Pre-Calculus – Chapter 2

1. Pre-Calculus – Chapter 2 Systems of Equations It’s time to play… Pre-Calc Jeopardy

2. Rules for the Game When it is your team’s turn, select a category and an amount. After Mr. Dillon has finished asking the question, any team may buzz in. If you buzz in early, you will not be called on. If the team that buzzes in answers correctly, they get those points and choose the next category. If the team answers incorrectly, they lose the points. Mr. Dillon will then re-read the question so the other teams can have a chance to answer. A team is NOT obligated to answer if they do not want to. There will be a Final Jeopardy question at the end of the game where teams can wager the points they have earned. Any questions?

3. Today’s Categories Solving Systems of Equations Matrix Stuff Augmented Matrices Linear Inequalities Linear Programming The Answer is One

4. Go to Final Jeopardy

5. 100 Points This method for solving systems is the most visual way to solve… Graphing Back to Game Board

6. 200 Points This method for solving systems involves replacing expressions that are equal. Substitution Back to Game Board

7. 300 Points This method for solving systems ends with “-limination.” Elimination Back to Game Board

8. 400 Points This method for solving systems of equations works great when you have 3 or more equations and 3 or more variables. Augmented Matrices Back to Game Board

9. 500 Points Solve the following system of equations: 3x – 4y = 360 5x + 2y = 340 (80, -30) Back to Game Board

10. 100 Points Two matrices are equal if… …they have the same dimensions and each corresponding element is equal. Back to Game Board

11. 200 Points Suppose that A is a 3 x 2 matrix and B is 2 x 3 matrix. Can you determine A + B? No. You can only add matrices with the same dimensions. Back to Game Board

12. 300 Points Suppose that A is a 3 x 2 matrix and B is 2 x 3 matrix. Can you determine AB? Yes. The number of columns in the first matrix must equal the number of rows in the second matrix. Back to Game Board

13. 400 Points Find AB: Back to Game Board

14. 500 Points Find the inverse: Back to Game Board

15. 100 Points This is one row operation that can be used to transform a matrix… Interchange rows. Back to Game Board

16. 200 Points This is another row operation that can be used to transform a matrix… Multiply a row by a scalar. Back to Game Board

17. 300 Points This is yet another row operation that can be used to transform a matrix… Multiply a row by a scalar and add it to the row (or a multiple of the row) that you are replacing. Back to Game Board

18. 400 Points When simplifying a matrix, you want this number in the triangular area below the main diagonal. ZERO Back to Game Board

19. 500 Points Solve this system using a matrix: x - 2y + z = 7 3x + y – z = 2 2x + 3y + 2z = 7 (2, -1, 3) Back to Game Board

20. 100 Points Use this type of line for the boundary when the inequality is less than or greater than. DOTTED LINE Back to Game Board

21. 200 Points Use this type of line for the boundary when the inequality is less than or equal to or greater than or equal to. SOLID LINE Back to Game Board

22. 300 Points When solving a system of linear inequalities, this is the region of the graph where the solutions are located. Where the shaded parts of each graph overlap. Back to Game Board

23. 400 Points This theorem states that the maximum and/or minimum values of a function constrained by a system of inequalities will be located at the vertices of polygonal region bounded by those inequalities. VERTEX THEOREM Back to Game Board

24. 500 Points Solve the following system of inequalities: y > 2x – 4 y ≤ -x + 5 See Mr. Dillon’s Sketch… Back to Game Board

25. 100 Points This is the first step in a linear programming problem. Define the Variables Back to Game Board

26. 200 Points This is the second step in a linear programming problem. Write the constraints in the form of linear inequalities. Back to Game Board

27. 300 Points This is the third step in a linear programming problem. Graph the inequalities and find the coordinates of the vertices. Back to Game Board

28. 400 Points This is the fourth step in a linear programming problem. Write a function to be maximized or minimized. Back to Game Board

29. 500 Points These are the final two steps in a linear programming problem. Substitute the ordered pairs to find the values and select the max/min value. Back to Game Board

30. 100 Points In an identity matrix, this number is found along the main diagonal. ONE Back to Game Board

31. 200 Points This is the number of “rows” in a row matrix. ONE Back to Game Board

32. 300 Points This is the number of “columns” in a column matrix. ONE Back to Game Board

33. 400 Points Find the determinant of the following matrix: ONE Back to Game Board

34. 500 Points This is “NOW” spelled backwards. “WON” Back to Game Board

35. FINAL JEOPARDY The category for Final Jeopardy is... LINEAR PROGRAMMING Write down your wager now. Here is the question…

36. FINAL JEOPARDY Open your books to page 95. Solve question #18. You must show work and your final answer is the amount of “maximum revenue.” Maximum Revenue: $170000

37. Pre-Calculus – Chapter 2 Systems of Equations And the winner is… Pre-Calc is fun and easy!