Math 208
Quiz 2
Concluded
Math 208
Quiz 2 +Answers
July 20, 2011
Each question is worth 6 points when answered correctly. However, Questions 11 and 12 are worth 5 points. Show your work to receive at least Partial Credit. Answer all questions somehow. Remember to breathe deeply every so often.
1. List all the real numbers in the set: { -10, , 0, 8/2, , 17/5 } 1. __all _____
2. List all of the rational numbers in the set of question 1. 2. all but pi and sqrt_
3. List all of the integers in the set of question 1. 3. __-10, 0, 8/2____
4. Simplify: 4. __–(1/4)X + (5/2)__
5. Simplify: 7( X – Y + Z ) – 3( -2X - 4Y + 1 ) 5. _13X + 5Y + 7Z -3_
7X -7Y + 7Z
-(-6)X -(-12)Y -3
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13X + 5Y + 7Z -3
6. Simplify: 21 + 5[ ( 2X + 9 ) – ( X + 3 ) ] 6. ___ 51 + 5X _____
21 + 10X + 45 - 5X - 15 = 21 + 45 - 15 +10X -5X = 51 + 5X
7. What Algebraic Property justifies this? 7. _Distributive Law_
8. The formula T = ( 3(A-20)2 / 50 ) + 10 describes
the average running time, T, in seconds, for a person
who is A years old to run the 100 yard dash event.
How long does it take a 25 year old runner to run the
100 yard dash? 8. __11.5 seconds ___
T = (3(25 - 20)2 /50 + 10 = 3*25/50 +10 = 11.5 seconds
9. The Dead Sea is 1312 feet below sea level. If a person
is in a helicopter flying 68 feet above the Dead Sea, what
is the person’s elevation? 9. _____ -1244 feet__
-1312 + 68 = -1244
10. Subtract 2X – 3Y + 3 from 6X –4Y –3 10. ___4X - Y - 6___
6X - 4Y -3
-(2X -3Y +3)
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4X - Y - 6
11. If = Find the value of 11. ____4/3______
A/B + 1 = 7/3 A/B = 7/3 - 1 = 4/3 ; B = 3, ? + 3 = 7 ? = 4, so 4/3
12. If = -1 What is the numerical value of X + Y ? 12. ______0______
X = -Y, so X + Y = 0; Let X = 2, then Y = -2 and 2/(-2) = -1 So X+Y=0
13. Represent the sum of and as a single fraction. 13. ____5/(6X)____
(2(1 - 2X) + 3 + 4X ) / 6X = 5/(6X)
14. The expression + is equivalent to:
(a) 1 (b) (c) (d) 14. ______c______
B(A+B) + A(A-B) = BA + B2 +A2 - AB = B2 + A2/A2B2
Let A = 1, B = 2, then expression is: (1 + 2)/1*2 + (1 – 2)/1*4 = 3/2 – 1/4 = 6/4 – 1/4 = 5/4
So not (a); b) 32 / 1*4 = 9/4, not (b); c) (1+4)/1*4 = 5/4 So (c)
15. If n represents an integer, the square of the next larger integer is:
(a) n2 + 1 (b) n2 + 4 (c) n2 + 2n + 1 (d) n2 + 4n + 4 15. ______c______
(n+1)2 = n2 + 2n + 1
let n=1, so n+1 = 2 and 22 = 4; a) 1+1=2 b)1+4=5 c) 1+2+1 = 4 so (c)
16. Ross jogs at a rate of one mile every 0.25 Hour. At what rate is he
jogging in Miles Per Hour? 16. ____4 mph____
17. If the average of two numbers is 2X + 1 and one of the numbers
is X, then the other number is:
(a) X + 1 (b) 2X + 1 (c) 3X + 1 (d) 3X + 2 17. ______d______
Average = 2X + 1 = (X + Y)/2
4X + 2 = X + Y
3X + 2 = Y
Average = sum of 2 numbers/2 Let X = 1, then (1 + Y)/2 = 2*1+1 = 3
So Y = 5 So a) 1 + 1 = 2 b) 2*1+1 = 3 c) 3*1+1 = 4 d) 3*1+2 = 5
So (d) is the answer
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