Algebra
Geometry/Trig
Number Theory
Combinatorics
Inequalities and Bounds
100
Every week Roger pays for a movie ticket and a soda out of his allowance. Last week, Roger's allowance was 
dollars. The cost of his movie ticket was 
of the difference between and the cost of his soda, while the cost of his soda was 
of the difference between and the cost of his movie ticket. To the nearest whole percent, what fraction of did Roger pay for his movie ticket and soda?
(D)23%
100
2016 AMC 10A Problems/Problem 15)
Seven cookies of radius 
inch are cut from a circle of cookie dough, as shown. Neighboring cookies are tangent, and all except the center cookie are tangent to the edge of the dough. The leftover scrap is reshaped to form another cookie of the same thickness. What is the radius in inches of the scrap cookie?
(A)root 2
100
2023 AMC 10B Problems/Problem 15)
What is the least positive integer 
such that 
is a perfect square?
(C)70
100
2005 AMC 10A Problems/Problem 15)
How many positive cubes divide 
?
(E)6
100
2015 AMC 10A Problems/Problem 15)
Consider the set of all fractions 
, where 
and 
are relatively prime positive integers. How many of these fractions have the property that if both numerator and denominator are increased by , the value of the fraction is increased by 
?
(B)1
200
The roots of the polynomial 10x3−39x2+29x−6 are the height, length, and width of a rectangular box (right rectangular prism). A new rectangular box is formed by lengthening each edge of the original box by 2 units. What is the volume of the new box?
(A) 524, (B) 542, (C) 581, (D) 30
(D)30
200
2014 AMC 10A Problems/Problem 18)
A square in the coordinate plane has vertices whose -coordinates are 
, , 
, and 
. What is the area of the square?
(B)17
200
What is the remainder when 
is divided by 
?
(D)201
200
2019 AMC 10A Problems/Problem 17)
A child builds towers using identically shaped cubes of different colors. How many different towers with a height 
cubes can the child build with 
red cubes, 
blue cubes, and green cubes? (One cube will be left out.)
(D)1260
200
2022 AMC 8 Problems/Problem 21)
Steph scored 
baskets out of 
attempts in the first half of a game, and 
baskets out of attempts in the second half. Candace took 
attempts in the first half and 
attempts in the second. In each half, Steph scored a higher percentage of baskets than Candace. Surprisingly they ended with the same overall percentage of baskets scored. How many more baskets did Candace score in the second half than in the first?
(C)9
300
2022 AMC 10A Problems/Problem 20)
A four-term sequence is formed by adding each term of a four-term arithmetic sequence of positive integers to the corresponding term of a four-term geometric sequence of positive integers. The first three terms of the resulting four-term sequence are 
, 
, and 
. What is the fourth term of this sequence?
(E)206
300
2020 AMC 10A Problems/Problem 19)
As shown in the figure below, a regular dodecahedron (the polyhedron consisting of congruent regular pentagonal faces) floats in space with two horizontal faces. Note that there is a ring of five slanted faces adjacent to the top face, and a ring of five slanted faces adjacent to the bottom face. How many ways are there to move from the top face to the bottom face via a sequence of adjacent faces so that each face is visited at most once and moves are not permitted from the bottom ring to the top ring?
(E)810
300
2018 AMC 10A Problems/Problem 22)
Let 
and 
be positive integers such that 
, 
, 
, and 
. Which of the following must be a divisor of 
? (gcd means greatest common factor)
(D)13
300
2015 AMC 10A Problems/Problem 22)
Eight people are sitting around a circular table, each holding a fair coin. All eight people flip their coins and those who flip heads stand while those who flip tails remain seated. What is the probability that no two adjacent people will stand?
(A)47/256
300
2014 AMC 10B Problems/Problem 20)
For how many integers is the number 
negative?
(C)12
400
2024 AMC 10A Problems/Problem 23)
Integers , 
, and 
satisfy 
, 
, and 
. What is 
?
(D)276
400
2022 AMC 10B Problems/Problem 20)
Let 
be a rhombus with 
. Let 
be the midpoint of 
, and let 
be the point on 
such that 
is perpendicular to . What is the degree measure of 
?
Diagram
(D)113
400
2023 AMC 10A Problems/Problem 23)
If the positive integer has positive integer divisors and with 
, then and are said to be 
divisors of . Suppose that 
is a positive integer that has one complementary pair of divisors that differ by and another pair of complementary divisors that differ by 
. What is the sum of the digits of ?
(C)15
400
2022 AMC 10A Problems/Problem 24)
How many strings of length formed from the digits , , , , are there such that for each 
, at least 
of the digits are less than ? (For example, 
satisfies this condition because it contains at least digit less than , at least digits less than , at least digits less than , and at least digits less than . The string 
does not satisfy the condition because it does not contain at least digits less than .)
(E)1296
400
2020 AMC 10B Problems/Problem 24)
How many positive integers 
satisfy 
(Recall that 
is the greatest integer not exceeding .)
(C)6
500
2021 AMC 10A Problems/Problem 24)
The interior of a quadrilateral is bounded by the graphs of 
and 
, where is a positive real number. What is the area of this region in terms of , valid for all 
?
(D)8a^2/(a^2+1)
500
2022 AMC 10A Problems/Problem 23)
Isosceles trapezoid has parallel sides 
and 
with 
and 
There is a point 
in the plane such that 
and 
What is 
(B)1/3
500
2017 AMC 10B Problems/Problem 25)
Last year Isabella took 
math tests and received different scores, each an integer between and 
, inclusive. After each test she noticed that the average of her test scores was an integer. Her score on the seventh test was 
. What was her score on the sixth test?
(E)100
500
2017 AMC 10A Problems/Problem 25)
How many integers between 100 and 999, inclusive, have the property that some permutation of its digits is a multiple of 11 between 100 and 999? For example, both 121 and 211 have this property.
(A)226
500
2018 AMC 10B Problems/Problem 25)
Let 
denote the greatest integer less than or equal to . How many real numbers satisfy the equation 
?
(C)199