legs meet perpendicularly to create a 90 degree angle. The right angle is represented by a square in the triangle and the legs of the triangle are represented by the letters a and b in the formula. It doesn t matter which leg is labeled a or b. Please note the sides a, b and c can be found across from the respective angles A, B, and C. If the length of both a and b are known, then c can be calculated as follows: You can find the length of a hypotenuse by using the formula: This example asks us to find the approximate length of the hypotenuse. Page 2 of 20
3 Try the question above and check the solution on the next page. Hint use: or this algebraically manipulated form of the same equation: This form of the formula is the same formula written in a different algebraic way: Page 3 of 20
4 Finding the length of the legs in a right triangle requires some algebraic manipulation of the Pythagorean Formula. If the length of hypotenuse c and one leg ( a or b ) are known, then the length of the other leg can be calculated with the following equations: or Page 4 of 20
5 Solve the triangle means to find all missing sides and angles possible. In this case we can only solve for the missing side: Please note in the previous and next solutions you may isolate the variable (unknown letter) before you insert the known values or after you insert the known values. Both methods lead to the correct answer. Page 5 of 20
6 We need to be able to find exact answers as well as the approximate decimal answers we ve been calculating in the previous examples. An exact answer is a real number not approximated by rounding the decimal portion of the answer. Example showing how to find the exact value (simplified using a square root symbol): 1) Find the exact value for the missing side: a 4m 6m Page 6 of 20
7 Solution 1) Subtract 16 from both sides to help isolate the unknown a Square root both sides to isolate a a = At this point you can calculate an approximation for this exact expression with your calculator to get an answer of 4.47cm however this question has asked for an exact answer. Therefore we will try to find a perfect root that is a factor of 20. Perfect roots are found by multiplying an integer by itself. For example 2 multiplied by 2 is 4. Four is a perfect root because the = 2. Other perfect roots include: 9, 16, 25, 36, 49, etc In this case 4 is the largest perfect root that is a factor of 20. That allows us to write the answer in the following simplified form: a = a= a = 2 cm Page 7 of 20
8 We have shown that if the lengths of any two sides are known the length of the third side can be found through the use of Pythagorean equation. If a triangle has three known sides we can also use the Pythagorean equation to prove if it is, or is not, a rightangled triangle: Determine if these Triangles are rightangled ones or not: 1a) 11m 11m 11 m Solution: Please note this triangle may look like it has a right angle in it but because there is no square symbol inside the triangle we cannot assume this triangle has a right angle. We can use the Pythagorean equation to determine if the triangle is rightangled = (121) (2) 242 = 242 We used the Pythagorean equation calculation to determine that both sides of the equation are equal. This is a true statement. That means all the conditions that allow the Pythagorean theorem to be true, are true. One of the key features of using the Pythagorean theorem is that you are using a rightangled triangle to do your calculations. Therefore this is a rightangled triangle. Page 8 of 20
9 1b) 12m 11m 16m Solution: We can use the Pythagorean equation to determine if the triangle is rightangled: = We used the Pythagorean equation calculation to determine that both sides of the equation are not equal. This means the equation creates a false statement. That means all the conditions that allow the Pythagorean Theorem to be true are NOT true and one of the key features of using Pythagorean s theorem is that you are using a rightangled triangle to do your calculations. Therefore this is a not a rightangled triangle. Page 9 of 20
