Competition · AMC preparation · step 4 of 4

AMC 8 2013: 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 2013 #1 grade 4+ number-theory
Danica wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the s…
AMC 8 2013 #2 grade 6+ arithmetic, rate-ratio
A sign at the fish market says, "50% off, today only: half-pound packages for just $3 per package." What is the regular…
AMC 8 2013 #3 grade 4+ arithmetic, pattern
What is the value of 4 · (-1+2-3+4-5+6-7+…+1000)?
AMC 8 2013 #4 grade 5+ arithmetic, algebra
Eight friends ate at a restaurant and agreed to share the bill equally. Because Judi forgot her money, each of her seven…
AMC 8 2013 #5 grade 6+ arithmetic
Hammie is in 6^th grade and weighs 106 pounds. His quadruplet sisters are tiny babies and weigh 5, 5, 6, and 8 pounds. W…
AMC 8 2013 #6 grade 4+ arithmetic, algebra
The number in each box below is the product of the numbers in the two boxes that touch it in the row above. For example,…
AMC 8 2013 #7 grade 6+ rate-ratio, arithmetic
Trey and his mom stopped at a railroad crossing to let a train pass. As the train began to pass, Trey counted 6 cars in…
AMC 8 2013 #8 grade 7+ probability, counting
A fair coin is tossed 3 times. What is the probability of at least two consecutive heads?
AMC 8 2013 #9 grade 6+ pattern, algebra
The Incredible Hulk can double the distance he jumps with each succeeding jump. If his first jump is 1 meter, the second…
AMC 8 2013 #10 grade 6+ number-theory
What is the ratio of the least common multiple of 180 and 594 to the greatest common factor of 180 and 594?
AMC 8 2013 #11 grade 6+ rate-ratio, arithmetic
Ted's grandfather used his treadmill on 3 days this week. He went 2 miles each day. On Monday he jogged at a speed of 5…
AMC 8 2013 #12 grade 6+ arithmetic, rate-ratio
At the 2013 Winnebago County Fair a vendor is offering a "fair special" on sandals. If you buy one pair of sandals at th…
AMC 8 2013 #13 grade 5+ number-theory, arithmetic
When Clara totaled her scores, she inadvertently reversed the units digit and the tens digit of one score. By which of t…
AMC 8 2013 #14 grade 7+ probability, counting
Abe holds 1 green and 1 red jelly bean in his hand. Bob holds 1 green, 1 yellow, and 2 red jelly beans in his hand. Each…
AMC 8 2013 #15 grade 6+ algebra, arithmetic
If 3^p + 3⁴ = 90, 2^r + 44 = 76, and 5³ + 6^s = 1421, what is the product of p, r, and s?
AMC 8 2013 #16 grade 6+ rate-ratio, number-theory
A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of 8^th-grad…
AMC 8 2013 #17 grade 6+ arithmetic, algebra
The sum of six consecutive positive integers is 2013. What is the largest of these six integers?
AMC 8 2013 #18 grade 5+ geometry-3d, arithmetic
Isabella uses one-foot cubical blocks to build a rectangular fort that is 12 feet long, 10 feet wide, and 5 feet high. T…
AMC 8 2013 #19 grade 6+ logic
Bridget, Cassie, and Hannah are discussing the results of their last math test. Hannah shows Bridget and Cassie her test…
AMC 8 2013 #20 grade 8+ geometry-2d
A 1× 2 rectangle is inscribed in a semicircle with the longer side on the diameter. What is the area of the semicircle?
AMC 8 2013 #21 grade 7+ counting
Samantha lives 2 blocks west and 1 block south of the southwest corner of City Park. Her school is 2 blocks east and 2 b…
AMC 8 2013 #22 grade 4+ counting, pattern
Toothpicks are used to make a grid that is 60 toothpicks long and 32 toothpicks wide. How many toothpicks are used altog…
AMC 8 2013 #23 grade 8+ geometry-2d
Angle ABC of △ ABC is a right angle. The sides of △ ABC are the diameters of semicircles as shown. The area of the semic…
AMC 8 2013 #24 grade 6+ geometry-2d
Squares ABCD, EFGH, and GHIJ are equal in area. Points C and D are the midpoints of sides IH and HE, respectively. What…
AMC 8 2013 #25 grade 7+ geometry-2d
A ball with diameter 4 inches starts at point A to roll along the track shown. The track is comprised of 3 semicircular…

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