MCF3M

**MCF3M - Functions and Applications** Grade 11, University/College Preparation


 * Important Reminders:

Course Calendar Test Dates | Assignment Dates | Summative Dates | Exam Dates

||  || Do Review Package and Chapter Self Tests - All Chapters || J14 || ||   || Summative Package || J01 || ||  || Complete Note & Questions: Quiz Next Class || =**ISU - Financial**= || ||   || M25 || ||   || Review: p.444 #2,3,4,5 a,c,e, 10,11,12,14 p.446 #6,7 || Decay: p.438-439 #3,6,7,8,9,12 Handouts from yesterday || M22 || Work Period || || Work on Thinking Task Assignment || plus handout || M17 || ||   || p.415-417 #1bf, 2cd, 10 cdef, 11 abf, 14, 15 || p.378 #2,3 (without graphing calc) p.380 #2,3,4,6 || p.379 #10,11 || & state Domain and Range, Equation of the axis of the curve, amplitude, and the period, #9 also || Hwk: p.340 #3,4,6,8,9 || Hwk: pg. 325 #1,2 (Sketches for each) || 5 ­ we will discuss next class, 6,7,8, 9 ­ no trig used || p.256 #7,8 || || [|Khan Academy - Complete the square] || p.214 #2bc,3,4,6,7,8,11 || =**Quadratics -**= ||  ||   || & M26 || Thinking Task #2 - Modelling Quadratics || ||  || ||  ||   || || p. 168 # 1, 2, 5, 6, 8, 9, 10 || ||  || p.139-140 #1,2abc,3b,4bc,5abf,6(Think about it but don't expand), 8bcf, 11,12 || Part 1 Only || ||  || Review - p.122 #1,3,5,6,7,8,9 Thinking Task Review: p.123 Part 1 Only || ||  || Worksheet || Read 1, Do 12b Try some from worksheet (handed out) || Returned Unit Test #1 || Videos for Algebra Tiles || p.110 #4 - Decomposition Method || || p.86 #4,5,6c (Draw Tiles), 7,10 + Worksheet || || Read p. 36, 66-67 || p.68-69m #1,4-6,8-10,12,14 p.70 #1,4-7 || ||  || p.33 #4,6 p.64-65 #2,4,7,9,10 || ||  || p.56-58 #3-7, 11ac, Also Graph the following f(x)=-(x+1)^2+2 g(x)=2(x-4)^2-5 h(x)=-1/2(x+3)^2+1 || || Handout - || p. 47 # 1 abdf,3cd,4cd,7cdef, 8 i) and ii) only, 9 ef || || Handout - || p.47 #1ce,3ab,4ab,6c,7ab,9bc || 4cd,5,7,8ab,11 & worksheet || A-­7 p.540 1,4bd,5,6 A-­11 p.546 #1def,2,cef,3a || A5: pg. 536 #1bc,2cd,3 || ||  || A1: p.530 # 1ef, 3ef, 4acef, 5cd A-­2: p.531-­532 #1ef, 4 A-­3: p.533 #2,3d,4b,5 || ||  ||   || **Overall Course Description** This course introduces basic features of the function by extending students’ experiences with quadratic relations. It focuses on quadratic, trigonometric, and exponential functions and their use in modeling real-world situations. Students will represent functions numerically, graphically, and algebraically; simplify expressions; solve equations; and solve problems relating to applications. Students will reason mathematically and communicate their thinking as they solve multi-step problems. (The Ontario Curriculum - Mathematics - Grades 11 and 12, page 57)
 * **Date** || **Topic/Lesson** || **Extra Resources** || **Assigned Work** ||
 * J19 || Last Day - Review
 * J18 || Summative Task ||  ||   ||
 * J15
 * J13 || Unit 5 Test - Part II ||  || Work on Exam Review ||
 * J12 || [[file:Unit 5 Part II - Review.pdf|Unit 5 Part II - Review.pdf]] ||  || Work on Review ||