10 Practice Questions a) b) Page 10 of 20
11 c) 2. In each diagram, calculate the indicated side exactly using Pythagorean Theorem: a) 3cm 5cm b a) Page 11 of 20
12 b) y 7km 3km b) 3. Prove which triangle is rightangled and which is not. Triangle B Triangle C Page 12 of 20
13 4) Find and prove which Triangles are right and which are not: a) A  B  C  D  Page 13 of 20
14 Practice Questions Answers 1a) h = approximately 4.70 cm 1b) r = approximately m 1c) f = approximately in 2a) b = 4 cm 2b) y = 2 km 3) Triangle B is not Right triangle and Triangle C is a right triangle. 4) Triangles A is a right triangle and Triangles B, C and D are not right triangles Page 14 of 20
15 Practice Questions Full Solutions a) 22.1 = h =h a) h = approximately 4.70 cm = r = r b) r = approximately m Page 15 of 20
16 = f = f c) f = approximately in 2. In each diagram, calculate the indicated side exactly using Pythagorean Theorem: a) 3cm 5cm b 9 = 25 = 259 b = b = 4 a) b = 4 cm Page 16 of 20
17 b) y 7km 3km 9 = 49 y = = 499 y = y= 2( ) y = 2 km 3. Prove which triangle is rightangled and which is not = = 196 This is a false statement Therefore B is not a rightangled triangle. Page 17 of 20
18 = = 100 This is a true statement Therefore C is a rightangled triangle. 4) Find and prove which Triangles are right and which are not: A right triangle B not a right triangle C  not a right triangle D  not a right triangle A) = = 81 This is a true statement B) = = 81 This is a false statement C) D) = = This is a false statement Page 18 of = = 225 This is a false statement
MAT 080Algebra II Applications of Quadratic Equations
MAT 080Algebra II Applications of Quadratic Equations Objectives a Applications involving rectangles b Applications involving right triangles a Applications involving rectangles One of the common applications
More informationGrade 6 Math Circles March 24/25, 2015 Pythagorean Theorem Solutions
Faculty of Mathematics Waterloo, Ontario NL 3G1 Centre for Education in Mathematics and Computing Grade 6 Math Circles March 4/5, 015 Pythagorean Theorem Solutions Triangles: They re Alright When They
More informationa c Pythagorean Theorem: a 2 + b 2 = c 2
Section 2.1: The Pythagorean Theorem The Pythagorean Theorem is a formula that gives a relationship between the sides of a right triangle The Pythagorean Theorem only applies to RIGHT triangles. A RIGHT
More informationPythagorean Theorem. Inquiry Based Unit Plan
Pythagorean Theorem Inquiry Based Unit Plan By: Renee Carey Grade: 8 Time: 5 days Tools: Geoboards, Calculators, Computers (Geometer s Sketchpad), Overhead projector, Pythagorean squares and triangle manipulatives,
More information1 Investigation of Rightangled Triangles
1 Investigation of Rightangled Triangles Answering this investigation Some tasks in this investigation require you to use Geogebra (www.geogebra. org). All the files are viewable online, so you will not
More informationB a. This means that if the measures of two of the sides of a right triangle are known, the measure of the third side can be found.
The Pythagorean Theorem One special kind of triangle is a right triangle a triangle with one interior angle of 90º. B A Note: In a polygon (like a triangle), the vertices (and corresponding angles) are
More informationModuMath Algebra Lessons
ModuMath Algebra Lessons Program Title 1 Getting Acquainted With Algebra 2 Order of Operations 3 Adding & Subtracting Algebraic Expressions 4 Multiplying Polynomials 5 Laws of Algebra 6 Solving Equations
More informationSolve each right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree.
