Difference between revisions of "2005 CEMC Gauss (Grade 7) Problems"
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== Problem 3 == | == Problem 3 == | ||
+ | <asy> | ||
+ | //make the picture small and square | ||
+ | size(80,80); | ||
+ | |||
+ | //draw an arc from 0 to 75 degrees of radius 1 centered at the origin | ||
+ | draw(arc((0,0),1,0,75)); | ||
+ | |||
+ | //draw a line with an arrow on the end pointing to 25 degrees (scale it down by .95 so that it stays inside the arc) | ||
+ | //dir(25) is a unit vector pointing 25 degrees | ||
+ | draw((0,0)--scale(.95)*dir(25),Arrow); | ||
+ | |||
+ | //put a label at the end of the 75 degree unit vector (and position it out 75 degrees) | ||
+ | MarkPoint("9",dir(75),dir(75)); | ||
+ | |||
+ | //put a label at the end of the 75 degree unit vector (rotate label 75 degrees to create a tick) | ||
+ | MarkPoint(75,"-",scale(.85)*dir(75),dir(75)); | ||
+ | MarkPoint("9.2",dir(60),dir(60)); | ||
+ | MarkPoint(60,"-",scale(.85)*dir(60),dir(60)); | ||
+ | MarkPoint("9.4",dir(45),dir(45)); | ||
+ | |||
+ | //put a label at the end of the 45 degree unit vector - use NE to move it slightly NorthEast of this point (or use dir(45)) | ||
+ | MarkPoint(45,"-",scale(.85)*dir(45),NE); | ||
+ | MarkPoint("9.6",dir(30),dir(30)); | ||
+ | MarkPoint(30,"-",scale(.85)*dir(30),dir(30)); | ||
+ | MarkPoint("9.8",dir(15),dir(15)); | ||
+ | MarkPoint(15,"-",scale(.85)*dir(15),dir(15)); | ||
+ | |||
+ | //put a label at the end of the 0 degree unit vector - use E to move it slightly East of this point (or use dir(0)) | ||
+ | MarkPoint("10",dir(0),E); | ||
+ | MarkPoint(0,"-",scale(.85)*dir(0),dir(0)); | ||
+ | </asy> | ||
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Revision as of 14:37, 22 October 2014
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 See also
Problem 1
The value of is
Problem 2
The value of is
Problem 3
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9.0.........9.2..........9.4.........9.6..^...9.8........10.0
Contestants on "Gauss Reality TV" are rated by an applause metre. In the diagram, the arrow for one of the contestants is pointing to a rating closest to:
Problem 4
Twelve million added to twelve thousand equals
Problem 5
The largest number in the set {} is
Problem 6
At a class party, each student randomly selects a wrapped prize from a bag. The prizes include books and calculators. There are prizes in the bag. Meghan is the first to choose a prize. If the probability of Meghan choosing a book for her prize is
, how many books are in the bag?
Problem 7
Karen has just been chosen the new “Math Idol”. A total of votes were cast and Karen received
of them. How many people voted for her?