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The Wellness Project-High

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 Printed on recyclable paper PL-WPHE-5B-00-CA23pp ISBN: 978-1-990714-08-5 T HE WELLNESS PROJE C T Ways Your Planner Supports Your Mental Wellness . ...... 2 August: MENTAL WELLNESS. ............................................ 3 September: SELF-CARE........................................................ 1O October: GROWTH MINDSET. ............................................ 22 November: STRESS.............................................................. 34 December: EMOTIONS.......................................................... 48 January: PURPOSE................................................................ 6O February: RELATIONSHIPS................................................. 72 March: RESILIENCE............................................................... 86 April: PHYSICAL HEALTH...................................................... 98 May: AUTHENTICITY .......................................................... 11O June: DIGITAL WELLNESS.................................................... 124 July: HOPE.............................................................................. 136 Self-Care Checklist................................................................ 144 Resource Pages: Language Arts, Math, Science, and More.......................... R–1 WELLNESS Welcome to THE PROJECT ! We are the greatest projects we’ll ever work on. So, let’s spend this year caring for ourselves and prioritizing our mental wellness.

September/septembre 2023 SELF-CARE fully CHARGEd • Trouble sleeping • Appetite changes • Frequent illness • Irritability • Frustration • Tense muscles • Increased stress • Apathy • Rest • Movement • Hydration • Nourishing food • Quality sleep • Time in nature • Fun with friends/family • Hobbies Failing to recharge your battery often can damage your mental wellness. 1:42 5:24 When our phone's battery is dying, we go into rapid response mode. We’ll go to great lengths to charge our phones, yet we tend to ignore our bodies’ low-battery signals. Why? Because we can function for a long time in the red without realizing it. 10

T HE WE L L NESS PROJEC T List ways you can care for your physical, mental, and emotional wellness.  Creating a consistent sleep schedule  Spending 3O minutes in nature  Stretching before heading to bed To make self-care a daily routine, try: 11

MONTHLY GOALS AND TO-DO’S LONG-TERM PROJECT PLANNING: LIST YOUR PROJECT STEPS: Sunday/dimanche Monday/lundi Tuesday/mardi Monthly goals are long-term goals. 3 4 5 10 1 1 12 17 18 19 24 25 26 * * * * * * * * * * * * Yom Kippur (sundown) Terry Fox Run Labour Day September septembre 2023 Plan Mindfully! Our planner is a support system that helps us get organized and manage stress. Using it daily is a form of self-care. CONNECT Feeling worn out or overwhelmed? Practise self-care. Form a plan with an adult you trust. 12

DUE DATE Wednesday/mercredi Thursday/jeudi Friday/vendredi Saturday/samedi Pick one long-term goal. Check a calendar box each day you work on it. 1 2 6 7 8 9 13 14 15 16 20 21 22 23 27 28 29 30 Rosh Hashanah (sundown) National Day for Truth and Reconciliation * * * * * * * * * * * * * * * * * * 13

Tuesday/mardi Wednesday/mercredi Monday/lundi Day Day Day WEEKLY GOALS S M T W T F S Labour Day What makes it hard for you to prioritize self-care? 4 5 6 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 September septembre 2023 14

T HE WE L L NESS PROJE C T Saturday/samedi Sunday/dimanche Thursday/jeudi Friday/vendredi WEEKLY CHECK MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY Day Day RECHARGE REGULARLY Regular self-care routines help prevent burnout and maintain our physical, mental, and emotional health. 7 8 9 10 You PRIORITy. are a 15

Tuesday/mardi Wednesday/mercredi Monday/lundi Day Day Day WEEKLY GOALS S M T W T F S Are you consuming anything that’s bringing you down? 1 1 12 13 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 September septembre 2023 16

T HE WE L L NESS PROJE C T Saturday/samedi Sunday/dimanche Thursday/jeudi Friday/vendredi WEEKLY CHECK MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY Day Day Terry Fox Run Rosh Hashanah (sundown) DID YOUKNOW? Everything we consume contributes to our health: food, books, music, social media, movies, and opinions. 14 15 16 17 CARe TAKE OF YOURSELF. 17

Tuesday/mardi Wednesday/mercredi Monday/lundi Day Day Day WEEKLY GOALS S M T W T F S List people and activities that energize you. 18 19 20 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 September septembre 2023 18

T HE WE L L NESS PROJE C T Saturday/samedi Sunday/dimanche Thursday/jeudi Friday/vendredi WEEKLY CHECK MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY Day Day Yom Kippur (sundown) SUPER STRATEGY Self-care is free. It’s anything we intentionally do to care for our mental, physical, and emotional health. 21 22 23 24 YOURSELf. SHOW UP FOR 19

