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2011 AMC 10B problems

All 25 problems from the 2011 AMC 10B, 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 1What is the value of the following expression? 2+4+6/1+3+5 - 1+3+5/2+4+6Algebra
  2. 2Problem 2Josanna’s test scores to date are 90, 80, 70, 60, and 85. Her goal is to raise her test average at least 3 points with her next test. What is the…Algebra
  3. 3Problem 3At a store, when a length is reported as x inches that means it is at least x - 0.5 inches and at most x + 0.5 inches. Suppose the dimensions of a…Algebra
  4. 4Problem 4LeRoy and Bernardo went on a week-long trip together and agreed to share the costs equally. Over the week, each of them paid for various joint…Algebra
  5. 5Problem 5In multiplying two positive integers a and b, Ron reversed the digits of the two-digit number a. His erroneous product was 161. What is the correct…Number Theory
  6. 6Problem 6On Halloween Casper ate 1/3 of his candies and then gave 2 candies to his brother. The next day he ate 1/3 of his remaining candies and then gave 4…Algebra
  7. 7Problem 7The sum of two angles of a triangle is 6/5 of a right angle, and one of these two angles is 30^° larger than the other. What is the degree measure of…Algebra
  8. 8Problem 8At a certain beach if it is at least 80^° F and sunny, then the beach will be crowded. On June 10 the beach was not crowded. What can be concluded…
  9. 9Problem 9The area of △ EBD is one third of the area of the 3-4-5 triangle ABC. Segment DE is perpendicular to segment AB. What is BD?Geometry
  10. 10Problem 10Consider the set of numbers {1, 10, 10^2, 10^3, …, 10^10}. The ratio of the largest element of the set to the sum of the other ten elements of the…Algebra
  11. 11Problem 11There are 52 people in a room. What is the largest value of n such that the statement “At least n people in this room have birthdays falling in the…Counting & Probability
  12. 12Problem 12Keiko walks once around a track at exactly the same constant speed every day. The sides of the track are straight, and the ends are semicircles. The…Algebra
  13. 13Problem 13Two real numbers are selected independently at random from the interval [-20, 10]. What is the probability that the product of those numbers is…Counting & Probability
  14. 14Problem 14A rectangular parking lot has a diagonal of 25 meters and an area of 168 square meters. In meters, what is the perimeter of the parking lot?Geometry
  15. 15Problem 15Let @ denote the “averaged with” operation: a @ b = a+b/2. Which of the following distributive laws hold for all numbers x, y, and z? I. x @ (y + z)…Algebra
  16. 16Problem 16A dart board is a regular octagon divided into regions as shown. Suppose that a dart thrown at the board is equally likely to land anywhere on the…Algebra
  17. 17Problem 17In the given circle, the diameter EB is parallel to DC, and AB is parallel to ED. The angles AEB and ABE are in the ratio 4: 5. What is the degree…Geometry
  18. 18Problem 18Rectangle ABCD has AB = 6 and BC = 3. Point M is chosen on side AB so that ∠ AMD = ∠ CMD. What is the degree measure of ∠ AMD?Geometry
  19. 19Problem 19What is the product of all the roots of the equation below? √(5 | x | + 8) = √(x^2 - 16)Algebra
  20. 20Problem 20Rhombus ABCD has side length 2 and ∠ B = 120°. Region R consists of all points inside the rhombus that are closer to vertex B than any of the other…Geometry
  21. 21Problem 21Brian writes down four integers w > x > y > z whose sum is 44. The pairwise positive differences of these numbers are 1, 3, 4, 5, 6, and 9. What is…Algebra
  22. 22Problem 22A pyramid has a square base with sides of length 1 and has lateral faces that are equilateral triangles. A cube is placed within the pyramid so that…Geometry
  23. 23Problem 23What is the hundreds digit of 2011^2011?Algebra
  24. 24Problem 24A lattice point in an xy-coordinate system is any point (x, y) where both x and y are integers. The graph of y = mx +2 passes through no lattice…Geometry
  25. 25Problem 25Let T_1 be a triangle with side lengths 2011, 2012, and 2013. For n ≥ 1, if T_n = △ ABC and D, E, and F are the points of tangency of the incircle of…Geometry

Practise the same ideas across every year on the topic pages, or browse the full AMC 10 archive.