Solve each right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree. 42. The sum of the measures of the angles of a triangle is 180. Therefore, The sine of an angle
More informationRoots of Real Numbers
Roots of Real Numbers Math 97 Supplement LEARNING OBJECTIVES. Calculate the exact and approximate value of the square root of a real number.. Calculate the exact and approximate value of the cube root
More informationThe Six Trigonometric Functions
CHAPTER 1 The Six Trigonometric Functions Copyright Cengage Learning. All rights reserved. SECTION 1.1 Angles, Degrees, and Special Triangles Copyright Cengage Learning. All rights reserved. Learning Objectives
More informationSquare Roots and the Pythagorean Theorem
4.8 Square Roots and the Pythagorean Theorem 4.8 OBJECTIVES 1. Find the square root of a perfect square 2. Use the Pythagorean theorem to find the length of a missing side of a right triangle 3. Approximate
More informationPythagoras Theorem. Page I can... 1... identify and label rightangled triangles. 2... explain Pythagoras Theorem. 4... calculate the hypotenuse
Pythagoras Theorem Page I can... 1... identify and label rightangled triangles 2... eplain Pythagoras Theorem 4... calculate the hypotenuse 5... calculate a shorter side 6... determine whether a triangle
More informationGrade 8 Unit 2 Pythagorean Theorem Applications. Assessment Plan
Grade 8 Unit 2 Pythagorean Theorem Applications Work with radicals and integer exponents Assessment Plan 8. EE.2 Use square root and cube root symbols to represent solutions to equations. Evaluate square
More informationG E O M E T R Y CHAPTER 9 RIGHT TRIANGLES AND TRIGONOMETRY. Notes & Study Guide
G E O M E T R Y CHAPTER 9 RIGHT TRIANGLES AND TRIGONOMETRY Notes & Study Guide 2 TABLE OF CONTENTS SIMILAR RIGHT TRIANGLES... 3 THE PYTHAGOREAN THEOREM... 4 SPECIAL RIGHT TRIANGLES... 5 TRIGONOMETRIC RATIOS...
More information1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5280 feet (ft) Replace 1 with 1 ft/12 in. 1ft
2 MODULE 6. GEOMETRY AND UNIT CONVERSION 6a Applications The most common units of length in the American system are inch, foot, yard, and mile. Converting from one unit of length to another is a requisite
More informationGeometry: Classifying, Identifying, and Constructing Triangles
Geometry: Classifying, Identifying, and Constructing Triangles Lesson Objectives Teacher's Notes Lesson Notes 1) Identify acute, right, and obtuse triangles. 2) Identify scalene, isosceles, equilateral
More informationThis page must be completed and submitted with your Substantive Assignment. Incomplete or missing information WILL NOT be processed.
Welcome to Math 11 Pre Calculus This page must be completed and submitted with your Substantive Assignment. Incomplete or missing information WILL NOT be processed. NOTE: Registration forms with attached,
More informationLooking for Pythagoras: Homework Examples from ACE
Looking for Pythagoras: Homework Examples from ACE Investigation 1: Coordinate Grids, ACE #20, #37 Investigation 2: Squaring Off, ACE #16, #44, #65 Investigation 3: The Pythagorean Theorem, ACE #2, #9,
More informationInClass Game. The Pythagorean Theorem Game (Lesson 34)
TEACHING SUGGESTIONS The Pythagorean Theorem Game (Lesson 34) Separate the class into groups of four. The Pythagorean Theorem Game master, p. 8 The Pythagorean Theorem Game Board master, p. 9 The Pythagorean
More informationUnit 6: Pythagorean Theorem
Approximate Time Frame: 2 weeks Connections to Previous Learning: In Unit 1, students learned to evaluate expressions and equations with exponents and solved equations of the form worked with triangles
More informationCOWLEY COUNTY COMMUNITY COLLEGE REVIEW GUIDE Compass Algebra Level 2
COWLEY COUNTY COMMUNITY COLLEGE REVIEW GUIDE Compass Algebra Level This study guide is for students trying to test into College Algebra. There are three levels of math study guides. 1. If x and y 1, what
More informationGeometry Unit 7 (Textbook Chapter 9) Solving a right triangle: Find all missing sides and all missing angles
Geometry Unit 7 (Textbook Chapter 9) Name Objective 1: Right Triangles and Pythagorean Theorem In many geometry problems, it is necessary to find a missing side or a missing angle of a right triangle.
More informationMATH 65 NOTEBOOK CERTIFICATIONS
MATH 65 NOTEBOOK CERTIFICATIONS Review Material from Math 60 2.5 4.3 4.4a Chapter #8: Systems of Linear Equations 8.1 8.2 8.3 Chapter #5: Exponents and Polynomials 5.1 5.2a 5.2b 5.3 5.4 5.5 5.6a 5.7a 1
More informationCHAPTER 8: ACUTE TRIANGLE TRIGONOMETRY
CHAPTER 8: ACUTE TRIANGLE TRIGONOMETRY Specific Expectations Addressed in the Chapter Explore the development of the sine law within acute triangles (e.g., use dynamic geometry software to determine that
More informationThe integer is the base number and the exponent (or power). The exponent tells how many times the base number is multiplied by itself.
