Functions
Course Description
This course introduces the mathematical concept of the function by extending students’ experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; investigate inverse functions; and develop facility in determining equivalent algebraic expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
Overall Curriculum Expectations
By the end of this course, students will:
A. CHARACTERISTICS OF FUNCTIONS
| A1 | demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations |
| A2 | determine the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic functions, including problems arising from real-world applications |
| A3 | demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions |
B. EXPONENTIAL FUNCTIONS
| B1 | evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways |
| B2 | make connections between the numeric, graphical, and algebraic representations of exponential functions |
| B3 | identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications |
C. DISCRETE FUNCTIONS
| C1 | demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal’s triangle |
| C2 | demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related problems; |
| C3 | make connections between sequences, series, and financial applications, and solve problems involving compound interest and ordinary annuities |
D. TRIGONOMETRIC FUNCTIONS
| D1 | determine the values of the trigonometric ratios for angles less than 360[degree sign]; prove simple trigonometric identities; and solve problems using the primary trigonometric ratios, the sine law, and the cosine law |
| D2 | demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions |
| D3 | identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including problems arising from real-world applications |
Course Content
| Unit | Title | Hours |
|---|---|---|
| Unit 1 |
Relations and Functions Function Notation Exploring Properties of Parent Functions Determining the Domain and Range of a Function The inverse function and its properties Exploring transformations of Parent function Investigating Horizontal stretches, compressions, and Reflections Using transformations to graph functions Adding and Subtracting Polynomials Properties of Quadratic functions |
25 hours |
| Unit 2 |
Exploring growth and decay Working with integer exponents Working with rational exponents Simplifying algebraic expressions involving exponents Exploring the properties of exponential function Transformations of exponential functions Applications involving exponential functions |
24 hours |
| Unit 3 |
Arithmetic sequences Geometric sequences Creating rules to define sequences Exploring Recursive sequences Arithmetic series Geometric series Pascal’s triangle and Binomial expansions Simple interest |
25 hours |
| Unit 4 |
Trigonometric ratios of acute angle Evaluation trigonometric ratios for special angles Exploring trigonometric ratios for angles greater than 90 degrees. Evaluating trigonometric ratios for any angle between 0 and 360. Trigonometric Identities The sine law The cosine Law Solving three-dimensional problems by using trigonometry Periodic function and their properties |
34 hours |
| Final Evaluation | 2 hours | |
| Total : 110 hours |
Strategies actually used in the classroom are indicated in the chart above and reflected in classroom instruction
- Assessment for learning (AFL) is diagnostic and formative for the purposes of greater learning achievement and is used at the beginning of a unit to help determine a starting point for instruction.
- Assessment as learning (AAL) is assessment as a process of developing and supporting students’ active participation in their own learning.
- Assessment of learning (AOL) is assessment for purposes of providing evidence of achievement for reporting. It is conducted at the end of each learning unit/work section and provides students with the opportunity to synthesize/apply/demonstrate their learning and their achievement of the stated expectations.
There are four levels of achievement for students who are passing the course:
- Level 1 (50-59%)
- Level 2 (60-69%)
- Level 3 (70-79%)
- Level 4 (80-100%)
Level 3 is the provincial standard for student achievement.
The percentage grade represents the quality of the students’ overall achievement of the expectations for the course and reflects the corresponding achievement as described in the achievement chart for mathematics. Term work will be 70% of the overall grade for the course; the summative evaluations will be 30% of the overall grade, incorporating summative evaluation and a final written examination.
| Percentage of Final Mark | Categories of Mark Breakdown |
|---|---|
| 70% | Term Work student product (tests) Observations(performance tasks) |
| 30% | Final Written Exam 30% |
Within the 70% term mark and the 30% summative mark, the breakdown of the achievement chart categories will be approximately 25% Knowledge/Understanding, Application 25%, Communication 25%, and Thinking/Inquiry 25%.
The evaluation for this course is based on the student’s achievement of curriculum expectations and the demonstrated skills required for effective learning. The final percentage grade represents the quality of the student’s overall achievement of the expectations for the course and reflects the corresponding level of achievement as described in the achievement chart for the discipline.
Proctoring
The tests are typically a paper-pen evaluation written at a mutually agreed time, date, and location. The tests will be proctored, meaning a suitable adult with a dedicated identifiable and authentic email address will supervise you writing the tests. This process ensures the security and integrity of the test. Any person related or affiliated to the student in a personal way cannot serve as a test supervisor.
Resources required by the student
- A non-programmable, non-graphing, scientific calculator
- A scanner, smartphone camera, or similar device to upload handwritten or hand-drawn work
- A front-facing camera on a desktop, laptop, or mobile device to allow for proctoring over the internet
- Internet access and a modern standards-compliant web browser
The tuition for this course is $800 for Canadian students and $2000 for international students.
Refunds
Maple Leaf School does not issue refunds. When a student enrolls in our course, MLS administration team undertakes many tasks including establishing electronic/physical files, assigning teachers and tracking the enrolment for Ministry purposes, etc. The work is completed by our school the moment you register online.
Course Curriculum
| Course Information | |||
| Course Outline | 00:00:00 | ||
| Hour Breakdown | 00:00:00 | ||
| Mark Breakdown | 00:00:00 | ||
| Unit 1 | |||
| U1L1 | 00:00:00 | ||
| U1L2 | 00:00:00 | ||
| U1L3 | 00:00:00 | ||
| U1L4 | 00:00:00 | ||
| U1L5 | 00:00:00 | ||
| Unit 2 | |||
| U2L1 | 00:00:00 | ||
| U2L2 | 00:00:00 | ||
| U2L3 | 00:00:00 | ||
| U2L4 | 00:00:00 | ||
| Unit 3 | |||
| U3L1 | 00:00:00 | ||
| U3L2 | 00:00:00 | ||
| U3L3 | 00:00:00 | ||
| Unit 4 | |||
| U4L1 | 00:00:00 | ||
| U4L2 | 00:00:00 | ||
| U4L3 | 00:00:00 | ||
| U4L4 | 00:00:00 | ||
| U4L5 | 00:00:00 | ||
| Course Culminating Activity | |||
| MCR3U CCA | 00:00:00 | ||
| Final Exam | |||
| How to request | 00:00:00 | ||
good course, good teacher
thank you very much!
Amazing
I learned a lot in this course.