 * J11 || Quiz on Chapter 8.7 || [[file:98 - 8_Review.pdf|HO - Review.pdf]] ||  ||
 * J08 || [[file:07x1 - Saving Plans and Loans - Amortization Tables (8.7).pdf|07x1 - Saving Plans and Loans - Amortization Tables (8.7).pdf]] || [[file:07 - HO Saving Plans and Loans - Amortization Tables _8.pdf|07 - HO Saving Plans and Loans - Amortization Tables _8.pdf]] || Review ||
 * J07 || [[file:06x1 - Regular Annuities - PV (8.6).pdf|06x1 - Regular Annuities - PV (8.6).pdf]] || [[file:06 - HO Regular Annuities - PV _8.pdf|06 - HO Regular Annuities - PV _8.pdf]] || Complete Note & Questions: Quiz Next Class ||
 * J06 || [[file:05x1 - Regular Annuities - FV (8.5).pdf|05x1 - Regular Annuities - FV (8.5).pdf]] || [[file:05 - HO Regular Annuities - FV _8.pdf|05 - HO Regular Annuities - FV _8.pdf]] || Complete Note & Questions: Quiz Next Class ||
 * J05 || [[file:04x1 - Compound Interest - Word Problems (8.4).pdf|04x1 - Compound Interest - Word Problems (8.4).pdf]] || [[file:04 - Compound Interest - Word Problems (8.4).pdf|04 - HO Compound Interest - Word Problems (8.4).pdf]] || Complete Note & Questions: Quiz Next Class ||
 * J04
 * M31 || [[file:02x1 - Compound Interest - FV (8.2).pdf|02x1 - Compound Interest - FV (8.2).pdf]] || [[file:02 - HO Compound Interest - FV.pdf|02 - HO Compound Interest - FV.pdf]] || Complete Note & Questions: Quiz Next Class ||
 * M30 || [[file:01 - Simple Interest vs. Compound (8.1).pdf|01 - Simple Interest vs. Compound (8.1).pdf]] || [[file:01 - HO Simple Interest vs. Compound _8.pdf|01 - HO Simple Interest vs. Compound _8.pdf]] || Complete Note & Questions: Quiz Next Class ||
 * || =**Unit 5 Part II -**=
 * M29 || Unit 5 Test - Part I ||  ||   ||
 * M28
 * M24 || [[file:mrlinseman/05x1 - Exponential Growth and Decay.pdf|05x1 - Exponential Growth and Decay.pdf]] ||  || Growth: p.430 #1-6, 8ab
 * M23
 * M18 || [[file:mrlinseman/04 - Exploring Exponential Functions.pdf|04 - Exploring Exponential Functions.pdf]] ||  || p.423 #2,3a,4
 * M16
 * M15 || [[file:mrlinseman/02 - Properties of Exponents.pdf|02 - Properties of Exponents.pdf]] ||  || Same as yesterday ||
 * M14 || [[file:mrlinseman/01 - Exponential Laws.pdf|01 - Exponential Laws.pdf]] ||  || p.408-409 #5,6,7,8,9,11,12 ||
 * || =**Unit 5 Part I - Exponential Functions**= ||  ||   ||
 * M11 || Thinking Task Introduction - Assignment [[file:mrlinseman/Thinking Task.pdf|Thinking Task.pdf]] || [[file:mrlinseman/Rubric - Periodic Functions Thinking Task.pdf|Rubric - Periodic Functions Thinking Task.pdf]] || Obtain picture for Tuesday ||
 * M10 || Unit Test ||  ||   ||
 * M09 || [[file:mrlinseman/08 - Application Problems Sinusoidal Fnx.pdf|09 - More Application Problems & Review]] ||  || Review: p.367 #15,16
 * 4,5,7b,8,9,10ce,11de
 * M08 || [[file:mrlinseman/08 - Application Problems Sinusoidal Fnx.pdf|08 - Application Problems Sinusoidal Fnx.pdf]] ||  || p.348-351 #3 acd, 5-7 ||
