r Bermuda C 60° Ft. taudercpe f L ^ sr Puerto Rico ***\ V, " emptier/ Mathematics 10 MEMMSMSA. / dlbcrra {(ZlMl\) TLeecahrnnionlgo gies r K B ranch LEARNING Digitized by the Internet Archive in 2016 with funding from University of Alberta Libraries https://archive.org/details/appliedmathemati03albe_5 RELATIONS AN Learning Technologies Branch LEARNING Applied Mathematics 10 Student Module Booklet Module 3 Relations and Functions Learning Technologies Branch ISBN 0-7741-1722-2 Cover photo: COREL CORPORATION 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 ://ww w.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 DIVERSITY OF ALBERTA Welcome Applied Mathematics 10 ivioauie c. Number Patterns in Tables Welcome to Module 3. We hope you'll Module 3 enjoy your study Relations and Functions of Relations and Functions. Module 4 Sampling Module 5 Line Segments Module 6 Linear Functions Module 7 Trigonometry Applied Mathematics 10 contains seven modules and a f inal test. Work through the modules in the order given, since several concepts build on each other as you progress through the course. IInnttrroodduuccttiioonn ttoo AApppplliieedd MMaatthheemmaattiiccss 1100 66 Module Overview Evaluation 13 Module Project: Epidemics Beginning the Project 14 Activity 1: Interpreting Graphs 16 Activity 2: Graphing from Tables of Data 21 Activity 3: Graphing from Equations 30 Activity 4: The Domain and Range of a F unction 41 Activity 5: Representing Functions in Many Ways 47 Follow-up Activities Extra Help 53 Enrichment 55 Module Project: Epidemics Completing the Project 56 Module Project 57 Submit the Module Project. Module Summary Module Assignment 58 Submit the Module Assignment. Appendix 60 Glossary 60 Suggested Answers 99 Credits introduction to Applied Mathematics 10 Applied Mathematics 10 is the first course in the Applied Mathematics 10-20-30 program of studies. Another program of studies is Pure Mathematics 10-20-30; students who complete Pure Mathematics 30 often choose to take Mathematics 31. A t hird program of studies is Mathematics 14-24. Each mathematics program is designed for students with different mathematical strengths and interests. • Pure Mathematics 10-20-30 is intended for students who are strong in algebra and mathematical theory. • Applied Mathematics 10-20-30 is better suited to students who prefer to solve problems using numerical reasoning or geometry. • Mathematics 14-24 is a g eneral mathematics program for high school students who have experienced difficulties in previous mathematics courses. Each sequence of courses is designed for students with different post-secondary and career plans. You may find it helpful to read mathematics updates on Alberta Learning’s website: http://www.learning.gov.ab.ca/studentprograms 6 Applied Mathematics 10 Before enrolling in Applied Mathematics 10, it is recommended that you talk with a school counsellor about your career plans. TRANSFERRING FROM THE APPLIED MATHEMATICS PROGRAM You should be aware that the applied and pure mathematics courses do have some topics in common; other topics are specific to either the applied or pure mathematics courses. The following table shows some of the common topics and some of the independent topics in the mathematics program. • linear programming • spreadsheets • irrational numbers • data tables and trends • line segments and linear • exponents • design and layout • scaling • polynomial and rational expressions • metric and imperial measure graphs • mathematical expectation • triangles • data presentation • surveys • growth patterns • vectors and matrices • linear and non-linear systems • periodic, fractal, and recursive patterns • financial mathematics • operations on functions • financial decision making • quadratic functions • mathematical reasoning • costing and design problems • circle geometry •• ceoxnpiocnse ntial and logarithmic functions • the bell curve • combinations • trigonometric functions Introduction 7 If y ou want to transfer from the Applied Mathematics 10-20-30 sequence to the Pure Mathematics 10-20-30 sequence at a f uture time, you won’t have to repeat the topics that are common to pure mathematics and applied mathematics. If y ou decide to transfer to Pure Mathematics 20 after successfully completing Applied Mathematics 10, you may take the 3-credit course called Pure Mathematics 10b. If y ou decide to transfer to Pure Mathematics 30 after successfully completing Applied Mathematics 20 or Applied Mathematics 30, you may take the 5-credit course called Pure Mathematics 20b. The two bridging courses are shown in the following diagram. For each module in Applied Mathematics 10, there is a S tudent Module Booklet, a P roject Booklet, and an Assignment Booklet. The document you are presently reading is called a Student Module Booklet. Each Student Module Booklet will show you, step by step, what to do and how to do it. There are readings, questions for you to answer in your mathematics binder, and applications that will give you hands-on experience. It is important to work systematically and carefully through the Student Module Booklets. This work will prepare you for the projects, assignments, and final test. Applied Mathematics 10