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MATHEMATICS 30-1 Course Outline Mrs. Orchard – Semester II, 2016-17 Course Schedule UNIT CLASSES EXAM DATES (may vary slightly) MARK % 1. Transformations and Functions; Radical Functions (Ch 1&2) 13 February 22 _______ 2. Polynomial Functions (Ch 3) 9 March 8 _______ 3. Rational Functions; Function Operations (Ch 9 & 10) 11 March 23 _______ 4. Exponents and Logarithms (Ch 7 & 8) 12 April 20 _______ 5. Trigonometry: unit circle, functions, graphs (Ch 4 & 5) 12 May 9 _______ 6. Trigonometric Identities (Ch 6) 12 May 30 _______ 7. Permutations and Combinations (Ch 11) 12 June 16 _______ RE-WRITE DIPLOMA EXAM Monday, June 26 Note: English Part A June 15, Social Part A June 16 Course Description Mathematics 30-1 builds on key concepts from Mathematics 20-1. Learning through problem solving is the key focus. Students develop and refine their own way of solving problems and show their work in a variety of ways. Students use mathematical vocabulary to explain how they solve problems and continue to acquire the mathematical processes of communication, making connections, mental mathematics, and visualization, and the use of technology as a tool. Students who believe they can learn, take risks and persevere in problem solving will be successful mathematics students. The topics in Mathematics 30-1 include: Trigonometry: develop trigonometric reasoning Relations and Functions: develop algebraic and graphical reasoning through the study of relations Permutations, Combinations and Binomial Theorem: develop algebraic and numeric reasoning that involves combinatorics Evaluation There will be a unit exam after each unit. In addition to the 7 unit exams, assignments designed to promote understanding will occur throughout the course. Opportunity to improve an exam mark will be offered at specified points throughout the semester. Rewrite opportunities will be at the teacher’s discretion after you have filled out a re-write form and have displayed evidence of practice and attention to further your learning. Staying on task and keeping pace with the class is important. With this in mind, UNIT STUDY NOTES should be presented to me prior to each unit exam in order for me to consider granting a re-write opportunity. The mark you achieve in class will be worth 70% of your final Math 30-1 mark, leaving the Diploma exam worth 30% of your final mark. Exams and assignments 1. If you are absent for an exam, you are required to write the exam upon your return at an agreed upon time and location. 2. Please be aware that everything counts. All work assigned (assignments, quizzes, exams) may be used to determine your grade in this course. Once an assignment or quiz is handed back to the students, any late assignments will not be accepted for the purpose of assessment. Required Materials Pre-Calculus 12 textbook, a binder, a pencil, and a graphing calculator. The Key is a booklet that contains an ample amount of previous Diploma questions and solutions to help you prepare for the Diploma Exam. There are also a number of useful websites. Please see Mrs. Cooke ASAP if you wish to purchase this booklet. Classroom Expectations 1. Give your best effort every day; ask questions when you don’t understand. DO NOT FALL BEHIND! 2. Attend class regularly. 3. Conduct yourself in a courteous, respectful manner and comply with all school rules listed in the online student agenda. 4. If you are late, get a late slip and enter the room in a respectful manner. 5. Use washrooms before class begins. 6. Be sitting at your desk when the bell rings. 7. Bring your required materials to class every day. 8. Please refrain from consuming any food or drink during the entire class, with the exception of water. 9. If the use of a personal device is deemed to be a distraction to the learning environment, it WILL result in confiscation of the device in question. No exceptions. No arguments. 10. Review notes and class work every night and complete homework as assigned. 11. Review notes and class work every night and complete homework as assigned. 12. Review notes and class work every night and complete homework as assigned. 13. Review notes and class work every night and complete homework as assigned. 