MATH 107 Quiz 1: Algebra Skills Assessment - UMUC, October 2018

This document provides a comprehensive solution to a MATH 107 Quiz 1, covering fundamental algebra concepts. The quiz includes problems on distance calculation on a number line, interval notation, simplification of algebraic expressions with exponents, scientific notation, factoring polynomials, performing operations on algebraic expressions, and solving linear equations. Additionally, it involves simplifying complex fractions and radical expressions. Each problem is solved step-by-step, showing the application of algebraic rules and principles to arrive at the correct answer. This quiz serves as a valuable resource for students to practice and reinforce their understanding of basic algebra concepts. Desklib provides access to this and many other solved assignments.

MATH 107 QUIZ 1 Oct. 8, 2018 Instr: J. Uccellini
Instructions:
 The quiz is worth 100 points. There are 12 problems. Your score on the quiz will be
converted to a percentage and posted in your Portfolio with comments.
 This quiz is open book and open notes, and you may take as long as you like on it
provided that you submit the quiz no later than the due date posted in our course schedule
of the syllabus. You may refer to your textbook, notes, and online classroom materials,
but you may not consult anyone or any other online resources than your course
material.
 You should show all of your work to receive full credit. If you do not show work, you
may earn only partial or no credit.
 Please type your work in your copy of the quiz, or if you prefer, create a document
containing your work. Scanned work is also acceptable. Be sure to include your name in
the document. Review instructions for submitting your quiz in the Quizzes and Exams
Conference.
 If you have any questions, please contact me by e-mail ([e-mail]).
Please remember to show ALL of your work on every problem. If there is no work to show,
then include a sentence or two explaining your answer.
Here are the basic rules of showing work:
 Each step should show the complete expression or equation rather than a piece of it.
 Each new step should follow logically from the previous step, following rules of algebra.
 Each new step should be beneath the previous step.
 The equal sign, =, should only connect equal numbers or expressions.
If you have questions about showing work, please ask.
At the end of taking your quiz you must sign the following dated statement with your name
typed in lieu of a signature. Without this signed statement you will receive a zero.
I have completed this quiz myself, working independently and not consulting anyone except the
instructor. I have neither given nor received help on this quiz.
Name: Date:

NAME: _______________________________ Math 107 Quiz 1 100 pts
1a. (2 pts) Which of the following represents the distance between -12.4 and–6.9on the number
line? Indicate your choice .
1a. ____C___
A. | -12.4|+ | -6.9|
B. | -6.9 - 12.4|
C. | -12.4 + 6.9 |
D. | –6.9| – | -12.4|
1b. (2 pts) Find the distance. Show your work.
Solution: The distance
2. (3 pts) Write the interval notation corresponding to the set notation{x | x≤– 4}.
Solution: Since , so on the number line
Hence, interval notation is
3. (6 pts) Consider the interval (–, 0]. For each numerical value below, is it in the interval or
not?
(Just answer Yes or No)
-7.1  10–3___Yes_____ (-10)0__No______|–0.09| _____No___
(Yes or No) (Yes or No) (Yes or No)
-32____Yes____ (–4)2___No_____ (-1.5) x (4.2)-1____Yes_______
(Yes or No) (Yes or No) (Yes or No)

4. (6 pts) Simplify 36 x3 y−2 z4
144 x5 y−3 z−3 .Show work. Make sure that your final answer has no negative
exponents.
Solution: Consider the expression,
Hence
5. (10 pts) Simplify(3 m2 n−5) ¿. Show work. Make sure that your final answer has no negative
exponents.
Solution:
Hence,
6. (8 pts) Compute 9 . 3 ×106
3 .1 ×10−5 . Show some work. Write the answer using scientific notation.
Solution:
Hence,

7. (6 pts. each) Factor. (Work not required to be shown).
(a) 3 x2−4 x −15
Solution:
(b) 4 a2−b2
Solution:
(c) 1−64 t3
Solution:
8. (12 pts) Perform the indicated operations and simplify: ( 2 x−3 ) ( x+6 ) −(4−2 x)2.Show work.
Solution: Consider the expression .
Now,
Hence
9. (8 pts) solve the equation 12(x−2)−10( x+7)=14. Show work.
Solution:
Consider the expression .
Now,

10. (8 pts) Solve the equation 6 x3−x2=12x. Show work.
Solution: Consider the expression .
Now,
Solve
Solve
Solve
Hence the solutions are
11. (9 pts) Simplify: 2 x
x2 −16 − 2 x−7
x2−7 x +12 . Show work.

Solution: Consider the expression .
Now,
Simplify further,
Simplify further and obtain,
12. (8 pts) Simplify: 8 √ 12−9 √ 20+ √ 75. Show work. Give the exact answer (including a radical).
Solution: Consider the expression .
Now,
Simplify further and obtain,