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2008 AMC 12B problems

All 25 problems from the 2008 AMC 12B, with answer choices, worked solutions and hints. Problems are roughly ordered by difficulty: 1–10 are the most approachable, 19–25 the hardest.

Problems

  1. 1Problem 1A basketball player made 5 baskets during a game. Each basket was worth either 2 or 3 points. How many different numbers could represent the total…Counting & Probability
  2. 2Problem 2A 4 × 4 block of calendar dates is shown. The order of the numbers in the second row is to be reversed. Then the order of the numbers in the fourth…Algebra
  3. 3Problem 3A semipro baseball league has teams with 21 players each. League rules state that a player must be paid at least $15,000, and that the total of all…Algebra
  4. 4Problem 4On 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 area of the smaller sector…Geometry
  5. 5Problem 5A class collects $50 to buy flowers for a classmate who is in the hospital. Roses cost $3 each, and carnations cost $2 each. No other flowers are to…Number Theory
  6. 6Problem 6Postman Pete has a pedometer to count his steps. The pedometer records up to 99999 steps, then flips over to 00000 on the next step. Pete plans to…Algebra
  7. 7Problem 7For real numbers a and b, define a $ b = (a - b)^2. What is (x - y)^2 $ (y - x)^2?Algebra
  8. 8Problem 8Points 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. The length of BC is what…Algebra
  9. 9Problem 9Points 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 the line segment AC?Geometry
  10. 10Problem 10Bricklayer Brenda would take 9 hours to build a chimney alone, and bricklayer Brandon would take 10 hours to build it alone. When they work together…Algebra
  11. 11Problem 11A 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 mountain is above water. What…Geometry
  12. 12Problem 12For each positive integer n, the mean of the first n terms of a sequence is n. What is the 2008th term of the sequence?Algebra
  13. 13Problem 13Vertex E of equilateral △ ABE is in the interior of unit square ABCD. Let R be the region consisting of all points inside ABCD and outside △ ABE…Geometry
  14. 14Problem 14A circle has a radius of log _10(a^2) and a circumference of log _10(b^4). What is log _a b?Algebra
  15. 15Problem 15On each side of a unit square, an equilateral triangle of side length 1 is constructed. On each new side of each equilateral triangle, another…Geometry
  16. 16Problem 16A rectangular floor measures a feet by b feet, where a and b are positive integers with b > a. An artist paints a rectangle on the floor with the…Algebra
  17. 17Problem 17Let A, B and C be three distinct points on the graph of y = x^2 such that line AB is parallel to the x-axis and △ ABC is a right triangle with area…Geometry
  18. 18Problem 18A 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 and 91, respectively. What is…Geometry
  19. 19Problem 19A function f is defined by f(z) = (4 + i)z^2 + alpha z + gamma for all complex numbers z, where alpha and gamma are complex numbers and i^2 = -1…Algebra
  20. 20Problem 20Michael walks at the rate of 5 feet per second on a long straight path. Trash pails are located every 200 feet along the path. A garbage truck…Algebra
  21. 21Problem 21Two circles of radius 1 are to be constructed as follows. The center of circle A is chosen uniformly and at random from the line segment joining (0…Geometry
  22. 22Problem 22A parking lot has 16 spaces in a row. Twelve cars arrive, each of which requires one parking space, and their drivers choose their spaces at random…Counting & Probability
  23. 23Problem 23The sum of the base-10 logarithms of the divisors of 10^n is 792. What is n?Algebra
  24. 24Problem 24Let A_0 = (0, 0). Distinct points A_1, A_2, … lie on the x-axis, and distinct points B_1, B_2, … lie on the graph of y = √(x). For every positive…Algebra
  25. 25Problem 25Let 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 ∠ B and ∠ C meet at…Geometry

Practise the same ideas across every year on the topic pages, or browse the full AMC 12 archive.