GEOMETRY
ALGEBRA 2
WORD PROBLEMS
ALGEBRA 1
MIXED
100
What is the perimeter of a square that has an area of 25?
20
100
Which functions below are one to one ?
Function #1 { (2,27), (3,28), (4,29), (5,30) }
Function #2 { (11,14), (12,14) , (16,7), (18,13) } Function #3 { (3,12), (4,13), (6,14), (8,1) }
Functions #1 and #3 are both one-to-one functions.
100
Brad’s class collected 320 cans of food. They boxed them in boxes of 40 cans each. How many boxes did they need?
320 ÷ 40 = 8 boxes.
100
If (23)2 = 4p, then 3p =
27
100
In how many different ways can five students be seated in three chairs?
60.
5x4x3=60
200
Angles A and B are complementary and the measure of angle A is twice the measure of angle B. Find the measures of angles A and B.
A = 2B
2B + B = 90
3B = 90
B = 90 / 3 = 30°
A = 2B = 60°
200
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?
f(7) = 3(7)-1 = 20
g(2) = 22 = 4
20 - 4 = 16
g(m) = 16 = x2 = 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
Simplify the expression: (20y-15)/(24y-18)
5/6
5(4y-3)/6(4y-3)
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.
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
5000(3)8
300
Justin earned scores of 85, 92, and 95 on his science tests. What does he need to earn on his next science test to have an average (arithmetic mean) of 93%?
To earn an average of 93% on four tests, the sum of those four tests must be (93)(4) or 372. The sum of the first three tests is 85 + 92 + 95 = 272. The difference between the needed sum of four tests and the sum of the first three tests is 100. He needs a 100 to earn a 93 average.
300
Simplify (x + 2)2 - x2
4(x+1)
x2+ 4x + 4 - x2
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
Find the area of the given shape.
.
Sides of the right triangle (red) are given by
15 - 10 = 5 cm and 20 - 8 = 12 cm
Area of given shape = 20 × 15 - (1/2) × 12 × 5 = 270 cm2
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
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
Working alone, Ryan can build a 10ft by 10ft hole in 5 hours. Bill can build the same hole in 6 hours. How long will it take if they work together?
2 8/11 hrs or 2 hours and 44 mins
R = 5; B = 6; X = together
(1/5) + (1/6) = 1/x
(6x/30x) + (5x/30x) = 30/30x
11x = 30; x = 30/11 or 2 8/11 or 2 hrs 44 mins
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.