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2003 AMC 12B problems

All 25 problems from the 2003 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 1Which of the following is the same as 2 - 4 + 6 - 8 + 10 - 12 + 14/3 - 6 + 9 - 12 + 15 - 18 + 21?Algebra
  2. 2Problem 2Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs $1 more than a pink pill…Algebra
  3. 3Problem 3Rose fills each of the rectangular regions of her rectangular flower bed with a different type of flower. The lengths, in feet, of the rectangular…Algebra
  4. 4Problem 4Moe uses a mower to cut his rectangular 90-foot by 150-foot lawn. The swath he cuts is 28 inches wide, but he overlaps each cut by 4 inches to make…Algebra
  5. 5Problem 5Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal length to the height in a…Algebra
  6. 6Problem 6The second and fourth terms of a geometric sequence are 2 and 6. Which of the following is a possible first term?Algebra
  7. 7Problem 7Penniless Pete’s piggy bank has no pennies in it, but it has 100 coins, all nickels, dimes, and quarters, whose total value is $8.35. It does not…Algebra
  8. 8Problem 8Let clubsuit (x) denote the sum of the digits of the positive integer x. For example, clubsuit (8) = 8 and clubsuit (123) = 1 + 2 + 3 = 6. For how…Number Theory
  9. 9Problem 9Let f be a linear function for which f(6) - f(2) = 12. What is f(12) - f(2)?Algebra
  10. 10Problem 10Several figures can be made by attaching two equilateral triangles to the regular pentagon ABCDE in two of the five positions shown. How many…
  11. 11Problem 11Cassandra sets her watch to the correct time at noon. At the actual time of 1:00 PM, she notices that her watch reads 12:57 and 36 seconds. Assuming…Algebra
  12. 12Problem 12What is the largest integer that is a divisor of (n + 1)(n + 3)(n + 5) · (n + 7)(n + 9) for all positive even integers n?Number Theory
  13. 13Problem 13An ice cream cone consists of a sphere of vanilla ice cream and a right circular cone that has the same diameter as the sphere. If the ice cream…Geometry
  14. 14Problem 14In rectangle ABCD, AB = 5 and BC = 3. Points F and G are on CD so that DF = 1 and GC = 2. Lines AF and BG intersect at E. Find the area of △ AEB.Geometry
  15. 15Problem 15A regular octagon ABCDEFGH has an area of one square unit. What is the area of the rectangle ABEF?Geometry
  16. 16Problem 16Three semicircles of radius 1 are constructed on diameter AB of a semicircle of radius 2. The centers of the small semicircles divide AB into four…Geometry
  17. 17Problem 17If log (xy^3) = 1 and log (x^2y) = 1, what is log (xy)?Algebra
  18. 18Problem 18Let x and y be positive integers such that 7x^5 = 11y^13. The minimum possible value of x has a prime factorization a^c b^d. What is a + b + c + d?Number Theory
  19. 19Problem 19Let S be the set of permutations of the sequence 1, 2, 3, 4, 5 for which the first term is not 1. A permutation is chosen randomly from S. The…Counting & Probability
  20. 20Problem 20Part of the graph of f(x) = ax^3 + bx^2 + cx + d is shown. What is b?Algebra
  21. 21Problem 21An object moves 8 cm in a straight line from A to B, turns at an angle alpha, measured in radians and chosen at random from the interval (0, π), and…Geometry
  22. 22Problem 22Let ABCD be a rhombus with AC = 16 and BD = 30. Let N be a point on AB, and let P and Q be the feet of the perpendiculars from N to AC and BD…Geometry
  23. 23Problem 23The number of x-intercepts on the graph of y = sin (1/x) in the interval (0.0001, 0.001) is closest toAlgebra
  24. 24Problem 24Positive integers a, b, and c are chosen so that a < b < c, and the system of equations 2x + y = 2003 and y = |x - a| + |x - b| + |x - c| has exactly…Algebra
  25. 25Problem 25Three points are chosen randomly and independently on a circle. What is the probability that all three pairwise distances between the points are less…Geometry

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