Tuesday/mardi Wednesday/mercredi Monday/lundi Day Day Day WEEKLY GOALS S M T W T F S Do you treat people differently when you’re stressed or tired? 25 26 27 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 September septembre 2023 20

T HE WE L L NESS PROJE C T Saturday/samedi Sunday/dimanche Thursday/jeudi Friday/vendredi WEEKLY CHECK MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY Day Day National Day for Truth and Reconciliation FILL UP FOR FRIENDS Taking time to care for ourselves gives us energy to listen well, empathize with others, and show compassion. 28 OCT. 29 30 1 break. ok it's A to TAKe 21

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

Problem Solving IDENTIFY Find out what the real problem is; check the data. GUESS AND CHECK • Think about strategies and relationships among variables. • Draw a picture, graph, or table. SOLVE Use the right strategy and formula. CHECK • Does the solution make sense? • Was your strategy effective? The Scientific Method STAGE 1 • Identify a question you want to solve. • Gather information. STAGE 2 Make your hypothesis, or predict what you will find out. STAGE 3 Research, experiment, and record the results. STAGE 4 • Analyze the data; ask, do the findings support the hypothesis? • Conduct more tests. • Publish your conclusion. UNIFORM MOTION m 1. DENSITY D m V density mass volume 2. MOTION d v t total distance m average velocity time s 3. AVERAGE VELOCITY AND ACCELERATION a vf vi t acceleration final velocity initial velocity time s 4. WITH CONSTANT ACCELERATION d vi t a distance m initial velocity time s acceleration 5. NEWTON’S SECOND LAW F m a net force N (= Newton) mass kg acceleration 6. GRAVITY Fg G 1,m2 d force of gravity N universal gravitational constant masses of the two objects kg distance between centres m 7. MOMENTUM p m v momentum mass kg velocity 8. WORK AND POWER W F d work J (= Joule) force N distance m 9. WORK AND POWER p W t power W (= Watt) work J time s 10. ENERGY KE m v kinetic energy J mass kg velocity 11. STATIC ELECTRICITY FE k q1,q2 d electrical force N Coulomb’s constant electrical charges C separation distance m 12. CURRENT ELECTRICITY V W q electrical potential difference V (= Volt) work done J electric charge C 13. CURRENT ELECTRICITY I q t electric current A (= Ampère) electric charge flowing C time s 14. CURRENT ELECTRICITY W V I t electrical energy J voltage V current A time s 15. CURRENT ELECTRICITY P V I power W voltage V current A 16. ENERGY TRANSFER q m ΔT c energy transfer J mass kg change in temperature °C specific heat capacity OTHER USEFUL CONSTANTS g = 9.80 m/s2 M = 5.98 x 1024 kg c = 3.00 x 108 m/s acceleration due to gravity on Earth mass of Earth speed of light 1 g 1000 kg ( cm3 = m3 ) m s m s m s m s m s2 m s2 m s2 ( k = 9x109 N·m2 ) C2 Kg · °C J m s Physics Equations ( G = 6.67x10–11 N·m2 ) kg2 s kg•m Problem Solving IDENTIFY Find out what the real problem is; check the data. GUESS AND CHECK • Think about strategies and relationships among variables. • Draw a picture, graph, or table. SOLVE Use the right strategy and formula. CHECK • Does the solution make sense? • Was your strategy effective? The Scientific Method STAGE 1 • Identify a question you want to solve. • Gather information. STAGE 2 Make your hypothesis, or predict what you will find out. STAGE 3 Research, experiment, and record the results. STAGE 4 • Analyze the data; ask, do the findings support the hypothesis? • Publish your conclusion. D = m V d = v·t a = vf–vi t d = vi·t+ 1 ·a·t 2 2 F = m·a Fg = G·m1 ·m2 d2 p = m·v W = F·d P = W t KE = 1 ·m·v2 2 V = W q W = V·I·t I = q t P = V·I q = m·c·ΔT FE = k·q1·q2 d2 m s R-12 RESOURCE PAGES SCIENCE Physics Equations R–13 RESOURCE PAGES

