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The Canadian-High

2023–2024 Copyright © 2023 PiQ Potential All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form without the written permission of the publisher. Website: www.PiQPotential.ca E-mail: yourvoice@PiQPotential.ca Meet Your Planner August: Developing Habits for Success......6 September: Getting Organized. ..............18 October: Being Prepared..........................28 November: Being an Active Listener........38 December: Setting Goals.........................50 January: Prioritizing. ................................60 February: Estimating Time........................70 March: Using Time Wisely.........................82 April: Doing Group Projects......................92 May: Completing Long-Term Projects.....102 June: Staying Motivated . .......................114 July: Learning to Adapt...........................124 Resources: Math, Language Arts, Science, and More!...................................126 Planning Activities: Learn to be a planning pro. Long-Term Project Planning: Create steps to complete big projects. Monthly Calendar: Jot down important dates. Monthly Calendar Hall Pass: Use this space as directed by your teacher. After-School Space: Jot down after-school plans, such as clubs or work. Day Block: Keep track of your daily schedule. Weekly Calendar MONTHLY GOALS AND TO-DO’S Sunday/dimanche Monday/lundi Tuesday/mardi 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Saint Patrick’s Day Daylight Saving Time begins Ramadan begins (sundown) Easter March mars 2024 TIME CRUNCHED? Smooth out your schedule with a well-formed plan. Act Planning helps you make the most of your time. Use your planner to determine which tasks you need to ACT on first. Honesty Being true to yourself and others 82 LONG-TERM PROJECT: PROJECT STEPS: DUE DATE Wednesday/mercredi Thursday/jeudi Friday/vendredi Saturday/samedi 1 2 Good Friday 83 S M T W T F S GOALS AND TO-DO’S After School After School After School Tuesday/mardi Wednesday/mercredi DAY DAY DAY Monday/lundi 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24/31 25 26 27 28 29 30 March mars 2024 4 5 6 Collars tracking caribou show they’re not only hunted by wolves, but by bears too. 84 After School After School Did I complete my responsibilities this week? Thursday/jeudi Friday/vendredi Saturday/samedi Sunday/dimanche DAY DAY HALL PASS/NOTES Date To Out In Sig. 7 8 9 10 Daylight Saving Time begins Ramadan begins (sundown) Stress has unhappy effects (nausea, headache)! Use time wisely to avoid it. The average Canadian teenager watches more than 12 hours of TV a week. Can’t fit everything in? Make a change. 85 Printed on recyclable paper

Plan with a Process It’s a process that helps you think through what you need to do, sort it out, and get it done. Planning isn’t just writing things down. T THINK about what you want and need to do—your goals. R RECORD them and make a plan. A ACT on your plans and get things done. C CHECK your progress and plan your next steps. 2

Follow these four simple steps to plan your goals, homework and activities. CHECK CHECK off work you’ve done. Did you complete your responsibilities? • Check off work you’ve finished. • Move work you haven’t finished to another day. • Plan time to complete unfinished tasks later in the week. • Reflect on your habits and what you need to change. LOOK BACK! RECORD RECORD things you want and need to do. MANAGE INFORMATION! WRITE IMPORTANT DATES ON YOURMONTHLY CALENDAR. WRITE HOMEWORK AND REMINDERS ON THE WEEKLY PAGES. BREAK BIG PROJECTS INTO SMALLERSTEPS. THINK THINK about your short- and long-term plans. SET GOALS! Set long-term goals to work on throughout the month. Think about things you need to do and remember. MONTHLY GOALS AND TO-DO’S Sunday/dimanche Monday/lundi 3 4 10 11 17 18 24 25 31 Sir John A. Macdonald January janvier 2021 Teamwork Sharing ideas and work wi Planning helps you prioritize! Write homework, proje planner. Then ACT on them in order of importance. Act FEELING LOST AT SEA? Let your priorities guide you to your top tasks. 60 S M T W T F S GOALS AND TO-DO’S After School After School After School Tuesday/mardi Wednesday/mercredi DAY DAY DAY Monday/lundi 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24/31 25 26 27 28 29 30 January janvier 2021 4 5 6 Runaway trains occurred often at Kicking Horse Pass until spiral tunnels were bu 62 ACT ACT on planning your time. Use this strategy to prioritize: 1. Finish stuff you need to do first. 2. Do the hard stuff before easy tasks. 3. Do tasks for tomorrow after tasks for today. 4. Break big stuff down into little pieces and start small. MANAGE TIME! 3

Long-term goals are things you work on all month or all year. List a bunch of your long-term goals. Plan Your Goal A plan starts with a goal—something you want to do or achieve. The best plans are formed when you start with a SMART goal! SSPECI FIC What exactly do you want to do? MMEASURABLE How will you know when you succeed? T TIMELY When will you complete your goal? RREALISTIC Is your goal possible? Why do you want to complete it? AACTION-ORIENTED What steps will you take to reach your goal? Step-by-Step Planning 4

Pick a goal from your list on the previous page. Write it here: Don’t stop there! Put your steps into action. First, set a deadline: Then schedule your goal steps in your planner. How’d things go? Look back on your plan and evaluate how it went. What went well? What would you change next time? Plan how you’ll reach your goal, by breaking it into small steps. List ’em all! Is your goal specific? Zero in on one thing you want to do or achieve. Can you finish each step in a day or a week? If not, break them down further. Did you schedule all your steps before your deadline? Try scheduling back from your final date. Use pencil to write in your planner. Plans often need to be modified and updated as you go! T I P 5

MONTHLY GOALS AND TO-DO’S Sunday/dimanche Monday/lundi Tuesday/mardi 3 4 5 10 11 12 17 18 19 24 25 26 31 Saint Patrick’s Day Daylight Saving Time begins Ramadan begins (sundown) Easter March mars 2024 TIME CRUNCHED? Smooth out your schedule with a well-formed plan. Act Planning helps you make the most of your time. Use your planner to determine which tasks you need to ACT on first. Honesty Being true to yourself and others 82

LONG-TERM PROJECT: PROJECT STEPS: DUE DATE Wednesday/mercredi Thursday/jeudi Friday/vendredi Saturday/samedi 1 2 6 7 8 9 13 14 15 16 20 21 22 23 27 28 29 30 Good Friday 83

S M T W T F S GOALS AND TO-DO’S After School After School After School Tuesday/mardi Wednesday/mercredi DAY DAY DAY Monday/lundi 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24/31 25 26 27 28 29 30 March mars 2024 4 5 6 Collars tracking caribou show they’re not only hunted by wolves, but by bears too. 84

After School After School Did I complete my responsibilities this week? Thursday/jeudi Friday/vendredi Saturday/samedi Sunday/dimanche DAY DAY HALL PASS/NOTES Date To Out In Sig. 7 8 9 10 Daylight Saving Time begins Ramadan begins (sundown) Stress has unhappy effects (nausea, headache)! Use time wisely to avoid it. The average Canadian teenager watches more than 12 hours of TV a week. Can’t fit everything in? Make a change. 85

