Mathletic | Practice Platform

QuestionDifficultyTopicSubject
1. For how many positive integers $n$ is $n^2 - 3n + 2$ a prime number?EasyNumber TheoryAMC 10
2. Liliane has $50\%$ more soda than Jacqueline, and Alice has $25\%$ …EasyAlgebraAMC 10
3. A box contains $5$ chips, numbered $1$ , $2$ , $3$ , $4$ , and $5$ …EasyCounting & ProbabilityAMC 10
4. Crystal has a running course marked out for her daily run. She starts this run by heading due north for one mile. She then runs northeast for one mile, then southeast for one mile. The last portion of her run takes her on a straight line ba …EasyGeometryAMC 10
5. In a table tennis tournament, every participant played every other participant exactly once. Although there were twice as many right-handed players as left-handed players, the number of games won by left-handed players was …Med.Number TheoryAMC 10
6. Real numbers $x$ and $y$ satisfy $x + y = 4$ and $x \cdot y = -2$ …Med.AlgebraAMC 10
7. Twelve fair dice are rolled. What is the probability that the product of the numbers on the top faces is prime? …Med.Counting & ProbabilityAMC 10
8. An even number of circles are nested, starting with a radius of $1$ and increasing by $1$ …Med.GeometryAMC 10
9. A finite sequence of three-digit integers has the property that the tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units digits of the last term are, respectively, the h …HardNumber TheoryAMC 10
10. How many four-digit integers $abcd$ , with $a \neq 0$ …HardAlgebraAMC 10
11. A square with side length $8$ is colored white except for $4$ …HardCounting & ProbabilityAMC 10
12. In triangle $ABC$ we have $AB=7$ , $AC=8$ , $BC=9$ . Point $D$ …HardGeometryAMC 10
13. Which of the following numbers is a perfect square?EasyNumber TheoryAMC 10
14. All lines with equation $ax+by=c$ such that $a,b,c$ …EasyAlgebraAMC 10
15. For how many positive integers $m$ …EasyCounting & ProbabilityAMC 10
16. What is the area of the shaded figure shown below?EasyGeometryAMC 10
17. Leap Day, February $29$ , $2004$ …Med.Number TheoryAMC 10
18. How many ordered pairs of integers $(m, n)$ satisfy $\sqrt{n^2 - 49} = m$ ?Med.AlgebraAMC 10
19. Two points on the circumference of a circle of radius $r$ …Med.Counting & ProbabilityAMC 10
20. A triangle with vertices $A(0, 2)$ , $B(-3, 2)$ , and $C(-3, 0)$ is reflected about the $x$ …Med.GeometryAMC 10
21. Let $S$ be the set of the $2005$ smallest positive multiples of $4$ , and let $T$ …HardNumber TheoryAMC 10
22. The polynomial $x^3-ax^2+bx-2010$ …HardAlgebraAMC 10
23. Three distinct vertices of a cube are chosen at random. What is the probability that the plane determined by these three vertices contains points inside the cube? …HardCounting & ProbabilityAMC 10
24. Travis has to babysit the terrible Thompson triplets. Knowing that they love big numbers, Travis devises a counting game for them. First Tadd will say the number …HardGeometryAMC 10
25. The numbers $16$ and $25$ are a pair of consecutive positive squares whose difference is …EasyNumber TheoryAMC 10
26. Tony works $2$ hours a day and is paid 0.50 …EasyAlgebraAMC 10
27. The faces of each of $7$ standard dice are labeled with the integers from $1$ to $6$ . Let …EasyCounting & ProbabilityAMC 10
28. Carl has $5$ cubes each having side length $1$ , and Kate has $5$ …EasyGeometryAMC 10
29. Define $L_n$ as the least common multiple of all the integers from $1$ to $n$ …Med.Number TheoryAMC 10
30. It takes Clea 60 seconds to walk down an escalator when it is not operating, and only 24 seconds to walk down the escalator when it is operating. How many seconds does it take Clea to ride down the operating escalator when she just stands o …Med.AlgebraAMC 10
31. Two concentric circles have radii $1$ and $2$ …Med.Counting & ProbabilityAMC 10
32. A company sells peanut butter in cylindrical jars. Marketing research suggests that using wider jars will increase sales. If the diameter of the jars is increased by …Med.GeometryAMC 10
