경시 · AMC 대비 · 4단계 중 4

AMC 10 2020A 문제 25개

문제마다 원리부터 푸는 풀이와 처음 풀 수 있는 학년(CCSS 기준)이 있습니다.

AMC 10 2020A #1 5학년부터 arithmetic
What value of x satisfies x- 3/4 = 5/12 - 1/3?
AMC 10 2020A #2 6학년부터 arithmetic
The numbers 3, 5, 7, a, and b have an average (arithmetic mean) of 15. What is the average of a and b?
AMC 10 2020A #3 7학년부터 algebra
Assuming a≠3, b≠4, and c≠5, what is the value in simplest form of the following expression? (a-3)/(5-c) · (b-4)/(3-a) ·…
AMC 10 2020A #4 6학년부터 rate-ratio
A driver travels for 2 hours at 60 miles per hour, during which her car gets 30 miles per gallon of gasoline. She is pai…
AMC 10 2020A #5 8학년부터 arithmetic
What is the sum of all real numbers x for which |x²-12x+34|=2?
AMC 10 2020A #6 4학년부터 number-theory
How many 4-digit positive integers (that is, integers between 1000 and 9999, inclusive) having only even digits are divi…
AMC 10 2020A #7 6학년부터 arithmetic
The 25 integers from -10 to 14, inclusive, can be arranged to form a 5-by-5 square in which the sum of the numbers in ea…
AMC 10 2020A #8 4학년부터 arithmetic
What is the value of 1+2+3-4+5+6+7-8+…+197+198+199-200?
AMC 10 2020A #9 6학년부터 arithmetic
A single bench section at a school event can hold either 7 adults or 11 children. When N bench sections are connected en…
AMC 10 2020A #10 8학년부터 geometry-3d
Seven cubes, whose volumes are 1, 8, 27, 64, 125, 216, and 343 cubic units, are stacked vertically to form a tower in wh…
AMC 10 2020A #11 6학년부터 arithmetic
What is the median of the following list of 4040 numbers? 1, 2, 3, …, 2020, 1², 2², 3², …, 2020²
AMC 10 2020A #12 7학년부터 geometry-2d
Triangle AMC is isosceles with AM = AC. Medians MV and CU are perpendicular to each other, and MV=CU=12. What is the are…
AMC 10 2020A #13 7학년부터 probability
A frog sitting at the point (1, 2) begins a sequence of jumps, where each jump is parallel to one of the coordinate axes…
AMC 10 2020A #14 7학년부터 arithmetic
Real numbers x and y satisfy x + y = 4 and x · y = -2. What is the value of x + x³/y² + y³/x² + y?
AMC 10 2020A #15 7학년부터 arithmetic
A positive integer divisor of 12! is chosen at random. The probability that the divisor chosen is a perfect square can b…
AMC 10 2020A #16 8학년부터 geometry-2d
A point is chosen at random within the square in the coordinate plane whose vertices are (0, 0), (2020, 0), (2020, 2020)…
AMC 10 2020A #17 8학년부터 arithmetic
Define P(x) =(x-1²)(x-2²)…(x-100²). How many integers n are there such that P(n)≤ 0?
AMC 10 2020A #18 7학년부터 arithmetic
Let (a,b,c,d) be an ordered quadruple of not necessarily distinct integers, each one of them in the set {0,1,2,3}. For h…
AMC 10 2020A #19 7학년부터 counting
As shown in the figure below, a regular dodecahedron (the polyhedron consisting of 12 congruent regular pentagonal faces…
AMC 10 2020A #20 8학년부터 geometry-2d
Quadrilateral ABCD satisfies ∠ ABC = ∠ ACD = 90°, AC=20, and CD=30. Diagonals AC and BD intersect at point E, and AE=5.…
AMC 10 2020A #21 8학년부터 arithmetic
There exists a unique strictly increasing sequence of nonnegative integers a₁ < a₂ < … < a_k such that(2²⁸⁹+1)/(2¹⁷+1) =…
AMC 10 2020A #22 6학년부터 number-theory
For how many positive integers n ≤ 1000 is⌊ 998/n ⌋+⌊ 999/n ⌋+⌊ 1000/n ⌋not divisible by 3? (Recall that ⌊ x ⌋ is the gr…
AMC 10 2020A #23 8학년부터 geometry-2d
Let T be the triangle in the coordinate plane with vertices (0,0), (4,0), and (0,3). Consider the following five isometr…
AMC 10 2020A #24 6학년부터 number-theory
Let n be the least positive integer greater than 1000 for which gcd(63, n+120) =21 그리고 gcd(n+63, 120)=60. What is the su…
AMC 10 2020A #25 7학년부터 probability
Jason rolls three fair standard six-sided dice. Then he looks at the rolls and chooses a subset of the dice (possibly em…

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