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Problem 1
What is
?
Solution
Problem 2
For real numbers
?
Solution
and
, define
. What is
Problem 3
A football game was played between two teams, the Cougars and the Panthers. The two teams scored a total of 34 points, and the Cougars won by a margin of 14 points. How many points did the Panthers score?
Solution
Problem 4
Circles of diameter 1 inch and 3 inches have the same center. The smaller circle is painted red, and the portion outside the smaller circle and inside the larger circle is painted blue. What is the ratio of the blue-painted area to the red-painted area?
Solution
Problem 5
A rectangle and a rectangle are contained within a square without overlapping at any point, and the sides of the square are parallel to the sides of the two given rectangles. What is the smallest possible area of the square?
Solution
Problem 6
A region is bounded by semicircular arcs constructed on the side of a square whose sides measure
, as shown. What is the perimeter of this region?
Solution
Problem 7
Which of the following is equivalent to
when
?
Solution
Problem 8
A square of area 40 is inscribed in a semicircle as shown. What is the area of the semicircle?
Solution
Problem 9
Francesca uses 100 grams of lemon juice, 100 grams of sugar, and 400 grams of water to make lemonade. There are 25 calories in 100 grams of lemon juice and 386 calories in 100 grams of sugar. Water contains no calories. How many calories are in 200 grams of her lemonade?
Solution
Problem 10
In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 15. What is the greatest possible perimeter of the triangle?
Solution
Problem 11
What is the tens digit in the sum
Solution
Problem 12
The lines
?
and
intersect at the point
. What is
Solution
Problem 13
Joe and JoAnn each bought 12 ounces of coffee in a 16 ounce cup. Joe drank 2 ounces of his coffee and then added 2 ounces of cream. JoAnn added 2 ounces of cream, stirred the coffee well, and then drank 2 ounces. What is the resulting ratio of the amount of cream in Joe's coffee to that in JoAnn's coffee?