The 2015 AMC 10 Papers A and B kept a high share of algebraic evaluation and combinatorial counting, with problems on factors and units digits of powers of 2, strictly-increasing-digit counting, cylinder surface area and divisibility tests demanding strong construction and categorization. Scan for the full papers and answer keys.
2015 AMC 10 A/B paper overview and exam highlights.
The 2015 AMC 10 was held in November 2015 in two papers (A and B), keeping a high share of algebraic evaluation and combinatorial counting.
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 2015 paper set more problems on divisors and units digits of powers of 2, strictly-increasing digit counting, cylinder surface area, and divisibility tests.
2015 AMC 10 main topic areas, weights and emphasis.
Evaluation, quadratics, word and speed problems; about 31%.
Square perimeter, triangle area, cylinder surface area; about 24%.
Divisibility, remainders, GCD and divisor counts of powers; about 15%.
Coin outcomes, combinations and strictly-increasing counting; about 20%.
Classical probability and dice sums; about 10%.
2015 AMC 10-style mock questions (Basic · Medium · Hard) — submit to grade and view step-by-step solutions.
If x = 3, what is the value of 3x2 + 5x - 1?
Correct answer: C
Substitute x = 3: 3(3)2 + 5(3) - 1 = 27 + 15 - 1 = 41. Answer C. Key: direct substitution.The sum of three consecutive integers is 96. What is the largest?
Correct answer: C
Let the middle integer be n: 3n = 96, so n = 32 and the largest is 33. Answer C. Key: model consecutive integers by their middle.How many positive divisors does 256 have?
Correct answer: B
256 = 28, so the number of divisors is 8+1 = 9. Answer B. Key: divisor count of a prime power.A large 5×5 square is built from 25 unit squares. What is its outer perimeter (in unit lengths)?
Correct answer: B
The 5×5 large square has side length 5, so the perimeter = 4×5 = 20. Answer B. (25 is the number of unit squares — do not confuse.) Key: square perimeter formula.An item is marked up 40% above cost to a price of $98. What was the cost?
Correct answer: C
cost × 1.4 = 98, so cost = 98 / 1.4 = 70. Answer C. Key: price = cost × (1 + markup).A fair six-sided die is rolled once. What is the probability of rolling a perfect square (1 or 4)?
Correct answer: B
Perfect squares up to 6 are 1 and 4 (2 of 6), so the probability is 2/6 = 1/3. Answer B. Key: classical probability = favorable / total.Five coins are tossed at once. How many heads/tails outcomes are possible?
Correct answer: C
Each coin has 2 outcomes, so 5 coins give 25 = 32. Answer C. Key: independent outcomes multiply.What is the remainder when 2015 is divided by 11?
Correct answer: C
11 × 183 = 2013, and 2015 - 2013 = 2, so the remainder is 2. Answer C. Key: division with remainder.If 5x - 4 = 26, what is x?
Correct answer: B
5x = 26 + 4 = 30, so x = 6. Answer B. Key: isolate the variable.A triangle has base 12 and height 6. What is its area?
Correct answer: B
Area = ½×12×6 = 72/2 = 36. Answer B. Key: triangle area formula.If x2 - 15x + 56 = 0, what is the sum of all possible values of x?
Correct answer: D
Factor: (x-7)(x-8) = 0, so x = 7 or 8, and the sum is 15. Answer D. Key: Vieta — sum of roots = -b/a = 15.What is the greatest common divisor of 64 and 96?
Correct answer: C
64 = 26 and 96 = 25×3, so GCD = 25 = 32. Answer C. Key: take the smallest power of each shared prime.A committee of 2 is chosen from 15 people. How many different committees are possible?
Correct answer: B
C(15,2) = (15×14)/(2×1) = 105. Answer B. Key: combinations are order-independent, C(n,k) = n!/(k!(n-k)!).In a triangle, two angles are 13° and 17°. What is the third angle?
Correct answer: C
Triangle angles sum to 180°, so the third angle = 180 - 13 - 17 = 150°. Answer C. Key: triangle angle-sum theorem.The average of 7 numbers is 17. After removing one number, the average of the remaining 6 is 15. What was the removed number?
