The 2011 AMC 10 Papers A and B balanced algebraic evaluation with geometric perimeter, with regular-polygon perimeter, coin-counting, units-digit and average-speed problem types taking sizeable shares, testing fluency in formulas and counting principles. Scan for the full papers and answer keys.
2011 AMC 10 A/B paper overview and exam highlights.
The 2011 AMC 10 was held in November 2011 in two papers (A and B), fairly balanced between algebraic evaluation and geometric perimeter.
Format: 25 multiple-choice questions, 75 minutes, 150 points max; a blank answer earns 1.5 points and a wrong answer earns 0. The AIME cut-off has recently been around 100 (Paper A).
The 2011 paper set more problems on regular-polygon perimeter, coin-outcome counting, units digits of powers, and average speed, combining formulas with counting.
2011 AMC 10 main topic areas, weights and emphasis.
Evaluation, quadratics, word and speed problems; about 30%.
Equilateral triangles, rectangle perimeter, circles and cylinder surface area; about 23%.
Divisibility, remainders, GCD and divisor counts; about 17%.
Coin outcomes, combinations and ordered counting; about 20%.
Classical probability and dice sums; about 10%.
2011 AMC 10-style mock questions (Basic · Medium · Hard) — submit to grade and view step-by-step solutions.
If x = 4, what is the value of x2 + 3x - 2?
Correct answer: A
Substitute x = 4: 42 + 3(4) - 2 = 16 + 12 - 2 = 26. Answer A. Key: direct substitution.The sum of three consecutive integers is 90. What is the largest?
Correct answer: B
Let the middle integer be n: 3n = 90, so n = 30 and the largest is 31. Answer B. Key: model consecutive integers by their middle.How many positive divisors does 180 have?
Correct answer: C
180 = 22×32×5, so the number of divisors is (2+1)(2+1)(1+1) = 18. Answer C. Key: divisor-count formula.An equilateral triangle has side length 12. What is its perimeter?
Correct answer: D
All three sides are equal, so the perimeter = 3×12 = 36. Answer D. Key: equilateral triangle perimeter.An item is marked up 10% above cost to a price of $88. What was the cost?
Correct answer: E
cost × 1.1 = 88, so cost = 88 / 1.1 = 80. Answer E. Key: price = cost × (1 + markup).A fair six-sided die is rolled once. What is the probability of rolling greater than 4 (5 or 6)?
Correct answer: A
Values greater than 4 are 5 and 6 (2 of 6), so the probability is 2/6 = 1/3. Answer A. Key: classical probability = favorable / total.Five coins are tossed at once. How many heads/tails outcomes are possible?
Correct answer: B
Each coin has 2 outcomes, so 5 coins give 25 = 32. Answer B. Key: independent outcomes multiply.What is the remainder when 2011 is divided by 13?
Correct answer: C
13 × 154 = 2002, and 2011 - 2002 = 9, so the remainder is 9. Answer C. Key: division with remainder.If 6x - 4 = 32, what is x?
Correct answer: D
6x = 32 + 4 = 36, so x = 6. Answer D. Key: isolate the variable.A triangle has base 12 and height 9. What is its area?
Correct answer: E
Area = ½×12×9 = 108/2 = 54. Answer E. Key: triangle area formula.If x2 - 11x + 24 = 0, what is the sum of all possible values of x?
Correct answer: A
Factor: (x-3)(x-8) = 0, so x = 3 or 8, and the sum is 11. Answer A. Key: Vieta — sum of roots = -b/a = 11.What is the greatest common divisor of 48 and 84?
Correct answer: B
48 = 24×3 and 84 = 22×3×7, so GCD = 22×3 = 12. Answer B. Key: take the smallest power of each shared prime.A committee of 2 is chosen from 17 people. How many different committees are possible?
Correct answer: C
C(17,2) = (17×16)/(2×1) = 136. Answer C. Key: combinations are order-independent, C(n,k) = n!/(k!(n-k)!).In a triangle, two angles are 55° and 65°. What is the third angle?
Correct answer: D
Triangle angles sum to 180°, so the third angle = 180 - 55 - 65 = 60°. Answer D. Key: triangle angle-sum theorem.The average of 7 numbers is 18. After removing one number, the average of the remaining 6 is 16. What was the removed number?
Correct answer: E
Sum of 7 = 7×18 = 126; sum of 6 = 6×16 = 96; the removed number = 126 - 96 = 30. Answer E. Key: average = sum / count.What is the units digit of 82011?