Exponents An integer is multiplied by itself one or more times. The integer is the base number and the exponent (or power). The exponent tells how many times the base number is multiplied by itself. Example:
More informationSample Problems. Lecture Notes Similar Triangles page 1
Lecture Notes Similar Triangles page 1 Sample Problems 1. The triangles shown below are similar. Find the exact values of a and b shown on the picture below. 2. Consider the picture shown below. a) Use
More informationLesson 19. Triangle Properties. Objectives
Student Name: Date: Contact Person Name: Phone Number: Lesson 19 Triangle Properties Objectives Understand the definition of a triangle Distinguish between different types of triangles Use the Pythagorean
More informationLesson 9: Radicals and Conjugates
Student Outcomes Students understand that the sum of two square roots (or two cube roots) is not equal to the square root (or cube root) of their sum. Students convert expressions to simplest radical form.
More informationReteaching Simplifying Radicals
Name Class Date Reteaching Simplifying Radicals You can remove perfectsquare factors from a radicand. Problem What is the simplified form of 80n? In the radicand, factor the coefficient and the variable
More informationIn a triangle with a right angle, there are 2 legs and the hypotenuse of a triangle.
PROBLEM STATEMENT In a triangle with a right angle, there are legs and the hypotenuse of a triangle. The hypotenuse of a triangle is the side of a right triangle that is opposite the 90 angle. The legs
More informationTypes of Angles acute right obtuse straight Types of Triangles acute right obtuse hypotenuse legs
MTH 065 Class Notes Lecture 18 (4.5 and 4.6) Lesson 4.5: Triangles and the Pythagorean Theorem Types of Triangles Triangles can be classified either by their sides or by their angles. Types of Angles An
More informationTrigonometry. Week 1 Right Triangle Trigonometry
Trigonometry Introduction Trigonometry is the study of triangle measurement, but it has expanded far beyond that. It is not an independent subject of mathematics. In fact, it depends on your knowledge
More informationUnit 10: Quadratic Equations Chapter Test
Unit 10: Quadratic Equations Chapter Test Part 1: Multiple Choice. Circle the correct answer. 1. The area of a square is 169 cm 2. What is the length of one side of the square? A. 84.5 cm C. 42.25 cm B.
More informationUnit 7: Right Triangles and Trigonometry Lesson 7.1 Use Inequalities in a Triangle Lesson 5.5 from textbook
Unit 7: Right Triangles and Trigonometry Lesson 7.1 Use Inequalities in a Triangle Lesson 5.5 from textbook Objectives Use the triangle measurements to decide which side is longest and which angle is largest.
More informationLaw of Cosines TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson. TINspire Navigator System
Math Objectives Students will be able to state the Law of Cosines Students will be able to apply the Law of Cosines to find missing sides and angles in a triangle Students will understand why the Law of
More informationProving Pythagoras. Lesson Plan
Proving Pythagoras Lesson Plan Cube Fellow: Kenneth A. Macpherson Goal: Get 10th Graders to understand and prove the Pythagorean Theorem Grade and Course: tenth grade geometry KY Standards: Geometry: MA112.1.3
More informationName Period Right Triangles and Trigonometry Section 9.1 Similar right Triangles
Name Period CHAPTER 9 Right Triangles and Trigonometry Section 9.1 Similar right Triangles Objectives: Solve problems involving similar right triangles. Use a geometric mean to solve problems. Ex. 1 Use
More informationParallel and Perpendicular. We show a small box in one of the angles to show that the lines are perpendicular.
