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MA 153 - Quiz 1 (5 minutes)
Solution
Statistics (out of 10):
Section 36 42
Average 5.5 6.7
Max
9
10
Min
1
1
1. (2 points) Evaluate (−4)|6(−2) + 3|.
Solution:
(−4)|6(−2) + 3| = (−4)| − 9| = (−4)(9) = −36
One point for the 36, one point for having a negative answer.
Common mistakes: Some people forgot that you can’t bring a number into absolute value symbols.
Remember: absolute values act as parentheses in that you should do everything inside of them first,
however they are unlike parentheses in that they don’t obey the distributive rule.
2. (6 points) Simplify the following expression. Your answer should not contain negative exponents.
−2 5 −2
3x y
x3 y 2
Solution:
3x−2 y 5
x3 y 2
−2
−2
3y 3
=
x3 x2
5 2
x
=
3y 3
x5·2
= 3·2
9y
=
3y 3
x5
−2
(x5 )2
32 (y 3 )2
x10
= 6.
9y
=
Points were awarded as follows: one point for the 9, one point for x10 and one point for y 6 . Then there
was one point given for having each of these in the correct spot (i.e. 1 point for x in the numerator,
etc.)
Common mistakes: Some people mixed up fractional exponents with negative ones, so had square roots
floating around in their answers. Others forgot to bring the exponent in to everything including the
number 3.
Remember the order of operations: Parentheses, exponents, multiplication, division, addition, subtraction (a good mnenomic for this is “Please Excuse My Dear Aunt Sally”). So first, you should simplify
things inside of the parentheses, in this case combining the x and y terms. Only then should the
exponent outside of the parentheses be worried about.
3. (2 points) Simplify the following expression. Remove numbers from the radical where possible.
√
4
32r12 .
Solution: Note: 32 = 25 = 24 · 2
√
4
32r12 =
√
4
√
4
√
4
32 r12
2 · 24 r12/4
√
√
4
4
= 24 2r3
√
4
= 2 2r3 .
=
√
One point for the correct exponent on the r, and one point for the correct number, 2 4 2.
Common mistakes: Lots of people thought that 321/4 = 8. The 1/4 is an exponent, not actual division
by 4. Instead, 32 should be broken up into 2 · 24 . Then when bringing in the fractional exponent, one
gets (2 · 24 )1/4 = 21/4 · 24/4 = 21/4 · 2.