SAT MATH JEOPARDY!! Mr. Henry

GEOMETRY

100

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

20

200

What is the circumference of a circle in which a 5 by 12 rectangle is inscribed?

13pi. The length of a diagonal of a 5 by 12 rectangle is 13 (pythagorean theorem). The diagonal of the rectangle is the diameter of the circle inscribed, and C = 2(pi)r.

300

The height h of a cylinder equals the circumference of the cylinder. In terms of h, what is the volume of the cylinder?

(h^3)/4pi. h=2(pi)r, so r=h/2pi. Volume of cylinder = pi(r^2)h = pi[(h/2pi)^2]h = (h^3)/4pi.

400

The length and width of a rectangle are in the ratio of 5:12. If the rectangle has an area of 240 square centimeters, what is the length, in centimeters, of its diagonal?

26. Draw the rectangle. If the length and width are in the ratio of 5:12, then they can be expressed as 5x and 12x. The area, then, is (5x)(12x) = 60x2 = 240. So x = 2, and the length and width are 10 and 24. Find the diagonal with the Pythagorean theorem:

500

A spider on a flat horizontal surface walks 10 inches east, then 6 inches south, then 4 inches west, then 2 inches south. At this point, how many inches is the spider from its starting point? (A) 8 (B) 10 (C) 12 (D) 16 (E) 18

10. The distance from the starting point to the finishing point is the hypotenuse of a right triangle with legs of 6 and 8. Therefore, the distance is found with Pythagoras: 6^2 + 8^2 = 36 + 64 = 100 = d^2, so d = 10. (Notice that this is a 3-4-5 triangle times 2.)

ALGEBRA II

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

Find the dimensions of a rectangle with and area of 10 square feet if its length is 8 feet more than 2 times the width.

Length = 8ft Width = 2ft

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

Allen can paint a room in 4 hours, and Bernie can paint a room in 2 hours. When they work together, their work rate is the sum of their rates working separately. How long should it take them to paint a room if they work together?

1 hours and 20 minutes. Allen can paint one room in 4 hours, so his rate is 1⁄4 room per hour. Bernie can paint one room in 2 hours, so his rate is 1⁄2 room per hour. When they work together, their rate is 1⁄4 + 1⁄2 = 3/4 room per hour. So to paint one room would take one room ÷ 3/4 room per hour = 4⁄3 hours, or 1.3333... hours, or 1 hour 20 minutes.

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

Francois baked just enough cookies to fill all the orders at his bakery. While the cookies were cooling, a kitchen assistant knocked over a cooling rack and spilled 15%, percent of the cookies onto the floor. Francois had to bake 12 more cookies to replace them.

80 cookies 12/0.15 = 80

300

The regular price of software at a computer superstore is 12% off the retail price. During an annual sale, the same software is 25% off the regular price. If the retail price is p, what is the sale price in terms of p?

0.66p. Since the regular price of software is 12% off the retail price p, the regular price of the software can be expressed as 0.88p. So the sale price is 0.75 x 0.88p = 0.66p.

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.

ARITHMETIC & ALGEBRA I

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

If 1/4 a=6+1/8 b , what is the value of 2a-b?

48. Bring the entire 1/8 b on the same side as 1/4a to obtain 1/4 a - 1/8 b = 6. Multiply the entire equation by 8 to obtain 2 a - b on the left side and 48 on the right side.

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.

MISCELLANEOUS

100

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

60. 5x4x3=60

200

What is the area of the circle whose radius is the average of the radii of two circles with areas of 16pi and 100pi?

49pi.

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

A fair six-sided die has faces bearing the numbers 1, 2, 3, 4, 5, and 6. When the die is thrown, the numbers on the five visible faces are added. What is the probability that this sum is greater than or equal to 18?

1/20. The six sides of a die add up to 1 + 2 + 3 + 4 + 5 +6 =21. The sum of any five faces can be greater than or equal to 18 only if the “down” face is 1, 2, or 3 (so that the sum ofthe other faces is either 21 − 1 = 20 , 21 − 2 = 19. Or 21-3 = 18. This is 3 possibilities out of 6 for a probability of 3/6 = 1/2.

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.