MATH 1111 Test 1

Fall 1998

Show all work for credit. Do all your work neatly on the paper provided. Write your name on each sheet you turn in. I will not grade any work done on the test sheet. When you are finished turn in all sheets including the test. Good Luck.

  1. Determine which of the following numbers are (a) natural numbers, (b) integers, (c) rational numbers, (d) irrational numbers, (e) real numbers.

    -9, 5/2, 15, Ö2, Ö4, [3/( Ö2)],1/2, 0

  2. Evaluate the following expressions:

    (a)   [(32)/( 34)]       (b)   8(-3)-2      (c)   [(5 ·32 ·40)/( 2·3-2)]

  3. Simplify the following expressions:

    (a)   (-z)4(2z3)      (b)   -z4(2z)3      (c)    ( [(r-3)/( q-3)] ) ( [(r3)/( q3)] )      (d)   (4a-2b3)-3

  4. Perform the indicated operations:

    (a)   (5x2-3x+8)-(x-3)       (b)   (5x2-3x+8)(x-3)

    (c)   (u+2)(u-2)(u2+4)          (d)   (x+1)3

  5. Completely factor the following expressions:

    1. 3x4-6x7

    2. 6x2+2x-4

    3. x2(x-3)3-x3(x-3)2-(x-3)2

    4. r6-q6

    5. 6(x-1)2+2(x-1)-4

  6. Perform the indicated operations and simplify:

    1. [(x2)/( x-2)] ·[(x2-4)/( x3)]

    2. [x/( x2+x-2)]+ [3/( x+2)]

    3. [(([(x+3)/( x-3)] )2)/( [1/( x+3)]+[1/( x-3)])]

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