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Difference between revisions of "2005 CEMC Gauss (Grade 7) Problems"

(→‎Problem 3)
(→‎Problem 8)
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== Problem 8 ==
 
== Problem 8 ==
 +
 +
In the diagram, what is the measure of <math>\angle ACB</math> in degrees?
 +
<asy>
 +
size(300);
 +
draw((-60,0)--(0,0));
 +
draw((0,0)--(64.3,76.6)--(166,0)--cycle);
 +
label("$A$",(64.3,76.6),N);
 +
label("$93^\circ$",(64.3,73),S);
 +
label("$130^\circ$",(0,0),NW);
 +
label("$B$",(0,0),S);
 +
label("$D$",(-60,0),S);
 +
label("$C$",(166,0),S);
 +
</asy>
  
 
[[2005 CEMC Gauss (Grade 7) Problems/Problem 8|Solution]]
 
[[2005 CEMC Gauss (Grade 7) Problems/Problem 8|Solution]]

Revision as of 14:13, 22 October 2014

Problem 1

The value of $\frac{3 \times 4}{6}$ is

$\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 6$

Solution

Problem 2

The value of $0.8 - 0.07$ is

$\text{(A)}\ 0.1 \qquad \text{(B)}\ 0.71 \qquad \text{(C)}\ 0.793 \qquad \text{(D)}\ 0.01 \qquad \text{(E)}\ 0.73$

Solution

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]


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:

$\text{(A)}\ 9.4 \qquad \text{(B)}\ 9.3 \qquad \text{(C)}\ 9.7 \qquad \text{(D)}\ 9.9 \qquad \text{(E)}\ 9.5$

Solution

Problem 4

Twelve million added to twelve thousand equals

$\text{(A)}\ 12,012,000 \qquad \text{(B)}\ 12,120,000 \qquad \text{(C)}\ 120,120,000 \qquad \text{(D)}\ 12,000,012,000 \qquad \text{(E)}\ 12,012,000,000$

Solution

Problem 5

The largest number in the set {$0.109, 0.2, 0.111, 0.114, 0.19$} is

$\text{(A)}\ 0.109 \qquad \text{(B)}\ 0.2 \qquad \text{(C)}\ 0.111 \qquad \text{(D)}\ 0.114 \qquad \text{(E)}\ 0.19$

Solution

Problem 6

At a class party, each student randomly selects a wrapped prize from a bag. The prizes include books and calculators. There are $27$ prizes in the bag. Meghan is the first to choose a prize. If the probability of Meghan choosing a book for her prize is $2/3$, how many books are in the bag?

$\text{(A)}\ 15 \qquad \text{(B)}\ 9 \qquad \text{(C)}\ 21 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 18$

Solution

Problem 7

Karen has just been chosen the new “Math Idol”. A total of $1,480,000$ votes were cast and Karen received $83\%$ of them. How many people voted for her?

$\text{(A)}\ 830,000 \qquad \text{(B)}\ 1,228,400 \qquad \text{(C)}\ 1,100,000 \qquad \text{(D)}\ 251,600 \qquad \text{(E)}\ 1,783,132$

Solution

Problem 8

In the diagram, what is the measure of $\angle ACB$ in degrees? [asy] size(300); draw((-60,0)--(0,0)); draw((0,0)--(64.3,76.6)--(166,0)--cycle); label("$A$",(64.3,76.6),N); label("$93^\circ$",(64.3,73),S); label("$130^\circ$",(0,0),NW); label("$B$",(0,0),S); label("$D$",(-60,0),S); label("$C$",(166,0),S); [/asy]

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

Problem 16

Solution

Problem 17

Solution

Problem 18

Solution

Problem 19

Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

See also

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