Download Math 58 Test # 2 Fall 2014

Math 58 Test # 2 Fall 2014
Chapter 8
Instructor: Smith-Subbarao
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Name
Score: _______________
If you are not sure about notation, please ask for help! (4 + 1 ) / x means 4 + 1 is in numerator and x is in the
denominator. (4 + 1) / (x + 2) means that 4 + 1 is in the numerator and (x + 2) is in the denominator. If there is a
mixed number, e.g., 3 1/2 , there will be a space between the number and the fraction. Compare with 31/2 where
then is no space, and it means 31 divided by 2.
Directions:
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Show all work and circle/box your answers.
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Partial credit may be given, even if the answer is incorrect, if your work is clear – attach additional scratch
pages you wish to be considered.
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If you do not show your work, you may not get credit.
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Unless otherwise instructed, leave all answers as fraction; improper fractions are OK, but you will lose one
point if you do not simplify your fractions.
Each problem is worth 10 points.
NO: Telephones, Books, Notes; CALCULATORS ARE NOT ALLOWEED
Suggestions:
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Choose the problems you understand best to work first.
If you get stuck, write down what you do understand for partial credit and move on
Show your work clearly
Check your solutions
Evaluate your solutions for “reasonableness”
1.
Give an example of
a. An integer: -4
b. A rational number that is not real: no such thing
c. An irrational number: √2
d. An integer that is neither rational nor real: no such thing
2. Sue and Joe are arguing about who ate the most pizza. Their mother says that she gave them each the
same sized pizza (although each child cut his/her pizza into however many equal pieces he/she
wished). Mom has a headache and told Sue and Joe to resolve their own argument.
Joe says that he ate 5 pieces of his pizza and that there are 3 left; he ate more pieces, so he ate more
pizza. Sue argues that she has eaten more – although she ate only 3 pieces she has just one piece left.
Can you help them figure out who ate more pizza, Sue or Joe, and explain you know?
Note: Both pizzas are the same total size!
Joe’s pizza has 8 pieces. He at 5, or 5/8 of a pizza
Sue’s pizza has 4 pieces. She at 3 or 3/4.
Which is bigger? 5/8 or 3/4. Find a common denominator of 8.
5/8 compared to 3/4 is the same as 5/8 compared to 6/8.
Sue ate more.
3. Does x = 2 satisfy the following equation?
|2x-3| - 4/x = - ( 2 – 2 x) / (-x)
Substituting for x:
|2 (2) – 3 | = - [ 2 – 2(2)]/ (- (2))
|4 – 3| = - (2 – 4) / (-2)
||1| = - (-2) / (-2)
1 = 2 / (-2) = -1;
Not equal, does not satisfy
4. Evaluate: y + 4x – (2x + y) + 1/(x+y) - 2, for y = 1 and x = -2
(1) + 4 (-2) – (2(-2) + 1 ) + 1/(-2 + 1)
1 – 8 – (-4 + 1) – 1/1
-7 – (-3) – 1 = - 5
5. a. If the additive inverse of a number is 5/2, what is the number?
- 5/2
b. If the multiplicative inverse of a number is -2, what is the number?
-1/2
6. Write an equation for the statements. You do not need to solve the equation:
a. Two times a number, less five, is the quotient of five and the number.
2n – 5 = 5/n
b. A number plus its multiplicative inverse is one-half the number.
n + 1/n = n/2
7. A spacecraft is orbiting earth at an altitude of 40 miles. In order to avoid an asteroid, it increases its
orbit by 4 miles. But, that move puts it on the path of an asteroid, so the craft decreases its orbit by
8 miles. What is its altitude after this second change?
Start 40
Increase by 4, 40 + 4 = 44
Decrease by 8, 44 – 8 = 36 miles
8. Give a brief explanation:
a. Kim says that she knows that 5 – 3 = 3 – 5 because of the commutative property of addition.
Is she right? Why or why not?
The commutative property of addition would be 5 + (-3) = -3 + 5 . she is trying to use
addition rules for subtraction, which is wrong.
b. Mike explains how to find the multiplicative inverse as follows: You take the number on the
top of the fraction and put it on the bottom, then you put the number that used to be on the
bottom of the fraction on the top. Finally, you put a minus sign in front of the whole fraction.
Is his explanation correct? Why or why not?
He is correct, except for the minus sign. The multiplicative inverse of a/b is b/a
9. Evaluate: [ |3-4|2 + 4 (3/2) – 5 (5-6) - (-3)3 ] =
[ |-1|2 + 6 – 5(-1) – (-27)] =
[ 1 + 6 + 5 + 27] = 39
10. Do the numbers x = -1 and y = 2 satisfy the following equation?
2 [3y + (x)5/2 - 4 ] = y – x
2 [ 3(2) + (-1) 5 / 2 – 4] = (2) – (-1)
2 [ 6 + (-1) /2 – 4 ] = 2 + 1
2 [ 6 - 1/2 – 4]= 3
2 ( 2 - 1/2] = 3
2 ( 4/2 – 1/2] = 3
2 (3/2) = 3 yes