S M T W T F S GOALS AND TO-DO’S After School After School After School Tuesday/mardi Wednesday/mercredi DAY DAY DAY Monday/lundi 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24/31 25 26 27 28 29 30 March mars 2024 11 12 13 In winter, Ottawa’s Rideau Canal is the world’s longest ice rink! 86

After School After School Did I complete my responsibilities this week? Thursday/jeudi Friday/vendredi Saturday/samedi Sunday/dimanche DAY DAY HALL PASS/NOTES Date To Out In Sig. 14 15 16 17 Saint Patrick’s Day TV and phones distract us. Don’t look! Focus to use your time wisely. Sticky notes, cell phone alarms— people can use up to 13 tools to manage their time. Make your planner one of them! 87

S M T W T F S GOALS AND TO-DO’S After School After School After School Tuesday/mardi Wednesday/mercredi DAY DAY DAY Monday/lundi 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24/31 25 26 27 28 29 30 March mars 2024 18 19 20 Glooscap is a hero in Mi’kmaq stories. He slept on NS and used PEI as his pillow! 88

After School After School Did I complete my responsibilities this week? Thursday/jeudi Friday/vendredi Saturday/samedi Sunday/dimanche DAY DAY HALL PASS/NOTES Date To Out In Sig. 21 22 23 24 Get blood to the brain by being active. Do 10 sit-ups before doing homework. Canadian scientists study the roles of brain power and behaviour to learn to treat many diseases. That’s a good use of time! 89

S M T W T F S GOALS AND TO-DO’S After School After School After School Tuesday/mardi Wednesday/mercredi DAY DAY DAY Monday/lundi 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24/31 25 26 27 28 29 30 March mars 2024 25 26 27 Canada is so cold that 40% of all energy produced here is needed for heating. 90

After School After School Did I complete my responsibilities this week? Thursday/jeudi Friday/vendredi Saturday/samedi Sunday/dimanche DAY DAY HALL PASS/NOTES Date To Out In Sig. 28 29 30 31 Good Friday Easter Using time wisely supports your personal life too. Plan time with friends! Want skills that impress employers? Teamwork and collaboration top the list because they get productivity buzzing! 91

10WAYS TO SUPPORT YOUR MENTAL WELLNESS T HE WE L L NESS PROJEC T Deep breathing reduces stress, fights anxiety, and refocuses thoughts. BREATHe just Be kind to yourself when you make mistakes. See mistakes as opportunities to learn and grow. mindset have a GROWTh Talking about things you’re going through can lift a weight from your shoulders. sHARe feelings The sights, sounds, and smells of nature can relieve stress and tension. sPEnd outside time Eating well, exercising, and getting enough sleep are habits that help your mental wellness. habits have HEALTHy If negative thoughts pop into your head, ask yourself if they’re true. Often they're not! thoughts CHALLENGe Speak to yourself as kindly as you’d talk to a friend, and give yourself pep talks. self-talk use PosITIVe You can’t control everything. Focus on things you CAN control, such as thoughts and actions. realistic be Focus on people, things, and opportunities that make you feel thankful and supported. PRACTise gratitude If you’re struggling, ask for help. People may not know what you’re going through. HELp for ask 126

STRESSe D alone when youfeel: sad HURt scared bullied confused Worri ed okto It’s Help ask for Talk to: A Teacher A School Counsellor Family Members Adults You Trust Your Friends A Family Doctor T HE WE L L NESS PROJEC T 127

Daily Physical Activity Tracker Exercise is essential for health. Being physically active keeps you fit. You will help yourself maintain a healthy weight and build healthy bones, muscles, and joints. There are many ways to get your heart working hard. Try for a good mix of aerobic and strengthening activities. Track your daily activity in this chart to start a new habit of making physical activity a regular part of your day. DATE ACTIVITY MINUTES DATE ACTIVITY MINUTES RESOURCE PAGES 128

Take Care of YOU To do your best, you need to feel your best. Take the quizzes below to find out how well you take care of YOU. 3 = Always 2 = Most of the time 1 = Never Healthy and Happy ___ I talk to others about my feelings. ___ I ask for help and support when I need it. ___ I treat others the way I want to be treated. ___ I take breaks when I am feeling overwhelmed. ___ I use coping mechanisms to reduce stress. ___ I am proud of who I am! ___ Score Healthy Eating ___ I have a fruit or vegetable with every meal. ___ I eat a dark-green and an orange vegetable every day. ___ At least half of my grains are whole grains. ___ I drink water or low-fat milk. ___ I eat small meals throughout the day. ___ I stop eating when I feel full. ___ Score Healthy Habits ___ I exercise for at least 30 minutes every day. ___ I try new kinds of physical activities. ___ I get 9–10 hours of sleep at night. ___ I go to bed and get up at the same time every day. ___ I use a nighttime routine to help me wind down. ___ I stay away from alcohol, tobacco, and drugs. ___ Score How did you do? If your scores are lower than you’d like, work on improving your habits and come back to try again. Aim for at least 15 on each quiz. Healthy Hygiene ___ I brush my teeth twice a day. ___ I floss my teeth every day. ___ I wash my hands throughout the day. ___ I shower or bathe every day. ___ I cover my nose and mouth when I sneeze or cough. ___ I feel confident I look my best. ___ Score R–1 RESOURCE PAGES

Study Skills LISTENING • Concentrate on your teacher. • Tune out noise and talking. • Listen for the main ideas. • Focus on the 5Ws and 1H: What? Why? Where? When? Who? How? Listen 80 per cent of the time, and write 20 per cent of the time. REMEMBERING • After school, quickly review your notes. • Highlight important notes or add explanations. • Apply what you’re learning as soon as possible. • Study with a friend; answer each other’s questions. When you’re well prepared, you experience less stress. TAKING NOTES • Don’t write down everything. • Record the main ideas and supporting facts. • Use your own words. • Keep your notes organized. Outlining I. Main idea or topic sentence A. Major point of the topic 1. Subpoint of the topic a. Detail Schedule short, frequent study sessions. This often works better than one long cram session! WORK SPACE • If possible, find your own quiet space to study. • Keep your workplace clean and uncluttered. • Make sure you have good lighting, a straight chair, and fresh air. Study DON’Ts: TV, radio, noise/ distractions, bed, hunger, and sleepiness. Test Tips GET READY • Find out what kind of test you will be taking (e.g., multiple choice or essay questions). • Avoid cramming. • Set up a study schedule to review everything well before the test; use your planner to keep track. • Write out likely test questions and answer them. • Get enough rest the night before. • Wear comfortable clothing. • Bring all the necessary tools: pens, pencils, erasers, calculator, highlighter, etc. GET SET • Don’t start writing as soon as you get the test. • First, read the instructions for each section. Ask your teacher to explain any that are not clear. • Highlight key words, such as discuss, compare, and list. • Quickly estimate how much time you have to answer questions. GO! • Answer easier questions first to boost your confidence. • Read questions thoroughly to be sure you understand exactly what is being asked. • Never rush through questions in a panic; be calm and pace yourself. • Try to leave some time before the test is over to review and correct errors. • If you run out of time on a certain question, leave some room and return to it later. Multiple Choice • Don’t guess unless there is no penalty for wrong answers. • Before looking at the possible answers, try to form the answer in your mind. • Don’t change an answer that comes to mind unless you’re absolutely sure it’s wrong. Essay Questions • Always write answers in paragraph form unless a list is specifically requested. • Answer essay questions this way: 1) Make a rough outline. 2) Begin with a topic sentence that includes the key words of the question. 3) Support your position with specific examples and detailed information. 4) Conclude by briefly summing up your answer. TIP TIP TIP TIP R–2 RESOURCE PAGES

