Algebra
Factor completely: x3 + 2x2 - 5x - 6
(x + 1)(x + 3)(x - 2)
What is the sum of the angles within 2 heptagons?
1800 degrees
What is the sum of the first 5 perfect squares that are natural numbers?
55
In how many ways can you rearrange the letters in the word “Wertman”
5040
What is the volume of sphere when the radius is 3?
36 pi
3x + 2y = 6
x - y = 2
Solve for x.
x = 2
What is the area of a triangle with side lengths of 8, 15, and 17?
60
What is the sum of first 10 numbers in the Fibonacci sequence, if the first two numbers of the sequence are 0 and 1?
88
You flip a coin 10 times. What is the chance you will get 9 or more heads.
3/1024
Find the simplified value
( 11! * 2! * 8! )/ ( 9! * 10! )
11/3
Find the inverse of f(x), if f(x) = (4x - 7)/(3 - x).
(3x + 7)/(x + 4)
Two supplementary angles are modeled by 2x + y and 2x + 2y, and two other complementary angles are modeled by x + 1.5y and x + 0.5y. How large is the first angle in degrees?
90 degrees
What is the greatest prime number under 10000?
9997
What is the chance of rolling a sum of 30 with 5 dice rolls?
1/7776
There are 13 people playing poker in the AP Calculus BC class. If there is a 75% chance somebody leaves the table every three hands and a 25% chance somebody joins the table every two hands, on average, how many rounds will it take for there to be one person left?
96
Michael scores a 95, 87, 85, 93, and a 94 on his first five math tests. If he wants to average at least a 90 after taking his sixth test, and each test is weighted the same, what must must he score at minimum to obtain that average?
86
A circle is modeled by 64 = (x - 3)2 + (y - 7)2. Another function is modeled by g(x) ≤ x + 4. What is the area of the portion bound by the two functions?
32π
What is the product of the integers from 1 to 10 that 648 is divisible by?
10368
In a normal deck of cards, what is the chance of pulling 2 face cards and then 2 number cards when pulling out 4 cards?
132/4165
What is the value of 15C6?
5005
Beth and Sam are 500 miles apart. Beth travels at 60mph and starts at 1 P.M. to Sam's house, and Sam travels at 90mph and starts at 4 P.M. to Beth's house, each not knowing the other is travelling. What two times will they be exactly 240 miles apart?
4:32 P.M. and 7:44 P.M.
In a regular hexagon, the distance of a perpendicular bisector at the center middle of one side has a length of 2sqrt(3) to the center of the hexagon. What is the area of the hexagon?
24sqrt(3)
What is the remainder when 77 is divided by 13?
6
A frog is sitting on a line of straight lily pads, stretching infinitely backwards and forwards. Every second, the frog has an equal chance to jump forward 1 lily pad, or backwards 1 lily pad. What is the chance that after 7 seconds the frog will be 5 or more lily pads forward from where it started?
1/16
Find the next term in the sequence
5, 12, 27/2, 25/3, 27/8
1