2020 AMC 10A Problems
2020 AMC 10A (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
| ||
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 |
Contents
[hide]- 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 value of satisfies
Problem 2
The numbers and
have an average (arithmetic mean) of
. What is the average of
and
?
Problem 3
Assuming ,
, and
, what is the value in simplest form of the following expression?
Problem 4
A driver travels for hours at
miles per hour, during which her car gets
miles per gallon of gasoline. She is paid
per mile, and her only expense is gasoline at
per gallon. What is her net rate of pay, in dollars per hour, after this expense?
Problem 5
What is the sum of all real numbers x for which |x^2-12x+34|=2
Problem 6
How many 4-digit positive integers (that is, integers between 1000 and 9999, inclusive) having only even digits are divisible by 5?
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
A positive integer divisor of is chosen at random. The probability that the divisor chosen is a perfect square can be expressed as
, where
and
are relatively prime positive integers. What is
?
Problem 16
A point is chosen at random within the square in the coordinate plane whose vertices are and
. The probability that the point is within
units of a lattice point is
. (A point
is a lattice point if
and
are both integers.) What is
to the nearest tenth
Problem 17
DefineHow many integers
are there such that
?
Problem 18
Let be an ordered quadruple of not necessarily distinct integers, each one of them in the set
For how many such quadruples is it true that
is odd? (For example,
is one such quadruple, because
is odd.)
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
See also
2020 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by 2019 AMC 10B Problems |
Followed by 2020 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.