Periodic Table of the Elements R–14 RESOURCE PAGES

PLANETS Photos of planets are not proportionally to scale. SYMBOL DIAMETER AVERAGE DISTANCE FROM SUN (MILLION MI OR KM) MASS ROTATIONAL PERIOD (LENGTH OF DAY IN EARTH DAYS) PERIOD OF REVOLUTION ABOUT THE SUN (1 PLANETARY YEAR IN EARTH DAYS) Mercury Inner Planet 3,032 mi 4,878 km 36.0 mi 57.9 km 3.30 x 10 23 kg 58.64 days 88.0 days Venus Inner Planet 7,521 mi 12,104 km 67.2 mi 108.2 km 4.87 x 10 24 kg 243 days (retrograde) 224.7 days Earth Inner Planet 7,926 mi 12,756 km 93.0 mi 149.6 km 5.98 x 10 24 kg 23 hrs, 56 min, 4.1 sec 365.2 days Mars Inner Planet 4,221 mi 6,794 km 141.6 mi 227.9 km 6.42 x 10 23 kg 24 hrs, 37 min, 22.3 sec 687 days Jupiter Outer Planet 88,846 mi 142,984 km 483.8 mi 778.6 km 1.90 x 10 27 kg 9 hrs, 50 min (equator) 9 hrs, 55 min (poles) 4,331 days Saturn Outer Planet 74,897 mi 120,536 km 890.8 mi 1,433.5 km 5.68 x 10 26 kg 10 hrs, 39 min 10,747 days Uranus Outer Planet 31,763 mi 51,118 km 1,784.8 mi 2,872.5 km 8.68 x 10 25 kg 17 hrs, 14 min (retrograde) 30,589 days Neptune Outer Planet 30,775 mi 49,528 km 2,793.1 mi 4,495.1 km 1.02 x 10 26 kg 16 hrs, 7 min 59,800 days SYMBOL DIAMETER MAX. DISTANCE FROM EARTH MASS ROTATIONAL PERIOD (LENGTH OF DAY IN EARTH DAYS) INTERIOR TEMPERATURE Sun 864,000 mi 1,390,000 km 94.5 million mi 152 million km 1.98 x 10 30 kg Rotates in 25 days (equator) or 34 days (poles) 15 million K ROTATIONAL PERIOD (LENGTH OF DAY IN EARTH DAYS) AVERAGE EARTH–MOON DISTANCE Moon 27.32 days 3.84 x 108 m INNER SOLAR SYSTEM SUN MERCURY: 0.39 VENUS: 0.72 EARTH: 1.0 MARS: 1.5 JUPITER: 5.2 SATURN: 9.5 URANUS: 19.2 NEPTUNE: 30.1 Our Solar System PLANETARY DISTANCES The average distance from a planet to the sun is measured in Astronomical Units (AU). 1.0 AU is defined as 9.3 x 107 miles or 1.5 x 108 km. Measurements given in the diagram are in AU. Not to scale. STATISTICS PHASES OF THE MOON THIRD QUARTER FIRST QUARTER WANING CRESCENT WAXING CRESCENT FULL WANING GIBBOUS WAXING GIBBOUS NEW Statistics from June 2017. Sources: nssdc.gsfc.nasa. gov/planetary/factsheet/planet_table_british.html nssdc.gsfc.nasa.gov/planetary/factsheet/index.html R–15 RESOURCE PAGES

3. Inform Yourself Investigate a variety of career paths. Know the facts: • What qualifications are required? • Is there room for personal and professional growth? • Are there jobs open now? • What’s the projected growth? • W hat are the working conditions? 4. Prepare Yourself Get ready. Prepare your job- hunting tools. • Create a resumé and cover letter. • Contact people for references. • Investigate companies that interest you. (Use the library.) 5. Present Yourself Make yourself stand out! • Prepare a great resumé. • Create a cover letter for each company. The more knowledge you have about a chosen career, the better your decision will be. 1. Assess Yourself Employers are looking for certain skills and attitudes. Think about it: • What interests and skills have you developed? • What do you like best: working with people, things, or ideas? • What goals and values have you set for yourself? 2. Explore Possibilities Interested in a few careers? Check them out: • Search the web. • Volunteer or work part-time. • Get to know what they are all about through talking to people in a specific field, observing them at work, or visiting professional meetings. Network. • Find out about internships, summer jobs, and other options. TIP Thinking About Career Planning? THINK ABOUT YOUR COMMUNITY! Your community is one of your best resources for information on careers, finances, etc. See your academic advisor or counsellor. Get informed! Success doesn’t happen by itself. Make a plan! Chart your course! The sooner you start, the sooner you will begin to achieve your goals. Here are some tips to help you reach your destination. STEPS TO TAKE Don’t base important decisions on only one experience. Give everything a fair trial, and keep your options open. TIP R–16 RESOURCE PAGES

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