Competition · AMC preparation · step 4 of 4

AMC 8 2006: 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 2006 #1 grade 5+ arithmetic
Mindy made three purchases for textdollar 1.98 dollars, textdollar 5.04 dollars, and textdollar 9.89 dollars. What was h…
AMC 8 2006 #2 grade 3+ arithmetic
On the AMC 8 contest Billy answers 13 questions correctly, answers 7 questions incorrectly and doesn't answer the last 5…
AMC 8 2006 #3 grade 6+ rate-ratio
Elisa swims laps in the pool. When she first started, she completed 10 laps in 25 minutes. Now, she can finish 12 laps i…
AMC 8 2006 #4 grade 4+ geometry-2d
Initially, a spinner points west. Chenille moves it clockwise 2 1/4 revolutions and then counterclockwise 3 3/4 revoluti…
AMC 8 2006 #5 grade 5+ geometry-2d
Points A, B, C and D are midpoints of the sides of the larger square. If the larger square has area 60, what is the area…
AMC 8 2006 #6 grade 3+ geometry-2d
The letter T is formed by placing two 2 × 4 inch rectangles next to each other, as shown. What is the perimeter of the T…
AMC 8 2006 #7 grade 7+ geometry-2d
Circle X has a radius of π. Circle Y has a circumference of 8 π. Circle Z has an area of 9 π. List the circles in order…
AMC 8 2006 #8 grade 6+ arithmetic
The table shows some of the results of a survey by radiostation KACL. What percentage of the males surveyed listen to th…
AMC 8 2006 #9 grade 5+ arithmetic
What is the product of 3/2×4/3×5/4×…×2006/2005 ?
AMC 8 2006 #10 grade 5+ geometry-2d
Jorge's teacher asks him to plot all the ordered pairs (w. l) of positive integers for which w is the width and l is the…
AMC 8 2006 #11 grade 3+ number-theory
How many two-digit numbers have digits whose sum is a perfect square?
AMC 8 2006 #12 grade 6+ rate-ratio
Antonette gets 70 % on a 10-problem test, 80 % on a 20-problem test and 90 % on a 30-problem test. If the three tests ar…
AMC 8 2006 #13 grade 6+ rate-ratio
Cassie leaves Escanaba at 8:30 AM heading for Marquette on her bike. She bikes at a uniform rate of 12 miles per hour. B…
AMC 8 2006 #14 grade 6+ rate-ratio
Problems 14, 15 and 16 involve Mrs. Reed's English assignment. A Novel Assignment The students in Mrs. Reed's English cl…
AMC 8 2006 #15 grade 6+ rate-ratio
Problems 14, 15 and 16 involve Mrs. Reed's English assignment. A Novel Assignment The students in Mrs. Reed's English cl…
AMC 8 2006 #16 grade 6+ rate-ratio
Problems 14, 15 and 16 involve Mrs. Reed's English assignment. A Novel Assignment The students in Mrs. Reed's English cl…
AMC 8 2006 #17 grade 7+ probability
Jeff rotates spinners P, Q and R and adds the resulting numbers. What is the probability that his sum is an odd number?
AMC 8 2006 #18 grade 6+ geometry-3d
A cube with 3-inch edges is made using 27 cubes with 1-inch edges. Nineteen of the smaller cubes are white and eight are…
AMC 8 2006 #19 grade 8+ geometry-2d
Triangle ABC is an isosceles triangle with AB=BC. Point D is the midpoint of both BC and AE, and CE is 11 units long. Tr…
AMC 8 2006 #20 grade 6+ counting
A singles tournament had six players. Each player played every other player only once, with no ties. If Helen won 4 game…
AMC 8 2006 #21 grade 5+ geometry-3d
An aquarium has a rectangular base that measures 100 cm by 40 cm and has a height of 50 cm. The aquarium is filled with…
AMC 8 2006 #22 grade 6+ arithmetic
Three different one-digit positive integers are placed in the bottom row of cells. Numbers in adjacent cells are added a…
AMC 8 2006 #23 grade 6+ number-theory
A box contains gold coins. If the coins are equally divided among six people, four coins are left over. If the coins are…
AMC 8 2006 #24 grade 6+ number-theory
In the multiplication problem below A, B, C, D are different digits. What is A+B? A B A × C D C D C D
AMC 8 2006 #25 grade 6+ number-theory
Barry wrote 6 different numbers, one on each side of 3 cards, and laid the cards on a table, as shown. The sums of the t…

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