The 2017 AMC 10 Papers A and B spread broadly across algebraic evaluation and counting problems, with triangle-area, coin-and-subset counting, units-digit and average-speed problems in the back half, deepening the demand on categorization and systematic enumeration. Scan for the full papers and answer keys.
2017 AMC 10 A/B paper overview and exam highlights.
The 2017 AMC 10 was held in November 2017 in two papers (A and B), with problems spread across algebraic evaluation and 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 100–105 (Paper A).
The 2017 paper set more problems on triangle area, coin and subset counting, units digits of powers, and average speed, stressing casework and enumeration.
2017 AMC 10 main topic areas, weights and emphasis.
Evaluation, Vieta, word and speed problems; about 30%.
Triangle area, rectangle perimeter, circles and cylinders; about 24%.
Divisibility, remainders, GCD and units digits of powers; about 15%.
Coin outcomes, subsets, permutations and combinations; about 21%.
Classical probability and dice sums; about 10%.
2017 AMC 10-style mock questions (Basic · Medium · Hard) — submit to grade and view step-by-step solutions.
If x = 2, what is the value of 2x3 - x2 + 3?
Correct answer: C
Substitute x = 2: 2(2)3 - 22 + 3 = 16 - 4 + 3 = 15. Answer C. Key: direct substitution.The sum of three consecutive integers is 84. What is the largest?
Correct answer: C
Let the middle integer be n: 3n = 84, so n = 28 and the largest is 29. Answer C. Key: model consecutive integers by their middle.How many positive divisors does 49 have?
Correct answer: A
49 = 72, so the number of divisors is 2+1 = 3 (namely 1,7,49). Answer A. Key: divisor count of a prime power.A rectangle has length 8 and width 3. What is its perimeter?
Correct answer: B
Perimeter = 2(8 + 3) = 2×11 = 22. Answer B. (24 is the area — do not confuse.) Key: rectangle perimeter formula.An item is marked up 45% above cost to a price of $87. What was the cost?
Correct answer: C
cost × 1.45 = 87, so cost = 87 / 1.45 = 60. Answer C. Key: price = cost × (1 + markup).A fair six-sided die is rolled once. What is the probability of rolling 1 or 6?
Correct answer: B
Faces 1 and 6 (2 of 6), so the probability is 2/6 = 1/3. Answer B. Key: classical probability = favorable / total.Three coins are tossed at once. How many heads/tails outcomes are possible?
Correct answer: C
Each coin has 2 outcomes, so 3 coins give 23 = 8. Answer C. Key: independent outcomes multiply.What is the remainder when 2017 is divided by 12?
Correct answer: B
12 × 168 = 2016, and 2017 - 2016 = 1, so the remainder is 1. Answer B. Key: division with remainder.If 2x + 11 = 21, what is x?
Correct answer: C
2x = 21 - 11 = 10, so x = 5. Answer C. Key: isolate the variable.A triangle has base 16 and height 3. What is its area?
Correct answer: B
Area = ½×16×3 = 8×3 = 24. Answer B. Key: triangle area formula.If x2 - 12x + 35 = 0, what is the sum of all possible values of x?
Correct answer: D
Factor: (x-5)(x-7) = 0, so x = 5 or 7, and the sum is 12. Answer D. Key: Vieta — sum of roots = -b/a = 12.What is the greatest common divisor of 75 and 100?
Correct answer: D
75 = 3×52 and 100 = 22×52, so GCD = 52 = 25. Answer D. Key: take the smallest power of each shared prime.A committee of 2 is chosen from 13 people. How many different committees are possible?
Correct answer: B
C(13,2) = (13×12)/(2×1) = 78. Answer B. Key: combinations are order-independent, C(n,k) = n!/(k!(n-k)!).In a triangle, two angles are 15° and 25°. What is the third angle?
Correct answer: C
Triangle angles sum to 180°, so the third angle = 180 - 15 - 25 = 140°. Answer C. Key: triangle angle-sum theorem.The average of 7 numbers is 16. After removing one number, the average of the remaining 6 is 15. What was the removed number?
Correct answer: C
Sum of 7 = 7×16 = 112; sum of 6 = 6×15 = 90; the removed number = 112 - 90 = 22. Answer C. Key: average = sum / count.What is the units digit of 22017?
Correct answer: A
The units digit of powers of 2 cycles as 2, 4, 8, 6 (period 4). Since 2017 = 4×504 + 1, the remainder is 1, corresponding to the 1st value, so the units digit is 2. Answer A. Key: cyclic units digits of powers.Two workers each need 14 hours alone to finish a job. How long do they need together?
Correct answer: D
Each rate is 1/14, so combined = 1/14 + 1/14 = 2/14 = 1/7 per hour, needing 1 / (1/7) = 7 hours. Answer D. Key: combined rate = sum of individual rates.A square and an equilateral triangle have the same perimeter. If the triangle side is 36, what is the square side?
Correct answer: C
Triangle perimeter = 3×36 = 108, so the square side = 108 / 4 = 27. Answer C. Key: equal perimeters split by side count.Two fair six-sided dice are rolled. What is the probability the sum is 3?
Correct answer: B
Sums to 3: (1,2),(2,1) — 2 outcomes out of 36, so 2/36 = 1/18. Answer B. Key: enumerate ordered dice pairs.A car travels 60 km at 20 km/h and returns at 30 km/h. What is the average speed for the whole trip (km/h)?
Correct answer: A
Outbound time = 60/20 = 3 h; return = 60/30 = 2 h. Total distance 120 km over 5 h gives 120/5 = 24 km/h. Answer A. 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 14?
Correct answer: B
Divisible by both 6 and 14 means divisible by LCM(6,14) = 42. The multiples of 42 below 100 are 42 and 84 — 2 of them. Answer B. Key: divisible by both ⟺ divisible by their LCM.A set has 4 elements. How many subsets does it have (including the empty set and itself)?
Correct answer: B
An n-element set has 2n subsets, so 24 = 16. Answer B. Key: subset count = 2n.A right cylinder has radius 2 and height 12. What is its total surface area? (in terms of π)
Correct answer: C
Surface area = 2πr2 + 2πrh = 2π(22) + 2π(2)(12) = 8π + 48π = 56π. Answer C. Key: cylinder surface = two bases + lateral area.Given x + y = 15 and xy = 56, what is x2 + y2?
Correct answer: A
x2 + y2 = (x+y)2 - 2xy = 152 - 2×56 = 225 - 112 = 113. Answer A. Key: identity linking sum of squares to sum and product.In how many ways can 18 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 = 18. For a=1: 8 ways — (1,1,16) to (1,8,9); a=2: 7 ways — (2,2,14) to (2,8,8); a=3: 5 ways — (3,3,12),(3,4,11),(3,5,10),(3,6,9),(3,7,8); a=4: 4 ways — (4,4,10),(4,5,9),(4,6,8),(4,7,7); a=5: 2 ways — (5,5,8),(5,6,7); a=6: 1 way — (6,6,6). Total 27. 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 2017 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 2017 AMC 10 A/B paper.
Finish all 25 within 75 minutes; do basics and medium first, leaving the last 15 minutes for the hardest.
Distinguish coin outcomes 2n, subsets 2n, permutations P, and combinations C.
Powers of 2, 3, 7 cycle with period 4; locate the result via the exponent remainder.
Triangle area = ½·base·height; do not mix with perimeter or rectangle area.
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 2017 AMC 10 papers and answers.
Scan to add the advisor for 2017 AMC 10 A/B past papers, answer keys and solutions, plus a custom prep plan.
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