Competition · AMC preparation · step 4 of 4

AMC 8 2018: all 25 problems

Each problem has a solution worked from first principles and the first grade (by CCSS standards) that can solve it.

AMC 8 2018 #1 grade 6+ rate-ratio
An amusement park has a collection of scale models, with a ratio of 1: 20, of buildings and other sights from around the…
AMC 8 2018 #2 grade 5+ arithmetic, pattern
What is the value of the product (1+1/1)·(1+1/2)·(1+1/3)·(1+1/4)·(1+1/5)·(1+1/6)?
AMC 8 2018 #3 grade 4+ logic
Students Arn, Bob, Cyd, Dan, Eve, and Fon are arranged in that order in a circle. They start counting: Arn first, then B…
AMC 8 2018 #4 grade 6+ geometry-2d
The twelve-sided figure shown has been drawn on 1 cm× 1 cm graph paper. What is the area of the figure in cm²?
AMC 8 2018 #5 grade 4+ arithmetic, pattern
What is the value of 1+3+5+…+2017+2019-2-4-6-…-2016-2018?
AMC 8 2018 #6 grade 4+ rate-ratio
On a trip to the beach, Anh traveled 50 miles on the highway and 10 miles on a coastal access road. He drove three times…
AMC 8 2018 #7 grade 4+ number-theory
The 5-digit number 2 0 1 8 U is divisible by 9. What is the remainder when this number is divided by 8?
AMC 8 2018 #8 grade 6+ arithmetic
Mr. Garcia asked the members of his health class how many days last week they exercised for at least 30 minutes. The res…
AMC 8 2018 #9 grade 3+ geometry-2d
Monica is tiling the floor of her 12-foot by 16-foot living room. She plans to place one-foot by one-foot square tiles t…
AMC 8 2018 #10 grade 5+ arithmetic
The harmonic mean of a set of non-zero numbers is the reciprocal of the average of the reciprocals of the numbers. What…
AMC 8 2018 #11 grade 7+ probability, counting
Abby, Bridget, and four of their classmates will be seated in two rows of three for a group picture, as shown. X X X X X…
AMC 8 2018 #12 grade 6+ rate-ratio
The clock in Sri's car, which is not accurate, gains time at a constant rate. One day as he begins shopping, he notes th…
AMC 8 2018 #13 grade 6+ arithmetic, algebra
Laila took five math tests, each worth a maximum of 100 points. Laila's score on each test was an integer between 0 and…
AMC 8 2018 #14 grade 4+ number-theory
Let N be the greatest five-digit number whose digits have a product of 120. What is the sum of the digits of N?
AMC 8 2018 #15 grade 7+ geometry-2d
In the diagram below, a diameter of each of the two smaller circles is a radius of the larger circle. If the two smaller…
AMC 8 2018 #16 grade 5+ counting
Professor Chang has nine different language books lined up on a bookshelf: two Arabic, three German, and four Spanish. H…
AMC 8 2018 #17 grade 5+ rate-ratio
Bella begins to walk from her house toward her friend Ella's house. At the same time, Ella begins to ride her bicycle to…
AMC 8 2018 #18 grade 6+ number-theory
How many positive factors does 23,232 have?
AMC 8 2018 #19 grade 4+ counting, pattern
In a sign pyramid a cell gets a "+" if the two cells below it have the same sign, and it gets a "-" if the two cells bel…
AMC 8 2018 #20 grade 8+ geometry-2d
In △ ABC, a point E is on AB with AE=1 and EB=2. Point D is on AC so that DE ∥ BC and point F is on BC so that EF ∥ AC.…
AMC 8 2018 #21 grade 6+ number-theory
How many positive three-digit integers have a remainder of 2 when divided by 6, a remainder of 5 when divided by 9, and…
AMC 8 2018 #22 grade 6+ geometry-2d
Point E is the midpoint of side CD in square ABCD, and BE meets diagonal AC at F. The area of quadrilateral AFED is 45.…
AMC 8 2018 #23 grade 7+ probability, counting
From a regular octagon, a triangle is formed by connecting three randomly chosen vertices of the octagon. What is the pr…
AMC 8 2018 #24 grade 8+ geometry-3d
In the cube ABCDEFGH with opposite vertices C and E, J and I are the midpoints of segments FB and HD, respectively. Let…
AMC 8 2018 #25 grade 8+ number-theory
How many perfect cubes lie between 2⁸+1 and 2¹⁸+1, inclusive?

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