CONDENSED L E S S O N. Parallel and Perpendicular In this lesson you will learn the meaning of parallel and perpendicular discover how the slopes of parallel and perpendicular lines are related use slopes
More informationCONNECT: Algebra. 3x = 20 5 REARRANGING FORMULAE
CONNECT: Algebra REARRANGING FORMULAE Before you read this resource, you need to be familiar with how to solve equations. If you are not sure of the techniques involved in that topic, please refer to CONNECT:
More informationPark Forest Math Team. Meet #5. Algebra. Selfstudy Packet
Park Forest Math Team Meet #5 Selfstudy Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. Geometry: Angle measures in plane figures including supplements and complements 3. Number
More informationLesson 9: Radicals and Conjugates
Student Outcomes Students understand that the sum of two square roots (or two cube roots) is not equal to the square root (or cube root) of their sum. Students convert expressions to simplest radical form.
More information1 Math 116 Supplemental Textbook (Pythagorean Theorem)
1 Math 116 Supplemental Textbook (Pythagorean Theorem) 1.1 Pythagorean Theorem 1.1.1 Right Triangles Before we begin to study the Pythagorean Theorem, let s discuss some facts about right triangles. The
More informationTeaching & Learning Plans. Using Pythagoras Theorem to establish the Distance Formula (Draft) Junior Certificate Syllabus
Teaching & Learning Plans Using Pythagoras Theorem to establish the Distance Formula (Draft) Junior Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson,
More informationMath Foundations IIB Grade Levels 912
Math Foundations IIB Grade Levels 912 Math Foundations IIB introduces students to the following concepts: integers coordinate graphing ratio and proportion multistep equations and inequalities points,
More informationPythagorean Theorem. Overview. Grade 8 Mathematics, Quarter 3, Unit 3.1. Number of instructional days: 15 (1 day = minutes) Essential questions
Grade 8 Mathematics, Quarter 3, Unit 3.1 Pythagorean Theorem Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned Prove the Pythagorean Theorem. Given three side lengths,
More informationIntroduction to the Mathematics of Zome
Introduction to the Mathematics of Zome Tom Davis tomrdavis@earthlink.net http://www.geometer.org/mathcircles July 1, 008 Abstract This article provides a gentle introduction to the Mathematics of Zome,
More information9.6 The Pythagorean Theorem
Section 9.6 The Pythagorean Theorem 959 9.6 The Pythagorean Theorem Pythagoras was a Greek mathematician and philosopher, born on the island of Samos (ca. 582 BC). He founded a number of schools, one in
More informationSection 7.2 Quadratic Applications
Section 7.2 Quadratic Applications Now that you are familiar with solving quadratic equations it is time to learn how to apply them to certain situations. That s right, it s time for word problems. The
More informationRight Triangles and Quadrilaterals
CHATER. RIGHT TRIANGLE AND UADRILATERAL 18 1 5 11 Choose always the way that seems the best, however rough it may be; custom will soon render it easy and agreeable. ythagoras CHATER Right Triangles and
More informationSolving Systems of Equations Algebraically Examples
Solving Systems of Equations Algebraically Examples 1. Graphing a system of equations is a good way to determine their solution if the intersection is an integer. However, if the solution is not an integer,
More informationSolving Quadratic Equations
9.3 Solving Quadratic Equations by Using the Quadratic Formula 9.3 OBJECTIVES 1. Solve a quadratic equation by using the quadratic formula 2. Determine the nature of the solutions of a quadratic equation
More informationUnit 3: Algebra. Date Topic Page (s) Algebra Terminology 2. Variables and Algebra Tiles 3 5. Like Terms 6 8. Adding/Subtracting Polynomials 9 12
Unit 3: Algebra Date Topic Page (s) Algebra Terminology Variables and Algebra Tiles 3 5 Like Terms 6 8 Adding/Subtracting Polynomials 9 1 Expanding Polynomials 13 15 Introduction to Equations 16 17 One
More informationPrentice 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
More informationSOLVING EQUATIONS WITH RADICALS AND EXPONENTS 9.5. section ( 3 5 3 2 )( 3 25 3 10 3 4 ). The OddRoot Property
498 (9 3) Chapter 9 Radicals and Rational Exponents Replace the question mark by an expression that makes the equation correct. Equations involving variables are to be identities. 75. 6 76. 3?? 1 77. 1
More informationMath 002 Intermediate Algebra
Math 002 Intermediate Algebra Student Notes & Assignments Unit 4 Rational Exponents, Radicals, Complex Numbers and Equation Solving Unit 5 Homework Topic Due Date 7.1 BOOK pg. 491: 62, 64, 66, 72, 78,
More informationLesson 2: Pythagorean Theorem
Lesson 2: Pythagorean Theorem Selected Content Standards Benchmarks Addressed: G5M Making and testing conjectures about geometric shapes and their properties G7M Demonstrating the connection of geometry
More informationKS4 Curriculum Plan Maths FOUNDATION TIER Year 9 Autumn Term 1 Unit 1: Number
KS4 Curriculum Plan Maths FOUNDATION TIER Year 9 Autumn Term 1 Unit 1: Number 1.1 Calculations 1.2 Decimal Numbers 1.3 Place Value Use priority of operations with positive and negative numbers. Simplify
More informationName Date Time. STUDY LINK 8 13 Unit 9: Family Letter. Please keep this Family Letter for reference as your child works through Unit 9.
