Pi-day Math 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 a side of a rectangle is (x+2) and the other is (x-3) Which is the expression to show the measure of the area?

19. x²-x-6

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 + x⁰?

3/2

200

What is the equation of the line which slope is -1/2 and intercepts in y =3

y=-1/2x +3

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=x² horizontally to the left 4 units and vertically down 3 units?

y = (x+4)² - 3

500

Let the function f be defined by f(x) = 3x-1 and let the function g be defined by g(x) = x². If m is a positive number such that f(7) = g(m) + g(2), what is the value of m?

4

Systems of equations

100

Solve the systems of equations using Elimination:

14x + 2y = 26

-14x - 6y = -50

(1, 6)

200

Which is the value of D in

-6x - 5y = 4

4x + 10y = 1

-40

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.

Factorization

100

Factor out GCF

30x⁴+6x³-18x²-24x

6x(5x³+x²-3x-4)

200

How can you factor x²-25

(x+5)(x-5)

300

Simplify (x + 2)² - x²

4(x+1)  or 4x+4

400

Factor

3x³-24y³

3(x-2y)(x²+2xy+4y²)

500

Factor completely

2x⁴-162

2(x²+9)(x+3)(x-3)

Warm-ups

100

In how many different ways can five students be seated in three chairs?

60. 5x4x3=60

200

The cost of admission to an event is $5.00 plus one half of its price. How much does the event cost?

$10.00 Because $5 + 0.5($10) = $10.

300

Three fair coins are tossed at the same time. What is the probability that all three coins will come up heads OR all will come up tails?

1/4

1/8 (all heads) + 1/8 (all tails) = 1/4.

400

Which is the next number in the following serie

1, 3, 4, 7, 11...

18

500

x, y, 22, 14, 10... In this sequence, each term after the first term x is obtained by halving the term that comes before it and then adding 3 to that number. What is the value of x-y?

32. 

x=70, y=38. 70-38=32.