The 2016 AMC 10 Papers A and B balanced algebra with geometry, with rectangle-perimeter, units-digit (constant units digit of 5), permutation-combination and divisibility-counting problems, stressing fluency with core formulas and computation speed. Scan for the full papers and answer keys.
2016 AMC 10 A/B paper overview and exam highlights.
The 2016 AMC 10 was held in November 2016 in two papers (A and B), fairly balanced between algebra and geometry.
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 2016 paper set more problems on rectangle perimeter, units digits of powers (the fixed digit of 5), permutations/combinations, and divisibility counting, stressing fluency with core formulas.
2016 AMC 10 main topic areas, weights and emphasis.
Evaluation, quadratics, word and speed problems; about 28%.
Rectangle perimeter, triangle area, circles and cylinder surface area; about 25%.
Divisibility, remainders, GCD and units digits of powers (incl. the fixed digit of 5); about 17%.
Permutations, combinations and coin-outcome counting; about 20%.
Classical probability and dice sums; about 10%.
2016 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 2x3 - x + 1?
Correct answer: C
Substitute x = 3: 2(3)3 - 3 + 1 = 2×27 - 3 + 1 = 54 - 3 + 1 = 52. Answer C. Key: direct substitution.The sum of three consecutive integers is 75. What is the largest?
Correct answer: C
Let the middle integer be n: 3n = 75, so n = 25 and the largest is 26. Answer C. Key: model consecutive integers by their middle.How many positive divisors does 144 have?
Correct answer: B
144 = 24×32, so the number of divisors is (4+1)(2+1) = 15. Answer B. Key: divisor-count formula.A rectangle has length 11 and width 7. What is its perimeter?
Correct answer: B
Perimeter = 2(11 + 7) = 2×18 = 36. Answer B. (77 is the area — do not confuse.) Key: rectangle perimeter formula.An item is marked up 25% above cost to a price of $50. What was the cost?
0Correct answer: C
cost × 1.25 = 50, so cost = 50 / 1.25 = 40. Answer C. Key: price = cost × (1 + markup).A fair six-sided die is rolled once. What is the probability of rolling a multiple of 3 (3 or 6)?
Correct answer: B
Multiples of 3 are 3 and 6 (2 of 6), so the probability is 2/6 = 1/3. Answer B. Key: classical probability = favorable / total.Two coins are tossed at once. How many heads/tails outcomes are possible?
Correct answer: C
Each coin has 2 outcomes, so 2 coins give 22 = 4. Answer C. Key: independent outcomes multiply.What is the remainder when 2016 is divided by 13?
Correct answer: B
13 × 155 = 2015, and 2016 - 2015 = 1, so the remainder is 1. Answer B. Key: division with remainder.If 4x + 5 = 17, what is x?
Correct answer: B
4x = 17 - 5 = 12, so x = 3. Answer B. Key: isolate the variable.A triangle has base 15 and height 6. What is its area?
Correct answer: B
Area = ½×15×6 = 90/2 = 45. Answer B. Key: triangle area formula.If x2 - 14x + 48 = 0, what is the sum of all possible values of x?
Correct answer: D
Factor: (x-6)(x-8) = 0, so x = 6 or 8, and the sum is 14. Answer D. Key: Vieta — sum of roots = -b/a = 14.What is the greatest common divisor of 52 and 78?
Correct answer: B
52 = 22×13 and 78 = 2×3×13, so GCD = 2×13 = 26. Answer B. Key: take the smallest power of each shared prime.A committee of 2 is chosen from 14 people. How many different committees are possible?
Correct answer: B
C(14,2) = (14×13)/(2×1) = 91. Answer B. Key: combinations are order-independent, C(n,k) = n!/(k!(n-k)!).In a triangle, two angles are 28° and 52°. What is the third angle?
Correct answer: B
Triangle angles sum to 180°, so the third angle = 180 - 28 - 52 = 100°. Answer B. Key: triangle angle-sum theorem.The average of 8 numbers is 16. After removing one number, the average of the remaining 7 is 15. What was the removed number?
Correct answer: C
Sum of 8 = 8×16 = 128; sum of 7 = 7×15 = 105; the removed number = 128 - 105 = 23. Answer C. Key: average = sum / count.What is the units digit of 52016?
Correct answer: D
Any positive power of 5 ends in 5 (51 = 5, 52 = 25, …). Answer D. Key: the units digit of powers of 5 is fixed.Two workers each need 16 hours alone to finish a job. How long do they need together?
Correct answer: C
Each rate is 1/16, so combined = 1/16 + 1/16 = 2/16 = 1/8 per hour, needing 1 / (1/8) = 8 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 40, what is the square side?
Correct answer: C
Triangle perimeter = 3×40 = 120, so the square side = 120 / 4 = 30. Answer C. Key: equal perimeters split by side count.Two fair six-sided dice are rolled. What is the probability the sum is 6?
Correct answer: E
Sums to 6: (1,5),(2,4),(3,3),(4,2),(5,1) — 5 outcomes out of 36, so 5/36. Answer E. 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: C
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 C. Key: average speed = total distance / total time, not the average of speeds.How many positive integers less than 100 are divisible by both 8 and 14?
Correct answer: A
Divisible by both 8 and 14 means divisible by LCM(8,14) = 56. The only multiple of 56 below 100 is 56 itself — 1 of them. Answer A. Key: divisible by both ⟺ divisible by their LCM.From 8 distinct objects, 3 are chosen. How many selections are possible?
Correct answer: C
C(8,3) = (8×7×6)/(3×2×1) = 336/6 = 56. Answer C. Key: combinations are order-independent, C(n,k) = n!/(k!(n-k)!).A right cylinder has radius 3 and height 2. What is its total surface area? (in terms of π)
Correct answer: C
Surface area = 2πr2 + 2πrh = 2π(32) + 2π(3)(2) = 18π + 12π = 30π. Answer C. Key: cylinder surface = two bases + lateral area.Given x + y = 16 and xy = 63, what is x2 + y2?
Correct answer: A
x2 + y2 = (x+y)2 - 2xy = 162 - 2×63 = 256 - 126 = 130. Answer A. Key: identity linking sum of squares to sum and product.In how many ways can 19 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 = 19. For a=1: 9 ways — (1,1,17) to (1,9,9); a=2: 7 ways — (2,2,15) to (2,8,9); a=3: 6 ways — (3,3,13),(3,4,12),(3,5,11),(3,6,10),(3,7,9),(3,8,8); a=4: 4 ways — (4,4,11),(4,5,10),(4,6,9),(4,7,8); a=5: 3 ways — (5,5,9),(5,6,8),(5,7,7); a=6: 1 way — (6,6,7). Total 30. 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 2016 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 2016 AMC 10 A/B paper.
Finish all 25 within 75 minutes, moving in order; flag hard ones and return to them.
Any power of 5 or 6 ends in that same digit; powers of 2, 3, 7, 8 cycle by period.
Rectangle perimeter = 2(l+w), area = l×w; triangle area = ½·base·height — do not mix them.
Decide ordered first, then choose P or C; watch constraints such as a non-zero leading digit.
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 2016 AMC 10 papers and answers.
Scan to add the advisor for 2016 AMC 10 A/B past papers, answer keys and solutions, plus a custom prep plan.
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