Algebra
Geometry
Counting/Probability
Number Theory
AMC Trivia
100
The sum of 25 consecutive even integers is 10,000. What is the largest of these 25 consecutive integers?
E(424)
100
In rectangle ABCD, AB=6 and AD=8. Point $M$ is the midpoint of AD. What is the area of triangle AMC?
A(12) B(15) C(18) D(20) E(24)
A(12)
100
At a gathering of 30 people, there are 20 people who all know each other and 10 people who know no one. People who know each other hug, and people who do not know each other shake hands. How many handshakes occur within the group?
A(240) B(245) C(290) D(480) E(490)
B(245)
100
What is the largest power of 2 that is a divisor of 
?
A(8) B(16) C(32) D(64) E(128)
C(32)
100
Who organizes the AMC?
MAA(Mathematical Association of America)
200
Joey and his five brothers are ages 3, 5, 7, 9, 11, and 13. One afternoon two of his brothers whose ages sum to 16 went to the movies, two brothers younger than 10 went to play baseball, and Joey and the 5-year-old stayed home. How old is Joey?
A(3) B(5) C(7) D(9) E(11)
E(11)
200
A circle is centered at O, segment AB is a diameter and C is a point on the circle with angle COB = 50 degrees. What is angle CAB?
A(20) B(25) C(50) D(100) E(150)
B(25)
200
A top hat contains 3 red chips and 2 green chips. Chips are drawn randomly, one at a time without replacement, until all 3 of the reds are drawn or until both green chips are drawn. What is the probability that the 3 reds are drawn?
B(2/5)
200
Which of the following is equivalent to
200
How many questions are on the AMC10/12, and what is the time limit?
25 questions, 75 minutes
300
A rectangle has integer length sides and an area of 2024. What is the least possible perimeter of the rectangle?
A(160) B(180) C(222) D(228) E(390)
B(180)
300
Isosceles triangle ABC has AB = AC = 3√6, and a circle with radius 5√2 is tangent to line AB at B and to line AC at C. What is the area of the circle that passes through vertices A, B, and C?
C(26pi)
300
Each of 6 balls is randomly and independently painted either black or white with equal probability. What is the probability that every ball is different in color from more than half of the other 5 balls?
D(5/16)
300
The digits 1, 2, 3, 4, and 5 are each used once to write a five-digit number PQRST. The three-digit number PQR is divisible by 4, the three-digit number QRS is divisible by 5, and the three-digit number RST is divisible by 3. What is P?
A(1) B(2) C(3) D(4) E(5)
A(1)
300
What competition comes after the AMC(FULL NAME NOT ACRONYM)
American Invitational Mathematics Examination
400
How many pairs of ordered numbers (x, y) satisfy the following equations:
x+3y=3
| |x| - |y| | = 1
A(1) B(2) C(3) D(4) E(8)
C(3)
400
Three equally spaced parallel lines intersect a circle, creating three chords of lengths 
and 
. What is the distance between two adjacent parallel lines?
B(6)
400
Amelia has a coin that lands heads with probability 1/3, and Blaine has a coin that lands on heads with probability 2/5. Amelia and Blaine alternately toss their coins until someone gets a head; the first one to get a head wins. All coin tosses are independent. Amelia goes first. The probability that Amelia wins is p/q, where p and q are relatively prime positive integers. What is q-p?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
D(4)
400
Which of the following expressions is never a prime number when p is a prime number?
A(p^2+16) B(p^2+24) C(p^2+26) D(p^2+46) E(p^2+96)
C(p^2+26)
400
When was the first AMC 12 held?
1950
500
The graph of
is symmetric about which of the following? (Here 
is the greatest integer not exceeding x.)
500
Let ABCDEF be an equiangular hexagon. The lines AB, CD, and EF determine a triangle with area 192sqrt(3), and the lines BC, DE, and FA determine a triangle with area 324sqrt(3). The perimeter of hexagon ABCDEF can be expressed as m +nsqrt(p), where m, n, and p are positive integers and p is not divisible by the square of any prime. What is m + n + p?
C(55)
500
A fair 6-sided die is repeatedly rolled until an odd number appears. What is the probability that every even number appears at least once before the first occurrence of an odd number?
C(1/20)
500
How many different remainders can result when you divide the 100th power of an integer by 125?
A(1) B(2) C(5) D(25) E(125)
B(2)
500
What was the AMC known as from 1983-2000?
AHSME(Annual High School Mathematics Examination)