Protect Yourself Online COMPUTER VIRUSES Computer viruses can damage your hard drive or digital devices. They can also jeopardize your personal information, files, and software. Viruses harm your computer when you run infected executable files. These files can pose as useful programs, pictures, e-cards, video clips, email attachments, or pop-up ads. Protect yourself by clicking with care. • Only visit sites you trust or know are safe. • D elete email attachments from people you don’t know. INFORMATION AND IDENTITY THEFT Thieves can use the personal information you provide online to steal your identity. Details such as your full name, birthdate, and social insurance number can be used to open accounts in your name. Additionally, some computer viruses allow thieves to hack into your computer to collect account, credit card, and PIN numbers, as well as your passwords. Protect yourself by guarding your privacy. • Never send sensitive information over unsecure wireless networks. • Don’t share personal information (e.g., full name and birthdate) online. • Keep your antivirus software up to date. ONLINE PERSONAL SAFETY Some adults use social-networking sites and chat rooms to target young people. They may lie and manipulate to gain trust or form relationships. Protect yourself by forming safe online relationships. • Don’t form online friendships with people you don’t know. • Never agree to meet online-only friends in real life. • End chats or block people if you feel upset or uncomfortable. Cyberbullying Cyberbullying is a form of bullying that uses technology to hurt, harass, or humiliate others. It’s a common form of bullying because it’s quick, can be anonymous, and allows bullies to reach their targets at any time of the day or night. COMMON FORMS OF CYBERBULLYING • Harassment: Continual, hurtful contact through phone calls or emails, instant or text messages, or posting cruel messages on bulletin boards or social-networking sites. • Outing: Making someone’s private information public by posting it on social-networking sites, blogs, or chat rooms, or by forwarding private photos to other people. • Gossip: Posting or passing along rumours about someone. • Impersonation: Pretending to be someone else in chat rooms or on social-networking sites in order to post messages that can make that person look bad. • Flaming: Fighting online using offensive or threatening language. Protect yourself by knowing how to respond to bullying. • B lock cyberbullies to prevent them from contacting you. • R eport cyberbullying to trusted adults and your Internet Service Provider (ISP). Break the cycle of cyberbullying. • Use netiquette online by being respectful, courteous, and truthful in your posts, email, and text messages. • Refuse to forward mean or threatening messages or embarrassing pictures. R–3 RESOURCE PAGES

Communication INPUTS: Reading, listening, viewing MAKING SENSE OF WHAT YOU READ, HEAR, AND SEE Improve your understanding. A good reader/listener/viewer pays attention to: 1. What is presented: • understand it. • connect it to what you already know. 2. How it is presented: • recognize purpose, tone, and possible bias. Literary elements to look for: form, voice, theme/plot, characterization, imagery, and figurative language. (See page R–5.) MAKING SENSE OF WORDS (VOCABULARY) You hear a new word. What does it mean? Attack strategies: a. Find out the meaning from the context. b. B reak the code (decode it). What is its root word? Does it have a prefix or suffix? c. C heck for it in a dictionary, or find words with a similar meaning in a thesaurus. MAKING SENSE OF THE BIG PICTURE The proven SQ4R method: S = Survey the chapter: Glance over it, paying attention to headings and organization. Q = Question: Check section headings and any questions provided at the end. What do you already know about this topic? What will you be learning? R = Read: Pay attention to words, diagrams, maps, pictures, and captions. Reread them if necessary. R = Recite: Summarize each paragraph or section in your own words. R = Relate: Link the new information to what you already know. R = Review: Quiz yourself; check your notes. OUTPUTS: Writing, speaking, other presentations Follow these basic steps to make a great presentation every time! 1. PLAN IT Brainstorm about your topic; clearly define it. Map ideas, research, and make the topic interesting to yourself and your audience. Think about the 5Ws/1H: who, what, when, where, why, and how. Being well prepared will make everything else easier! 2. DRAFT IT Make a blueprint of what you will present and what your message will be. Decide on your point of view and how you intend to get it across. Prepare an outline with subtopics. Remember the three basic parts: introduction, main body, and conclusion. 3. CREATE IT Write or make your first draft based on your outline. Remember, be original; don’t copy what others have produced. 4. IMPROVE IT Take the time to revise and edit. Ask others for their feedback. If your teacher has provided a rubric, check that you’ve covered all the requirements. Check your work for spelling, grammar, and formatting. 5. PUBLISH IT Share what you’ve created! If you need to show or cite sources, make sure to check out the information on page R–8. When you take notes, immediately jot down the work’s title, author, publisher, and publication date. This saves time later! TIP R–4 RESOURCE PAGES

1. TOPIC Choose what you will write about. Your topic should be clear and well defined. 2. RESEARCH Gather facts to support your statements or opinions. 3. FORMAT The requirements for writing a letter, essay, speech, or journal entry are different. Make sure you follow the requirements of the format you are using. 4. PURPOSE Your purpose will focus your writing. Are you writing to inform, entertain, instruct, or persuade your audience? 5. AUDIENCE Your choice of words and writing style should be shaped by your audience. Are you writing for your peers, younger children, or adults? 6. OUTLINE Write a clear thesis (topic) statement. Then write your subtopics in a logical order that leads to a conclusion. (See Outlining, page R–2.) 7. POINT OF VIEW Determine the point of view (e.g., I, he/she, etc.) from which you will write. Your understanding of a topic might increase when you consider different points of view. 8. ROUGH DRAFT Write a rough draft that follows your outline, keeping your audience and point of view in mind. Each paragraph should deal with one main idea only. Your composition should follow a logical order to a conclusion. 9. EDIT AND REVISE Check your work for clarity and for spelling, punctuation, and formatting errors. Revise the content if necessary. Then proofread carefully. 10. SOURCES Cite a source for each quote, fact, and idea used that is not your own. DO NOT PLAGIARIZE. Use footnotes and/or a bibliography or Works Cited page. (See page R–8.) 11. FINAL DRAFT Prepare a neat final copy for submission. Be proud of your work! Many of these steps apply to other projects as well, such as oral or PowerPoint presentations. The Writing Process These steps are part of the writing process. PLOT The main events in a story put in a particular order THEME The subject, topic, or recurring idea SETTING The time period(s) and location(s) in the story CHARACTERS The people or participants in the story MOOD The overall tone or feeling; the atmosphere and imagery VOICE/STYLE The unique way a writer tells his or her story FIGURATIVE LANGUAGE The use of figures of speech or word images, such as: • Metaphor: A comparison of two things without using “like” or “as” • Simile: A comparison of two things using “like” or “as” • Personification: The giving of human qualities to nonhuman things • Hyperbole: The use of exaggeration for effect Literary Elements Essential features of a piece of writing Literary elements vary depending on the format and genre of a piece of writing. They include but are not limited to: TIP R–5 RESOURCE PAGES