Name Date Time STUDY LINK Unit 9: Family Letter More about Variables, Formulas, and Graphs You may be surprised at some of the topics that are covered in Unit 9. Several of them would be traditionally
More informationFunctions  Inverse Trigonometry
10.9 Functions  Inverse Trigonometry We used a special function, one of the trig functions, to take an angle of a triangle and find the side length. Here we will do the opposite, take the side lengths
More informationGeometry Notes RIGHT TRIANGLE TRIGONOMETRY
Right Triangle Trigonometry Page 1 of 15 RIGHT TRIANGLE TRIGONOMETRY Objectives: After completing this section, you should be able to do the following: Calculate the lengths of sides and angles of a right
More informationAnnotated work sample portfolios are provided to support implementation of the Foundation Year 10 Australian Curriculum.
Work sample portfolio summary WORK SAMPLE PORTFOLIO Annotated work sample portfolios are provided to support implementation of the Foundation Year 10 Australian Curriculum. Each portfolio is an example
More informationCOGNITIVE TUTOR ALGEBRA
COGNITIVE TUTOR ALGEBRA Numbers and Operations Standard: Understands and applies concepts of numbers and operations Power 1: Understands numbers, ways of representing numbers, relationships among numbers,
More informationPythagorean Theorem Differentiated Instruction for Use in an Inclusion Classroom
Pythagorean Theorem Differentiated Instruction for Use in an Inclusion Classroom Grade Level: Seven Time Span: Four Days Tools: Calculators, The Proofs of Pythagoras, GSP, Internet Colleen Parker Objectives
More information91 Similar Right Triangles (Day 1) 1. Review:
91 Similar Right Triangles (Day 1) 1. Review: Given: ACB is right and AB CD Prove: ΔADC ~ ΔACB ~ ΔCDB. Statement Reason 2. In the diagram in #1, suppose AD = 27 and BD = 3. Find CD. (You may find it helps
More informationALGEBRA 2/ TRIGONOMETRY
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/ TRIGONOMETRY Tuesday, January 28, 2014 1:15 4:15 p.m. SAMPLE RESPONSE SET Table of Contents Question 28...................
More informationChapter 8. Right Triangles
Chapter 8 Right Triangles Objectives A. Use the terms defined in the chapter correctly. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately apply the
More informationPreAlgebra Interactive Chalkboard Copyright by The McGrawHill Companies, Inc. Send all inquiries to:
PreAlgebra Interactive Chalkboard Copyright by The McGrawHill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGrawHill 8787 Orion Place Columbus, Ohio 43240 Click the mouse button
More informationHiker. A hiker sets off at 10am and walks at a steady speed for 2 hours due north, then turns and walks for a further 5 hours due west.
