Algebra 2 TEST 1



Algebra 2 SIX WEEKS TEST Review DO ON OWN PAPER!

This review covers problems from TEST 2.1 and TEST 2.2. It would be wise to look over your old reviews and your graded tests in addition to completing this review.

I. Linear Programming

|1. Graph the region and find the vertices. |2. Maximize and minimize [pic] for problem #1. |3. Which restrictions are graphed? |

|[pic] | |[pic] |

II. Use the matrices provided for #4-11.

|[pic] [pic] [pic] [pic] [pic] |

|4. [pic] |5. [pic] |6. [pic] |7. [pic] |

|8. [pic] |9. [pic] |10. [pic] |11. dimensions of [pic] |

III. Matrix Products.

|Given that [pic], [pic], [pic], and [pic], state what the dimensions of the products would be, if they are defined. |

|12. [pic] |13. [pic] |14. [pic] |15. [pic] |16. [pic] |

1V. Find the inverse of each matrix.

|17. [pic] |18. [pic] |

VI. Solve using inverse matrices. Set up a matrix equation first!

|19. [pic] |20. [pic] |

VI. Solve the matrix for each variable.

|21. [pic] |

VII. Simplify. No decimals.

|22. [pic] |23. [pic] |24. [pic] |

|25. [pic] |26. [pic] |

VIII. Simplify. No negative exponents in your final answer!

|27. [pic] |28. [pic] |

|29. [pic] |

IX. State the transformations for each and then graph.

|30. [pic] |31. [pic] |32. [pic] |

X. Write the equation of each function. State the Domain and Range.

|33. |34. |

|[pic] |[pic] |

XI. Find the vertex and the axis of symmetry. Then state the maximum or minimum value.

|35. [pic] |

Rewrite in vertex form.

|36. [pic] |

XI. Factor:

|37. [pic] |38. [pic] |39. [pic] |40. [pic] |

XII. Find the zeros:

|41. [pic] |42. [pic] |

Write the quadratic in standard form, given the following roots.

|43. 3 and -1 |

Answers:

1. Vertices [pic], [pic], [pic], and [pic] 2. Maximum value of 55 at [pic],

Minimum value of –21 at [pic]

3. [pic] 4. not possible 5. [pic]

6. [pic] 7. [pic] 8. not possible

9. 10. [pic] 11. [pic] 12. [pic] 13. not possible

14. not possible 15. [pic] 16. [pic]

17. [pic] 18[pic] 19. [pic] 20. [pic]

21. [pic] 22. [pic] 23. [pic] 24. [pic] 25. [pic] 26. [pic] 27. [pic] 28. [pic] 29. [pic]

30. Reflected over the x-axis 31. left 3, up 1 32. Vertical stretch of 3; right 1, up 2

up 4

33. [pic] 34. [pic] 35. [pic] 36. [pic]

37. (x+3)(x+4) 38. (2x+3)(2x-3) 39. (x-4)(x+3) 40. (2x-1)(x+3) 41. -7; 2

42. [pic] 43. [pic]

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[pic]

[pic]

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