14. Preparation to leave the classroom at the end of the period includes ensuring that your work area is neat. Unit 1 Transformations and Functions; Radical Functions (Ch 1&2) 1.1 Horizontal and Vertical Translations – pg. 6–15 Assignment: pg. 12–15 #1, 2a, 3, 4b sketch only, 5 - 9, 17, 19, C3 1.2 Stretches and Reflections – pg. 16–31 Assignment: pg 28–31 #2, 5ab, 6, 7ac, 8,9 14acd, 15cd, C4 Assignment: pg. 28–31 #1ad, 3, 4, 5cd, 7bd, 14b, 15ab, 16, C2, C3 1.3 Combining Transformations – pg. 32–43 Assignment: pg. 38–43 #2,3,4,5a (graph paper),6, 7 PC3, 9 PC 3 (graphs), 10, C2, C3 1.4 Inverse of a Relation – pg. 44–55 Assignment: Page 51 #2-4, 5a,c,e, 6, 7a,8a,c, 9a,d, 11, 12a,b,c, 13,15,16,17,21 Chapter Review and Practice Test – pg. 56–58 Assignment: pg. 56–57 #1–17 2.1 Radical Functions and Transformations – pg. 62–77 Assignment: pg. 72–77 #3, 4, 6, 9, 10, 13, 16 2.2 Square Root of a Function – pg. 78–89 Assignment: pg. #2-6, 8, 9, 16 2.3 Solving Radical Equations Graphically – pg. 90–98 Assignment: pg. 96–98 #1, 2, 3 PC2, 4, 5 PC2, 6, 7 PC2, 9, 10, 12, 13, 16 Chapter Review and Practice Test– pg. 99 - 102 Unit 1 Exam Date:______________________________ Need to review/remember: Unit 2 Polynomial Functions (Ch 3) 3.1 Characteristics of Polynomial Functions – pg. 106–117 Assignment: pg. 114–117 #1–9 3.2 The Remainder Theorem – pg. 118–125 Assignment: pg. 124–125 #2, 4 PC3 for each, 6 ab, 8 ac, 10, 11a, 16 3.3 The Factor Theorem – pg. 126 – 135 Assignment: pg. 133–135 #1-4 PC 2 for each, 5 and 6 PC 5 total, 7-9, 11, 15, 16 i,ii,iii omit d) 3.4 Equations and Graphs of Polynomial Functions – pg. 136–152 Assignment: pg. 147–152 #3-6, 7 bd, 9 bef, 10 Assignment: pg. 147–152 # pg. 150–151 #12-16, 18 Chapter Review and Practice Test – pg. 153–156, pg 160 Assignment: Pg. 153–156 #1, 2(odd), 3, 4cd, 5a, 6, 7, 8(odd), 10–14 Unit 2 Exam Date:______________________________ Need to review/remember: Unit 3 Rational Functions; Function Operations (Ch 9 & 10) 9.1 Rational Functions using Transformations I – pg. 430–445 Assignment: pg. 442 Rational Functions using Transformations II – pg. 430–445 Assignment: pg. 443–445 9.2 Analyzing Rational Functions – pg. 446–456 Assignment: pg. 451–456 9.3 Graphs and Rational Equations – pg. 457–467 Assignment: pg. 465–467 10.1 Sums and Differences of Functions – pg. 474–487 Assignment: pg. 483–487 10.2 Products and Quotients of Functions – pg. 488–498 Assignment: pg. 496–498 10.3 Composite Functions – pg. 499–509 Assignment: pg. 507–509 Chapter Review – pg. 468–469, pg. 510–511 Assignment: pg. 468–469 Unit 6 Exam Date:______________________________ Need to review/remember: Unit 4 Exponents and Logarithms (Ch 7 & 8) 7.1 Exponential Functions – pg. 334–345 Assignment: pg. 342–345 #1-8, 10-12, 15 7.2 Transformations of Exponential Functions – pg. 346–357 Assignment: pg. 354–357 #1, 2, 4, 5ab, 6 PC2, 7, 9, 10, 11, 14 7.3 Solving Exponential Equations – pg. 358–365 Assignment: pg. 364–365 #2-5, 7-9 8.1 Logarithms and their functions – pg. 372–382 Assignment: pg. 380–382 8.2 Transformations of Logarithmic Functions – pg. 383–391 Assignment: pg. 389–391 8.3 Laws of Logarithms I – pg. 392–403 Assignment: pg. 400–403 Laws of Logarithms II – pg. 392–403 Assignment: pg. 401–403 8.4 Logarithmic and Exponential Equations – pg. 404–415 Assignment: pg. 412–413 Applications of Logarithmic and Exponential Equations – pg. 404–415 Assignment: pg. 413–415 Chapter Review – pg. 366–367, pg. 416–418 Assignment: Unit 5 Exam Date:______________________________ Need to review/remember: Unit 5 Trigonometry: unit circle, functions, graphs (Ch 4 & 5) 4.1 Angles and Angle Measure – pg. 166–179 Assignment: pg. 175–179 # 1-8 PC 2 for each, 11 adh, 12 bc, 15, 17 a-f, 18, 27 abc 4.2 The Unit Circle – pg. 180–190 Assignment: pg. 186–190 #1–5(odd), 6, 10, 11, 12a, 13 4.3 Trigonometric Ratios – pg. 191–205 (I) Assignment: pg. 201–205 #1 PC4, 3, 6, 8, 12 PC2 (II) Assignment: pg. 202–205 #2, 7, 9, 10ab, 11ab, 13, 16 4.4 Trigonometric Equations – pg. 206–214 Assignment: pg. 211–214 #1, 2, 4 PC 3, 5 PC 1, 6, 7ac, 8–11, 15, 16, 18 5.1 Graphing Sine and Cosine Functions – pg. 222–237 Assignment: pg.233–237 #4–10, 15, 18, 19 5.2 Transformations of Sinusoidal Functions I – pg. 238–255 Assignment: pg. 250–255 #1 PC3, 2 PC3, 3-5, 6a, 7ab Assignment: pg. 250–255 #8, 9, 11, 14-16, 