Difference between revisions of "2019 AMC 8 Problems"
(→Problem 24: the triangle) |
Scrabbler94 (talk | contribs) (Undo revision 208053 by Anniehyacinth (talk)) (Tag: Undo) |
||
Line 362: | Line 362: | ||
[[2019 AMC 8 Problems/Problem 23|Solution]] | [[2019 AMC 8 Problems/Problem 23|Solution]] | ||
− | == Problem | + | == Problem 25: the triangle == |
Name the sum of the first 1000000 areas of squares in the Golden Ratio. | Name the sum of the first 1000000 areas of squares in the Golden Ratio. | ||
Revision as of 19:00, 21 December 2023
2019 AMC 8 (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 addition
- 2 x and y basics
- 3 3=
- 3.1 Snakes and ladders
- 3.2 Problem 5
- 3.3 Problem 6
- 3.4 Problem 7
- 3.5 Problem 8
- 3.6 Problem 9
- 3.7 Problem 10
- 3.8 Problem 12
- 3.9 Problem 13
- 3.10 Problem 14
- 3.11 Problem 15
- 3.12 Problem 16
- 3.13 Problem 17
- 3.14 Problem 18
- 3.15 Problem 19
- 3.16 Problem 20
- 3.17 Problem 21
- 3.18 Problem 22
- 3.19 Problem 23 ghost problem
- 3.20 Problem 25: the triangle
- 3.21 The Boss: Demolition crew: =
- 3.22 Sponsor for today's video
addition
What is 5+3+4+6+7+_+6)*(&^_*__*&+&_)_*&&(_+?
x and y basics
A rectangle has measures of side lengths x and y. If the area is 5, how many values are there?
3=
Which of the following is the correct order of the fractions and from least to greatest?
Snakes and ladders
What is a probability that occurs when throwing 2 dice on a snake and ladders board, if there are 54 snakes and 4747 ladders?
Problem 5
A tortoise challenges a hare to a race. The hare eagerly agrees and quickly runs ahead, leaving the slow-moving tortoise behind. Confident that he will win, the hare stops to take a nap. Meanwhile, the tortoise walks at a slow steady pace for the entire race. The hare awakes and runs to the finish line, only to find the tortoise already there. Which of the following graphs matches the description of the race, showing the distance traveled by the two animals over time from start to finish?
Problem 6
There are grid points (uniformly spaced) in the square shown in the diagram below, including the points on the edges. Point is in the center of the square. Given that point is randomly chosen among the other points, what is the probability that the line is a line of symmetry for the square?
Problem 7
Shauna takes five tests, each worth a maximum of points. Her scores on the first three tests are , , and . In order to average for all five tests, what is the lowest score she could earn on one of the other two tests?
Problem 8
Gilda has a bag of marbles. She gives of them to her friend Pedro. Then Gilda gives of what is left to another friend, Ebony. Finally, Gilda gives of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself?
Problem 9
Alex and Felicia each have cats as pets. Alex buys cat food in cylindrical cans that are cm in diameter and cm high. Felicia buys cat food in cylindrical cans that are cm in diameter and cm high. What is the ratio of the volume of one of Alex's cans to the volume one of Felicia's cans?
Problem 10
The diagram shows the number of students at soccer practice each weekday during last week. After computing the mean and median values, Coach discovers that there were actually participants on Wednesday. Which of the following statements describes the change in the mean and median after the correction is made?
The mean increases by and the median does not change.
The mean increases by and the median increases by .
The mean increases by and the median increases by .
The mean increases by and the median increases by .
The mean increases by and the median increases by .
Each student takes a math class or a foreign language class or both. There are eighth graders taking a math class, and there are eight graders taking a foreign language class. How many eight graders take only a math class and not a foreign language class?
