Learning lecnnoiogies tsrancn Display Purposes Only Do Not Remove University,?]. Alberta^Ubrar , L \ Module 4 0 1 620 3366854 0 Digitized by the Internet Archive in 2016 with funding from University of Alberta Libraries https://archive.org/details/puremathematics304albe Module 4 Conics Liberia Learning Technologies Branch LEARNING Pure Mathematics 30 Module 4: Conics Student Module Booklet Learning Technologies Branch ISBN 0-7741-1688-9 This document is intended for The Learning Technologies Branch has an Internet site that you may find useful. The address is as follows: Students / http://www.learning.gov.ab.ca/ltb Teachers / Administrators The use of the Internet is optional. Exploring the electronic information superhighway can be Parents educational and entertaining. However, be aware that these computer networks are not censored. Students may unintentionally or purposely find articles on the Internet that may be offensive or General Public inappropriate. As well, the sources of information are not always cited and the content may not be Other accurate. Therefore, students may wish to confirm facts with a second source. ALL RIGHTS RESERVED Copyright © 2 000, the Crown in Right of Alberta, as represented by the Minister of Learning, Alberta Learning, 11160 Jasper Avenue, Edmonton, Alberta T5K 0L2. All rights reserved. Additional copies may be obtained from the Learning Resources Distributing Centre. No part of this courseware may be reproduced in any form, including photocopying (unless otherwise indicated), without the written permission of Alberta Learning. Every effort has been made both to provide proper acknowledgement of the original source and to comply with copyright law. If cases are identified where this effort has been unsuccessful, please notify Alberta Learning so that appropriate corrective action can be taken. IT IS STRICTLY PROHIBITED TO COPY ANY PART OF THESE MATERIALS UNDER THE TERMS OF A LICENCE FROM A C OLLECTIVE OR A L ICENSING BODY. UNIVERSITY LIBRARY UNIVERSITY OF ALBERTA Welcome to Module 4. 1 Pure PPaPuc-rr^fpc.Q gfj We hope you'll enjoy your study of Conics. Module 1 Transformations Module 2 Exponents and Logarithms Module 3 Sequences and Series Module 4 Conics Module 5 Trigonometry Module 6 Combinatorics Module 7 Probability and Statistics 30 y<yW High School Mathematics Courses Pure Mathematics 30 is the third course in the Pure Mathematics 10-20-30 sequence of courses. Many students who take the Pure Mathematics 10-20-30 Mathematics 31 will also choose to take Mathematics 3 1 . A nother sequence of courses is V. J Applied Mathematics 10-20-30. * \ f r \ f Pure Pure Pure Mathematics 10 Mathematics 20 Mathematics 30 V J J MathAepmpaltiiecds 20 j MathAepmpaltiiecds 30 Each sequence of courses is designed for students with different mathematical strengths and interests. The Pure Mathematics 10-20-30 sequence is intended for students who are strong in mathematical theory and algebra. The Applied Mathematics 10-20-30 sequence is better suited to students who prefer to solve mathematical problems using numerical reasoning or geometry. Each sequence of courses is designed for students with different career plans. Students who plan to take courses such as commerce, engineering, physics, and engineering technologies in post-secondary education will need to take Pure Mathematics 30 in high school. Some of these students will also need to take Mathematics 31. Alberta Students will write a d iploma examination at the end of the course. Alberta Learning provides several documents to help students prepare for this examination. These documents are found in the directory under “Students and Learning” on the Alberta Learning website, http://www.learning.gov.ab.ca. Information like course expectations, the makeup of the diploma examination, keyed copies of previous examinations, preparation guides, and calculator policies are available to students at this site. Each year, in February and September, Alberta Learning provides teachers with information on a student project, which teachers may use as part of your overall assessment. Information to students will also be posted on the Alberta Learning website. Check with your teacher to determine what you will be expected to do. Be aware that one of the diploma examination’s written-response questions is worth 10% of your diploma examination mark and will deal with elements of this project. You should take advantage of the many sources of information about Pure Mathematics 30. Your success depends on your understanding of course expectations and evaluation procedures. Work closely with your teacher and do not hesitate to ask questions. Remember, take the initiative to find out all you can about Pure Mathematics 30. If y ou do not successfully complete Pure Mathematics 30, you can repeat the course or you can transfer