Advanced Functions – MHF4U

Course Prerequisite

Functions 11, MCR3U; or Mathematics for College Technology 12, MCT4C

Description

This course extends students’ experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programs.

Course Info

Course Outline & Units

Unit Order

Unit Name

Suggested Time

Unit 1

Functions: Characteristics and Properties

Many situations can be modelled graphically. Interpreting those graphs is something that requires you to become familiar with all of the aspects of these graphs. Students will recall a few basic facts of a distance time graph. In previous math courses, students saw some transformations and studied their effects on a given graph. These will also be reviewed. The concepts of function notation, relation, range, domain, and function notation will all be reviewed.

10 hours
Unit 2

Polynomial Functions

In this unit students learn to identify and describe some key features of polynomial functions and to make connections between the numeric, graphical, and algebraic representations of polynomial functions. Transformations of Cubic and Quartic functions. Dividing and Factoring Polynomials.

10 hours
Unit 3

Polynomial Equations and Inequalities

Solving polynomial equations. Solving linear and polynomial equations by using factoring and graphing

12 hours
Unit 4

Rational Functions, Equations and Inequalities

The concepts of identifying and describing some key features of the graphs of rational functions are also presented. Students will represent rational functions graphically; solve problems involving polynomial and simple rational equations graphically and algebraically so they can demonstrate an understanding of how to solve rational inequalities.

12 hours
Unit 5

Trigonometric Functions

This unit examines the meaning and application of radian measure. Students will make connections between trigonometric ratios and the graphical and algebraic representations of the corresponding trigonometric functions and between trigonometric functions and their reciprocals. Transformations of Trigonometric Functions

13 hours
Unit 6

Trigonometric Identities and Equations

Exploring equivalent trigonometric functions. Compound and Double angle formulas. Proving Trigonometric Identities. Solving linear and quadratic trigonometric equations.

12 hours
Final Evaluation 30%

Final Assignment

Final Exam

6 hours

2 hours

Total 110 Hours
Learning Strategies

A wide variety of instructional strategies are used to provide learning opportunities to accommodate a variety of learning styles, interests and ability levels. These strategies include, but are not limited to:

Think-Pair-Share                                           

Peer Assessment

Model Analysis                                          

Anticipation Guide                                  

Graphing Applications                                

Investigate                                             

Research                                                    

Graphic Organizers                                        

 

Concept Attainment

Entry Slip

Group Discussion

Problem Solving

Self-Assessments

KWL Chart

Direct Instruction

Exit card

 

Course FAQ
The course duration is 110 hours, delivered in an online school format. 
Functions 11, MCR3U; or Mathematics for College Technology 12, MCT4C
The course fee is based on the selected option of Online Instructor-Class Credit For detailed information and pricing, please check our website.
Assessment & Resources

Purpose   

The primary purpose of assessment is to improve student learning. Assessment relates directly to the expectations for the course.

A variety of assessments for and as learning are conducted on a regular basis to allow ample opportunities for students to improve and ultimately demonstrate their full range of learning and for the teacher to gather information to provide feedback. Assessment tasks relate to the success criteria set out in lesson plans. Success criteria allow students to see what quality looks like.

Evaluation is the process of judging the quality of student work in relation to the achievement chart categories and criteria and assigning a percentage grade to represent that quality. Evaluation is based on gathering evidence of student achievement through:

  • Products
  • Observations
  • Conversations

Assessment for Learning – we provide feedback and coaching. Assessment FOR Learning is the process of seeking and interpreting evidence for the use of learners and their teachers to decide where the learners are in their learning, where they need to go, and how best to go there.

Assessment as Learning – we help students monitor progress, set goals, reflect on their learning

Assessment AS Learning is the process of the explicit fostering of students’ capacity over time to be their own best assessors, but teachers need to start by presenting and modeling external, structured opportunities for students to assess themselves.

Assessment of Learning – we use assessments to provide evaluative statements about student achievement. Assessment OF Learning is the assessment that becomes public and results in statements of symbols

(marks/grades/levels of achievement) about how well students are learning. It often contributes to pivotal decisions that will affect students’ future.

ASSESSMENT TOOLS  

  Units Duration Overall Expectations AFL AAL AOL K

25%

A

25%

C

25%

T

25%

  A 25 hours A1-A3 Diagnostic Assessment

Homework

Unit Review

Practice Test

Exit card

 

 

 

Reflective Discussion on Learning  

 

Unit Assignment Test

Presentation

 

 

 

  70% 

B 28 hours B1-B3 Diagnostic Assessment

Assigned Questions

Unit Wrap Up

Exit card

 

KWL Chart Unit Test

Presentation

C 36 hours C1-C4 Prior Knowledge Assessment Worksheet Unit Review

Unit Wrap Up

Discussion

Exit card

 

KWL Chart

 

 

Unit Assignment

Test

Presentation

 

  D 21 hours D1-D3 Homework

Unit Review

Unit Wrap Up

Exit card

 

Pair Peer Assessment Assignment Presentation

Test

 

30%     Final Project (A1-D3)

 

Final Evaluation 30% Summative

Final Exam

 

 

 

 

 

 

 

 

These learning skills and work habits will be taught, assessed and evaluated throughout the course.

Responsibility

Fulfils responsibilities and commitments within the learning environment

Completes and submits class work, homework, and assignments according to agreed-upon timelines.

Takes responsibility for and manages own behaviour

Collaboration

Accepts various roles and an equitable share of work in a group

Responds positively to the ideas, opinions, values, and traditions of others

Builds healthy peer-to-peer relationships through personal and media-assisted interactions

Works with others to resolve conflicts and build consensus to achieve group goals

Shares information, resources, and expertise, and promotes critical thinking to solve problems and make decisions

Organization

Devises and follows a plan and process for completing work and tasks

Establishes priorities and manages time to complete tasks and meet goals

Identifies, gathers, evaluates, and uses information, technology, and resources to complete tasks

Self- Regulation

Sets own individual goals and monitors progress towards achieving them

Seeks clarification or assistance when needed

Assesses and reflects critically on own strengths, needs and interests

Identifies learning opportunities, choices, and strategies to meet personal needs and meet goals

Perseveres and makes an effort when responding to challenges

Independent Work

Independently monitors, assesses, and revises plans to complete tasks and meet goals

Uses class time appropriately to complete tasks

Follows instructions with minimal supervision

Initiative

Looks for and acts on new ideas and opportunities for learning

Demonstrates the capacity for innovation and a willingness to take risks

Demonstrates curiosity and interest in learning

Approaches new tasks with a positive attitude

Recognizes and advocates appropriately for the rights of self and others

E – Excellent          G – Good          S – Satisfactory          N – Needs Improvement

Resources 

Course Final Grade & Report Card

Grading  

  • The final grade is based on performance in 3 areas: products, observations, conversations.
  • 70% of the grade is based on evaluations conducted throughout the course.
  • 30% is based on a final evaluation.

Weighting of categories 

Knowledge/Understanding  Thinking/Inquiry  Communication  Application 
25%  25%  25%  25% 
Play Video

Course Grade

Grade 12

Course Code

MHF4U

Course Category

Mathematics

Course Type

University Preparation

Course Delivery

Online

Course Duration

110h

Course Credit

1.00

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