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Unformatted text preview: Instr: Paul Terwilliger
Spring 07
Math 130 Midterm II Your Name U GM NO CALCULATORS ALLOWED. Show all yourwork. CLEAR AND APPROPRIATE»
EXPLANATIONS COUNT FOR JUST AS MUCH AS THE CORRECT NUMERICAL
ANSWER. ' ‘ 1. The numbers A and B are shown on the number line below. Find the points on the
number line that correspond to thefollowing: —A + B; (ii) —(A + B); (iii) A + B; (iv)
——(B — A). Label your answers clearly. ' V A l a I 5 .
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' (6 W4) ‘( W”) Are "5“6 2. Compute 3/4 — 2/3 and express your answer as a fraction. Explain why your method is
valid using the number line below. r e 3
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your reasoning using the deﬁnition of percent. «‘7‘ t: 26 : J.
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Cr: 0 $26. What was the original price? Explain
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2c, VANS uh (EFL? EVCBxLE‘Eﬂ art? 9%,. a} pace 5. Describe a way to solve 204 — 81' mentally, by using reasoning other than the standard
subtraction algorithm. Then write a coherent sequence of equations that correSpond to your
reasoning. ' ’ "20435; arr—2’0 6. One type of ﬂoor tile costs $70 per square yard. A second type of ﬂoor tile costs $7.90
per square foot. Which type of tile is more expensive? Explain your reasoning. :va
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'  Iglt. numbers can be mad .
re eated di ‘ , . ‘ € usmg only the divits 2. I :1
priblem “rjiitsaare alioxned (so that 232 and 334 are counted)? Show hOCW t 3;: \mere
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ex 1 _ Vh _ 1 Organlzed ﬂat and tree dlagram. Use the meanin f . .O,.80 V? this
p am V" Y thls pTOblem can be solved by multimin g 0 muﬁlpncamon to
u ‘ ‘ b, Calf/(15V “44 F! L; 56 Drum Ear/f1 74455 # fi/Qh’md 1) 3 x3 :7 ktA 8. A cube that is 1 foot tall, 1 foot wide, and 1 foot deep is made out of smaller cubes that
are each 1 inch tall, 1 inch Wide, and 1 inch deep. The large cube is painted on the outside. 12? (ii) How many of the smaller cubes have paint on exactly two sides? ans (i) How many of the smaller cubes have paint on them? ans
1 L 0 1 8 (iii) How many of the smaller cubes have paint on exactly three sides? ans 23,10): [12? ’1000
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[.wa’llo 9. Determine which of the foilowing two numbers is larger, withou
number explicitly. Explain your reasoning. The numbers are: (i) 1000, 000 x (1+2+3+~+1,000,001);
(ii) 1:000, 001 X (1 + 2+3++1=000,000). t actually calculating each n ‘ 715 5 W14 56" {3 a»; of / ("71 : Aéiafﬁvqak m: i/OOL7KC7éu
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I'sz n4 (my; / 5 t 51% //VW (0V etc/MW s ‘— W ; 5 ghqgécd' axe”; ‘ I Ix ( Ck/LE/é’k
ALL/aw) a : ; Ch 10. Draw a subdivided array to show that 7 x 6 = 5 X 5+ 5 x 1 + 2 X 5 + 2 x 1. Then
write a coherent sequence of equations and use the properties of arithmetic to Show Why the
preceding equation is true. 9 “H ' . r—j'f—
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:' §'*(§3frlj «k 2% 5‘“) + 1X57“ 7“" 11. Use the partial products algorithm to calculate 27 x 2 8. Illustrate the meaning of this
algorithm using a rectangular array diagram. ' 9’2? glue: 7%
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 Spring '07
 TERWILLIGER
 Inch, smaller cubes, ﬂoor tile costs

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