Download Chapter 1 Test

Math 58 Test # 2 Fall 2015
Chapter 8-9 (sect. 1 -3, 7)
Instructor: Smith-Subbarao
______________________________
Name
Score: _______________
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 4 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:
-1, 3, 10986, -30985
b. A rational number that is not real:
not possible; all rationals are real
c. An irrational number:
√2, √14 , 𝜋 (There are many of them)
d. An integer that is neither rational nor real:
not possible; all integers are rational and all rational are real
2. (Hint: Use the picture below to help work your solution.) 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 8 pieces of his pizza and that there are 4 left; he ate more pieces, so he ate more
pizza. Sue argues that she has eaten more – although she ate only 4 pieces, she has just 2 pieces left.
Can you help them figure out who ate more pizza, Sue or Joe, and explain you know?
Sue’s
Pizza
Joe’s
Pizza
Joe’s pizza has 12 pieces. He ate 8/12 or 2/3 of it
Sue’s pizza has 6 pieces. She ate 4/6 or 2/3 of it.
Which is bigger? They are the same
3. Does x = 2 satisfy the following equation?
|2x-3| -
4
𝑥
=-
2−2𝑥
−𝑥
left side: |4-3| - 4/2 = 1-2 = -1
right side: -(2-4)/(-2) = 2/-2 = -1
yes
4. Evaluate:
y + 3x – (4x + y) +
1
𝑥+𝑦
- 2, for y = 1 and x = -2
1 + -6 – (-8 + 1) + 1/(-1) -2
1 - 6 + 7 + 1 – 2 = -1
5. a. If the additive inverse of a number is 5/2, what is the number?
-5/2; 5/2 – 5/2 = 0; a number plus its additive inverse is zero
b. If the multiplicative inverse of a number is -2, what is the number?
-1/2; (-1/2)(-2) = 1; a number times its multiplicative inverse is one
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.
2x – 5 = 5/x
b. A number equals one-half the number plus its multiplicative inverse.
x = x/2 +1/x
7. A spacecraft is orbiting earth at an altitude of 30 miles. In order to avoid an asteroid, it increases its
orbit by 5 miles. But, that move puts it on the path of another asteroid, so the craft decreases its orbit
by 4 miles. What is its altitude after this second change?
30 + 5 - 4 = 31
8. If the solution to mx = 5 is x = 1/2, what is m?
10
9. Evaluate the expression –x3 + y4 + 3xy for x = -1 and y = -2.
1 + 16 + 6 = 23
10. Joe came home from school very excited. He has learned a new way to multiply by a two digit
number: “You take the larger number and make it into the number of tens plus the number of ones.
Then you multiply each of those by the smaller number and add them together”. He gives the
example that 5 x 31 = 5 (30 + 1) = 5 x 30 + 5 = 150 + 5 = 155.
a. What property(s) of arithmetic is he using in this method?
distributive
b. Using Joe’s method, multiply 6 x 21. Show all the steps for full credit.
6 x 21 = 6(20 + 1) = 120 + 6 = 126
11. Evaluate:
a. The product of a number and its multiplicative inverse.
1; by definition
b. The quotient of a number and its additive inverse.
x/(-x) = -1
12. The longest interstate in the US is I-90, which connects Seattle to Boston. The second longest is
I-80, which connects San Francisco to Teaneck NJ, and is 178.5 miles shorter than I-90. If the length
of I-80 is m miles, express the length of I-90 in terms of an algebraic expression containing m.
length of I-90 = m + 178.5
13. Solve for y: 7(2y + 1) = 18 y – 19 y.
14y + 7 = -y
15y = -7
y = -7/15
14. There are five classrooms on one side of a school’s science building. They are numbered with
consecutive even integers. If the last room (the one with the highest number) on that side of the
building is numbered x, write an expression for the sum of the five classroom numbers. (Hint: draw
a picture of the classrooms and label them with their numbers to discover a pattern.)
x + x-2 + x-4 + x-6 + x-8 = 5x –(2 + 4 + 6 + 8) = 5x - 20
15. Solve for n: -3n –
1
2
=
8
3
I mistyped the problem in my version. If I marked you wrong, and you got it right, please let me
know and I will correct your grade.
-3n =
-3n =
8
3
+
1
2
16+3
=
6
19
6
−19
n=
18
16. Combine terms: 8wz + 6wzk – 3wz + 5wk2 – 3zk + ½ wk2.
5wz + 6wzk +
11
2
wk2 - 3zk
17. Solve for r: 2r – 8.6 = - 8.1
2r=0.5, r =0.25
18. Solve for x: 10 – 3x – 6 – 9x = 7.
-12x = 3
x = - 3/12 = -1/4
19. Solve for a: -5(3-a) =
10𝑎−25
2
-
5
2
left side: -15 + 5a
right side 5a – 25/2 – 5/2 = 5a – 30/2 = 5a – 15;
all values satisfy
20. Solve for c: c + 1/6 = 3/8 + 2c
c = 1/6 – 3/8 = 4/24 – 9/24 = -5/24
21. Evaluate (1/3)(4 + 1/2)  5 – 3
=(1/3)(9/2)  5 – 3 = (3/2)(1/5) – 3 = 3/10 – 3 = -27/10
22. Solve for x: 3x – 4 < 8
3x < 12, x < 4
23. Solve for t: 3 - 4t ≥ 9
-6 ≥ 4t, -3/2≥ t
24. Solve for y: 3(2y – 5) = - (4 – 6y)
6y – 15 = -4 + 6y no solutions
25. If the perimeter of a triangle is 36 feet, the first side is 4x + 3 feet, the second side is 2x feet, and the
remaining side is x – 2 feet, how long are each of the three sides?
Perimeter = 36 = 4x+3 + 2x + x-2 = 7x + 1
7x = 35
x=5
Sides are 23, 10, 3