High School 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

The angle of elevation to the top C of a building from two points A and B on level ground are 50 degrees and 60 degrees respectively. The distance between points A and B is 30 meters. Points A, B and C are in the same vertical plane. Find the height h of the building(round your answer to the nearest unit).

h = (approximately) 115 meters.

500

Two ships leave port at 4 p.m. One is headed at a bearing of N 38 E and is travelling at 11.5 miles per hour. The other is travelling 13 miles per hour at a bearing of S 47 E. How far apart are they when dinner is served at 6 p.m.?

36.2miles

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

Adam and Andrej bought sweets. Adam paid € 2.9 for three chocolates and 2 bars, and Andrej paid € 4 for four chocolates and 3 bars. How much did the chocolate cost, and how much did the bar cost?

c =  0.7 eur
t =  0.4 eur

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.

MIXED

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($5) = $7.5.

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

Five students, all of different heights, are randomly arranged in a line. What is the probability that the tallest student will be first in line and the shortest student will be last in line?

1/20. 1x3x2x1x1=6, 6 ways in which students can be arranged under given conditions. Under no conditions, the ways are 5x4x3x2x1=120. 6/120=1/20.

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.