Download Exam 1 Solutions

(8 points) 1. Mark the following as rational, irrational, integer, whole, natural (list all that apply).
(a) 0
(a)
(b) −
7
3
(b)
(c) −8
(c)
(d) 1.41421356237 . . .
(d)
(5 points) 2. Factor 264 completely into a product of prime numbers.
2.
(8 points) 3. Are the fractions
7
21
and
equivalent? Why or why not?
9
27
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Math 100A
Exam #1 (Continued)
(5 points) 4. Based on the readings and class discussions, explain what it means for two algebraic expressions
to be equivalent. You may use an example, such as 3x + 9 and 3(x + 3), or a non-example,
such as 3x + 9 and 3(3x + 3), but if you merely perform multiplication/simplification you will
receive no credit.
(8 points) 5. Simplify completely.
−2 +
10 − 4
+ (15 − 13)3
3
5.
(9 points) 6. Britta plans to buy a few pairs of jeans for $60 each and some skirts for $27 each. Write an
algebraic expression that describes the cost of Britta’s shopping spree.
6.
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Math 100A
Exam #1 (Continued)
(6 points) 7. Jeff simplified 10 − 8 · 2 − 32 as follows:
10 − 8 · 2 − 32 = 2 · 2 + 9
=4+9
= 13.
Where did Jeff go wrong? Explain what he did wrong and how to correct his mistake(s).
(12 points) 8. Vicki is thinking of a real number between (and possibly including) −20 and 77.
(a) Graph the set of possibilities of Vicki’s number on a number line.
(b) Express this set in set builder notation.
(b)
(c) Express this set in interval notation.
(c)
(d) Does this set have a finite or infinite number of elements?
(d)
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Math 100A
Exam #1 (Continued)
(8 points) 9. Assume C and D represent the sizes of the populations of two cities, where C > D. For each
of the following pair of expressions, determine which is larger. Briefly explain your reasoning
in terms of the two populations.
(a) C + D and 2C
(b)
C
C+D
and
C+D
C
(12 points) 10. Simplify the following expressions completely.
(a) 7x + 10y − 40 + x − 13y
(a)
(b) 18 − 2w + 7z − 4z + 8w − 10
(b)
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Math 100A
Exam #1 (Continued)
(10 points) 11. Express each English expression as an algebraic expression.
(a) The sum of 3 and the product of 7 and x.
(a)
(b) Twice the sum of a and 17, subtracted from 3.
(b)
(9 points) 12. The algebraic expression 11x represents the approximate number of snack cookies that can be
purchased for x dollars. How many cookies can you buy for $3? $12? $100?
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