22-24, 27 PC2 5.3 The Tangent Function – pg. 256–265 Assignment: pg. pg. 262–265 #1-4, 6, 8, 9, 12 5.4 Equations and Graphs of Trigonometric Functions I– pg. 266–280 Assignment: pg. 275 #1, 3, 4ab, 6z Assignment: pg. 275–279 #9, 10, 12, 13, 15, 16, 19 Chapter Review (2 days)– pg. 215–217, pg. 282–285 Assignment: pg. 215–217 #1, 2, 5, 7, 9, 11, 13–15, 17, 19–21, 23 pg. 282–285 #3–7, 8, 10–13, 15, 16, 18, 19, 20, 22, 23 Unit 3 Exam Date:______________________________ Need to review/remember: Unit 6 Trigonometric Identities (Ch 6) 6.1 Reciprocal, Quotient, and Pythagorean Identities – pg. 290–297 Assignment: pg. 296–297 #1, 3 – 6, 10, 11, 13 6.2 Sum, Difference, and Double–Angle Identities – pg. 299–308 Assignment: pg. 306–308 6.3 Proving Identities – pg. 309–315 Assignment: pg. 314–315 6.4 Solving Trigonometric Equations Using Identities – pg. 316 – 321 Assignment: pg. 320–321 Chapter Review – pg. 322–323 Assignment: pg. 322–323 Unit 4 Exam Date:______________________________ Need to review/remember: Unit 7 Permutations and Combinations (Ch 11) 1. Fundamental Counting Principle Assignment: Absolute Value Workbook: pg. 375 – 378 #1–14 2. Permutations and Factorial Notation Assignment: Absolute Value Workbook pg. 524–527 #1–7,12, 18, 22, 23–25, pg. 526 of text #22 3. Permutations with Repetitions and Restrictions Assignment: Absolute Value Workbook: pg. 388 – 391 #1–15, pg. 525 of text #8 4. Combinations – pg. 528–536 Assignment: Absolute Value Workbook: pg. 396 –398 #1–12, pg. 402–404 #1–16, pg. 534 of text #6 5. The Binomial Theorem Assignment: Absolute Value Workbook: pg. 410 – 412 #1–13 Chapter Review – pg. 546–547 Assignment: pg. 546–547 #1–12, 14–18 Unit 7 Exam Date:______________________________ Need to review/remember: Period for sine and cosine: 360o or 2π Period for tangent: 180o or π In an equation: 2 360 period = (for degrees) period = (for radians) b b Transformations of Trigonometric Functions y = asin[b(x - c)] + d amplitude (vertical stretch by a factor of 'a') Amplitude = max - min 2 Think: distance away from 'centre line', which is the value of 'd' horizontal stretch by a factor of 1/b value of b HELPS you find the period horizontal translation (Phase shift) vertical translation (Vertical displacement) -just like before ('b' is NOT the period!!!!!!) -just like before, PLUS, it cuts the graph in half horizontally...good to know! **Reflection: -a, +a Interval Notation: (description) Open Interval: (a, b) is interpreted as a < x < b where the endpoints are NOT included. (diagram) (1, 5) (While this notation resembles an ordered pair, in this context it refers to the interval upon which you are working.) Closed Interval: [a, b] is interpreted as a < x < b where the endpoints are included. Half–Open Interval: (a, b] is interpreted as a < x < b where a is not included, but b is included. Half–Open Interval: [a, b) is interpreted as a < x < b where a is included, but b is not included. [1, 5] (1, 5] [1, 5) Non–ending Interval: (𝑎, ∞) is interpreted as x > a where a is not included and infinity is always expressed as being "open" (not included). (1, ∞) Non–ending Interval: (−∞, 𝑏] is interpreted as x < b where b is included and again, infinity is always expressed as being "open" (not included). (−∞, 5] Mathematics 30-1 Formula Sheet For ax 2 bx c 0, x Trigonometry b b 2 4ac 2a Relations and Functions Graphic Calculator Window Format x : xmin , xmax , xsc1 y : ymin , ymax , ysc1 Laws of Logarithms log b M N log b M log b N M log b N log b M log b N log b M n n log b M log b c sin x cos x cot x cos x sin x csc x 1 sin x sec x 1 cos x cot x 1 tan x sin 2 x cos 2 x 1 1 tan 2 x sec 2 x 1 cot 2 x csc 2 x sin A B sin A cos B cos A sin B log a c log a b cos A B cos A cos B sin A sin B cos A B cos A cos B sin A sin B t p General Function y af b x h k Permutations, Combinations, and the Binomial Theorem n! n n 1 n 2 ...3 2 1, where n N and 0! = 1 tan A B tan A tan B 1 tan A tan B tan A B tan A tan B 1 tan A tan B sin 2 A 2sin A cos A cos 2 A cos 2 A sin 2 A cos 2 A 2cos 2 A 1 cos 2 A 1 2sin 2 A n! n Pr n r ! n! n Cr n r !r ! tan x sin A B sin A cos B cos A sin B Growth/Decay Formula y ab a r n n Cr r In the expansion of x y , n the general term is tk 1 n Ck x n k y k tan 2 A 2 tan A 1 tan 2 A y a sin b x c d y a cos b x c d