Parts of Speech NOUNS Common nouns refer to any place, person, thing, or idea. examples: woman, country Proper nouns refer to any particular place, person, thing, or idea. examples: Greta, Norway PRONOUNS take the place of a noun. Nominative case is used for the subject of a sentence or clause. example: He went to bed. Possessive case shows ownership. example: The waterbed is his. Objective case receives action or is after a preposition. example: They sold him a leaky waterbed. VERBS show action or state of being and the time of that action or state. examples: Past: She waited in the car. Present: She needs gas now. Future: She will enjoy her trip. ADVERBS describe verbs, adjectives, or other adverbs and specify in what manner, when, where, or how much. examples: He whimpered miserably as the doctor injected the antidote. It hurt much more than he expected. ADJECTIVES describe nouns and specify size, colour, number, and so on. This is called modifying. examples: A small light showed in the upper window of the old factory. ARTICLES introduce nouns and are sometimes classified as adjectives. There are only three articles in the English language: a, an, and the. examples: The taxi screeched to a stop. PREPOSITIONS show how a noun or pronoun is related to another word in a sentence. Note: Prepositions can also be used as adverbs. examples: Preposition: I fell down the stairs. Adverb: I fell down. CONJUNCTIONS join words, phrases, or clauses. Coordinating conjunctions connect elements of the same value. example: Take the cookie and eat it. Subordinating conjunctions join a main clause and a dependent (subordinate) clause. example: The cookie is overdone because the timer was slow. INTERJECTIONS are also known as exclamations and are indicated by the use of the exclamation mark (!). example: Wow! Look at that horse go! • I before E, except after C—or when sounded as A, as in neighing and weigh. • Final consonants are not doubled when the word ends in more than one consonant. examples: conform conformed conforming help helped helping • When words end in soft ce or ge, keep the e before able and ous. examples: advantageous changeable chargeable courageous enforceable manageable noticeable outrageous peaceable • When verbs end in ie, change the ending to y before adding ing. examples: die dying (died) lie lying (lied) tie tying (tied) Spelling Rules R–6 RESOURCE PAGES

. , ; : Punctuation Drop the final e before a suffix beginning with a vowel. example: love + ing = loving exceptions: canoe + ing = canoeing hoe + ing = hoeing Keep the final e before a suffix beginning with a consonant. example: care + ful = careful exceptions: true + ly = truly argue + ment = argument Final consonants might or might not be doubled when the accent is thrown forward. Canadian and British usage is to double the final consonant; the American tendency is not to double it. examples: benefit benefitting or benefiting benefitted or benefited cancel cancelling or canceling cancelled or canceled travel travelling or traveling travelled or traveled “” ’ — ? ! PERIOD Put a period at the end of a: • Declarative sentence example: Rain is wet. • Indirect question example: She wondered what was wrong. COMMA Use a comma to separate words or phrases in a series. example: Her hobbies were reading, watching old movies, driving, and running. SEMICOLON Use a semicolon between clauses in a compound sentence when the conjunction is omitted or when the connection is close. example: The statistical evidence is there; it cannot be denied. COLON Use a colon to: • Begin a list example: He studied three subjects: biology, chemistry, and English. • Formally introduce a statement example: She stated: “I never saw the new contract.” QUOTATION MARKS Use double quotation marks around a direct quotation. example: He said, “Go away.” Do not use quotation marks for indirect statements. example: She said she was happy. APOSTROPHE Use an apostrophe for: • Contractions example: It’s all right. • The possessive case of a noun example: That is Bart’s dog. EM DASH Use em dashes to set off intensifying or explanatory parts of a sentence. example: My cats—Leo, Theo, and Marv—enjoy racing through the house at midnight. QUESTION MARK Use a question mark for questions. example: What on earth do you mean? EXCLAMATION MARK Express strong feeling with an exclamation mark. example: That’s funny! R–7 RESOURCE PAGES

COMPONENTS Most print periodical entries (e.g., newspapers, magazines, and journals) will include the author’s name, article’s title in quotation marks, periodical’s name in italics, number or name of series, volume number, issue number, date of publication, relevant page numbers, and publication medium. Most print nonperiodical entries (e.g., books and pamphlets) will include the name of the author, editor, translator, or compiler; work’s title in italics; edition used; number of volumes; city of publication; publisher’s name, shortened according to MLA’s guidelines (7.5); year of publication; and publication medium. Most web publication entries will include the name of the author, editor, compiler, narrator, translator, or performer; work’s title in italics if it’s independent, or in quotation marks if it’s part of another work; website title in italics; version or edition; city of publication; website’s publisher or sponsor; date of publication; publication medium; and date accessed. SAMPLE ENTRIES A book with one author Leung, Mary. Purcell: The English Orpheus. London: Heinemann, 2006. Print. A book with two or three authors Avandez, Diana, and Andrew Janowicz. Art Deco. Acadie: Moncton, 2004. Print. Burney, Chuck, Tyler Capriotti, and Ann Kovak. A History of Aviation. Toronto: Doubleday, 2009. Print. A book with more than three authors may list all authors or use “et al.” Silverstein, Gordon, et al. The Eleusinian Mysteries. New York: Penguin, 2004. Print. A book with an editor that does not name an author listed on the title page Faber, K. R., ed. Shakespeare’s Great Tragedies: Critical Essays. London: Oxford UP, 2000. Print. An article in a newspaper Kurozumi, T. “How the West Was Won.” The Calgary Herald 14 June 2009: F3. Print. An article in a magazine Wheatley, Meaghan. “Swans in Danger.” Wide World Mar. 2001: 18–21. Print. An entry in an encyclopedia “Theseus.” Encyclopedia of Myth and Legend. 2000 ed. Print. A work without print publication; data accessed online Eng, C. “The Missing Shoe.” Kids’ Lit Online. Premier Publications, 11 Jan. 2006. Web. 25 Apr. 2006. A work with print publication; data accessed online Chekhov, Anton. The Sea-Gull. Fairfield: 1st World Library, 2004. Google Books Search. Web. 20 June 2011. References Your Works Cited page should have a separate entry for every book, website, article, and other source you use. List the entries alphabetically by each one’s first word. TIP There are different citation styles; your teacher might give you guidelines for a different style. The examples on this page are based on MLA (Modern Language Association) style, which is commonly used for academic writing in the humanities (literature, philosophy, art, and classical studies). R–8 RESOURCE PAGES

