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2007 AMC 12B problems

All 25 problems from the 2007 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 1Isabella’s house has 3 bedrooms. Each bedroom is 12 feet long, 10 feet wide, and 8 feet high. Isabella must paint the walls of all the bedrooms…Geometry
  2. 2Problem 2A college student drove his compact car 120 miles home for the weekend and averaged 30 miles per gallon. On the return trip the student drove his…Algebra
  3. 3Problem 3The point O is the center of the circle circumscribed about △ ABC, with ∠ BOC=120° and ∠ AOB=140°, as shown. What is the degree measure of ∠ ABC?Geometry
  4. 4Problem 4At Frank’s Fruit Market, 3 bananas cost as much as 2 apples, and 6 apples cost as much as 4 oranges. How many oranges cost as much as 18 bananas?Algebra
  5. 5Problem 5The 2007 AMC 12 contests will be scored by awarding 6 points for each correct response, 0 points for each incorrect response, and 1.5 points for each…Algebra
  6. 6Problem 6Triangle ABC has side lengths AB=5, BC=6, and AC=7. Two bugs start simultaneously from A and crawl along the sides of the triangle in opposite…Algebra
  7. 7Problem 7All sides of the convex pentagon ABCDE are of equal length, and ∠ A=∠ B=90°. What is the degree measure of ∠ E?Geometry
  8. 8Problem 8Tom’s age is T years, which is also the sum of the ages of his three children. His age N years ago was twice the sum of their ages then. What is T/N?Algebra
  9. 9Problem 9A function f has the property that f(3x-1)=x^2+x+1 for all real numbers x. What is f(5)?Algebra
  10. 10Problem 10Some boys and girls are having a car wash to raise money for a class trip to China. Initially 40% of the group are girls. Shortly thereafter two…Algebra
  11. 11Problem 11The angles of quadrilateral ABCD satisfy ∠ A=2∠ B=3∠ C=4∠ D. What is the degree measure of ∠ A, rounded to the nearest whole number?Algebra
  12. 12Problem 12A teacher gave a test to a class in which 10% of the students are juniors and 90% are seniors. The average score on the test was 84. The juniors all…Algebra
  13. 13Problem 13A traffic light runs repeatedly through the following cycle: green for 30 seconds, then yellow for 3 seconds, and then red for 30 seconds. Leah picks…Counting & Probability
  14. 14Problem 14Point P is inside equilateral △ ABC. Points Q, R, and S are the feet of the perpendiculars from P to AB, BC, and CA, respectively. Given that PQ=1…Geometry
  15. 15Problem 15The geometric series a+ar+ar^2+… has a sum of 7, and the terms involving odd powers of r have a sum of 3. What is a+r?Algebra
  16. 16Problem 16Each face of a regular tetrahedron is painted either red, white, or blue. Two colorings are considered indistinguishable if two congruent tetrahedra…Counting & Probability
  17. 17Problem 17If a is a nonzero integer and b is a positive number such that ab^2=log _10b, what is the median of the set {0,1,a,b,1/b}?Algebra
  18. 18Problem 18Let a, b, and c be digits with ane 0. The three-digit integer abc lies one third of the way from the square of a positive integer to the square of…Number Theory
  19. 19Problem 19Rhombus ABCD, with side length 6, is rolled to form a cylinder of volume 6 by taping AB to DC. What is sin (∠ ABC)?Geometry
  20. 20Problem 20The parallelogram bounded by the lines y=ax+c, y=ax+d, y=bx+c, and y=bx+d has area 18. The parallelogram bounded by the lines y=ax+c, y=ax-d, y=bx+c…Geometry
  21. 21Problem 21The first 2007 positive integers are each written in base 3. How many of these base-3 representations are palindromes? (A palindrome is a number that…Number Theory
  22. 22Problem 22Two particles move along the edges of equilateral △ ABC in the direction A→ B→ C→ A, starting simultaneously and moving at the same speed. One starts…Geometry
  23. 23Problem 23How many non-congruent right triangles with positive integer leg lengths have areas that are numerically equal to 3 times their perimeters?Algebra
  24. 24Problem 24How many pairs of positive integers (a,b) are there such that gcd (a,b)=1 and a/b+14b/9a is an integer?Number Theory
  25. 25Problem 25Points A, B, C, D, and E are located in 3-dimensional space with AB=BC=CD =DE=EA=2 and ∠ ABC=∠ CDE =∠ DEA=90°. The plane of △ ABC is parallel to DE…Geometry

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