33. For how many positive integers $n$ less than or equal to $24$ is $n!$ evenly divisible by …HardNumber TheoryAMC 10
34. Aaron the ant walks on the coordinate plane according to the following rules. He starts at the origin …HardAlgebraAMC 10
35. Let $D(n)$ denote the number of ways of writing the positive integer $n$ …HardCounting & ProbabilityAMC 10
36. What is the perimeter of the boundary of the region consisting of all points which can be expressed as …HardGeometryAMC 10
37. Consider the statement, "If $n$ is not prime, then $n-2$ …EasyNumber TheoryAMC 10
38. What is $\frac{2+4+6}{1+3+5} - \frac{1+3+5}{2+4+6}$ ?EasyAlgebraAMC 10
39. How many distinguishable arrangements are there of $1$ brown tile, $1$ purple tile, $2$ …EasyCounting & ProbabilityAMC 10
40. The polygon enclosed by the solid lines in the figure consists of 4 congruent squares joined edge -to-edge. One more congruent square is attached to an edge at one of the nine positions indicated. How many of the nine resulting polygons can …EasyGeometryAMC 10
41. The number $2013$ …Med.Number TheoryAMC 10
42. The sum of an infinite geometric series is a positive number $S$ …Med.AlgebraAMC 10
43. In how many ways can the sequence $1,2,3,4,5$ …Med.Counting & ProbabilityAMC 10
44. Rhombus $ABCD$ is similar to rhombus $BFDE$ . The area of rhombus $ABCD$ is $24$ and …Med.GeometryAMC 10
45. Let $x$ and $y$ be two-digit integers such that $y$ …HardNumber TheoryAMC 10
46. In how many zeroes does the number $\frac{2002!}{(1001!)^2}$ end?HardAlgebraAMC 10
47. A player chooses one of the numbers $1$ through $4$ …HardCounting & ProbabilityAMC 10
48. A rectangular piece of paper whose length is $\sqrt3$ times the width has area $A$ …HardGeometryAMC 10
49. How many two-digit positive integers have at least one $7$ as a digit?EasyNumber TheoryAMC 10
50. The sum of $5$ consecutive even integers is $4$ less than the sum of the first $8$ …EasyAlgebraAMC 10
51. Three tiles are marked $X$ and two other tiles are marked $O$ …EasyCounting & ProbabilityAMC 10
52. Triangle $ABC$ has a right angle at $B$ . Point $D$ is the foot of the altitude from $B$ , …EasyGeometryAMC 10
53. How many positive integer divisors of $201^9$ …Med.Number TheoryAMC 10
54. Points $( \sqrt{\pi} , a)$ and $( \sqrt{\pi} , b)$ are distinct points on the graph of …Med.AlgebraAMC 10
55. In a certain card game, a player is dealt a hand of $10$ cards from a deck of $52$ …Med.Counting & ProbabilityAMC 10
56. Three semicircles of radius $1$ are constructed on diameter $\overline{AB}$ …Med.GeometryAMC 10
57. Bernardo chooses a three-digit positive integer $N$ …HardNumber TheoryAMC 10
58. What is the area of the region enclosed by the graph of the equation $x^2+y^2=|x|+|y|?$ HardAlgebraAMC 10
59. The number $5^{867}$ is between $2^{2013}$ and $2^{2014}$ . How many pairs of integers …HardCounting & ProbabilityAMC 10
60. A lattice point in an $xy$ -coordinate system is any point $(x, y)$ where both $x$ and $y$ …HardGeometryAMC 10
61. Mary thought of a positive two-digit number. She multiplied it by $3$ and added $11$ …EasyNumber TheoryAMC 10
62. Suppose that $a$ cows give $b$ gallons of milk in $c$ …EasyAlgebraAMC 10
63. A pair of six-sided dice are labeled so that one die has only even numbers (two each of 2, 4, and 6), and the other die has only odd numbers (two of each 1, 3, and 5). The pair of dice is rolled. What is the probability that the sum of the …EasyCounting & ProbabilityAMC 10
64. Points $A(11, 9)$ and $B(2, -3)$ are vertices of $\triangle ABC$ with $AB=AC$ …EasyGeometryAMC 10
65. A sequence of numbers is defined recursively by $a_1 = 1$ , $a_2 = \frac{3}{7}$ …Med.Number TheoryAMC 10
66. Which of the following describes the graph of the equation $(x+y)^2=x^2+y^2$ ?Med.AlgebraAMC 10
67. There are 5 yellow pegs, 4 red pegs, 3 green pegs, 2 blue pegs, and 1 orange peg to be placed on a triangular peg board. In how many ways can the pegs be placed so that no (horizontal) row or (vertical) column contains two pegs of the same …Med.Counting & ProbabilityAMC 10