NUMBER NOTATION The decimal number system uses base 10. Place value: 123,456,789.012 MILLIONS THOUSANDS ONES Each section shows hundreds, tens, and ones. Expanded notation: 6,824 = 6 x 103 + 8 x 102 + 2 x 101 + 4 x 100 Scientific notation: 6,800 = 6.8 x 103 SYMBOLS ORDER OF OPERATIONS P Do operations within Parentheses ( ) and other grouping symbols, such as absolute value and square root. E Do Exponents 2 and roots . MD Do Multiplication x and Division ÷ in order from left to right. AS Do Addition + and Subtraction – in order from left to right. FRACTIONS, DECIMALS, PERCENTAGES 3 – numerator _ 5 – denominator To add or subtract fractions, first obtain a common denominator: 1 2 5 6 11 --- + --- = ----- + ----- = ----- 3 5 15 15 15 To multiply: 1 2 1 x 2 2 --- x --- = ------------ = ----- 3 5 3 x 5 15 To divide, multiply the first fraction by the reciprocal of the second fraction: 2 1 2 6 12 =4 --- ÷ --- = --- x --- = ----- 3 6 3 1 3 1 = 1.0 = 100% 3/4 = 0.75 = 75% 2/3 = 0. –6 = 66. –6% 1/2 = 0.5 = 50% 1/3 = 0. –3 = 33. –3% 1/4 = 0.25 = 25% 1/5 = 0.2 = 20% 1/6 = 0.1 –6 = 16. –6% 1/8 = 0.125 = 12.5% 1/9 = 0.1– = 11.1– % 1/10 = 0.1 = 10% 1/12 = 0.08 –3 = 8. –3%  Is less than  Is greater than  Is equal to  Is approximate to  Is less than or equal to  Is greater than or equal to SQUARES AND SQUARE ROOTS n 1 2 3 4 5 6 7 8 9 10 12 15 20 25 100 1/2 1/4 n2 1 4 9 16 25 36 49 64 81 100 144 225 400 625 10,000 1/4 1/16  n 1 1.414 1.732 2 2.236 2.449 2.646 2.828 3 3.162 3.464 3.873 4.472 5 10 0.707 1/2 Length 1 millimetre (mm) = 0.04 inches (in.) 1 metre (m) = 39.4 inches (in.) = 3.3 feet (ft.) = 1.1 yards (yd.) 1 kilometre (km) = 1093.6 yards (yd.) = 0.6 miles (mi.) Capacity 1 tablespoon (Tbsp.) = 3 teaspoons (tsp.) = 14.787 mL 1 cup (c.) = 8 fl.oz. = 236.59 mL 1 pint (pt.) = 2 c. = 473.18 mL 1 quart (qt.) = 2 pt. = 4 c. = 32 fl.oz. = 946.35 mL 1 gallon (gal.) = 3.7854 L Area 1 ft.2 = 144 in.2 1 yd.2 = 9 ft.2 1 acre = 4,840 yd.2 1 m2 = 10,000 cm2 1 hectare (ha) = 10,000 m2 1 km2 = 100 ha Mass 1 pound (lb.) = 16 ounces (oz.) 1 ton, UK (tn.) = 2,240 lbs. 1 kg = 1,000 g 1 tonne (t) = 1,000 kg Length/Area to go from to multiply by cm → in. 0.39 in. → cm 2.54 m → ft. 3.28 ft. → m 0.30 km → mi. 0.62 mi. → km 1.61 m2 → ft.2 10.76 ft.2 → m2 0.09 km2 → mi.2 0.39 mi.2 → km2 2.59 Weight/Capacity to go from to multiply by g → oz. 0.0353 oz. → g 28.35 kg → lbs. 2.2046 lbs. → kg 0.4536 t → tn. 0.9842 tn. → t 1.0161 mL → fl.oz. 0.0338 fl.oz. → mL 29.574 L → US gal. 0.2642 US gal.→ L 3.785 MEASUREMENTS AND CONVERSIONS 1,000 100 10 1 .1 .01 .001 KILO HECTO DECA DECI CENTI MILLI km hm dam m dm cm mm kg hg dag g dg cg mg kL hL daL L dL cL mL Mathematics and Units of Measurement COMMON UNITS used with the International System MEASUREMENT ABBREV. RELATION metre................m.....length hectare. ............ha.....area kelvin. ................K. .... thermodynamic temp. kilogram...........kg.....mass litre.....................L...... volume or capacity second............... s......time hertz..................Hz. ...frequency degree Celsius. .. ˚C.....temperature joule...................J......energy, work pascal. ..............Pa..... pressure, stress newton............. N.....force watt...................W..... power, radiant flux ampere............. A. .... electric current volt.....................V...... electric potential TEMPERATURE °C = 5/9 (°F – 32) °F = 9/5 °C + 32 TENTHS HUNDREDTHS THOUSANDTHS R–9 RESOURCE PAGES

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 3 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 4 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 6 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 7 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140 8 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120 128 136 144 152 160 9 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144 153 162 171 180 10 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 11 11 22 33 44 55 66 77 88 99 110 121 132 143 154 165 176 187 198 209 220 12 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 MULTIPLICATION CHART EXPANDING a(b + c) = ab + ac (a – b)2 = a2 – 2ab + b2 (a + b)2 = a2 + 2ab + b2 (a + b) (c + d) = ac + ad + bc + bd (a + b)3 = a3 + 3a2b + 3ab2 + b3 (a – b)3 = a3 – 3a2b + 3ab2 – b3 FACTORING a2 – b2 = (a + b) (a – b) a3b – ab = ab (a + 1) (a – 1) a2 + 2ab + b2 = (a + b)2 a3 + b3 = (a + b) (a2 – ab + b2) a2 – 2ab + b2 = (a – b)2 a3 – b3 = (a – b) (a2 + ab + b2) ROOTS OF A QUADRATIC The solution for a quadratic equation in the form of ax2 + bx + c = 0 can be found by using the quadratic formula: Algebra Properties of Addition and Multiplication Commutative property of addition a + b = b + a Commutative property of multiplication ab = ba Associative property of addition a + (b + c) = (a + b) + c Associative property of multiplication a(bc) = (ab)c Distributive property of multiplication over addition a(b + c) = ab + ac Distributive property of multiplication over subtraction a(b – c) = ab – ac x-axis y-axis quadrant -5 -4 -3 -2 -1 0 1 2 3 4 5 5 4 3 2 1 -1 -2 -3 -4 -5 (4,3) (4,-3) (-4,-3) (-4,3) THE COORDINATE PLANE LOGARITHMS log a x = n ↔ x = an (log to the base a) loga (xy) = loga x + loga y loga ( x ) = loga x – loga y loga xp = p log a x loga ax = x alog a x = x loga x = logb x logb a y Common log: A log that is written without a base: log x = n, the base is 10: log10 x = n. All loga rules apply. Natural log: A log that is written ln x = n, where the base is e: loge x = n. All loga rules apply. LAW OF EXPONENTS x = –b + b2 – 4ac =+++++++++++++ 2a If a, b e R, a, b 0 and p, q e Q, then: a– p = 1 (a 0) ap 1 2 3 4 5 6 7 8 apaq = ap+q ap aq = ap–q a p= ap (b 0) (b) bp (ap)q = apq (ab)p = apbp ap = q ap q =+++ a0 = 1 (a 0) (a 0) R–10 RESOURCE PAGES

