Algebra
Guts
Random
Numbers
Theorems
100
Factor 3x2-16x-12 completely.
(x-6)(3x+2)
100
Mr. Patrick teaches math to 15 students. He was grading tests and found that when he graded everyone's test except Payton's, the average grade for the class was 80. After he graded Payton's test, the class average became 81. What was Payton's score on the test?
95
100
Samia set off on her bicycle to visit her friend, traveling at an average speed of 17 kilometers per hour. When she had gone half the distance to her friend's house, a tire went flat, and she walked the rest of the way at 5 kilometers per hour. In all it took her 44 minutes to reach her friend's house. In kilometers rounded to the nearest tenth, how far did Samia walk?
2.8
100
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 scores of the students' scores on this quiz?
3
100
Name the spiral figure below.
Fibonacci Spiral
Golden Spiral
200
For a positive integer n, the factorial notation n! represents the product of the integers from n to 1. For example, 6! = 6*5*4*3*2*1 = 720. What value of N satisfies the following equation?
5! * 9! = 12! * N!
N=10
200
How many positive integers less than 1000 are 6 times the sum of their digits?
1; the number is 54.
200
A power boat and a raft both left dock A on a river and headed downstream. The raft drifted at the speed of the river current. The power boat maintained a constant speed with respect to the river. The power boat reached dock B downriver, then immediately turned and traveled back upriver. It eventually met the raft on the river 9 hours after leaving dock A. How many hours did it take the power boat to go from A to B?
4.5 or 9/2
200
How many proper divisors does 524,000 have?
47
200
Which theorem states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color?
Four color theorem
Four color map theorem
Four color map problem
300
For what value of n is 
?
n=97
300
A triangular array of 2016 coins has 1 coin in the first row, 2 coins in the second row, 3 coins in the third row, and so on up to N coins in the Nth row. What is the sum of the digits of N?
9
300
Two trains are on the same line, 100 miles apart, heading towards each other, each traveling at 25 mph. A fly that can travel at 60mph leaves one engine flying towards the other. Upon reaching the other engine, it instantaneously turns around, and heads back to the other engine. This is repeated until the two trains crash and the fly is squashed at the same time. How far does the fly travel before it is "splatted"?
120 mi
300
Let 
and 
be two different infinite geometric series of positive numbers with the same first term. The sum of the first series is r1, and the sum of the second series is r2. What is r1+r2?
1
300
This theorem states that every non-constant single-variable polynomial with complex (or real) coefficients has at least one complex root.
Fundamental Theorem of Algebra
400
Brian writes down four integers w > x > y > z whose sum is 44. The pairwise positive differences of these numbers are 1, 3, 4, 5, 6, and 9. What is the sum of the possible values for w?
31
400
Find the number of positive integers less than or equal to 2017 whose base-three representation contains no digit equal to 0.
222
400
There is an old car that needs to go up and down a hill. The hill is 1 mile going up, and since the car is old, it can only travel up the hill at 15 mph. The hill is also 1 mile going down. What is the needed speed for the car to go down the hill such that the car speed averages 30 mph for the 2 mile trip?
Trick question: it's impossible.
400
Find the number of positive integers n < 2018 such that 25n + 9n is divisible by 13.
336
400
Which theorem states that for any real x and complex n, 
.
DeMoivre's Theorem
500
Find the sum of all positive integers n such that sqrt(n^2+85n+2017) is an integer.
195
500
Abby, Bernardo, Carl, and Debra play a game in which each of them starts with four coins. The game consists of four rounds. In each round, four balls are placed in an urn---one green, one red, and two white. The players each draw a ball at random without replacement. Whoever gets the green ball gives one coin to whoever gets the red ball. What is the probability that, at the end of the fourth round, each of the players has four coins?
5/192
500
Albert and Bernard are perfect logicians, and became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.
May 15 May 16 May 19
June 17 June 18
July 14 July 16
Aug 14 Aug 15 Aug 17
Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.
Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.
Bernard: At first I don’t know when Cheryl’s birthday is, but I know now.
Albert: Then I also know when Cheryl’s birthday is.
When is Cheryl’s birthday?
July 16
500
Find the least positive integer such that when its leftmost digit is deleted, the resulting integer is 1/29 of the original integer.
725
500
Which theorem gives the area K of a cyclic quadrilateral (a quadrilateral that can be inscribed in a circle) whose sides have lengths a, b, c, d as
K=sqrt[(s-a)(s-b)(s-c)(s-d)] ?
Brahmagupta's formula