Duration: 1 hour
Objectives:
- To understand the concepts of polynomial equations and functions
- To understand the concept of limits and differentiation
- To be able to differentiate and simplify algebraic expressions
Materials:
- Whiteboard and markers
- Graphing calculator or graph paper
- Handout with practice problems
Introduction (10 minutes):
- Ask students if they have studied algebra and calculus before and what they know about it
- Introduce polynomial equations and functions and how they can be used to model real-world situations
- Explain the concept of limits and how they relate to calculus
Body (35 minutes):
- Demonstrate how to differentiate simple algebraic expressions
- Provide examples for students to differentiate in pairs or independently
- Discuss the meaning of the derivative and its relationship to the original function
- Demonstrate how to graph polynomial equations and use the graph to find the maximum and minimum points
- Provide practice problems for students to graph and differentiate in pairs or independently
Conclusion (15 minutes):
- Review the key concepts covered in the lesson
- Answer any questions students may have
- Assign homework (e.g. additional practice problems or a worksheet)
- Summarize what will be covered in the next lesson
Assessment:
- Observe students during the practice problems to assess understanding
- Collect and grade the homework to see how well students have retained the material
Note: This is just a sample lesson plan, and can be adjusted to fit the needs of your students and curriculum.
handout:
Title: Further Algebra and Calculus Practice Problems
Introduction:
In this handout, we will practice further algebraic concepts and the basics of calculus. The following topics will be covered:
- Simplifying and solving complex algebraic expressions
- Solving systems of linear equations using matrices
- Differentiation and optimization
- Integration and areas under curves
Practice Problems:
- Simplify the following expression: (x^2 + 2x - 3) + (2x^2 - x + 4)
- Solve the following system of linear equations using matrices: x + y = 7 2x - y = 4
- Find the derivative of the function y = x^3
- Use differentiation to find the maximum value of the function y = x^2 - 6x + 8
- Evaluate the definite integral of the function y = x^2 from x = 1 to x = 3
Answers:
- 3x^2 + x + 1
- x = 5, y = 2
- y' = 3x^2
- The maximum value is at x = 3 and the maximum value is 7.
- The definite integral is equal to 8.