Geometry b1 b b Square Area = b2 Perimeter = 4b Rectangle Area = ab Perimeter = 2(a + b) Parallelogram Area = bh Perimeter = 2(a + b) Trapezoid Area = 1 2 (b1 + b2 )h Perimeter = a + b1 + b2 + c b2 a c h b a Rhombus Area = 1 2 d1 d2 Perimeter = 4b b h a d2 d1 LINES ANGLES Circumference = 2 r Area = r2 approximates 3.14159 or 3 1/7 Arc C = center d = diameter r = radius s = secant t = tangent c = chord s d r C c t x a b C A B x y C y x C Semicircle Circle theorems m x = 90˚ if and only if ab is the diameter m x = m y if both angles are subtended on the same arc, AB 2m x = m y CIRCLES QUADRILATERALS Pentagon 5 sides Hexagon 6 sides Heptagon 7 sides Decagon 10 sides Octagon 8 sides Sum of Interior Angles = 180 (n-2). (n = number of angles) REGULAR POLYGONS Sum of interior angles for any polygon = 180 (n–2). (n = number of angles) SOLIDS s s s Cube Volume = s3 Surface area = 6s2 l w h Pyramid Volume = 1/3· lwh r Sphere Volume = 4/3• r3 Surface area = 4 r2 r h Cylinder Volume = r2h Surface area = 2 rh + 2 r2 l w h Rectangular prism Volume = lwh Surface area = 2wl + 2wh + 2hl r h Cone Volume = 1/3· r2h Surface area = r2+ r r 2+ h2 Volume = B 3 B = area of base s s s Cube Volume = s3 Surface area = 6s2 l w h Pyramid Volume = 1/3· lwh r Sphere Volume = 4/3• r3 Surface area = 4 r2 r h Cylinder Volume = r2h Surface area = 2 rh + 2 r2 l w h Rectangular prism Volume = lwh Surface area = 2wl + 2wh + 2hl r h Cone Volume = 1/3· r2h Surface area = r2+ r r 2+ h2 OR Scalene triangle 0 congruent sides. b h Right triangle 1 right angle. The side opposite the right angle is called the hypotenuse. b h Area = 1/2 bh Isosceles triangle 2 congruent sides. b h Equilateral triangle 3 congruent sides. b h Pythagorean theorem a2 + b2 = c2 b c a Congruency cases Angle, Side, Angle Side, Angle, Side Side, Side, Side Hypotenuse Leg Scalene triangle 0 congruent sides. Scal ne triangle 0 congruent sides. b h Right triangle 1 right angle. The side pposite the right angle is called t e hypotenuse. b h Area = 1/2 bh I osceles triangle 2 congruent sides. b h Equilateral triangle 3 congruent sides. b h Pythagorean th orem a2 + b2 = c2 b c a Congruen y ca es Angle, Side, Angle Side, Angle, Side Side, Side, Side Hypotenuse Leg Scalene tri ngle 0 congruent sides. b h Right riangle 1 right angle. The side opposite the right angle is called the hypotenuse. b h Area = 1/2 bh Isosceles triangle 2 congruent sides. b h Equilateral triangle 3 congruent sides. b h Pythagorean theorem a2 + b2 = c2 b c a Congruency cases Angle, Side, Ang Side, Side Hypote Scalen ri ngle 0 congruent side . b h Right triangl 1 right angle. The side opp site th right angle is called the ypotenuse. b h Area = 1/2 bh Iso celes triangle 2 congruent side . b h Equilateral triangle 3 congruent sides. b h Pythagorean theor m a2 + b2 = c2 b c a Congruency ase Angle, Side Side, Angle, S Side, Side, Sid Hypotenus l o e l ot s TRIANGLES Area = bh 2 Perpendicular lines Line segment Transversal line Ray Line of symmetry Line Parallel lines Reflex angle 180˚ < m x < 360˚ Obtuse angle 90˚ < m x < 180˚ x Straight angle m x = 180˚ x Right angle m x = 90˚ x x Complementary add up to 90˚ Acute angle m x < 90˚ x Supplementary add up to 180˚ R–11 RESOURCE PAGES

