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) 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.

1)
2)
3)
4)
5)
6) .

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

 1) 3x + 2 < 5x – 6 2) x2 + 4x > 12 3) 4) 5) | 3x – 5| > 22

 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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