Hiker A hiker sets off at 10am and walks at a steady speed for hours due north, then turns and walks for a further 5 hours due west. If he continues at the same speed, what s the earliest time he could
More informationTRIGONOMETRY Compound & Double angle formulae
TRIGONOMETRY Compound & Double angle formulae In order to master this section you must first learn the formulae, even though they will be given to you on the matric formula sheet. We call these formulae
More informationGrade 7 Math Course Lesson Plan: 34 weeks
Grade 7 Math Course Lesson Plan: 34 weeks Welcome to Thinkwell s 7th Grade Math! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson plan is meant to be a guide
More informationProblem 3.2 A Proof of the Pythagorean Theorem
Problem 3.2 A Proof of the Pythagorean Theorem Use the puzzles your teacher gives you. Puzzle frames Puzzle pieces A. Study a triangle piece and the three square pieces. How do the side lengths of the
More informationIf A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C?
Problem 3 If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C? Suggested Questions to ask students about Problem 3 The key to this question
More informationas a fraction and as a decimal to the nearest hundredth.
Express each ratio as a fraction and as a decimal to the nearest hundredth. 1. sin A The sine of an angle is defined as the ratio of the opposite side to the hypotenuse. So, 2. tan C The tangent of an
More informationTHE PYTHAGOREAN THEOREM
THE PYTHAGOREAN THEOREM a 2 + b 2 = c 2 CFE 3285V OPEN CAPTIONED ALLIED VIDEO CORPORTATION 1993 Grade Levels: 912 14 minutes DESCRIPTION Reviews the definition of a right triangle before a brief history
More informationExact Values of the Sine and Cosine Functions in Increments of 3 degrees
Exact Values of the Sine and Cosine Functions in Increments of 3 degrees The sine and cosine values for all angle measurements in multiples of 3 degrees can be determined exactly, represented in terms
More informationDefinition of an nth Root
Radicals and Complex Numbers 7 7. Definition of an nth Root 7.2 Rational Exponents 7.3 Simplifying Radical Expressions 7.4 Addition and Subtraction of Radicals 7.5 Multiplication of Radicals 7.6 Rationalization
More informationFoundation. Scheme of Work. Year 10 September 2016July 2017
Foundation Scheme of Work Year 10 September 016July 017 Foundation Tier Students will be assessed by completing two tests (topic) each Half Term. PERCENTAGES Use percentages in reallife situations VAT
More informationIntermediate Algebra with Trigonometry. J. Avery 4/99 (last revised 11/03)
Intermediate lgebra with Trigonometry J. very 4/99 (last revised 11/0) TOPIC PGE TRIGONOMETRIC FUNCTIONS OF CUTE NGLES.................. SPECIL TRINGLES............................................ 6 FINDING
More informationWarm Up. Use A ( 2, 3) and B (1, 0) 1. Find the slope of AB. 2. Find the midpoint of AB. 3. Find the distance of AB. 4. Simplify.
Use A ( 2, 3) and B (1, 0) 1. Find the slope of AB. 2. Find the midpoint of AB. 3. Find the distance of AB. Warm Up 4. Simplify. 5. Draw an example of vertical angles. GOALS Develop and apply the
More informationSample Problems. 3. Find the missing leg of the right triangle shown on the picture below.
Lecture Notes The Pythagorean Theorem page 1 Sample Problems 1. Could the three line segments given below be the three sides of a right triangle? Explain your answer. a) 6 cm; 10 cm; and 8 cm b) 7 ft,
More informationEXPONENTS. To the applicant: KEY WORDS AND CONVERTING WORDS TO EQUATIONS
To the applicant: The following information will help you review math that is included in the Paraprofessional written examination for the Conejo Valley Unified School District. The Education Code requires
More informationPythagoras. 1 of 60. (Pythagoras)
Pythagoras 1 of 60 http://www.youtube.com/watch?v=8fjlxrudhg4 (Pythagoras) 2 of 60 The history of Pythagoras Theorem The theorem is named after the Greek mathematician and philosopher, Pythagoras. He lived
More information2. Simplify. College Algebra Student SelfAssessment of Mathematics (SSAM) Answer Key. Use the distributive property to remove the parentheses
College Algebra Student SelfAssessment of Mathematics (SSAM) Answer Key 1. Multiply 2 3 5 1 Use the distributive property to remove the parentheses 2 3 5 1 2 25 21 3 35 31 2 10 2 3 15 3 2 13 2 15 3 2
More informationG C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Performance Assessment Task Circle and Squares Grade 10 This task challenges a student to analyze characteristics of 2 dimensional shapes to develop mathematical arguments about geometric relationships.