RESOU PAGES MATHEMATICS y x x 1 x y x2 0 b y1 y2 x y r θ 1 45˚ 45˚ 1 2 1 60˚ 30˚ 2 3 a c b B r r r y x θ Equation of a straight line y – y 1 = m(x – x 1 ) where m = slope = rise run = y = y 2 – y 1 x x2 – x 1 or y = mx + b where m = slope, b = y-intercept sin = y (opposite/hypotenuse) =1/ csc r cos = x (adjacent/hypotenuse) =1/ sec r tan = y (opposite/adjacent) =1/ cot x tan = 1+cot2 = csc2 sin2 +cos2 = 1 cos 2 –sin2 = cos2 1+tan2 = sec2 sec = 1 sin 45° = 1 cos 45° = = 1 = tan 45° = 1 2 2 2 2 3 3 2 2 sin (A+B) = sin A cos B + cos A sin B sin (A–B) = sin A cos B – cos A sin B tan (A+B) = tan A+ tan B 1– tan A tan B tan (A–B) = tan A – tan B 1 + tan A tan B cos (A+B) = cos A cos B – sin A sin B cos (A–B) = cos A cos B + sin A sin B Quad II Quad I sin+ all ratios+ Quad III Quad IV tan+ cos+ *undefined for and = 1 radian 2π radians = 360° 0 π/2 π/2 π 3π/2 3π/2 2π sin 0 1 0 –1 0 cos 1 0 * –1 0 1 tan 0 0 0 a = b = c sinA sinB sinC a2 = b2+ c2– 2bc cos A b2 = a2+ c2– 2ac cos B c2 = a2+ b2– 2ab cos C y = sin(x) y = cos(x) y = tan(x) sin 30° = 1 cos 30° = 3 tan 30° = 1 = 2 2 3 sin 60° = 3 cos 60° = 1 tan 60° = 3 2 2 cot = cos cos sin sin A C cos * y x -360° -270° -180° -90° 0 90° 180° 270° 360° -2 - 2 1 1 2 -1 2 -1 RESOU PAGES AT EMATICS y x x 1 x y x2 0 b y1 y2 x y r θ 1 45˚ 45˚ 1 2 1 60˚ 30˚ 2 3 a c b B r r r y x θ Equation of a straight line y – y 1 = m(x – x 1 ) where m = slope = rise run = y = y 2 – y 1 x x2 – x 1 or y = mx + b where m = slope, b = y-intercept sin = y (opposite/hypotenuse) =1/ csc r cos = x (adjacent/hypotenuse) =1/ sec r tan = y (opposite/adjacent) =1/ cot x tan = 1+cot2 = csc2 sin2 +cos2 = 1 cos 2 –sin2 = cos2 1+tan2 = sec2 sec = 1 sin 45° = 1 cos 45° = = 1 = tan 45° = 1 2 2 2 2 3 3 2 2 sin (A+B) = sin A cos B + cos A sin B sin (A–B) = sin A cos B – cos A sin B tan (A+B) = tan A+ tan B 1– tan A tan B tan (A–B) = tan A – tan B 1 + tan A tan B cos (A+B) = cos A cos B – sin A sin B cos (A–B) = cos A cos B + sin A sin B Quad II Quad I sin+ all ratios+ Quad III Quad IV tan+ cos+ *undefined for and = 1 radian 2π radians = 360° 0 π/2 π/2 π 3π/2 3π/2 2π sin 0 1 0 –1 0 cos 1 0 * –1 0 1 tan 0 0 0 a = b = c sinA sinB sinC a2 = b2+ c2– 2bc cos A b2 = a2+ c2– 2ac cos B c2 = a2+ b2– 2ab cos C y = sin(x) y = cos(x) y = tan(x) sin 30° = 1 cos 30° = 3 tan 30° = 1 = 2 2 3 sin 60° = 3 cos 60° = 1 tan 60° = 3 2 2 cot = cos cos sin sin A C cos * y x -360° -270° -180° -90° 0 90° 180° 270° 360° -2 - 2 1 1 2 -1 2 -1 RES PAG MATHEMATICS y x x 1 x y x2 0 b y1 y2 x y r θ 1 45˚ 45˚ 1 2 1 60˚ 30˚ 2 3 a c b B r r r y x θ Equation of a straight line y – y 1 = m(x – x 1 ) where m = slope = rise run = y = y 2 – y 1 x x2 – x 1 or y = mx + b where m = slope, b = y-intercept sin = y (opposite/hypotenuse) =1/ csc r cos = x (adjacent/hypotenuse) =1/ sec r tan = y (opposite/adjacent) =1/ cot x tan = 1+cot2 = csc2 sin2 +cos2 = 1 cos 2 –sin2 = cos2 1+tan2 = sec2 sec = 1 sin 45° = 1 cos 45° = = 1 = tan 45° = 1 2 2 2 2 3 3 2 2 sin (A+B) = sin A cos B + cos A sin B sin (A–B) = sin A cos B – cos A sin B tan (A+B) = tan A+ tan B 1– tan A tan B tan (A–B) = tan A – tan B 1 + tan A tan B cos (A+B) = cos A cos B – sin A sin B cos (A–B) = cos A cos B + sin A sin B Quad II Quad I sin+ all ratios+ Quad III Quad IV tan+ c s+ *undefined for and = 1 radian 2π radians = 360° 0 π/2 π/2 π 3π/2 3π/2 2π sin 0 1 0 –1 0 cos 1 0 * –1 0 1 tan 0 0 0 a = b = c sinA sinB sinC a2 = b2+ c2– 2bc cos A b2 = a2+ c2– 2ac cos B c2 = a2+ b2– 2ab cos C y = sin(x) y = cos(x) y = tan(x) sin 30° = 1 cos 30° = 3 tan 30° = 1 = 2 2 3 sin 60° = 3 cos 60° = 1 tan 60° = 3 2 2 cot = cos cos sin sin A C cos * y x -360° -270° -180° -90° 0 90° 180° 270° 360° -2 - 2 1 1 2 -1 2 -1 RESOU PAGES MATHEMATICS y x x 1 x y x2 0 b y1 y2 x y r θ 1 45˚ 45˚ 1 2 1 60˚ 30˚ 2 3 a c b B r r r y x θ Equation of a straight line y – y 1 = m(x – x 1 ) where = slope = rise run = y = y 2 – y 1 x x2 – x 1 or y = mx + b where m = slope, b = y-intercept sin = y (opposite/hypotenuse) =1/ csc r cos = x (adjacent/hypotenuse) =1/ sec r tan = y (opposite/adjacent) =1/ cot x tan = 1+ t2 = csc2 si 2 + o 2 1 cos 2 –sin2 = cos2 1+tan2 = sec2 sec = 1 sin 45° = 1 cos 45° = = 1 = tan 45° = 1 2 2 3 2 sin (A+B) = sin A cos B + cos A sin B si ( – ) i os B – c s si tan (A+B) = tan A+ tan B 1– tan A tan B tan (A–B) = tan A – tan B 1 + tan A t B cos (A+B) = cos A cos B – sin A sin B s ( – ) + i i Quad II Quad I sin+ all ratios+ Quad III Quad IV tan+ cos+ *undefined for and = 1 radian 2π radians = 360° 0 π/2 π/2 π 3π/2 3π/2 2π sin 1 0 –1 0 cos 1 0 * –1 0 1 tan 0 0 0 a = b = c sinA sinB sinC a2 = b2+ c2– 2bc cos A b2 a + 2 a c B c = b2 b c s C y = sin(x) y = cos(x) y = tan(x) sin 30° = 1 cos 30° = 3 tan 30° = 1 = 2 2 3 sin 60° = 3 cos 60° = 1 tan 60° = 3 2 2 cot = cos cos sin A C cos * y x -360° -270° -180° -90° 0 90° 180° 270° 360° -2 - 2 1 1 2 -1 2 -1 RESOU MATHE I S y x x 1 x y x2 0 y1 y2 x y r θ 1 45˚ 45˚ 1 2 1 60˚ 30˚ 2 3 a c b r r r y x θ Equation f str i t li y 1 m( – 1 ) wher sl ise run y 2 – 1 x2 – x 1 or w r sl , -i t r t sin = y ( sit / t s ) / csc c s x ( j t/hypote use) 1/ sec r tan = (opposite/adjacent) = / cot x t c t2 csc2 sin2 +cos2 = 1 c s 2 si 2 = cos2 1+tan2 sec2 sec = 1 si ° 1 cos 45° = 1 = tan 45° = 1 2 2 2 3 2 + ) i c + s si sin ( ) sin A cos c s si t ( ) tan A+ tan B t t B t n (A–B) t A t