Correct answer: C
Sum of 7 = 7×17 = 119; sum of 6 = 6×15 = 90; the removed number = 119 - 90 = 29. Answer C. Key: average = sum / count.What is the units digit of 92015?
Correct answer: D
The units digit of powers of 9 cycles as 9, 1 (period 2); odd exponents give a units digit of 9. Since 2015 is odd, the units digit is 9. Answer D. Key: cyclic units digits of powers.One worker can finish a job in 20 hours and another in 30 hours. How long does it take them together?
Correct answer: C
Rates: 1/20 + 1/30 = 3/60 + 2/60 = 5/60 = 1/12 per hour, so together they need 1 / (1/12) = 12 hours. Answer C. Key: combined rate = sum of individual rates.A square and an equilateral triangle have the same perimeter. If the triangle side is 52, what is the square side?
Correct answer: C
Triangle perimeter = 3×52 = 156, so the square side = 156 / 4 = 39. Answer C. Key: equal perimeters split by side count.Two fair six-sided dice are rolled. What is the probability the sum is 5?
Correct answer: D
Sums to 5: (1,4),(2,3),(3,2),(4,1) — 4 outcomes out of 36, so 4/36 = 1/9. Answer D. Key: enumerate ordered dice pairs.A car travels 240 km at 80 km/h and returns at 120 km/h. What is the average speed for the whole trip (km/h)?
Correct answer: C
Outbound time = 240/80 = 3 h; return = 240/120 = 2 h. Total distance 480 km over 5 h gives 480/5 = 96 km/h. Answer C. Key: average speed = total distance / total time, not the average of speeds.How many positive integers less than 100 are divisible by both 9 and 12?
Correct answer: B
Divisible by both 9 and 12 means divisible by LCM(9,12) = 36. The multiples of 36 below 100 are 36 and 72 — 2 of them. Answer B. Key: divisible by both ⟺ divisible by their LCM.Using the digits 1 through 9, choose 4 distinct digits to form a four-digit number whose digits are strictly increasing from left to right. How many such numbers are there?
Correct answer: C
Each choice of 4 distinct digits determines exactly one strictly-increasing four-digit number, so the count is C(9,4) = (9×8×7×6)/(4×3×2×1) = 3024/24 = 126. Answer C. Key: strictly increasing corresponds to a unique combination.A right cylinder has radius 8 and height 2. What is its total surface area? (in terms of π)
Correct answer: C
Surface area = 2πr2 + 2πrh = 2π(82) + 2π(8)(2) = 128π + 32π = 160π. Answer C. Key: cylinder surface = two bases + lateral area.Given x + y = 17 and xy = 72, what is x2 + y2?
Correct answer: A
x2 + y2 = (x+y)2 - 2xy = 172 - 2×72 = 289 - 144 = 145. Answer A. Key: identity linking sum of squares to sum and product.In how many ways can 20 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 = 20. For a=1: 9 ways — (1,1,18) to (1,9,10); a=2: 8 ways — (2,2,16) to (2,9,9); a=3: 6 ways — (3,3,14),(3,4,13),(3,5,12),(3,6,11),(3,7,10),(3,8,9); a=4: 5 ways — (4,4,12),(4,5,11),(4,6,10),(4,7,9),(4,8,8); a=5: 3 ways — (5,5,10),(5,6,9),(5,7,8); a=6: 2 ways — (6,6,8),(6,7,7). Total 33. 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 2015 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 2015 AMC 10 A/B paper.
Finish all 25 within 75 minutes; tackle basics and medium first, saving the last 15 minutes for hard ones.
A number pk has k+1 divisors; pkqj has (k+1)(j+1).
Choosing k of n items and ordering them strictly increasing gives exactly C(n,k).
Odd/even powers of 9 end in 9/1; a power of 2 has (exponent + 1) divisors.
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 2015 AMC 10 papers and answers.
Scan to add the advisor for 2015 AMC 10 A/B past papers, answer keys and solutions, plus a custom prep plan.
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