Geometry
What is the sum of the exterior angles of any polygon, one per vertex?
360 degrees
A rectangular garden has a perimeter of 70 meters. Its length is 5 meters longer than twice its width. Find the dimensions of the garden.
10x25
Find the derivative: f(x)=3x^2+2x−5.
f′(x)=6x+2.
What is the median of the following data set: 96, 68, 256, 49, 21, 84, 195, 73, 42, 58?
70.5
What are the first 6 digits of pi?
3.14159
What is the formula for the volume of a sphere?
4/3πr^3
A tank is 4/5 full of water, after drawing 70 liters it became 1/3 full. How many liters of water does it carry when full?
150 liters
Find the derivative of 1/(x^2+1).
-2x/((x^2+1)^2)
A box contains 6 red balls, 5 green balls, and 4 blue balls. Two balls are drawn without replacement. What is the probability that at least one of the balls is red?
23/35
What is the determinant of the following matrix?
2 3
5 7
-1
On square ABCD, point E lies on side AD and point F lies on side BC, so that BE = EF = FD = 30. Find the area of the square.
810
A line with slope 2 intersects a line with slope 6 at the point (40,30). What is the distance between the x-intercepts of these two lines?
10
What are the critical points of the graph: x^3-6x^2+9x?
x=1 and x=3
If you roll two fair sided die, what is the probability of getting a sum greater than or equal to 7?
21/36 or 7/12
What is the sum of the interior angles of a polygon with 12 sides?
1800 degrees
A regular hexagon is inscribed in a circle with a radius of 10 units. What is the area of the hexagon?
150sqrt3 or 259.81
On an algebra quiz, 10% of the students scored 70 points, 35% scored 80 points, 30% scored 90 points, and the rest scored 100 points. What is the difference between the mean and median score of the students' scores on this quiz?
3
As x approaches 0, what is the limit of sin(3x)/x?
3
A standard deck of 52 cards contains 13 cards of each suit. If two cards are drawn at random, what is the probability that both cards are either both hearts or both spades?
2/17
What in the 13th number in the Fibonacci sequence?
Four distinct points are arranged on a plane so that the segments connecting them have lengths a, a, a, a, 2a, and b. What is the ratio of b to a?
a) sqrt3 b) 2 c) sqrt5 d) 3 e) Π
a) sqrt3
If α≠b and α^2=5α−3 and b^2=5b−3, find the equation whose roots are α/b and b/α.
3x^2−19x+3=0.
What is the y value of the point of inflection for the function: -15x^3+9x+2?
2
A factory produces light bulbs, and 95% of the bulbs are non-defective. A sample of 3 light bulbs is randomly selected. What is the probability that exactly 1 of the bulbs is defective?
13.54%
How many distinct ways are there to arrange the letters in the word "MISSISSIPPI"?
34650