 * M07 || [[file:mrlinseman/07 - Horizontal stretch and compression and Finding Eqns day 2.pdf|07 - Horizontal stretch and compression and Finding Eqns.pdf]] ||  || p.376 #19,20
 * M04 || Quiz on Graphing ||  || None ||
 * M03 || [[file:mrlinseman/06 - Graphing Periodic Functions (Incl. Cosine).pdf|06 - Graphing Periodic Functions (Incl. Cosine).pdf]] ||  || p.374 #5 + graph c,f
 * 6, #13 ||
 * M02 || [[file:mrlinseman/05 - Sine Trans. V. Stretch and Comp.pdf|05 - Sine Trans. V. Stretch and Comp.pdf]] ||  || p.373 #4 Graph a,c,e,
 * M01 || [[file:mrlinseman/04 - Transformation of Sinusoidal Curves (Vert and Horizontal Shifts).pdf|04 - Transformation of Sinusoidal Curves (Vert and Horizontal Shifts).pdf]] ||  || p.365 #1-4,7,8,10 ||
 * A30 || [[file:mrlinseman/03x1 - Sinusoidal Curve.pdf|03x1 - Sinusoidal Curve.pdf]] || [[file:mrlinseman/03 - HO - Sinusoidal Function Diagram.pdf|03 - HO - Sinusoidal Function Diagram.pdf]] || See Handout plus Read Example 2 from p. 338
 * A26 || [[file:mrlinseman/02 - Periodic Motion.pdf|02 - Periodic Motion.pdf]] ||  || p.331 #2,3,5 ||
 * A25 || Unit 4 Part I - Test ||  || Same as yesterday ||
 * A24 || [[file:mrlinseman/01 - HO - Exploring Periodic Motion using the CBR.doc|01 - HO - Exploring Periodic Motion using the CBR.doc]] || [[file:mrlinseman/Homework Take-Up.pdf|Homework Take-Up.pdf]] || Finish Handout &
 * || =**Unit 4 - Part II - Representing Trigonometric Functions**= ||  ||   ||
 * A23 || Unit 4 - Thinking Task ||  ||   ||
 * A20 || [[file:mrlinseman/07 - Work Period & Review.pdf|07 - Work Period & Review.pdf]] ||  || pg. 316 all ||
 * A19 || [[file:mrlinseman/06 - Work Period & Review.pdf|06 - Work Period & Review.pdf]] ||  || pg. 314-­315 #1­4. 5bc, 6,7bc,8,9c,10 ||
 * A18 || [[file:mrlinseman/05x1 - Trigometric Application Problems.pdf|05x1 - Trigometric Application Problems.pdf]] ||  || pg.309 #3,4,7,9,10,11,12,13 ||
 * A17 || [[file:mrlinseman/04x1 - The Cosine Law.pdf|04x1 - The Cosine Law.pdf]] ||  || p. 299-300
 * 1,2,3,5cd,7 ||
 * A16 || [[file:mrlinseman/03 - The Sine Law.pdf|03 - The Sine Law.pdf]] ||  || pg.288-289
 * 5,6abc,7,8cd,9af ||
 * A12,A13 || [[file:mrlinseman/02x1 - Solving Right Trangle Problems.pdf|02x1 - Solving Right Trangle Problems.pdf]] ||  || Pg. 280-­282
 * 1b,3,4b,
 * A11 || [[file:mrlinseman/01 - Primary Trig Ratios.pdf|01 - Primary Trig Ratios.pdf]] ||  || pg.271-­273 #1,2,3b,4b,5cd,7,8,10,12,14 ||
 * || =**Unit 4 - Part I - Using Trigometry in Geometric Situations**= ||  ||   ||
 * A10 || Unit 3 Test ||  ||   ||
 * A05 || Review ||  || p.254-255 #1bc,2bc,3,4ab,5-10
 * A04 || [[file:mrlinseman/05 - Application - Cost, Revenue, Profit Quadratics.pdf|05 - Application - Cost, Revenue, Profit Quadratics.pdf]] ||  || p. 240 & 241 #5-13 ||
 * A03 || [[file:mrlinseman/04 - The Discriminant.pdf|04 - The Discriminant.pdf]] ||  || p. 232-233 #2,4,5,6,7,9 ||
 * A02 || [[file:mrlinseman/03 - Quadratic Formula.pdf|03 - Quadratic Formula.pdf]] ||  || p.222 #3abc, 5abdc, 6,7 ||
 * M30 || Completing the Square
