Algebra
Geometry
Graphing
Probability
Riddles
100
What value of x satisfies
5/6
100
For how many of the following types of quadrilaterals does there exist a point in the plane of the quadrilateral that is equidistant from all four vertices of the quadrilateral?
- a square
- a rectangle that is not a square
- a rhombus that is not a square
- a parallelogram that is not a rectangle or a rhombus
- an isosceles trapezoid that is not a parallelogram
3
100
Two lines with slopes 1/2 and 2 intersect at (2,2). What is the area of the triangle enclosed by these two lines and the line x + y = 10?
6
100
How many ways can a student schedule 3 mathematics courses -- algebra, geometry, and number theory -- in a 6-period day if no two mathematics courses can be taken in consecutive periods? (What courses the student takes during the other 3 periods is of no concern here.)
24
100
Ana and Bonita are born on the same date in different years, n years apart. Last year Ana was 5 times as old as Bonita. This year Ana's age is the square of Bonita's age. What is n?
12
200
For what value x does 
?
3
200
All of the triangles in the diagram below are similar to isosceles triangle ABC, in which AB = AC. Each of the 7 smallest triangles has area 1, and Triangle ABC has area 40. What is the area of trapezoid DBCE?
24
200
Let S be a set of points (x,y) in the coordinate plane such that two of the three quantities 3, x+2, and y-4 are equal and the third of the three quantities is no greater than this common value. Which of the following is a correct description for S?
E
200
A box contains 28 red balls, 20 green balls, 19 yellow balls, 13 blue balls, 11 white balls, and 9 black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 15 balls of a single color will be drawn?
76
200
Alice, Bob, and Charlie were on a hike and were wondering how far away the nearest town was. When Alice said, "We are at least 6 miles away," Bob replied, "We are at most 5 miles away." Charlie then remarked, "Actually the nearest town is at most 4 miles away." It turned out that none of the three statements were true. Let d be the distance in miles to the nearest town. What interval is the set of all possible values of d?
(5,6)
300
What is the sum of all real numbers x for which 
18
300
Triangle AMC is isosceles with AM = AC. Medians MV and CU are perpendicular to each other, and MV = CU = 12. What is the area of Triangle AMC?
96
300
All lines with equation ax + by = c such that a, b, c form an arithmetic progression pass through a common point. What are the coordinates of that point?
(-1,2)
300
When 7 fair standard 6-sided dice are thrown, the probability that the sum of the numbers on the top faces is 10 can be written as n/67, where n is a positive integer. What is n?
84
300
Ms. Carroll promised that anyone who got all the multiple choice questions right on the upcoming exam would receive an A on the exam. Which of these statements necessarily follows logically?
B
400
Suppose that real number x satisfies
What is the value of 
?
8
400
Let Triangle ABC be an isosceles triangle with BC = AC and Angle ACB = 40o. Construct the circle with diameter BC, and let D and E be the other intersection points of the circle with the sides AC and AB, respectively. Let F be the intersection of the diagonals of the quadrilateral BCDE. What is the degree measure of Angle BCF?
110o
400
The lines with equations ax - 2y = c and 2x + by = -c are perpendicular and intersect at (1,-5). What is c?
13
400
Three distinct integers are selected at random between 1 and 2016, inclusive. Which of the following is a correct statement about the probability p that the product of the three integers is odd?
A
400
Trickster Rabbit agrees with Foolish Fox to double Fox's money every time Fox crosses the bridge by Rabbit's house, as long as Fox pays 40 coins in toll to Rabbit after each crossing. The payment is made after the doubling, Fox is excited about his good fortune until he discovers that all his money is gone after crossing the bridge three times. How many coins did Fox have at the beginning?
35
500
How many ordered pairs of real numbers (x,y) satisfy the following system of equations?
3
500
Two circles of radius 5 are externally tangent to each other and are internally tangent to a circle of radius 13 at points A and B, as shown in the diagram. The distance AB can be written in the form m/n, where m and n are relatively prime positive integers. What is m+n?
69
500
The y-intercepts, P and Q, of two perpendicular lines intersecting at the point A(6,8) have a sum of zero. What is the area of Triangle APQ?
60
500
Chloé chooses a real number uniformly at random from the interval [0,2017]. Independently, Laurent chooses a real number uniformly at random from the interval [0,4034]. What is the probability that Laurent's number is greater than Chloé's number? (Assume they cannot be equal)
3/4
500
The figure below shows line l with a regular, infinite, recurring pattern of squares and line segments.
How many of the following four kinds of rigid motion transformations of the plane in which this figure is drawn, other than the identity transformation, will transform this figure into itself?
- some rotation around a point of line l
- some translation in the direction parallel to line l
- the reflection across line l
- some reflection across a line perpendicular to line l
2