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Unformatted text preview: Final Exam —— Spring 2007  Math 130 100 Points
Name:
Section gcircle): 9:30 1:00 Do FIVE out of the SIX problems. Put an X through the question you do not want graded (or do not
write anything). If every problem is solved and no X is placed, then problem 6 will be left out. You have one hour and fifteen minutes. Show all your work and make sure your explanations are
crystal clear. If you need a clariﬁcation, raise your hand. Five minutes before the end of class I will ask everyone to stay in their seats until the end, so that
everyone may concentrate. No calculators are allowed. 1) Base Five [20 points}
You have given the following problem to your students:
Without converting to base 10, multiply (43); by (14),— ( in base 5). A student gives the following solution. Find all errors in it and give a correct solution. 7')“: : (g2)§ (g)£o : 00);
1. lg a I, .q. 37+ 3 (73:0 : (I 2); '2 o . 12:3 Name:
2) Estimation [20 points] Estimate the fraction below using the standard method from class. Give an integer upper bound and an integer lower bound whose difference is at most 5. Show how you found them, and explain why you
know they are smaller or greater than the following fraction. Q11
55 3) Divisibility and Primes
The following is a divisibility test for 13:
i) Let a be the one's digit of your number, and let b be your number with one's digit chopped off.
Your number is 10 x b + a.
ii) Your number is divible by 13 exactly when b + (4 x a) is divisible by 13.
iii) Let b + (4 X a) be your new number, and repeat the above steps until your number is less than
50. Note: the only multiples 0f13 less than 50 are 13, 26, and 39. a) Demonstrate this test for the number 104 [5 points] 13) How would you check if a number is divisible by 39, using divisibility tests? Explain why
your method works, and demonstrate it for 104. [5 points] c) Using any method, factorize 4844. [10 points] Name: 4) Critical Thinking Explanations
3) Absolute Values [10 points] i) For any positive integer X, two of the following three are equal. Which two? Explain.
X X 1 X 1 ii) For any negative integer X, two of the following three are equal. Which two? Explain.
X X l X f b) Student Solution [10 points]
You‘ve given the following word problem to your students: Jack and Jill '5 tourist shop sells TShirts for $10 each. Jack reduced that price by 20% today because
they weren’t selling well. Now they're selling great, so Jill will increase prices tomorrow by 10%.
How much will a T—Shirt tomorrow? Your student Julie gets correct answer, but mixed up the percents. Here is her solution: I 0‘ percent of $1 0 is $1. A 10% increase is $1].
20 percent of $ 1 1 is $2.20. A 20% decrease is $11  $2.20 = $8. 80. Explain why this solution is wrong. Also, explain why for any other combination of prices and '
percentages’you can mix up the percentages, and still get the correct answer. 5) Computations (remember to show your work!) 21) Rates [5 points] 1
One hose ﬁlls a swimming pool in 10 hours, while the other hose ﬁlls the swimming pool in 40 hours.
How long would it take to ﬁll up the swimming pool using both hoses together? b) Conversions [5 points each]
1) Write Oli'as a fraction in lowest terms. ii) Write the following as an exact decimal: _2_ c) Simplify each of the following; any fractions should be put in lowest terms. You do not need to show any work. [1 point each]
i) xz(xy)<x)(x+<y))
ii) 1.5. +39
13 39
iii) 5(3/7)+2(3/7)
iv) (2‘+(1/9))(1+(2/9)) v) 52 Name: 6) Prove that the square root of 2 is irrational [20 points]
Hint: every rational number can be written as a ratio of two integers, and every integer has a prime factorization. ...
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 Spring '07
 TERWILLIGER

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