to the Applied Mathematics sequence. If y ou decide to transfer to the Applied Mathematics sequence, you may take the five-credit course called Applied Mathematics 20b or you may take the five-credit course called Applied Mathematics 20. Mathematical Processes Throughout the course you will be expected to do the following: • communicate mathematically • connect mathematical ideas to everyday experiences and to concepts in other disciplines • develop and use estimation strategies • develop and use mental math strategies • develop and use problem-solving strategies • reason and justify your thinking • select and use appropriate technologies as tools to solve problems • use visualization to assist in processing information, making connections, and solving problems Mathematical Process ■ C ommunication 8 C onnection ■ E stimation This icon will show which mathematical B M ental Math process you are expected to perform. IB Problem Solving SI Reasoning H T echnology | V isualization In order to develop these mathematical processes more fully, you are encouraged to ask someone who is also taking Pure Mathematics 30 to be your study partner. You may find that having a f riend to discuss mathematics with makes your studying more enjoyable. You are also encouraged to record your mathematical ideas in a j ournal. Here are some suggestions for organizing your journal: • Keep a section on new concepts and procedures you have learned. Get in the habit of describing new concepts, procedures, and strategies in your own words. If y ou are having difficulty, write your questions in your journal before discussing them with your teacher or study partner. Record useful ways to help you remember what a concept means. Make graphic organizers (such as context webs, Venn diagrams, or organizational charts) to help you connect mathematical ideas. • Keep a section on your mathematical accomplishments. This can include solutions to problems that you are proud of solving. It can also include landmark events, such as when you finally grasped a d ifficult concept (an “aha!”) or when you first used a calculator or spreadsheet program in a new way. • Keep a section on mathematics in the everyday world. This could include newspaper articles, cartoons, and descriptions of careers that require a mathematical background. Resources You Will Need In order to complete Pure Mathematics 30 successfully, you will need to have access to the following resources, which can be purchased through the Learning Resources Distributing Centre: • the MATHPOWER™ 12 textbook, Western Edition, published by McGraw-Hill Ryerson (2000) • a g raphing calculator Any of the following graphing calculators may be used: Texas Instruments TI-83, TI-83 Plus, TI-82, TI-86, TI-89, TI-92, or TI-92 Plus; Casio CFX-9850Ga-Plus, CFX-9850G, CFX-9800G, or FX-9700 series; or Sharp EL-9600c, EL-9600, EL-9300, or EL-9200. Note: Some of these calculators are no longer commercially manufactured. • a computer and a spreadsheet program Any of the following spreadsheet programs may be used: ClarisWorks™ 4.0 (or higher) for Macintosh, ClarisWorks™ 4.0 (or higher) for Windows, Microsoft® Works 3.0 (or higher) for Windows, or Microsoft® Access 97 and Microsoft® Excel 97 for Windows (a part of Microsoft® Office Professional 95 or Microsoft® Office Professional 97). Note: Examples in this course show the TI-83 graphing calculator and the Microsoft® Excel 97 spreadsheet program where applicable. If y ou have access to a videocassette recorder, you may wish to view the video The TI-83 Graphing Calculator Video Tutor to review some of the calculator’s features. Check with your distance learning provider concerning the availability of this video. Finally, you will need the following resources, which can be purchased locally: • a mathematical instrument set (compass, protractor, ruler, and triangles) • a notebook or binder in which to respond to the questions asked • a notebook or binder for journal writing Other Visual Cues In addition to the Mathematical Process icon described earlier, you will find other visual cues throughout this course. Read the explanations given to discover what each icon prompts you to do. Use the Internet Refer to the View a to explore a textbook. videocassette. topic. l(e member : . < //n y Answer the Internet website address Use the questions in Pure Mathematics 30 given in this module is the Assignment subject to change. Booklet. Companion CD. CONTENTS Circles and Ellipses HypPearrbaobloalsa s and Evaluation Activity 1: Conic Sections Activity 1: 6 Th9e Hyperbola 2 6 Strategies for Completing Activity 21: 6 Th e Circle Activity 2: The Parabola a M odule 54 Activity 3: The Ellipse 26 Follow-up Activities 79 Extra Help Follow-up Activities 44 83 Extra Help 79 Enrichment 44 Enrichment 48 Conclusion 86 Conclusion Assignment 86 Assignment 51 51