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What is the value of
What is the hundreds digit of 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
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 2019 AMC 10A Problems
Problem 1
Problem 2
Problem 3
Problem 4
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What is the greatest number of concutive integers who sum is
For how many of the following types of quadrilaterals does there exist a point in the plane of the quadrilateral that is equidistant from all four vertices of the quadrilateral?
a square
a rectangle that is not a square
a rhombus that is not a square
a parallelogram that is not a rectangle or a rhombus
致辞英文an isosceles trapezoid that is not a parallelogram
Two lines with slopes and interct at . What is the area of the triangle enclod by the two lines and the line
Problem 5
Problem 6
Problem 7
The figure below shows line with a regular, infinite, recurring pattern of squares and line gments.
How many of the following four kinds of rigid motion transformations of the plane in which this figure is drawn, other than the identity transformation, will transform this figure into itlf?some rotation around a point of line some translation in the direction parallel to line the reflection across line
some reflection across a line perpendicular to line What is the greatest three-digit positive integer for which the sum of the first positive integers is a divisor of the product of the
first positive integers?
A rectangular floor that is feet wide and feet long is tiled with one-foot square tiles. A bug walks from one corner to the opposite corner in a straight line. Including the first and the last tile, how many tiles does the bug visit?
Problem 8
Problem 9
Problem 10How many positive integer divisors of are perfect squares or perfect cubes (or both)?
Melanie computes the mean , the median
, and the modes of the values that are the dates in the months of . Thus her
ccbpdata consist of
, , . . . ,
, , , and . Let be the median of the modes. Which of the following statements is true?Let
be an isosceles triangle with
and
. Construct the circle with diameter , and let and be the other interction points of the circle with the sides
and , respectively. Let be the interction of the diagonals
of the quadrilateral . What is the degree measure of Problem 11
Problem 12
马航翻译Problem 13
For a t 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 ? A quence of numbers is defined recursively by
, , and for all . Then can be written as , where and
are relatively prime positive integers. What is The figure below shows circles of radius
within a larger circle. All the interctions 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 14Problem 15
Problem 16 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.)For some positive integer , the repeating ba-
reprentation of the (ba-ten) fraction is . What is ?
Problem 17
Problem 18
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What is the least possible value of where
is a real number?The numbers are randomly placed into the squares of a grid. Each square gets one number, and each of the英语名字大全
numbers is ud once. What is the probability that the sum of the numbers in each row and each column is odd? 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 19Problem 20Problem 21
Real numbers between 0 and 1, inclusive, are chon in the following manner. A fair coin is flipped. If it lands heads, then it is flipped again and the chon number is 0 if the cond flip is heads and 1 if
the cond flip is tails. On the other hand, if the first coin flip is tails, then the
number is chon uniformly at random from the clod interval . Two random numbers and are chon independently in this manner. What is the probability that ?
Travis has to babysit the terrible Thompson triplets. Knowing that they love big numbers, Travis devis a counting game for them. First Tadd will say the number , then Todd must say the next two numbers ( and ), then Tucker must say the next three numbers (, , ),then Tadd must say the next four numbers (,
, , ), and the process continues to rotate through the three children in order, each saying one more number than the previous child did, until the number is reached. What is the th number said by Tadd?Let ,
, and be the distinct roots of the polynomial . It is given that there exist real numbers ,
, and such that for all . What is
?
For how many integers between and , inclusive, is
an integer? (Recall that .)
Problem 22
Problem 23
Problem 24
Problem 25
2019 AMC 10A Answer Key
1. C
2. A
3. D
4. B
5. D
6. C
7. C
8. C
乐趣 英文9. B
10. C
11. C
12. E
13. D
14. D
15. E
16. A
17. D
18. D
19. B
初代吸血鬼第二季15
20. B
21. D
22. B
23. C
24. B
star net25. D
