Competition · AMC preparation · step 4 of 4

AMC 8 2003: 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 2003 #1 grade 2+ geometry-3d
Jamie counted the number of edges of a cube, Jimmy counted the numbers of corners, and Judy counted the number of faces.…
AMC 8 2003 #2 grade 4+ number-theory
Which of the following numbers has the smallest prime factor?
AMC 8 2003 #3 grade 6+ rate-ratio
A burger at Ricky C's weighs 120 grams, of which 30 grams are filler. What percent of the burger is not filler?
AMC 8 2003 #4 grade 4+ arithmetic
A group of children riding on bicycles and tricycles rode past Billy Bob's house. Billy Bob counted 7 children and 19 wh…
AMC 8 2003 #5 grade 6+ rate-ratio
If 20% of a number is 12, what is 30% of the same number?
AMC 8 2003 #6 grade 8+ geometry-2d
Given the areas of the three squares in the figure, what is the area of the interior triangle?
AMC 8 2003 #7 grade 6+ arithmetic
Blake and Jenny each took four 100-point tests. Blake averaged 78 on the four tests. Jenny scored 10 points higher than…
AMC 8 2003 #8 grade 6+ geometry-2d
Problems 8, 9 and 10 use the data found in the accompanying paragraph and figures Four friends, Art, Roger, Paul and Tri…
AMC 8 2003 #9 grade 6+ rate-ratio
Problems 8, 9 and 10 use the data found in the accompanying paragraph and figures Four friends, Art, Roger, Paul and Tri…
AMC 8 2003 #10 grade 6+ geometry-2d
Problems 8, 9 and 10 use the data found in the accompanying paragraph and figures Four friends, Art, Roger, Paul and Tri…
AMC 8 2003 #11 grade 7+ rate-ratio
Business is a little slow at Lou's Fine Shoes, so Lou decides to have a sale. On Friday, Lou increases all of Thursday's…
AMC 8 2003 #12 grade 7+ probability
When a fair six-sided dice is tossed on a table top, the bottom face cannot be seen. What is the probability that the pr…
AMC 8 2003 #13 grade 4+ geometry-3d
Fourteen white cubes are put together to form the figure on the right. The complete surface of the figure, including the…
AMC 8 2003 #14 grade 4+ number-theory
In this addition problem, each letter stands for a different digit. 0.5mm T W O + T W O F O U R If T = 7 and the letter…
AMC 8 2003 #15 grade 5+ geometry-3d
A figure is constructed from unit cubes. Each cube shares at least one face with another cube. What is the minimum numbe…
AMC 8 2003 #16 grade 4+ counting
Ali, Bonnie, Carlo, and Dianna are going to drive together to a nearby theme park. The car they are using has 4 seats: 1…
AMC 8 2003 #17 grade 1+ logic
The six children listed below are from two families of three siblings each. Each child has blue or brown eyes and black…
AMC 8 2003 #18 grade 4+ counting
Each of the twenty dots on the graph below represents one of Sarah's classmates. Classmates who are friends are connecte…
AMC 8 2003 #19 grade 6+ number-theory
How many integers between 1000 and 2000 have all three of the numbers 15, 20, and 25 as factors?
AMC 8 2003 #20 grade 5+ geometry-2d
What is the measure of the acute angle formed by the hands of the clock at 4:20 PM?
AMC 8 2003 #21 grade 8+ geometry-2d
The area of trapezoid ABCD is 164 cm². The altitude is 8 cm, AB is 10 cm, and CD is 17 cm. What is BC, in centimeters?
AMC 8 2003 #22 grade 7+ geometry-2d
The following figures are composed of squares and circles. Which figure has a shaded region with largest area?
AMC 8 2003 #23 grade 4+ pattern
In the pattern below, the cat moves clockwise through the four squares, and the mouse moves counterclockwise through the…
AMC 8 2003 #24 grade 8+ rate-ratio
A ship travels from point A to point B along a semicircular path, centered at Island X. Then it travels along a straight…
AMC 8 2003 #25 grade 8+ geometry-2d
In the figure, the area of square WXYZ is 25 cm². The four smaller squares have sides 1 cm long, either parallel to or c…

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