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Difference between revisions of "2005 CEMC Gauss (Grade 7) Problems"
Line 127: Line 127:
  
 
== Problem 11 ==
 
== Problem 11 ==
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 +
The temperature range on a given day is the difference between the daily high and the daily low temperatures. On the graph shown, which day has the greatest temperature range?
 +
 +
<math>\text{(A)}\ Monday \qquad \text{(B)}\ Tuesday \qquad \text{(C)}\ Wednesday \qquad \text{(D)}\ Thursday \qquad \text{(E)}\ Friday</math>
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 +
<asy>
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size(300);
 +
draw((0,-10)--(0,10),EndArrow);
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draw((0,0)--(16,0),EndArrow);
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picture temp;
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label(temp,"Temperature ($^\circ$C)");
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add(rotate(90)*temp,(-2,0));
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picture mon;
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label(mon,"Mon.");
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add(rotate(90)*mon,(2,7.3));
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picture tues;
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label(tues,"Tues.");
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add(rotate(90)*tues,(4,4.3));
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picture Wed;
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label(Wed,"Wed.");
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add(rotate(90)*Wed,(6,5.3));
 +
picture Thurs;
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label(Thurs,"Thurs.");
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add(rotate(90)*Thurs,(8,5.4));
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picture Fri;
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label(Fri,"Fri.");
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add(rotate(90)*Fri,(10,9));
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draw((-0.3,-8)--(0.3,-8));
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draw((-0.3,-6)--(0.3,-6));
 +
draw((-0.3,-4)--(0.3,-4));
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draw((-0.3,-2)--(0.3,-2));
 +
draw((-0.3,2)--(0.3,2));
 +
draw((-0.3,4)--(0.3,4));
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draw((-0.3,6)--(0.3,6));
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draw((-0.3,8)--(0.3,8));
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dot((2,6));
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dot((4,3));
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dot((6,4));
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dot((8,4));
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dot((10,8));
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draw((1.8,-3.8)--(2.2,-3.8)--(2.2,-4.2)--(1.8,-4.2)--cycle);
 +
draw((3.8,-5.8)--(4.2,-5.8)--(4.2,-6.2)--(3.8,-6.2)--cycle);
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draw((5.8,-1.8)--(6.2,-1.8)--(6.2,-2.2)--(5.8,-2.2)--cycle);
 +
draw((7.8,-4.8)--(8.2,-4.8)--(8.2,-5.2)--(7.8,-5.2)--cycle);
 +
draw((9.8,0.2)--(10.2,0.2)--(10.2,-0.2)--(9.8,-0.2)--cycle);
 +
label("-8",(-0.3,-8),W);
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label("-6",(-0.3,-6),W);
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label("-4",(-0.3,-4),W);
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label("-2",(-0.3,-2),W);
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label("0",(-0.3,0),W);
 +
label("2",(-0.3,2),W);
 +
label("4",(-0.3,4),W);
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label("6",(-0.3,6),W);
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label("8",(-0.3,8),W);
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dot((12,-6.5));
 +
label("Daily High",(12,-6.5),E);
 +
draw((11.8,-7.7)--(11.8,-7.3)--(12.2,-7.3)--(12.2,-7.7)--cycle);
 +
label("Daily Low",(12,-7.5),E);
 +
</asy>
  
 
[[2005 CEMC Gauss (Grade 7) Problems/Problem 11|Solution]]
 
[[2005 CEMC Gauss (Grade 7) Problems/Problem 11|Solution]]

Revision as of 21:12, 22 October 2014

Part A: Each correct answer is worth 5 points

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]

$\text{(A)}\ 57^\circ \qquad \text{(B)}\ 37^\circ \qquad \text{(C)}\ 47^\circ \qquad \text{(D)}\ 60^\circ \qquad \text{(E)}\ 17^\circ$

Solution

Problem 9

A movie theatre has eleven rows of seats. The rows are numbered from $1$ to $11$. Odd-numbered rows have $15$ seats and even-numbered rows have $16$ seats. How many seats are there in the theatre?

$\text{(A)}\ 176 \qquad \text{(B)}\ 186 \qquad \text{(C)}\ 165 \qquad \text{(D)}\ 170 \qquad \text{(E)}\ 171$

Solution

Problem 10

In relation to Smiths Falls, Ontario, the local time in St. John’s, Newfoundland, is $90$ minutes ahead, and the local time in Whitehorse, Yukon, is $3$ hours behind. When the local time in St. John’s is 5:36 p.m., the local time in Whitehorse is

$\text{(A)}$ 1:06 p.m. $\text{(B)}$ 2:36 p.m. $\text{(C)}$ 4:06 p.m. $\text{(D)}$ 12:06 p.m. $\text{(E)}$ 10:06 p.m.

Solution

Part B: Each correct answer is worth 6 points

Problem 11

The temperature range on a given day is the difference between the daily high and the daily low temperatures. On the graph shown, which day has the greatest temperature range?

$\text{(A)}\ Monday \qquad \text{(B)}\ Tuesday \qquad \text{(C)}\ Wednesday \qquad \text{(D)}\ Thursday \qquad \text{(E)}\ Friday$

[asy] size(300); draw((0,-10)--(0,10),EndArrow); draw((0,0)--(16,0),EndArrow); picture temp; label(temp,"Temperature ($^\circ$C)"); add(rotate(90)*temp,(-2,0)); picture mon; label(mon,"Mon."); add(rotate(90)*mon,(2,7.3)); picture tues; label(tues,"Tues."); add(rotate(90)*tues,(4,4.3)); picture Wed; label(Wed,"Wed."); add(rotate(90)*Wed,(6,5.3)); picture Thurs; label(Thurs,"Thurs."); add(rotate(90)*Thurs,(8,5.4)); picture Fri; label(Fri,"Fri."); add(rotate(90)*Fri,(10,9)); draw((-0.3,-8)--(0.3,-8)); draw((-0.3,-6)--(0.3,-6)); draw((-0.3,-4)--(0.3,-4)); draw((-0.3,-2)--(0.3,-2)); draw((-0.3,2)--(0.3,2)); draw((-0.3,4)--(0.3,4)); draw((-0.3,6)--(0.3,6)); draw((-0.3,8)--(0.3,8)); dot((2,6)); dot((4,3)); dot((6,4)); dot((8,4)); dot((10,8)); draw((1.8,-3.8)--(2.2,-3.8)--(2.2,-4.2)--(1.8,-4.2)--cycle); draw((3.8,-5.8)--(4.2,-5.8)--(4.2,-6.2)--(3.8,-6.2)--cycle); draw((5.8,-1.8)--(6.2,-1.8)--(6.2,-2.2)--(5.8,-2.2)--cycle); draw((7.8,-4.8)--(8.2,-4.8)--(8.2,-5.2)--(7.8,-5.2)--cycle); draw((9.8,0.2)--(10.2,0.2)--(10.2,-0.2)--(9.8,-0.2)--cycle); label("-8",(-0.3,-8),W); label("-6",(-0.3,-6),W); label("-4",(-0.3,-4),W); label("-2",(-0.3,-2),W); label("0",(-0.3,0),W); label("2",(-0.3,2),W); label("4",(-0.3,4),W); label("6",(-0.3,6),W); label("8",(-0.3,8),W); dot((12,-6.5)); label("Daily High",(12,-6.5),E); draw((11.8,-7.7)--(11.8,-7.3)--(12.2,-7.3)--(12.2,-7.7)--cycle); label("Daily Low",(12,-7.5),E); [/asy]

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

Part C: Each correct answer is worth 8 points

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

See also

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