GEOMETRY
ALGEBRA 2
WORD PROBLEMS
ALGEBRA 1
MIXED
1000
What is the perimeter of a square that has an area of 25?
20
1000
If x^2 = 64, what is the value of the square root of x?
+1000 points if in simplified radical form
sqrt8
OR
2sqrt2
1000
A jacket you really want is on sale for 40% off. You end up paying $180 (without tax). What was the original price?
If it was 40% off, that means you paid 60% of the original price.
.6x = 180
1000
What whole number is this equivalent to?
(23)2
64
1000
In how many different ways can five students be seated in three chairs?
60.
5x4x3=60
2000
What is the area of a circle with a diameter of 12?
36pi
Diameter of 12 means the radius is 6. Area = pi*r^2
so 36pi
2000
Solve the system of equations
(6, 5)
2000
A perimeter of a rectangle is 40 cm. Its length is 3cm greater than its width.
Find the dimensions of the rectangle
5cm x 8cm
length = w+3, width = w.
Area = length * width, or w(w+3), or w2+3w.
w2+3w = 40. then, w2+3w-40 = 0.
Factoring, we get (w+8)(w-5), giving us a valid width of 5cm. Plugging back in, we get a 5x8 rectangle
2000
A giant axelotl steals your car and drives 210 miles. It took you 4 hours to catch up to the little thief. What was his average speed, in miles per hour?
52.5 mph
He went 210 miles in 4 hours,
so 210/4 = 52.5 mph
2000
The cost of admission to an event is $5.00 plus one half of its price. How much does the event cost?
$10.00
Because $5 + 0.5($10) = $10.
3000
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.
3000
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
3000
A boat moored in Richardson Bay (Sausalito) 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.
This number of rungs will be exposed. As the tide comes in, the boat will rise up.
3000
Simplify (x + 2)^2 - x^2
4(x+1)
Note: x^2 + 4x + 4 - x^2
3000
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.
4000
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
4000
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
4000
If a virus population doubles each day, and continues unabated (without stopping) for 30 days, when every person on earth is infected ...
On which day is 50% of the earth infected?
Day 29.
Every day the virus population doubles, so if day 30 is 100%, day 29 = 50%, day 28 = 25% and so on.
4000
Solve: x2 - 9x = -20
x = 4, 5
4000
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.
5000
What is the measure of each interior angle in a regular decagon?
Sum of interior angles, S = (n-2)180 where n=number of sides. Solving for (10-2) = 8 x 180 = 1440. Since there are 10 angles, each interior angle is 144 degrees.
5000
Solve for x:
x=17
rewrites as 24 = x-1. So x = 17
5000
Fruit for a dessert costs $1.20 a pound. If 4 pounds of fruit are needed to make a dessert that serves 20 people, what is the cost of the fruit needed to make enough of the same dessert to serve 32 people?
$8.00. If 4 pounds of fruit serve 20 people, then 1/4 pound serves one person, so 32 x 1/4 = 8 pounds. Since the fruit costs $1.20 a pound, the cost of the fruit needed to serve 32 people is 8 x $1.20 = $9.60.
5000
If f(x) = 2x2-3x+6
What is the value of f(4)?
26
5000
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 and y?
x=70, y=38.