Exam Review with answers

MCR3U FINAL EXAM REVIEW

• Preparation for the MCR3U examination is crucial as the end of semester two approaches.

• Recommended study guidelines:

  1. FINAL REVIEW HANDOUT: Complete the provided exam review.

  2. TESTS and QUIZZES: Review questions from all past tests and quizzes. Reattempt any incorrect responses and seek help if necessary (e.g., teachers, parents, friends). Extra help available Monday to Friday at lunch until exams.

  3. GROUP STUDY SESSIONS: Organize study sessions with peers focusing on specific themes (e.g., Sinusoidal Functions). Bring quizzes and tests for discussion. Aim for small, focused groups.

• Planning and preparation are key. DO NOT WAIT UNTIL THE LAST MINUTE TO STUDY. Topics may include everything from the curriculum.

• STUDY QUESTIONS: Cumulative Review page 206 #1-32; page 408 #1-28; page 538 #2, 9-10.

Unit 1 – Functions

1. Inverse Functions:

   • a) Find the inverse equation in function notation.

   • b) Determine the domain (D) and range (R) of f.

   • c) Determine the domain (D) and range (R) of f⁻¹.

2. Function Analysis:

   • Given a function’s graph, identify the domain.

   • Calculate specific values of the function (e.g., for x = 5) and (e.g., for x = 2 or 3.5).

3. Graph Transformations:

   • a) Graph transformations: horizontal stretches, reflections, and shifts. Determine key points and their new coordinates based on transformations (e.g., from (1, 4) to (½, 4)).

   • b) Clarify whether each transformation maintains the function property (passes the vertical line test).

   • c) Specify the domains and ranges of transformed relations.

4. Transformation Descriptions:

   • Describe the step-by-step transformations needed to morph one function into another in the correct order (e.g., stretch, reflection, shift).

   • Second example: g(x) = -3f(-2x - 6) - 7 detailing reflections, stretches, and shifts.

5. Function Evaluation:

   • Given g, evaluate g(3) = 13.

   • For f(x) = 2x – 1, evaluate f⁻¹(7) = 4.

   • a) Convert f(t) = -3t² – 18t + 3 into vertex form to find its inverse equation.

   • b) Analyze if f⁻¹ is a function.

   • c) Discuss what restriction ensures the inverse behaves as a function.

6. Algebra Simplification:

   • Work through various algebraic problems, ensuring to state restrictions on variables when necessary.

Unit 2 – Algebra

7-12. Algebra Exercises:

• Simplify expressions, leaving as few terms and positive exponents as possible.

• Describe restrictions dictated by the variable conditions.

Unit 3 – Quadratics

13. Quadratic Solutions: Solve for x in specific quadratic equations, reporting results in exact forms.

14. Max/Min Values: For given quadratic functions, identify maximum/minimum locations and their open/closed nature. 15-17. Profit Analysis and Quadratic Functions: Analyze revenue functions, break-even equations, and profit maximization scenarios.

Unit 4 – Exponential Functions

18-20. Financial Models and Roots: Graph functions, model profit, and determine break-even points and root evaluations.

Unit 5 – Trigonometry

21. Graphing and Ratios: Sketch trigonometric functions, determine ratios, and solve for side lengths in given figures. 22-32. Trigonometric Applications: Solve for angles, side lengths, areas, and relationships in various triangles.

Unit 6 – Sinusoidal Functions

39-48. Modeling and Cycles: Evaluate sinusoidal functions, discuss transformations, and analyze periodic behavior in diverse contexts (e.g., swings, height in water). State amplitude and period, and interpret results for real-world applications.