Competition · AMC preparation · step 4 of 4

AMC 8 2012: 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 2012 #1 grade 6+ arithmetic
Rachelle uses 3 pounds of meat to make 8 hamburgers for her family. How many pounds of meat does she need to make 24 ham…
AMC 8 2012 #2 grade 4+ arithmetic
In the country of East Westmore, statisticians estimate there is a baby born every 8 hours and a death every day. To the…
AMC 8 2012 #3 grade 4+ arithmetic
On February 13 The Oshkosh Northwester listed the length of daylight as 10 hours and 24 minutes, the sunrise was 6:57tex…
AMC 8 2012 #4 grade 4+ rate-ratio
Peter's family ordered a 12-slice pizza for dinner. Peter ate one slice and shared another slice equally with his brothe…
AMC 8 2012 #5 grade 4+ geometry-2d
In the diagram, all angles are right angles and the lengths of the sides are given in centimeters. Note the diagram is n…
AMC 8 2012 #6 grade 4+ geometry-2d
A rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. The ph…
AMC 8 2012 #7 grade 6+ arithmetic
Isabella must take four 100-point tests in her math class. Her goal is to achieve an average grade of 95 on the tests. H…
AMC 8 2012 #8 grade 7+ arithmetic
A shop advertises everything is "half price in today's sale." In addition, a coupon gives a 20% discount on sale prices.…
AMC 8 2012 #9 grade 4+ algebra
The Fort Worth Zoo has a number of two-legged birds and a number of four-legged mammals. On one visit to the zoo, Margie…
AMC 8 2012 #10 grade 7+ counting
How many 4-digit numbers greater than 1000 are there that use the four digits of 2012?
AMC 8 2012 #11 grade 6+ arithmetic
The mean, median, and unique mode of the positive integers 3, 4, 5, 6, 6, 7, and x are all equal. What is the value of x…
AMC 8 2012 #12 grade 4+ number-theory
What is the units digit of 13²⁰¹²?
AMC 8 2012 #13 grade 6+ number-theory
Jamar bought some pencils costing more than a penny each at the school bookstore and paid textdollar 1.43. Sharona bough…
AMC 8 2012 #14 grade 5+ counting
In the BIG N, a middle school football conference, each team plays every other team exactly once. If a total of 21 confe…
AMC 8 2012 #15 grade 6+ number-theory
The smallest number greater than 2 that leaves a remainder of 2 when divided by 3, 4, 5, or 6 lies between what numbers?
AMC 8 2012 #16 grade 4+ number-theory
Each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is used only once to make two five-digit numbers so that they have t…
AMC 8 2012 #17 grade 4+ geometry-2d
A square with integer side length is cut into 10 squares, all of which have integer side length and at least 8 of which…
AMC 8 2012 #18 grade 6+ number-theory
What is the smallest positive integer that is neither prime nor square and that has no prime factor less than 50?
AMC 8 2012 #19 grade 6+ algebra
In a jar of red, green, and blue marbles, all but 6 are red marbles, all but 8 are green, and all but 4 are blue. How ma…
AMC 8 2012 #20 grade 6+ arithmetic
What is the correct ordering of the three numbers 5/19, 7/21, and 9/23, in increasing order?
AMC 8 2012 #21 grade 6+ geometry-3d
Marla has a large white cube that has an edge of 10 feet. She also has enough green paint to cover 300 square feet. Marl…
AMC 8 2012 #22 grade 6+ arithmetic
Let R be a set of nine distinct integers. Six of the elements are 2, 3, 4, 6, 9, and 14. What is the number of possible…
AMC 8 2012 #23 grade 7+ geometry-2d
An equilateral triangle and a regular hexagon have equal perimeters. If the triangle's area is 4, what is the area of th…
AMC 8 2012 #24 grade 7+ geometry-2d
A circle of radius 2 is cut into four congruent arcs. The four arcs are joined to form the star figure shown. What is th…
AMC 8 2012 #25 grade 6+ geometry-2d
A square with area 4 is inscribed in a square with area 5, with each vertex of the smaller square on a side of the large…

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