MHF4U – Advanced Functions

Upcoming Evaluations:

 Evaluation Topics Date Quiz Characteristics and graphs of polynomials/even and odd functions/transformations (Sept 10 – 17) Sept 20 Quiz Slopes/Remainder and Factor Theorem (Sept 18 – 26) Sept 28 Unit Test #1 All of Unit 1 Oct 4

Unit 1:  Polynomial Functions

 Date Topic/Learning goals Daily Work/Assignments Wed Sep 5 Introduction To determine what the expectations are for the course and to begin to get to know each other. Click here to see the course info sheet   We will complete a diagnostic and begin review of previous material. Handout:  Essential Skills Review Click here for answers Thu Sep 6 Review Day 2 We will review the concept of factoring. Handouts: ·        Exercise ·        Advanced Factoring Click here for more advanced factoring Click here for more factoring fun!! Fri Sep 7 Review Day 3 To recall our knowledge of equations and functions.  This includes simplifying, solving, finite differences, domain and range, and transformations. Handout: Polynomial Expressions and Equations   Photocopy: p. 2 – 3 #5 – 12 Click here for a copy Mon  Sep 10 Power Functions To discover the properties and graphs of power functions. Click here for the class lesson   Click here for the textbook lesson for section 1.1 p. 12 #3 – 11, 14, 16 – 18   For those without a textbook click here for the homework with answers Tue Sep 11 Characteristics of Polynomial Functions (Day 1) We will investigate the properties of polynomial functions. p.26 #1, 2, 3i, 5, 6 Click here for a copy Wed Sep 12 Characteristics of Polynomial Functions (Day 2) To determine the connections between the finite differences and properties of a polynomial function. p. 26 #3ii, iii, 7, 8acdef, 11 – 18 Click here for a copy Thu Sep 13 Equations and graphs of Polynomial functions We will determine how to graph a polynomial function from factored form and learn about order of roots. p. 39 #1, 2, 6, 9 – 11, 13 Click here for a copy Fri Sep 14 Even and Odd Functions To understand the differences between, and the properties of odd and even functions. Click here for today’s textbook lesson p. 39 #3 – 5, 7, 8(omit 8c), 12, 14   Click here for a copy Mon Sep 17 Transformations We will apply our previous knowledge of transformations to power functions.  To recall proper terminology and notation. p. 49 #1 – 7, 10, 12, 15 Tue Sep 18 Slopes of Secants/Average Rates of Change We will discover how to calculate the average rate of change and use it in different applications. p. 62 #1 – 5, 7, 9, 10, 12, 13 Wed Sep 19 Slopes of Tangents/Instantaneous Rates of Change To understand the difference between instantaneous and average rates of change.  We will also learn to approximate an instantaneous rate of change. p. 71 #1 – 4, 7 – 10, 12 Thu Sep 20 Quiz Dividing Polynomials To discover the method for polynomial long division and learn to write the division in different forms. p. 91 #1 – 6 Handout:  Polynomial Long Division Fri Sep 21 Remainder Theorem We will determine the remainder theorem and use it to find the remainder of polynomial division. p. 91 #7 – 10, 11ab, 12 – 16, 18, 20 – 23 Tue Sep 25 Factor Theorem – Day 1 We extend the remainder theorem to the factor theorem and use it to factor polynomials with a leading coefficient of 1. p. 102 #1 – 4, 6, 9, 12 – 15, 20 – 22   Click here for a solution to #22 Wed Sep 26 Factor Theorem – Day 2 To learn how to apply the factor theorem to factor polynomials with a leading coefficient other than 1. p. 102 #5, 7, 10, 11, 17 – 19 Thu Sep 27 Solving Polynomial Equations We will use factor theorem and our knowledge of solving linear and quadratic equations to solve polynomial equations. p. 110 #3, 4, 7, 8eop, 12 – 15, 18, 20, 24   Click here for a solution to #24 Fri Sep 28   Quiz More Solving Polynomial Equations/Families of Polynomial Equations To define what a family of equations is, and to determine equations of polynomial functions with given properties. p. 119 #1 – 3, 6, 7, 9, 11, 13, 15, 19, 22 Mon Oct 1 Solving Polynomial Inequalities We will determine a graphical and algebraic solution to solve polynomial inequalities. p. 138 #2, 4, 6bc, 9, 12, 14*, 16* Tue Oct 2 Review – Day 1 Text p. 74 – 77 (omit 8d, 18)         p. 78 – 79 Wed Oct 3 Review – Day 2 Text p. 140 – 141 (omit 10b, 15, 16, 18c)         p. 142 – 143 (omit 14, 15) Thu Oct 4 UNIT TEST #1 UNIT TEST #1