Math II Final ProjectDue: June 4, 2015

Objectives:

  1. Demonstrate mastery of key advanced algebra topics covered this year
  2. Investigate real world applications of one of these topics

Task I:

In this part, you will show that you can solve all of the types of algebra problems that we have covered. For each topic, you will create one problem to model the correct method to solve it. Each student should have a unique problem. You may use any resources to find appropriate problems, but it should NOT be a problem that you have solved before. A Level 3 solution will show all steps in a logical and mathematically correct manner. You must show a mathematical check to ensure that you have solved your problem correctly. In addition you will include a written description of the steps involved in creating and solving each problem. No Level 4 option will be available for this task.

Below are the required problems for Task I.

  1. Solve a quadratic using factoring of a trinomial with a leading coefficient greater than 1.
  2. Solve a quadratic using complete the square for a function with irrational roots.
  3. Solve a quadratic using the quadratic formula for a function with imaginary roots.
  4. Graph and algebraically solve a system of equations with a consistent and independent solution.
  5. Graph and algebraically solve a system that includes a circle and a quadratic that intersect at 4 points.
  6. Write a system of inequalities that has a quadrilateral shaded region as the solution. Graph the solution and name all of the vertices in the solution.
  7. Write two complex numbers. Show the sum, difference, product, and quotient of the 2 numbers.
  8. Write a fraction that includes numbers with rational exponents in both the numerator and the denominator. Use the conjugate then rationalize the denominator.
  9. Write and graph a piecewise function then state its domain and range in interval notation.
  10. Choose a parent graph that we discussed. Write the equation and graph the function after a horizontal shift, vertical shift, reflection, and compression have been applied to the parent graph. (Apply all changes at the same time.)
  11. Write and solve a word problem using the formula for discretely compounded interest.
  12. Write and solve a word problem using the formula for continuously compounded interest.
  13. Find a set of linearly correlated data. On graph paper, create a scatter plot for the data and find the regression equation and r value. Describe how the regression data could be used to make future predictions.
  14. Write an equation for a circle in expanded form. Use complete the square techniques to change it to standard form.
  15. Write the equation of a parabola in trinomial form. Use complete the square techniques to change it to vertex form.

Task 2:

Perform an investigation of a real world application of one of the topics studied this year. Choose from the list below or come up with your own topic. Create a product that demonstrates your understanding of the topic. The product can take any form (3D model, digital presentation, video, painting, song, etc.). Ensure that through your product you can clearly communicate how this real world application is connected to a specific algebra/geometry topic. Level 3 work requires a completed product along with a clearly written description of the reason why this product is connected to an algebra topic.

Fractals in the world or art (self-similarity, recursion, complex numbers)

Electric circuitry (complex numbers)

Parabolic motion (quadratics)

Real world devices that use the foci of a parabola

The occurrence of “e” in the real world

Tessellations in architecture and/or art (parent function transformations)

Linear programming (systems of equations and inequalities)

Regression analysis in a world real data set (linear, quadratic, or exponential regression)

Financial decision making for the stock market (rate of return, compound interest)

A topic of your choice with prior permission

Recommended Pacing of Project Work:

Class Day 1 – Introduction and begin investigating the requirements (5/20)

Class Day 2 – Start work on problem solving – finish draft work of the first 3 problems (5/21)

Class Day 3 – Solve 4 more problems (5/22)

Memorial Class Day Weekend – 3 Class Days off, research project ideas and make a decision about your product

Class Day 4 – Solve 4 more problems (5/26)

Class Day 5 – Solve the last 4 problems (5/27)

5/28 and 5/29 – no class for EOG – create your final draft for the problems

Class Day 6 – Create your product (6-1)

Class Day 7 – Continue to work on your product (6-2)

Class Day 8 – Finish your product (6-3)

Class Day 9 – Present your product to the class (6-4)