2019 AMC 10A Problems
2019 AMC 10A (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
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Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 See also
Problem 1
What is the value of
Problem 2
What is the hundreds digit of
Problem 3
Ana and Bonita were born on the same date in different years, years apart. Last year Ana was times as old as Bonita. This year Ana's age is the square of Bonita's age. What is
Problem 4
A box contains red balls, green balls, yellow balls, blue balls, white balls, and black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least balls of a single color will be drawn
Problem 5
What is the greatest number of consecutive integers whose sum is
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Let be an isosceles triangle with and . Contruct the circle with diameter , and let and be the other intersection points of the circle with the sides and , respectively. Let be the intersection of the diagonals of the quadrilateral . What is the degree measure of
Problem 14
For a set of four distinct lines in a plane, there are exactly distinct points that lie on two or more of the lines. What is the sum of all possible values of ?
Problem 15
A sequence of numbers is defined recursively by , , and for all Then can be written as , where and are relatively prime positive inegers. What is
Problem 16
The figure below shows circles of radius within a larger circle. All the intersections occur at points of tangency. What is the area of the region, shaded in the figure, inside the larger circle but outside all the circles of radius
Problem 17
A child builds towers using identically shaped cubes of different color. 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.)
Problem 18
For some positive integer , the repeating base- representation of the (base-ten) fraction is . What is ?
Problem 19
What is the least possible value of where is a real number?
Problem 20
Problem 21
A sphere with center has radius 6. A triangle with sides of length , , and is situated in space so that each of its sides is tangent to the sphere. What is the distance between and the plane determined by the triangle?
Problem 22
Problem 23
Problem 24
Problem 25
For how many integers between and , inclusive, is an integer? (Recall that .)
See also
2019 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by 2018 AMC 10B Problems |
Followed by 2019 AMC 10B Problems | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.