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MHF4U – 1-6H: X-Plore the Polynomial Realm
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Total Marks |
38 |
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|
KICA |
K |
I |
C |
A |
|
8 |
26 |
2 |
2 |
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Weight |
10% |
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Learning Goals:
- Solve polynomial equations by selecting an appropriate strategy and verify with technology.
- Determine key features of a function including intercepts, end behaviour and factors.
- Factor polynomials using the appropriate strategy then sketch and list key features.
- Make connections between the x-intercepts of a polynomial function and the real roots of the corresponding equation and solve linear and factorable polynomial inequalities.
- Write solutions on a number line and in interval form.
- Apply factor theorem, integral zero theorem, and rational zero theorem to solve polynomials.
- Use the steps learnt to solve inequalities.
- Solve factorable polynomial inequalities algebraically (considering all cases and testing the values in each interval) and graph solutions on number lines.
- Use a table and number lines to organize intervals and provide a visual clue to solutions.
- Solve inequalities and write their solution on a number line as well as in interval form using the correct parenthesis.
- Solve inequalities by using factor theorem to factor inequalities in order to test the x values.
- Use roots to break number lines into intervals to test the inequalities.
- Use a graph to determine the solution of an inequality by checking when the graph is above and below the x-axis.
- Provide all reasoning, thinking and logic to justify responses where necessary.
- Use correct notation as learned in LMS.
- All responses and answers must be supported by detailed work and thought process.
- Provide all reasoning, thinking and logic to justify responses where necessary.
- Proper notation from LMS must be present in this evaluation.
- All graphs/sketches done by hand, must have appropriate end behaviors/arrows to correspond to domain/range and intervals. All sketches must be clear, organized, and well labeled with an appropriate scale.
Part A)
b) Provide an example of an equation and explain how its solution demonstrates that it is an equation. (Thinking: 2 marks)
c) Provide an example of an inequality and explain how its solution demonstrates that it is an inequality. (Thinking: 2 marks)
Question 2:
Describe how you can represent the solutions to these inequalities, both graphically and algebraically. (Communication: 2 marks)
Question 4:
Part B (Thinking 13 marks)
- The polynomial function must be of degree 4.
- The polynomial function must be fully factorable (each factor must be an integer and/or rational number).
- The polynomial function must not contain zero as a factor.
- The polynomial function must not be identical to a classmate, nor a polynomial provided on LMS. Your polynomial must be unique.
b) Rewrite your polynomial function from Part B a) in standard form. Show all of your steps. (Thinking: 2 marks)
c) Fully factor your polynomial function from Part B b). You must use the full process as done in your Graded Formative 1. You must use long division at least once. (Thinking: 10 marks)
Part C
b) Verify your solution using Desmos. Enter your function into Desmos, including the inequality. Include the screenshot. Your screenshot must include the inequality expression, and the inequality graph. State whether or not your solution is confirmed. (Application: 2 marks)