 * M28 || **[[file:mrlinseman/01 - Vertex and Standard Forms.pdf|01 - Vertex and Standard Forms.pdf]]** ||  || p.203-205 (#1,2,3)(ab), 4f,5bc,6,7,9cd,10 ||
 * || =**Unit 3 -** **Part II**=
 * M27
 * M23 || [[file:mrlinseman/05 - Creating a model from data.pdf|05 - Creating a model from data.pdf]] ||  || p.177 #1,3,4,8,10 ||
 * M21 || Work Period
 * M20 ||  || [[file:mrlinseman/03 BR - Quadratic Factoring Word Problem .doc|03 BR - Quadratic Factoring Word Problem .doc]]
 * M19 || [[file:mrlinseman/03 - Solving Quadratics by Factoring.pdf|03 - Solving Quadratics by Factoring.pdf]] ||  || p.161 #1,2ab,3a,4bef,5,6,7def,8,10,11,13 ||
 * M09 || [[file:mrlinseman/02 - Quadratic Application Problems.pdf|02 - Quadratic Application Problems.pdf]] || Download the free applet [|Geogebra] || p.149 #1,2,4-11, (Use [|Geogebra]for questions 6 through 11) ||
 * M08 || Standard and Factored Forms
 * || =**Unit 3 - Part I - Representing Quadratic Functions**= ||  ||   ||
 * M07 || Unit 2 - Thinking Task ||  ||   ||
 * M06 || Unit #2 Test ||  || Thinking Task Review: p.123
 * M05 || Review || Handout - Factoring Question || Handout - For Hand In ||
 * M02 || Quiz - Factoring
 * M01 || Mixing Factoring Up
 * F29 || Lead Up Thinking Task ||  || Complete Handout - factor expressions on worksheet ||
 * F28 || [[file:mrlinseman/03x3 Factoring (Special Cases).pdf|03x1 Factoring (Special Cases).pdf]] || Factoring Worksheet || p.115 #3,4,11
 * F27 || [[file:mrlinseman/02x2 Factoring (a not equal to zero).pdf|02x1 Factoring (a not equal to zero).pdf]]
 * 1) 5 - Produc/ Sum Method
 * 9,10 - Your choice ||
 * F24 || Assembly ||  || p.92-94 #6,7,9,16 ||
 * F23 || Factoring Quadratics - Using Algebra Tiles - Common Factoring
 * || =**Unit 2 - Factoring Quadratics**= ||  ||   ||
 * F22 || Redo Thinking Inquiry Question From Test ||  || None ||
 * F21 || Unit Test ||  ||   ||
 * F16 || Review Period
 * F15 || Quadratic Application Problems
 * F14 || Graphing Quadratics Cont.
 * F13 || Handed Back Quiz
 * F10 || Functions Quiz
 * F09 || [[file:mrlinseman/1.2 Lesson - Function Notation.pdf|02x1 - Function Notation.pdf]] ||  || p.32-34 1,2,4,6,10a (v,vi), 11a,(v,vi),12 ||
 * F08 || [[file:mrlinseman/1.1 Lesson - Characteristics of a function.pdf|01x1 - Characteristics of a function.pdf]] ||  || p.13­-15 #1cd,2bc,3(part ii only),
 * || =**Unit 1 - Quadratic Functions**= || Open this file in GeoGebra - [[file:mrlinseman/Transformations of Quadratic Relations.ggb|Transformations of Quadratic Relations.ggb]] ||  ||
 * F07 || Review Quiz ||  ||   ||
 * F06 || [[file:mrlinseman/04x1 - Linear Relations & Equations A6,A7,A11.pdf|04x1 - Linear Relations & Equations A6,A7,A11.pdf]] ||  || A-­6 p.538 #1bf,2c,4
 * F03 || [[file:mrlinseman/03x1 - Pythagorean Theorem & Algebraic Expressions.pdf|03x1 - Pythagorean Theorem & Algebraic Expressions.pdf]] ||  || A4: pg. 534 #1bd, 3cd, 4b,
 * F02 || Integers & Order of Operations, Rational Numbers, Exponent Laws
 * F01 || Welcome to MCF3M
 * || **Unit 0 - Introduction & Review** ||  ||   ||

