Competition · AMC preparation · step 4 of 4

AMC 12 2008B: all 25 problems

Each problem has a solution worked from first principles and the first grade (by CCSS standards) that can solve it.

AMC 12 2008B #1 grade 4+ counting
A basketball player made 5 baskets during a game. Each basket was worth either 2 or 3 points. How many different numbers…
AMC 12 2008B #2 grade 2+ arithmetic
A 4× 4 block of calendar dates is shown. First, the order of the numbers in the second and the fourth rows are reversed.…
AMC 12 2008B #3 grade 5+ arithmetic
A semipro baseball league has teams with 21 players each. League rules state that a player must be paid at least 15,000…
AMC 12 2008B #4 grade 7+ geometry-2d
On circle O, points C and D are on the same side of diameter AB, ∠ AOC = 30°, and ∠ DOB = 45°. What is the ratio of the…
AMC 12 2008B #5 grade 6+ counting
A class collects 50 dollars to buy flowers for a classmate who is in the hospital. Roses cost 3 dollars each, and carnat…
AMC 12 2008B #6 grade 6+ arithmetic
Postman Pete has a pedometer to count his steps. The pedometer records up to 99999 steps, then flips over to 00000 on th…
AMC 12 2008B #7 grade 7+ algebra
For real numbers a and b, define atextdollar b = (a - b)². What is (x - y)²textdollar(y - x)²?
AMC 12 2008B #8 grade 6+ rate-ratio
Points B and C lie on AD. The length of AB is 4 times the length of BD, and the length of AC is 9 times the length of CD…
AMC 12 2008B #9 grade 8+ geometry-2d
Points A and B are on a circle of radius 5 and AB=6. Point C is the midpoint of the minor arc AB. What is the length of…
AMC 12 2008B #10 grade 6+ rate-ratio
Bricklayer Brenda would take 9 hours to build a chimney alone, and bricklayer Brandon would take 10 hours to build it al…
AMC 12 2008B #11 grade 8+ geometry-3d
A cone-shaped mountain has its base on the ocean floor and has a height of 8000 feet. The top 1/8 of the volume of the m…
AMC 12 2008B #12 grade 6+ algebra
For each positive integer n, the mean of the first n terms of a sequence is n. What is the 2008th term of the sequence?
AMC 12 2008B #13 grade 8+ geometry-2d
Vertex E of equilateral △ABE is in the interior of unit square ABCD. Let R be the region consisting of all points inside…
AMC 12 2008B #14 grade 11+ algebra, geometry-2d
A circle has a radius of log₁₀(a²) and a circumference of log₁₀(b⁴). What is log_ab?
AMC 12 2008B #15 grade 10+ geometry-2d
On each side of a unit square, an equilateral triangle of side length 1 is constructed. On each new side of each equilat…
AMC 12 2008B #16 grade 7+ geometry-2d, number-theory
A rectangular floor measures a by b feet, where a and b are positive integers with b > a. An artist paints a rectangle o…
AMC 12 2008B #17 grade 10+ geometry-2d
Let A, B and C be three distinct points on the graph of y=x² such that line AB is parallel to the x-axis and △ ABC is a…
AMC 12 2008B #18 grade 10+ geometry-3d
A pyramid has a square base ABCD and vertex E. The area of square ABCD is 196, and the areas of △ ABE and △ CDE are 105…
AMC 12 2008B #19 grade 11+ algebra
A function f is defined by f(z) = (4 + i) z² + α z + γ for all complex numbers z, where α and γ are complex numbers and…
AMC 12 2008B #20 grade 7+ rate-ratio
Michael walks at the rate of 5 feet per second on a long straight path. Trash pails are located every 200 feet along the…
AMC 12 2008B #21 grade 10+ probability, geometry-2d
Two circles of radius 1 are to be constructed as follows. The center of circle A is chosen uniformly and at random from…
AMC 12 2008B #22 grade 11+ probability
A parking lot has 16 spaces in a row. Twelve cars arrive, each of which requires one parking space, and their drivers ch…
AMC 12 2008B #23 grade 11+ number-theory, algebra
The sum of the base-10 logarithms of the divisors of 10ⁿ is 792. What is n?
AMC 12 2008B #24 grade 9+ geometry-2d
Let A₀=(0,0). Distinct points A₁,A₂,… lie on the x-axis, and distinct points B₁,B₂,… lie on the graph of y=√x. For every…
AMC 12 2008B #25 grade 10+ geometry-2d
Let ABCD be a trapezoid with AB||CD, AB=11, BC=5, CD=19, and DA=7. Bisectors of ∠ A and ∠ D meet at P, and bisectors of…

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