Problem 12
unitsize(2 cm); pair x, y, z, trans; int i; x = dir(-5); y = (0.6,0.5); z = (0,1); trans = (2,0); for (i = 0; i <= 2; ++i) { draw(shift(i*trans)*((0,0)--x--(x + y)--(x + y + z)--(y + z)--z--cycle)); draw(shift(i*trans)*((x + z)--x)); draw(shift(i*trans)*((x + z)--(x + y + z))); draw(shift(i*trans)*((x + z)--z)); } label(rotate(-3)*"$R$", (x + z)/2); label(rotate(-5)*slant(0.5)*"$B$", ((x + z) + (y + z))/2); label(rotate(35)*slant(0.5)*"$G$", ((x + z) + (x + y))/2); label(rotate(-3)*"$W$", (x + z)/2 + trans); label(rotate(50)*slant(-1)*"$B$", ((x + z) + (y + z))/2 + trans); label(rotate(35)*slant(0.5)*"$R$", ((x + z) + (x + y))/2 + trans); label(rotate(-3)*"$P$", (x + z)/2 + 2*trans); label(rotate(-5)*slant(0.5)*"$R$", ((x + z) + (y + z))/2 + 2*trans); label(rotate(-85)*slant(-1)*"$G$", ((x + z) + (x + y))/2 + 2*trans); (Error making remote request. Unexpected URL sent back)
Problem 13
A palindrome is a number that has the same value when read from left to right or from right to left. (For example, 12321 is a palindrome.) Let be the least three-digit integer which is not a palindrome but which is the sum of three distinct two-digit palindromes. What is the sum of the digits of ?
Problem 14
Isabella has coupons that can be redeemed for free ice cream cones at Pete's Sweet Treats. In order to make the coupons last, she decides that she will redeem one every days until she has used them all. She knows that Pete's is closed on Sundays, but as she circles the dates on her calendar, she realizes that no circled date falls on a Sunday. On what day of the week does Isabella redeem her first coupon?
Problem 15
On a beach people are wearing sunglasses and people are wearing caps. Some people are wearing both sunglasses and caps. If one of the people wearing a cap is selected at random, the probability that this person is also wearing sunglasses is . If instead, someone wearing sunglasses is selected at random, what is the probability that this person is also wearing a cap?
Problem 16
Qiang drives miles at an average speed of miles per hour. How many additional miles will he have to drive at miles per hour to average miles per hour for the entire trip?
Problem 17
What is the value of the product
Problem 18
The faces of each of two fair dice are numbered , , , , , and . When the two dice are tossed, what is the probability that their sum will be an even number?
Problem 19
In a tournament there are six teams that play each other twice. A team earns points for a win, point for a draw, and points for a loss. After all the games have been played it turns out that the top three teams earned the same number of total points. What is the greatest possible number of total points for each of the top three teams?
Problem 20
How many different real numbers satisfy the equation
Problem 21
What is the area of the triangle formed by the lines , , and ?
Problem 22
A store increased the original price of a shirt by a certain percent and then decreased the new price by the same amount. Given that the resulting price was of the original price, by what percent was the price increased and decreased?
Problem 23 ghost problem
Problem 25: the triangle
Name the sum of the first 1000000 areas of squares in the Golden Ratio.
The Boss: Demolition crew: =
The demolition crew can destroy eighteen buildings with their invention, the wrecking ball thirty thousand. After destroying them in the mere of 3 seconds, the tractors need to come pick them up. The tractor moves at 5 miles/hour. Each tractor can carry 300 kg of materials over the long course of five hundred miles. While both events are happening, the cranes slowly construct the buildings at a rate of 15 buildings per hour. After the tractor collects the broken materials, it will return to the crane. The crane will continue constructing. A man is currently watching the team at work. If he started watching at 5:00 am on July 3rd, 2020, and finished watching on March 12th, 2024 (assuming he doesn't die), how many buildings would he have seen?
Sponsor for today's video
riot powshadowpsh nexus zzoink doggie blank ai michigun evw viprin xender game mulpan aethervernus snakevine aximos fresh salt lake andromeda cyclic space uk noctafly npesta sdslayer vortrox vision tride moldy ender bli