Functions (MCR3U)

During this initial unit, learners will engage deeply with the study of functions, their various forms of representation, and their inverse forms. They'll acquire the skill to link algebraic expressions with their graphical counterparts using transformation techniques. The emphasis of this unit is on guiding students to identify zeros and discern the peak or trough of quadratic functions. In addition, it will enhance their ability to solve problems related to quadratic functions, especially those stemming from real-life scenarios.

At the end of this unit, students are expected to have a thorough grasp of the concept of equivalence, especially in simplifying expressions that involve polynomials, radicals, and rational terms.

This unit immerses students in a range of topics related to exponential functions. They will explore evaluating powers with rational exponents, streamlining expressions with exponents, and understanding the characteristics of exponential functions presented in different forms. The focal point of this unit is practical problem-solving, encouraging students to utilize these concepts in real-world contexts.

In this unit, learners focus on mastering the calculation of trigonometric ratios for angles under 360º. They will engage in proving straightforward trigonometric identities and solving challenges using the fundamental trigonometric ratios. This unit introduces and elaborates on the sine and cosine laws. Students will develop a clear comprehension of periodic relationships and sinusoidal functions. They will also learn to draw connections among numeric, graphical, and algebraic portrayals of sinusoidal functions. This knowledge will be applied in solving sinusoidal function problems, including those derived from real-life situations.

This unit begins by investigating recursive sequences, covering a range of representational methods. Linking these concepts to Pascal’s Triangle, students will move on to grasping the underlying principles in arithmetic and geometric sequences and series. The unit then transitions to applying these concepts to practical scenarios involving compound interest and ordinary annuities, rounding off the unit's comprehensive study.

This final examination is supervised and represents 30% of your total grade.

This is a monitored examination, accounts for 30% of the overall grade.

• A scanner, a smartphone camera, or an equivalent device to upload work that's handwritten or hand-drawn.
• A laptop or personal computer, ideally with Google Chrome or Mozilla Firefox installed as the web browser.
• A reliable internet connection.
• Facilities for video recording and scanning of handwritten work, which can be achieved using a mobile phone, tablet, iPad, or a webcam.
• A scientific calculator that is non-programmable and non-graphing.

• Access to Google Suites or Microsoft Education for essential software, with accounts provided by the school.
• Supplemental reading materials.
• Tutorial and solution videos through Screencast.
• Student accounts for Gizmos, Labster, Mathletics, GeoGebra, and Padlet.

Note: The course is fully online; no textbooks required.