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 .
A/ Factor Completely if Possible
|1) 6a2b2 54b4||2) c2 a2 10ab 25b2||3) 81 m4|
|4) 3cx2 + 6cx 9c||5) 64 x6||6) a2b3 b3 + a2 1|
|7) 3x2 + 11x + 10||8) 25 x2 6x 9||9) 7x2 27x 4|
|10) 3x3 + 24|
B/ Perform the Indicated Operations. Reduce to Lowest Terms.
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)|
|5)||6) x2 = 2x + 15|
|7) 3x2 + 2x = 7||8)|
|9) 3x + 2y = 16(eq.1)
....7x + y = 19(eq.2)
|10) 4r2 + t2 = 25(eq.1)|
.........2r + t = 7(eq.2)
D/ Solve These Inequalities and Check Your Answers.
|1) 3x + 2 < 5x 6||2) x2 + 4x > 12|
|5) | 3x 5| > 22|
E/ Simplify these Radical Expressions:
F/ Rationalize these denominators
G/ Simplify. Leave no negative exponents
H/ Solve these word problems:
(remember to make a "let" statement and a table or diagram when helpful.)
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