Math Club Jeopardy

GEOMETRY

100

What is the perimeter of a square that has an area of 25?

20

200

What is the area of a circle in which a 3 by 4 rectangle is inscribed?

25pi. The length of a diagonal of a 6 by 8 rectangle is 10 (pythagorean theorem). The diagonal of the rectangle is the diameter of the circle inscribed, and A = pi*r^2

300

At a certain time of day, a 25-foot telephone pole casts a 10-foot shadow. At that same time, how high would a tree have to be in order to cast a 25-food shadow?

62.5 feet. Proportional reasoning with similar triangles.

400

If the integer lengths of the three sides of a triangle are 4, x, and 9, what is the least possible perimeter of the triangle?

19. In the given triangle, 9-4

500

What is the number of sides of a polygon in which the sum of the degree measures of the interior angles is 4 times the sum of the degree measures of the exterior angles?

10. Sum of the degree measures of exterior angles is 360. S = (n-2)180 = 4 x 360, where n=number of sides. Solving for (n-2) = 8 or n=10.

ALGEBRA 2

100

If x^-2 = 64, what is the value of x^(1/3) + x^0?

3/2

200

Let the function f be defined by f(x) = 3x-1 and let the function g be defined by g(x) = x^2. If m is a positive number such that f(7) = g(m) + g(2), what is the value of m?

4

300

A culture of 5000 bacteria triples every 15 minutes. What is the size of the bacteria population after 2 hours have elapsed? (Calculator needed.)

32,805,000

400

What is the equation of the graph obtained by shifting the graph of y=x^2 horizontally to the left 4 units and vertically down 3 units?

y = (x+4)^2 - 3

500

Working alone, Bill takes three times the amount of time to paint a fence that Mike takes. If Bill and Mike work together, they can paint the fence in 2 hours. If Mike works at the same rate as when he worked with Bill, how long would it take Mike working alone to paint the same fence?

2 hours and 40 minutes. If x represents the number of hours it takes Mike working alone to paint the fence, then 3x is the number of hours it takes Bill working alone to paint the fence. So 2(1/x) + 2(1/3x) = 1 gives x=8/3 hours.

WORD PROBLEMS

100

If 1/3 of a number is 4 less than 1/2 of the number, the number is

24. Let x represent the unknown number. Since 1/3 of x is 4 less than 1/2 of x, x/3 = x/2 - 4. So, 2x = 3x - 24, giving x = 24.

200

Susan weighs p pounds. If Susan gains 17 pounds, she will weigh as much as Carol, who weighs 8 pounds less than Judy. If Judy weighs x pounds, then Susan's weight, p, in terms of x is

x-25

300

A boat moored in Richardson Bay (Sausalito) has a ladder that hangs down from the deck of the boat and touches the flat sea surface. The rungs are 1 foot apart. At low tide, ten rungs of the ladder are exposed. At high tide, the water level rises 6 feet. How many of the rungs will remain exposed?

5 rungs. This number of rungs will be exposed. As the tide comes in, the boat will rise up.

400

Jars A, B, and C each contain 8 marbles. What is the minimum number of marbles that must be transferred among the jars so that the ratio of the number of marbles in jar A to the number in jar B to the number in jar C is 1:2:3?

4. Since jars A, B, and C each contain 8 marbles, there are 24 marbles in the three jars. Let x, 2x, and 3x represent the new numbers of marbles in jars A, B, and C, respectively. Hence, x + 2x + 3x = 24 or 6x = 24, so x=4.

500

Fruit for a dessert costs $1.20 a pound. If 5 pounds of fruit are needed to make a dessert that serves 18 people, what is the cost of the fruit needed to make enough of the same dessert to serve 24 people?

$8.00. If 5 pounds of fruit serve 18 people, then 5/18 pound serves one person, so 24 x 5/18 = 20/3 pounds. Since the fruit costs $1.20 a pound, the cost of the fruit needed to serve 24 people is 20/3 x $1.20 = $8.00.

ALGEBRA 1

100

If (2^3)^2 = 4^p, then 3^p =

27

200

When the number of people who contribute equally to a gift decreases from four to three, each person must pay an additional $10. What is the cost of the gift?

$120.

300

Simplify (x + 2)^2 - x^2

4(x+1) Note: x^2 + 4x + 4 - x^2

400

For the system of three equations: x-z=7, x+y=3, z-y=6, what is x?

8

500

For how many integer values of b is b+3>0 and 1>2b-9?

Seven. b>-3, and b<5. Since b is an integer, b may be equal to any of the following: -2, -1, 0, 1, 2, 3, or 4.

Challenge (2X points)

100

Mr. Dickson is good in what sports?

Table tennis

200

How many Math passes do you need to skip one homework?

You need 3 math passes to skip 1 homework

300

Heewon got d/dx 100 in her math test. What is her score?

0

400

Which is bigger?
2^100 or 3^75

3^75 is bigger

500

3^x - 3^y = 234

Find x and y

y=2, x=5