More informationIndiana State Core Curriculum Standards updated 2009 Algebra I
Indiana State Core Curriculum Standards updated 2009 Algebra I Strand Description Boardworks High School Algebra presentations Operations With Real Numbers Linear Equations and A1.1 Students simplify and
More informationHow do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.
The verbal answers to all of the following questions should be memorized before completion of prealgebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics
More informationCourse Title: Honors Algebra Course Level: Honors Textbook: Algebra 1 Publisher: McDougall Littell
Course Title: Honors Algebra Course Level: Honors Textbook: Algebra Publisher: McDougall Littell The following is a list of key topics studied in Honors Algebra. Identify and use the properties of operations
More informationTime Topic What students should know Mathswatch links for revision
Time Topic What students should know Mathswatch links for revision 1.1 Pythagoras' theorem 1 Understand Pythagoras theorem. Calculate the length of the hypotenuse in a rightangled triangle. Solve problems
More information1. The volume of the object below is 186 cm 3. Calculate the Length of x. (a) 3.1 cm (b) 2.5 cm (c) 1.75 cm (d) 1.25 cm
Volume and Surface Area On the provincial exam students will need to use the formulas for volume and surface area of geometric solids to solve problems. These problems will not simply ask, Find the volume
More informationWentzville School District Curriculum Development Template Stage 1 Desired Results
Wentzville School District Curriculum Development Template Stage 1 Desired Results Unit Title: Radicals and Radical Expressions Course: Middle School Algebra 1 Unit 10 Radicals and Radical Expressions
More informationMath 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
More informationMATHEMATICAL VECTOR ADDITION
MATHEMATICAL VECTOR ADDITION Part One: The Basics When combining two vectors that act at a right angle to each other, you are able to use some basic geometry to find the magnitude and direction of the
More information5.4 The Quadratic Formula
Section 5.4 The Quadratic Formula 481 5.4 The Quadratic Formula Consider the general quadratic function f(x) = ax + bx + c. In the previous section, we learned that we can find the zeros of this function
More informationMath Content
20122013 Math Content PATHWAY TO ALGEBRA I Unit Lesson Section Number and Operations in Base Ten Place Value with Whole Numbers Place Value and Rounding Addition and Subtraction Concepts Regrouping Concepts
More information10.2 4545 90 Triangles
Page of 6 0. 0 Triangles Goal Find the side lengths of 0 triangles. Key Words 0 triangle isosceles triangle p. 7 leg of a right triangle p. hypotenuse p. GeoActivity Eploring an Isosceles Right
More informationEach pair of opposite sides of a parallelogram is congruent to each other.
Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. 2. Each pair of opposite
More informationSect 6.7  Solving Equations Using the Zero Product Rule
Sect 6.7  Solving Equations Using the Zero Product Rule 116 Concept #1: Definition of a Quadratic Equation A quadratic equation is an equation that can be written in the form ax 2 + bx + c = 0 (referred
More information111 Areas of Parallelograms and Triangles. Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary.
Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 2. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. Each pair of opposite
More informationTrigonometry Lesson Objectives
Trigonometry Lesson Unit 1: RIGHT TRIANGLE TRIGONOMETRY Lengths of Sides Evaluate trigonometric expressions. Express trigonometric functions as ratios in terms of the sides of a right triangle. Use the
More informationPilot Flyskole AS Hangarveien 13 N3241 Sandefjord Tlf Epost Preparatory Course.
Pilot Flyskole AS Hangarveien 13 N3241 Sandefjord Tlf +47 9705 6840 Epost post@pilot.no www.pilot.no Preparatory Course Mathematics Pilot Flight School 2014 Order of operations Operations means things
More information