Competition · AMC preparation · step 4 of 4

AMC 8 2009: 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 2009 #1 grade 4+ arithmetic
Bridget bought a bag of apples at the grocery store. She gave half of the apples to Ann. Then she gave Cassie 3 apples,…
AMC 8 2009 #2 grade 6+ rate-ratio
On average, for every 4 sports cars sold at the local dealership, 7 sedans are sold. The dealership predicts that it wil…
AMC 8 2009 #3 grade 6+ rate-ratio
The graph shows the constant rate at which Suzanna rides her bike. If she rides a total of a half an hour at the same sp…
AMC 8 2009 #4 grade 3+ geometry-2d
The five pieces shown below can be arranged to form four of the five figures shown in the choices. Which figure cannot b…
AMC 8 2009 #5 grade 4+ pattern
A sequence of numbers starts with 1, 2, and 3. The fourth number of the sequence is the sum of the previous three number…
AMC 8 2009 #6 grade 6+ rate-ratio
Steve's empty swimming pool will hold 24,000 gallons of water when full. It will be filled by 4 hoses, each of which sup…
AMC 8 2009 #7 grade 6+ geometry-2d
The triangular plot of ACD lies between Aspen Road, Brown Road and a railroad. Main Street runs east and west, and the r…
AMC 8 2009 #8 grade 6+ geometry-2d
The length of a rectangle is increased by 10% percent and the width is decreased by 10% percent. What percent of the old…
AMC 8 2009 #9 grade 4+ geometry-2d
Construct a square on one side of an equilateral triangle. On one non-adjacent side of the square, construct a regular p…
AMC 8 2009 #10 grade 7+ probability
On a checkerboard composed of 64 unit squares, what is the probability that a randomly chosen unit square does not touch…
AMC 8 2009 #11 grade 6+ number-theory
The Amaco Middle School bookstore sells pencils costing a whole number of cents. Some seventh graders each bought a penc…
AMC 8 2009 #12 grade 7+ probability
The two spinners shown are spun once and each lands on one of the numbered sectors. What is the probability that the sum…
AMC 8 2009 #13 grade 7+ probability
A three-digit integer contains one of each of the digits 1, 3, and 5. What is the probability that the integer is divisi…
AMC 8 2009 #14 grade 6+ rate-ratio
Austin and Temple are 50 miles apart along Interstate 35. Bonnie drove from Austin to her daughter's house in Temple, av…
AMC 8 2009 #15 grade 6+ rate-ratio
A recipe that makes 5 servings of hot chocolate requires 2 squares of chocolate, 1/4 cup sugar, 1 cup water and 4 cups m…
AMC 8 2009 #16 grade 4+ counting
How many 3-digit positive integers have digits whose product equals 24?
AMC 8 2009 #17 grade 8+ number-theory
The positive integers x and y are the two smallest positive integers for which the product of 360 and x is a square and…
AMC 8 2009 #18 grade 4+ pattern
The diagram represents a 7-foot-by-7-foot floor that is tiled with 1-square-foot black tiles and white tiles. Notice tha…
AMC 8 2009 #19 grade 8+ geometry-2d
Two angles of an isosceles triangle measure 70° and x°. What is the sum of the three possible values of x?
AMC 8 2009 #20 grade 8+ geometry-2d
How many non-congruent triangles have vertices at three of the eight points in the array shown below?
AMC 8 2009 #21 grade 6+ arithmetic
Andy and Bethany have a rectangular array of numbers with 40 rows and 75 columns. Andy adds the numbers in each row. The…
AMC 8 2009 #22 grade 5+ counting
How many whole numbers between 1 and 1000 do not contain the digit 1?
AMC 8 2009 #23 grade 4+ algebra
On the last day of school, Mrs. Wonderful gave jelly beans to her class. She gave each boy as many jelly beans as there…
AMC 8 2009 #24 grade 4+ logic
The letters A, B, C and D represent digits. If A B + C A D Aand A B - C A A,what digit does D represent?
AMC 8 2009 #25 grade 6+ geometry-3d
A one-cubic-foot cube is cut into four pieces by three cuts parallel to the top face of the cube. The first cut is 1/2 f…

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