Knowledge
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Thinking
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Communication
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Application
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Total
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/15
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/15
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/15
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/15
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/60
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Project – Applications of Calculus
Overall Curriculum Expectations :
1. demonstrate an understanding of rate of change by making connections between average rate of change over an interval and instantaneous rate of change at a point, using the slopes of secants and tangents and the concept of the limit;
2. graph the derivatives of polynomial, sinusoidal, and exponential functions, and make connections between the numeric, graphical, and algebraic representations of a function and its derivative;
3. verify graphically and algebraically the rules for determining derivatives; apply these rules to determine the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions, and simple combinations of functions; and solve related problems.
4. make connections, graphically and algebraically, between the key features of a function and its first and second derivatives, and use the connections in curve sketching;
5. solve problems, including optimization problems, that require the use of the concepts and procedures associated with the derivative, including problems arising from real-world applications and involving the development of mathematical models.
1. demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications;
2. perform. operations on vectors in two-space and three-space, and use the properties of these operations to solve problems, including those arising from real-world applications;
3. distinguish between the geometric representations of a single linear equation or a system of two linear equations in two-space and three-space, and determine different geometric configurations of lines and planes in three-space;
4. represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances and intersections.
Objective:
Create a project that demonstrates a thorough understanding of one particular aspect of Calculus. Ideally, this project will extend the knowledge you have acquired during the course.
Possible Topics:
Please choose from the below given topics :
- Build 5 optimization problems used in geometry , finance, and other sectors
· Demonstrate how derivatives can be used in the field of chemistry, physics , biology , medicine engineering, economics, environmental studies, or any other scientific discipline of interest to you
· Demonstrate the application of vectors in the real life in 5 examples
· Build 5 examples stating the use of the rate of change in the field of physics, chemistry, biology , medicine engineering, economics, environmental studies, or any other scientific discipline of interest to you
Format:
The format of this project is flexible; choose a format that best allows you to demonstrate your understanding of your chosen topic. Options include (but are not limited to):
· Written report with graphs and diagrams
· Visual and/or audio presentation (Prezi/PowerPoint slides, video, etc.)
· Creation of physical models with supporting written work
References:
Any references that are used in the completion of your project must be cited using APA format. Include references somewhere near the end of your project/report
Evaluation Rubrics
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Category
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Description
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Grade
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Knowledge and Understanding
Background
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A brief opening paragraph (or 2) should introduce the chosen topic and clearly explain its place in (or connection to) the study of Calculus.
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/3
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Knowledge and Understanding
Calculus Content
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Content is presented in a way that shows you clearly understand the material and could explain it to me or to a classmate. Marking scheme is based on the level of calculus content as follows:
Level 4 (11–12): Project’s content is beyond level of course.
Level 3 (9–10): Project’s content is similar to level of course.
Level 2 (6–8): Project’s content is slightly below level of course.
Level 1 (0–6): Project’s content is significantly below level of course.
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/12
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Thinking & Inquiry
Graphs, Diagrams & Models
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Any graphs used in the report are accurately drawn and clearly described.
Any diagrams included in report are well-constructed, clearly labeled, and relevant to the chosen topic.
Any models created are precisely constructed and clearly demonstrate the chosen concept.
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/15
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Communication
Organization & Format
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Submitted work is very well-organized, well presented, using clear language that is easy to follow (assume that your target audience is one of your classmates)
Use of correct mathematical units, formula and show the steps
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/10
/5
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Application
References
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All materials must be cited in APA format. Plagiarism will be penalized.
Use of the correct language as required .
Use of correct mathematical notations
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/5
/5
/5
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Total:
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/30
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