**Prerequisite:**
Principles of Mathematics, Grade 10, Academic OR Foundations of Mathematics, Grade 10, Applied

**Units:**
These units are based on the McGraw – Hill Ryerson Functions and Applications 11 textbook.

**Unit 1 – Review & Quadratic Functions**
**Goals:**
 * Define function and identify a function from a relation that is not a function
 * Evaluate linear and quadratic functions
 * Define and identify restrictions domain and range by investigating numerical, graphical and algebraic representations
 * Investigate quadratic functions in vertex form, describe the roles of variables in the transformation of f(x) = x² and the corresponding sketch.
 * Collect data that represents a quadratic relation and determine the equations of curves of best fit where applicable

===**Unit 2 – Factor Quadratic Expressions** ===

**Goals:**
 * Expand and simplify, solve, and factor quadratic expressions in one variable using a variety of strategies (i.e. perfect square and difference of squares)
 * Connect factored form, standard form, and vertex form through investigation of the key variables.
 * Describe and sketch the intercepts, the maximum and minimum and other key features of a quadratic function.

===**Unit 3 (Part 1) – Represent Quadratic Function in Factored and Standard Forms** === **Goals:**
 * Factor and Expand Quadratic Functions to solve problems involving real world applications.

Unit 3 (Part 2) - Vertex to Standard
**Goals:**
 * Find the real roots of a quadratic equation using various methods, including the quadratic formula
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Use the discriminant to determine the number of real roots of a quadratic equation
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Complete the square
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Solve real world applications of quadratic functions

<span style="font-size: 1.1em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**Unit 4 (Part 1) – Trigonometry**
**Goals:**
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Use primary trigonometry ratios to determine measures of sides and angles of right triangles
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Solve problems using two triangles
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Use the sine law and cosine law to determine the measures of sides and angles in acute triangle

<span style="font-size: 1.1em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**Unit 4 (Part 2) – Sine Functions**
**Goals:**
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Describe key properties of periodic functions
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Graph the sine function and make connections to the sine ratio
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Determine the roles of a, c, and d in f(x) = a sin (x - d) + c and sketch the resulting graphs
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Identify periodic and sinusoidal functions and restrictions of domain and range

===<span style="font-size: 1.1em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**Unit 5 (Part 1) – Exponential Functions** === **Goals:**
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Evaluate expressions containing integer and rational exponents and rational bases
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Graph exponential relations and explain why it is a function
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Describe key properties of exponential relations
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Identify functions as linear, quadratic or exponential
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Collect data and solve problems with real-world applications that can be modeled as an exponential function

===<span style="font-size: 1.1em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**Unit 5 (Part 2) – Financial Math** ===

**Goals:**

 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Compare simple and compound interest for a given principle and fixed interest rate over a certain period of time
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Solve problems for any unknown using simple and compound interest and investigate compound interest as an example of exponential growth
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Define and explore annuity through numerical and graphical representations
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Explore the affects of changing the conditions of ordinary simple annuities
 * <span style="margin: 0.5em 0px 0px; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Solve annuity problems involving amount, present value and regular payment


 * Resources **

<span style="font-size: 1.1em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**Textbooks:**

 * Nelson Functions and Applications 11**
 * Publisher: Nelson Education Ltd. **
 * ISBN: 0-176-33204-9 **

Other: McGraw-Hill Ryerson Functions and Applications 11 Publisher: McGraw-Hill Ryerson ISBN: 0-070-72596-9

Functions and Relations Publisher: Addison - Wesley ISBN: 0-201-72657-2

<span style="font-size: 1.1em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**Online Resources:**
<span style="background-clip: initial; background-origin: initial; background-position: 100% 50%; cursor: pointer; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px;">OAME - Ontario Association for Mathematics Education [|Wolfram Alpha] - Online calculator - Downloadable Student Calculator Geogebra - Online graphing tool applet

<span style="font-size: 1.1em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**Ontario Ministry of Education:**
<span style="background-clip: initial; background-origin: initial; background-position: 100% 50%; cursor: pointer; padding-right: 10px;">The Ontario Curriculum - Mathematics - Grades 11 and 12 (Page 57) <span style="background-clip: initial; background-origin: initial; background-position: 100% 50%; cursor: pointer; padding-right: 10px;">The Ontario Curriculum Exemplars, Grade 11, Mathematics (Section: Functions University/College Preparation)