Competition · AMC preparation · step 4 of 4

AMC 8 2011: 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 2011 #1 grade 4+ arithmetic
Margie bought 3 apples at a cost of 50 cents per apple. She paid with a 5-dollar bill. How much change did Margie receiv…
AMC 8 2011 #2 grade 4+ geometry-2d
Karl's rectangular vegetable garden is 20 feet by 45 feet, and Makenna's is 25 feet by 40 feet. Whose garden is larger i…
AMC 8 2011 #3 grade 6+ geometry-2d
Extend the square pattern of 8 black and 17 white square tiles by attaching a border of black tiles around the square. W…
AMC 8 2011 #4 grade 6+ arithmetic
Here is a list of the numbers of fish that Tyler caught in nine outings last summer: 2,0,1,3,0,3,3,1,2. Which statement…
AMC 8 2011 #5 grade 4+ arithmetic
What time was it 2011 minutes after midnight on January 1, 2011?
AMC 8 2011 #6 grade 4+ arithmetic
In a town of 351 adults, every adult owns a car, motorcycle, or both. If 331 adults own cars and 45 adults own motorcycl…
AMC 8 2011 #7 grade 6+ geometry-2d
Each of the following four large congruent squares is subdivided into combinations of congruent triangles or rectangles…
AMC 8 2011 #8 grade 3+ counting
Bag A has three chips labeled 1, 3, and 5. Bag B has three chips labeled 2, 4, and 6. If one chip is drawn from each bag…
AMC 8 2011 #9 grade 6+ rate-ratio
Carmen takes a long bike ride on a hilly highway. The graph indicates the miles traveled during the time of her ride. Wh…
AMC 8 2011 #10 grade 6+ algebra
The taxi fare in Gotham City is 2.40 for the first 1/2 mile and additional mileage charged at the rate 0.20 for each add…
AMC 8 2011 #11 grade 6+ arithmetic
The graph shows the number of minutes studied by both Asha (black bar) and Sasha (grey bar) in one week. On the average,…
AMC 8 2011 #12 grade 7+ probability
Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the probabil…
AMC 8 2011 #13 grade 6+ geometry-2d
Two congruent squares, ABCD and PQRS, have side length 15. They overlap to form the 15 by 25 rectangle AQRD shown. What…
AMC 8 2011 #14 grade 6+ rate-ratio
There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5 : 4. There are 180 students at Win…
AMC 8 2011 #15 grade 6+ arithmetic
How many digits are in the product 4⁵ · 5¹⁰?
AMC 8 2011 #16 grade 8+ geometry-2d
Let A be the area of the triangle with sides of length 25, 25, and 30. Let B be the area of the triangle with sides of l…
AMC 8 2011 #17 grade 6+ number-theory
Let w, x, y, and z be whole numbers. If 2^w · 3^x · 5^y · 7^z = 588, then what does 2w + 3x + 5y + 7z equal?
AMC 8 2011 #18 grade 7+ probability
A fair 6 sided die is rolled twice. What is the probability that the first number that comes up is greater than or equal…
AMC 8 2011 #19 grade 4+ counting
How many rectangles are in this figure?
AMC 8 2011 #20 grade 8+ geometry-2d
Quadrilateral ABCD is a trapezoid, AD = 15, AB = 50, BC = 20, and the altitude is 12. What is the area of the trapezoid?
AMC 8 2011 #21 grade 4+ number-theory
Students guess that Norb's age is 24, 28, 30, 32, 36, 38, 41, 44, 47, and 49. Norb says, "At least half of you guessed t…
AMC 8 2011 #22 grade 6+ number-theory
What is the tens digit of 7²⁰¹¹?
AMC 8 2011 #23 grade 5+ counting
How many 4-digit positive integers have four different digits, where the leading digit is not zero, the integer is a mul…
AMC 8 2011 #24 grade 4+ number-theory
In how many ways can 10001 be written as the sum of two primes?
AMC 8 2011 #25 grade 8+ geometry-2d
A circle with radius 1 is inscribed in a square and circumscribed about another square as shown. Which fraction is close…

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