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. 
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

Nate walks 25 meters in 13.7 seconds. If he walks at this same rate, how far will he walk in 4 minutes?

438
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 number of radians in a 720-degree angle can be written as aπ, where a is a constant. What is the value of a? 

4
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

In triangle ABC, the measure of ∠B is 90°, BC=16, and AC=20.  Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is 1/3 the length of the corresponding side of triangle ABC. What is the value of sin F ?

3/5
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

At a lunch stand, each hamburger has 50 more calories than each order of fries.  If 2 hamburgers and 3 orders of fries have a total of 1700 calories, how many calories does a hamburger have?

370
400
For the system of three equations:  x-z=7,  x+y=3,       z-y=6, what is x?
8
400

In a circle with center O, central angle AOB has a measure of 5π/4 radians. The area of the sector formed by central angle AOB is what fraction of the area of the circle?

5/8 or .625
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

In the xy-plane, the parabola with equation              y=( − 11)^2 intersects the line with equation y=25 at two points, A and B. What is the length of AB ?

10
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. 
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.
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