68. Given a triangle with side lengths 15, 20, and 25, find the triangle's shortest altitude.Med.GeometryAMC 10
69. Mr. Jones has eight children of different ages. On a family trip his oldest child, who is 9, spots a license plate with a 4-digit number in which each of two digits appears two times. "Look, daddy!" she exclaims. "That number is evenly divi …HardNumber TheoryAMC 10
70. A sequence of natural numbers is constructed by listing the first $4$ …HardAlgebraAMC 10
71. In a small pond there are eleven lily pads in a row labeled 0 through 10. A frog is sitting on pad 1. When the frog is on pad …HardCounting & ProbabilityAMC 10
72. Eight semicircles line the inside of a square with side length 2 as shown. What is the radius of the circle tangent to all of these semicircles? …HardGeometryAMC 10
73. What is the units digit of $2022^{2023} + 2023^{2022}$ ?EasyNumber TheoryAMC 10
74. Mr. Lopez has a choice of two routes to get to work. Route A is $6$ …EasyAlgebraAMC 10
75. At a gathering of $30$ people, there are $20$ people who all know each other and $10$ …EasyCounting & ProbabilityAMC 10
76. In rectangle $ABCD$ , $AD=1$ , $P$ is on $\overline{AB}$ , and $\overline{DB}$ and …EasyGeometryAMC 10
77. The base-nine representation of the number $N$ is $27{,}006{,}000{,}052_{\text{nine}}.$ …Med.Number TheoryAMC 10
78. How many ordered pairs of real numbers $(x,y)$ satisfy the following system of equations? …Med.AlgebraAMC 10
79. Ms. Carr asks her students to read any $5$ of the $10$ …Med.Counting & ProbabilityAMC 10
80. Let $B$ be a right rectangular prism (box) with edges lengths $1, 3,$ and $4$ …Med.GeometryAMC 10
81. How many four-digit positive integers have at least one digit that is a $2$ or a $3$ ?HardNumber TheoryAMC 10
82. Michael walks at the rate of $5$ …HardAlgebraAMC 10
83. A group of $12$ …HardCounting & ProbabilityAMC 10
84. A square with side length $x$ is inscribed in a right triangle with sides of length $3$ , …HardGeometryAMC 10
85. Which of the following numbers is a perfect square?EasyNumber TheoryAMC 10
86. What is the difference between the sum of the first $2003$ …EasyAlgebraAMC 10
87. A student must choose a program of four courses from a menu of courses consisting of English, Algebra, Geometry, History, Art, and Latin. This program must contain English and at least one mathematics course. In how many ways can this progr …EasyCounting & ProbabilityAMC 10
88. Kate bakes a $20$ -inch by $18$ …EasyGeometryAMC 10
89. Suppose $a$ , $b$ , and $c$ …Med.Number TheoryAMC 10
90. Three runners start running simultaneously from the same point on a 500-meter circular track. They each run clockwise around the course maintaining constant speeds of 4.4, 4.8, and 5.0 meters per second. The runners stop once they are all t …Med.AlgebraAMC 10
91. Bob and Alice each have a bag that contains one ball of each of the colors blue, green, orange, red, and violet. Alice randomly selects one ball from her bag and puts it into Bob's bag. Bob then randomly selects one ball from his bag and pu …Med.Counting & ProbabilityAMC 10
92. Let $A$ , $M$ , and $C$ be nonnegative integers such that $A+M+C=10$ …Med.GeometryAMC 10
93. For how many positive integers $n \le 1000$ …HardNumber TheoryAMC 10
94. Let $\{a_k\}$ be a sequence of integers such that $a_1=1$ and $a_{m+n}=a_m+a_n+mn,$ …HardAlgebraAMC 10
95. Each of $2010$ boxes in a line contains a single red marble, and for $1 \le k \le 2010$ …HardCounting & ProbabilityAMC 10
96. Tetrahedron $ABCD$ has $AB=5$ , $AC=3$ , $BC=4$ , $BD=4$ , $AD=3$ , and $CD=\tfrac{12}5\sqrt2$ …HardGeometryAMC 10
97. Marvin had a birthday on Tuesday, May 27 in the leap year $2008$ …EasyNumber TheoryAMC 10
98. The sum of two positive numbers is $5$ …EasyAlgebraAMC 10
99. A rectangle is partitioned into $5$ …EasyCounting & ProbabilityAMC 10
100. A triangle has side lengths $10$ , $10$ , and $12$ . A rectangle has width $4$ …EasyGeometryAMC 10

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