Correct answer: A
The units digit of powers of 8 cycles as 8, 4, 2, 6 (period 4). Since 2011 = 4×502 + 3, the remainder is 3, corresponding to the 3rd value, so the units digit is 2. Answer A. Key: cyclic units digits of powers.One worker can finish a job in 6 hours and another in 12 hours. How long does it take them together?
Correct answer: B
Rates: 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4 per hour, so together they need 1 / (1/4) = 4 hours. Answer B. Key: combined rate = sum of individual rates.A square and an equilateral triangle have the same perimeter. If the triangle side is 44, what is the square side?
Correct answer: C
Triangle perimeter = 3×44 = 132, so the square side = 132 / 4 = 33. Answer C. Key: equal perimeters split by side count.Two fair six-sided dice are rolled. What is the probability the sum is 8?
Correct answer: D
Sums to 8: (2,6),(3,5),(4,4),(5,3),(6,2) — 5 outcomes out of 36, so 5/36. Answer D. Key: enumerate ordered dice pairs.A car travels 90 km at 30 km/h and returns at 90 km/h. What is the average speed for the whole trip (km/h)?
Correct answer: E
Outbound time = 90/30 = 3 h; return = 90/90 = 1 h. Total distance 180 km over 4 h gives 180/4 = 45 km/h. Answer E. Key: average speed = total distance / total time, not the average of speeds.How many positive integers less than 100 are divisible by both 6 and 9?
Correct answer: A
Divisible by both 6 and 9 means divisible by LCM(6,9) = 18. The multiples of 18 below 100 are 18, 36, 54, 72, 90 — 5 of them. Answer A. Key: divisible by both ⟺ divisible by their LCM.From the integers 1 through 9, 3 different numbers are chosen to form a set. How many such sets are there?
Correct answer: B
C(9,3) = (9×8×7)/(3×2×1) = 504/6 = 84. Answer B. Key: combinations are order-independent, C(n,k) = n!/(k!(n-k)!).A right cylinder has radius 2 and height 9. What is its total surface area? (in terms of π)
Correct answer: C
Surface area = 2πr2 + 2πrh = 2π(22) + 2π(2)(9) = 8π + 36π = 44π. Answer C. Key: cylinder surface = two bases + lateral area.Given x + y = 23 and xy = 120, what is x2 + y2?
Correct answer: D
x2 + y2 = (x+y)2 - 2xy = 232 - 2×120 = 529 - 240 = 289. Answer D. Key: identity linking sum of squares to sum and product.In how many ways can 24 be written as a sum of three positive integers, where order does not matter?
Correct answer: C
Let a ≤ b ≤ c with a+b+c = 24. For a=1: 11 ways — (1,1,22) to (1,11,12); a=2: 10 ways — (2,2,20) to (2,11,11); a=3: 8 ways — (3,3,18) to (3,10,11); a=4: 7 ways — (4,4,16) to (4,10,10); a=5: 5 ways — (5,5,14) to (5,9,10); a=6: 4 ways — (6,6,12) to (6,9,9); a=7: 2 ways — (7,7,10) to (7,8,9); a=8: 1 way — (8,8,8). Total 48. Answer C. Key: ordered enumeration to avoid duplicates.Unified AMC 10 specs, consistent across years.
Papers A and B are comparable in difficulty and scope. Students may take either, or both — the higher score is used for awards and AIME qualification.
Four steps · Overview / Topics / Practice / Prep
Read the 2011 AMC 10 A/B overview and format specs to grasp the year’s style.
Review the key topics and weights, and locate your weak areas.
Complete the 25 mock questions (75-minute limit); submit for auto-grading and right/wrong marks.
Open the step-by-step solutions, learn from mistakes, and scan for full papers to push for AIME.
Prep tips and score-boosting advice for the 2011 AMC 10 A/B paper.
Finish all 25 within 75 minutes; skip when stuck and bank the solvable ones first.
Factor N into prime powers; the divisor count is the product of (exponent + 1).
Divisible by both numbers means divisible by their LCM — find the LCM, then count multiples.
Units digits cycle by the base; locate the result via the exponent mod the period.
Aiming above 100? Lock the basics and medium questions, then take the last 5 step by step; scan for full papers and a plan.
Frequent questions about the 2011 AMC 10 papers and answers.
Scan to add the advisor for 2011 AMC 10 A/B past papers, answer keys and solutions, plus a custom prep plan.
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