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GEOMETRY
ALGEBRA II
WORD PROBLEMS
ARITHMETIC & ALGEBRA I
MISCELLANEOUS
100
What is the perimeter of a square that has an area of 25?
20
100
If x^-2 = 64, what is the value of x^(1/3) + x^0?
3/2
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.
100
If (2^3)^2 = 4^p, then 3^p =
27
100
In how many different ways can five students be seated in three chairs?
60. 5x4x3=60
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.
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
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
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.
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
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.
300
A culture of 5000 bacteria triples every 15 minutes. What is the size of the bacteria population after 2 hours have elapsed?
32,805,000
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.
300
Simplify (4a+a-3)(4b-2b-b)
5ab-3b
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
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
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
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.
400
For the system of three equations: x-z=7, x+y=3, z-y=6, what is x?
8
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
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.
500

Nisha can solve a set of 5 math problems in 12 minutes. At this rate, in hours and minutes, how long will it take her to solve 20 sets of 7 math problems?

5 hours and 36 minutes. Using a proportion, you find that 1 set of 7 problems takes 16.8 minutes. Multiply that by 20 sets and it will take 336 minutes which is 5 hours and 36 minutes

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.
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.
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.