ALGEBRA TEST |

This Algebra test is not meant to be done in one sitting. If you can accomplish that -- good on you -- not only do you know your algebra, you've become efficient and precise, so you're ready to tackle other things! Check out some Analytic Geometry.

This test is meant chiefly as a comprehensive review of the material in the lessons of the Algebra MathRoom to help the student evaluate his/her familiarity with the material. It should also serve to pinpoint weaknesses or topics that could use a little more practice. In such a case, go back to the **Algebra MathRoom** and review those topics.

You will find no **multiple guess** questions on this test. I despise them. They encourage you to "guess" rather than solve. You should write a clear response for each question. Your response should be properly presented in conventional math format.

Before you start, you might check out the article entitled "**So You're Writing a Math Exam**" in **MathRoom Musings**. And here's a link to the solutions .

__ALGEBRA TEST__

**A/ Factor Completely if Possible**

1) 6a^{2}b^{2} – 54b^{4} |
2) c^{2} – a^{2} – 10ab – 25b^{2} |
3) 81 – m^{4} |

4) 3cx^{2} + 6cx – 9c |
5) 64 – x^{6} |
6) a^{2}b^{3} – b^{3} + a^{2} – 1 |

7) 3x^{2} + 11x + 10 |
8) 25 – x^{2} – 6x – 9 |
9) 7x^{2} – 27x – 4 |

10) 3x^{3} + 24 |

**B/ Perform the Indicated Operations. Reduce to Lowest Terms.**

- 1)

- 2)

- 3)

- 4)

- 5)

- 6) .

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**C/ Solve These Equations and Check Your Answer(s).**

1) 12 + 3(m + 4) = 5m – 2 |
2) 8(n + 3) + (6 + 2n) = 2(n – 2) + 5(5 + n) |

3) | 4) |

5) | 6) x^{2} = 2x + 15 |

7) 3x^{2} + 2x = 7 |
8) |

9) 3x + 2y = 16_{(eq.1)}....7 |
10) 4r^{2} + t^{2} = 25_{(eq.1)}.........2 |

**D/ Solve These Inequalities and Check Your Answers.**

1) 3x + 2 < 5x – 6 |
2) x^{2} + 4x > 12 |

3) | 4) |

5) | 3x – 5| > 22 |

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**E/ Simplify these Radical Expressions:**

1) | 2) |

3) | 4) |

5) | 6) |

7) | 8) |

__F/ Rationalize these denominators__

1) | 2) | 3) | 4) |

**G/ Simplify. Leave no negative exponents**

1) | 2) | 3) | 4) |

**H/** **Solve these word problems:**

(remember to make a **"let"** statement and a table or diagram when helpful.)

- 1) The larger of two numbers exceeds the smaller by 4. Eight times the smaller decreased by four times the larger is 12. What are the two numbers?

- 2) The perimeter of a rectangle is 72 dm. Three times the width exceeds twice the length

by 3 cm. Find the length and width of the rectangle.

- 3) Sam is presently 7 years older than Fred. One year ago, Sam was twice as old as Fred was then. How old is each now?

- 4) The sum of the squares of two consecutive integers is 221. Find 2 solutions for these integers.

- 5) A grocer wishes to make a mixture of 80 Kg. of coffee to sell at $4.00 per Kg. He has some coffee that sells for $5.50/kg and cheaper coffee that sells for $3.00/kg. How many kilograms of each type of coffee must he put in the mixture?

- 6) A bicycle party travels at 25 km/h. At what speed must a second bicycle party travel in order to overtake the first party in 3 hours if they start from the same place 1 hour later than the first party?

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