t t c ) i i c s ( ) = cos A cos B + sin A si Q II I sin+ ll r ti s+ Quad III I t c s *undefined for = 1 radian 2π radians = ° 0 π/ π/2 π 3π/ 3π/ si 1 0 1 cos 1 0 * –1 0 1 t 0 = = c si sinB si a2 = 2 2 c b2 = 2 c c c s B c2 2 2 c s C i ( ) ( ) t ( ) sin 30° = cos 30° tan 30° = = 2 3 sin 60° = c s ° ta ° cot cos cos sin sin A C cos * y x -360° -270° -180° -90° ° 180° ° ° - - 1 2 -1 2 -1 RESOU PAGES MATHEMATICS y x x 1 x y x2 0 b y1 y2 x y r θ 1 45˚ 45˚ 1 2 1 60˚ 30˚ 2 3 a c b B r r r y x θ Equation of a straight line y – y 1 = m(x – x 1 ) where m = slope = rise run = y = y 2 – y 1 x x2 – x 1 or y = mx + b where m = slope, b = y-intercept sin = y (opposite/hypotenuse) / csc r cos = x (adjacent/hypotenuse) =1/ sec r tan = y (opposite/adjacent) =1/ cot x tan = 1+cot2 = csc2 sin2 +cos2 = 1 cos 2 –sin2 = cos 1+tan2 = sec2 sec = 1 sin ° cos ° 1 = tan 45° = 1 2 2 2 3 3 sin (A+B) = sin A cos B + cos A sin B sin (A–B) = sin A cos B – cos A sin B tan (A+B) = an + t – t ta tan (A–B) = tan A – tan B 1 + tan A tan B cos (A+B) = cos A cos B – sin A sin B cos (A–B) = cos A cos B + sin A sin B Quad II ua I si all ratios+ Quad III Quad IV tan+ cos+ *undefined for and = 1 radian 2π radians = 360° π/2 π/2 π 3π/2 3π/2 2π sin 0 1 0 –1 0 cos 1 0 * –1 0 1 tan 0 0 0 a = b = c sinA sinB sinC a2 = b2+ c2– 2bc cos A b2 = a2+ c2– 2ac cos B c2 = a2+ b2– 2ab cos C y = sin(x) y = cos(x) y = tan(x) sin ° 1 cos ° 3 tan 30° = 1 = 2 3 sin 60° 3 cos 60° = 1 tan 60° = 3 2 cot = o cos sin sin A C cos * y x -360° -270° -180° -90° 0 90° 180° 270° 360° -2 - 2 1 1 2 -1 2 -1 RESOURCE PAGES EMATICS y x x 1 x y x2 0 b y1 y2 x y r θ 45˚ 1 2 1 60˚ 30˚ 2 3 a c b B r r r y x θ on of a straight line m(x – x 1 ) m = slope = rise run = y = y 2 – y 1 x x2 – x 1 or y = mx + b where m = slope, b = y-intercept y (opposite/hyp tenu e) =1/ csc r x (adjacent/hypotenuse) =1/ sec r y (opposite/adjacent) =1/ cot x tan = 1+cot2 = csc2 sin2 +cos2 = 1 cos 2 –sin2 = cos2 1+tan2 = sec2 c = 1 sin 45° = 1 cos 45° = = 1 = tan 45° = 1 2 2 2 2 3 3 2 2 +B) = sin A cos B + co A sin B –B) = sin A cos B – cos A sin B tan (A+B) = tan A+ tan B 1– tan A tan B tan (A–B) = tan A – tan B 1 + tan A tan B cos (A+B) = cos A cos B – sin A sin B cos (A–B) = cos A cos B + sin A in B Quad II sin+ all r tios+ Quad III uad IV tan+ cos *undefined for and = 1 radian 2π radians = 360° 0 π/2 π/2 π 3π/2 3π/2 2π sin 0 1 0 –1 0 cos 1 0 * –1 0 1 tan 0 0 0 a = b = c sinA sinB sinC a2 = b2+ c2– 2bc cos A b2 = a2+ c2– 2ac cos B c2 = a2+ b2– 2ab cos C in(x) y = co (x) y = tan(x) sin 30° = 1 cos 30° = 3 tan 30° = 1 = 2 2 3 sin 60° = 3 cos 60° = 1 tan 60° = 3 2 2 cot = cos cos sin sin A C cos * y x -360° -270° -180° -90° 0 90° 180° 270° 360° -2 - 2 1 1 2 -1 2 -1 RESOU PAGES MATHEMATICS y x x 1 x y x2 0 b y1 y2 x y r θ 1 45˚ 45˚ 1 2 1 60˚ 30˚ 2 3 a c b B r r r y x θ Equation of a straight line y – y 1 = m(x – x 1 ) where m = slope = rise run = y = y 2 – y 1 x x2 – x 1 or y = mx + b where m = slope, b = y-intercept sin = y (opposite/hypotenuse) =1/ csc r cos = x (adjacent/hypotenuse) =1/ sec r tan = y (opposite/adjacent) =1/ cot x tan = 1+cot2 = csc2 sin2 +cos2 = 1 cos 2 –sin2 = cos2 1+tan2 = sec2 sec = 1 sin 45° = 1 cos 45° = = 1 = ta ° 1 2 2 2 3 3 2 2 sin (A+B) = sin A cos B + cos A sin B sin (A–B) = sin A cos B – cos A sin B tan (A+B) = tan A+ tan B 1– tan A tan B tan (A–B) = tan A – tan B 1 + tan A ta cos (A+B) = cos A cos B – sin A sin B cos (A–B) = cos A cos B + sin A sin B Quad II Quad I sin+ all ratios+ Quad III Quad IV tan+ cos+ *undefi ed for and = 1 radian 2π radians = 360° 0 π/2 π/2 π 3π/2 3π/2 2π sin 0 1 0 –1 0 cos 1 0 * –1 0 1 tan 0 0 0 a = b = c sinA sinB sinC a2 = b2+ c2– 2bc cos A b2 = a2+ c2– 2ac cos B c2 = a2+ b2– ab cos C y = sin(x) y = cos(x) y = tan(x) sin 30° = 1 cos 30° = 3 tan 30° = 1 = 2 2 3 sin 60° = 3 cos 60° = 1 tan 60° 2 2 cot = cos co sin sin A C cos * y x -360° -270° -180° -90° 0 90° 180° 270° 360° -2 - 2 1 1 2 -2 -1 RESOU PAGES AT E ATICS y x x 1 x y x2 0 b y1 y2 x y r θ 1 45˚ 45˚ 1 2 1 60˚ ˚ 2 3 a c b B r r r y x θ Equation of a straight line y – y 1 = m(x – x 1 ) where m = slope = rise run = y = y 2 – y 1 x x2 – x 1 or y = mx + b where = slope, b = y-intercept sin = y (opposite/hypotenuse) =1/ csc r cos = x (adjacent/hypotenuse) =1/ sec r tan = y (opposite/adjacent) =1/ cot x tan = 1+cot2 = csc2 sin2 +cos2 = 1 cos 2 –sin2 = cos2 1+tan2 = sec2 sec = 1 sin 45° = 1 cos 45° = = 1 = tan 45° = 1 2 2 2 2 3 3 2 2 sin (A+B) = sin A cos B + cos A sin B sin (A–B) = sin A cos B – cos A sin B tan (A+B) = tan A+ tan B 1– tan A tan B tan (A–B) = t A – tan B 1 + tan A tan B cos (A+B) = cos A cos B – sin A sin B cos (A–B) = cos A cos B + sin A sin B Quad II Qu d I sin+ all ratios+ Qu d III Quad IV tan+ cos+ *undefined for and = 1 radian 2π radians = 360° 0 π/2 π/2 π 3π/2 3π/2 2π sin 0 1 0 –1 0 cos 1 0 * –1 0 1 ta 0 0 0 a = b = c sinA sinB sinC a2 = b2+ c2– 2bc cos A b2 = a2+ c2– 2ac cos B c2 = a2+ b2– 2ab cos C y = sin(x) y = cos(x) y = tan(x) sin 30° = 1 cos 30° = 3 ta 30° = 1 = 2 2 3 sin 60° = 3 cos 60° = 1 tan 60° = 3 2 2 cot = cos cos sin sin A C cos * y x -360° -270° -180° -90° 0 90° 180° 270° 360° -2 - 2 1 1 2 -1 2 -1 Linear Trigonometry TRIGONOMETRIC RATIOS C A S T Value of trig ratio SINE LAW COSINE LAW R–12 RESOURCE PAGES

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