ALGEBRA 1
Evaluate:
6 + 9[10 – 2(2 + 3(9 + 2))]
-534
What is the perimeter of a square that has an area of 196 units2?
56 units
If x-2= 64, what is the value of x1/3 + x0?
3/2
What is the probability of rolling 3 dice, and them all landing on a 6?
1/216
If 1/3 of a number is 4 less than 1/2 of the number, what is the number?
24
Explanation: 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.
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
What is the area of a circle in which a 6 by 8 rectangle is inscribed?
25pi
Explanation: 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)(r2)
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?
4
What is the median of this set of numbers?
50, 39, 32, 47, 36, 52, 38, 44
41.5 (83/2)
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 what is Susan's weight, p, in terms of x?
x - 25 pounds
Simplify: (x + 2)2 - x2 - x +179
3(x+61)
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-foot shadow?
62.5 feet (125/2 feet)
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
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
Explanation: 1/8 (all heads) + 1/8 (all tails) = 1/4
A boat moored in McManus Bay has a ladder that hangs down from the deck of the boat and touches the flat sea surface. The rungs are 1 foot apart. At low tide, ten rungs of the ladder are exposed. At high tide, the water level rises 6 feet. How many of the rungs will remain exposed?
5 rungs
Explanation: This number of rungs will be exposed. As the tide comes in, the boat will rise up.
For the system of three equations:
x-z=7, x+y=3, z-y=6, what is x?
x = 8
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?
18 units
Explanation: Let a, b and c be the sides of a scalene triangle, c being the longest in length. The statement a+b≥c must be true, because otherwise the shape formed would not be a triangle since the sides wouldn't be touching at the vertices. Let b represent x. Then 4+b≥9, or the least possible value of b is 5.
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
There are four students, all of different heights, who are to be 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?
1/12
Explanation: (Assuming you have a set front and end of the line) The probability that the tallest student is 1st in line =1/4. Now, the probability that the shortest student is 4th in line =1/3 (If the tallest person is first in line, he can't also be last).
The total probability =1/4⋅1/3=1/12
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
Therefore, x=4.
For how many integer values of b is b+3>0 and 1>2b-9?
7
Explanation: 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, which are seven integers in total.
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
Explanation: The sum of the degree measures of exterior angles is 360. (n-2)(180) = (4)(360), where n=number of sides. Solve (n-2) = 8 to get n=10.
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
Explanation: 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.
Craps is played with two dice. If you roll a 7 or an 11 on your first roll, you win. What are the chances that you win on your first roll?
2/9
Explanation: Let's assume you have one red die and one blue die. Whatever number the red die shows, if the blue die lands on the opposite side, the two numbers will add up to 7. Thus there is a 1/6 chance of rolling a 7.
In order to roll an 11, you need the red die to be either a 5 or a 6. There is a 1/3 chance of this. Once that happens, you have a 1/6 chance of the blue die being the other number that adds to 11. (The red die could be either a 5 or a 6 but the blue die can only be the one the red die is not.) (1/3)(1/6) = 1/18.
If we add the chances of a 7 (1/6) and an 11 (1/18) we get 3/18 + 1/18 = 4/18 or 2/9.
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
Explanation: 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.