The 2020 AMC 10 Papers A and B saw a slightly higher share of number-theory divisibility and geometric computation, with foundational algebra-equation and permutation-combination usage throughout, and comprehensive categorization-counting and divisibility-test items in the back half testing integrated application. Scan for the full papers and answer keys.
2020 AMC 10 A/B paper overview and exam highlights.
The 2020 AMC 10 was held in November 2020 in two papers (A and B), with divisibility in number theory and computational geometry taking a slightly larger share.
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 2020 paper focused on basic use of algebraic equations and permutations/combinations, with mid-to-late problems combining casework counting and divisibility tests.
2020 AMC 10 main topic areas, weights and emphasis.
Evaluation, Vieta, word and speed problems; about 26%.
Rectangle perimeter, circle circumference, triangles and cylinder surface area; about 25%.
Divisibility, remainders, GCD and units digits of powers; about 19%.
Permutations, combinations and counting with zero; about 20%.
Classical probability and dice sums; about 10%.
2020 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 4x2 - x + 2?
Correct answer: C
Substitute x = 3: 4(3)2 - 3 + 2 = 36 - 3 + 2 = 35. Answer C. Key: direct substitution.The sum of three consecutive integers is 90. What is the largest?
Correct answer: C
Let the middle integer be n: 3n = 90, so n = 30 and the largest is 31. Answer C. Key: model consecutive integers by their middle.How many positive divisors does 48 have?
Correct answer: C
48 = 24×3, so the number of divisors is (4+1)(1+1) = 10. Answer C. Key: divisor-count formula.A rectangle has length 13 and width 3. What is its perimeter?
Correct answer: B
Perimeter = 2(13 + 3) = 2×16 = 32. Answer B. (39 is the area — do not confuse.) Key: rectangle perimeter formula.An item is marked up 50% above cost to a price of $90. What was the cost?
Correct answer: C
cost × 1.5 = 90, so cost = 90 / 1.5 = 60. Answer C. Key: price = cost × (1 + markup).A fair six-sided die is rolled once. What is the probability of rolling at least 5 (5 or 6)?
Correct answer: B
Outcomes at least 5 are 5 and 6 (2 of 6), so the probability is 2/6 = 1/3. Answer B. Key: classical probability = favorable / total.In how many ways can 7 different books be arranged in a row?
Correct answer: C
Permutations of 7 distinct items: 7! = 7×6×5×4×3×2×1 = 5040. Answer C. Key: n distinct items have n! arrangements.What is the remainder when 2020 is divided by 5?
Correct answer: A
2020 ends in 0, so it is divisible by 5 and the remainder is 0. Answer A. Key: divisibility-by-5 test.If 9 - 2x = 1, what is x?
Correct answer: C
2x = 9 - 1 = 8, so x = 4. Answer C. Key: isolate the variable.A circle has diameter 28. What is its circumference? (Use π ≈ 22/7)
Correct answer: B
Circumference = π × diameter = (22/7) × 28 = 22 × 4 = 88. Answer B. Key: circle circumference = πd.If x2 - 11x + 30 = 0, what is the sum of all possible values of x?
Correct answer: D
Factor: (x-5)(x-6) = 0, so x = 5 or 6, and the sum is 11. Answer D. Key: Vieta — sum of roots = -b/a = 11.What is the greatest common divisor of 40 and 100?
Correct answer: B
40 = 23×5 and 100 = 22×52, so GCD = 22×5 = 20. Answer B. Key: take the smallest power of each shared prime.A committee of 2 is chosen from 10 people. How many different committees are possible?
Correct answer: B
C(10,2) = (10×9)/(2×1) = 45. Answer B. Key: combinations are order-independent, C(n,k) = n!/(k!(n-k)!).In a triangle, two angles are 20° and 50°. What is the third angle?
Correct answer: D
Triangle angles sum to 180°, so the third angle = 180 - 20 - 50 = 110°. Answer D. Key: triangle angle-sum theorem.The average of 8 numbers is 14. After removing one number, the average of the remaining 7 is 13. What was the removed number?
Correct answer: C
Sum of 8 = 8×14 = 112; sum of 7 = 7×13 = 91; the removed number = 112 - 91 = 21. Answer C. Key: average = sum / count.What is the units digit of 92020?
Correct answer: A
The units digit of powers of 9 cycles as 9, 1 (period 2); even exponents give a units digit of 1. Since 2020 is even, the units digit is 1. Answer A. Key: cyclic units digits of powers.One worker can finish a job in 9 hours and another in 18 hours. How long does it take them together?
Correct answer: C
Rates: 1/9 + 1/18 = 2/18 + 1/18 = 3/18 = 1/6 per hour, so together they need 1 / (1/6) = 6 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 28, what is the square side?
Correct answer: C
Triangle perimeter = 3×28 = 84, so the square side = 84 / 4 = 21. Answer C. Key: equal perimeters split by side count.Two fair six-sided dice are rolled. What is the probability the sum is 11?
Correct answer: A
Sums to 11: (5,6),(6,5) — 2 outcomes out of 36, so 2/36 = 1/18. Answer A. Key: enumerate ordered dice pairs.A car travels 360 km at 60 km/h and returns at 90 km/h. What is the average speed for the whole trip (km/h)?
Correct answer: C
Outbound time = 360/60 = 6 h; return = 360/90 = 4 h. Total distance 720 km over 10 h gives 720/10 = 72 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 6 and 9?
Correct answer: B
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 B. Key: divisible by both ⟺ divisible by their LCM.Using the digits 0, 1, 2, 3, 4, 5 (each at most once), how many three-digit numbers can be formed?
Correct answer: B
Hundreds digit cannot be 0: 5 choices; tens 5 remaining (including 0); units 4. Total 5×5×4 = 100. Answer B. Key: place-by-place counting with a non-zero leading digit.A right cylinder has radius 3 and height 10. What is its total surface area? (in terms of π)
Correct answer: C
Surface area = 2πr2 + 2πrh = 2π(32) + 2π(3)(10) = 18π + 60π = 78π. Answer C. Key: cylinder surface = two bases + lateral area.Given x + y = 12 and xy = 35, what is x2 + y2?
Correct answer: C
x2 + y2 = (x+y)2 - 2xy = 122 - 2×35 = 144 - 70 = 74. Answer C. Key: identity linking sum of squares to sum and product.In how many ways can 15 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 = 15. For a=1: 7 ways — (1,1,13) to (1,7,7); a=2: 5 ways — (2,2,11),(2,3,10),(2,4,9),(2,5,8),(2,6,7); a=3: 4 ways — (3,3,9),(3,4,8),(3,5,7),(3,6,6); a=4: 2 ways — (4,4,7),(4,5,6); a=5: 1 way — (5,5,5). Total 19. 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 2020 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 2020 AMC 10 A/B paper.
Finish all 25 within 75 minutes, moving in order; flag hard ones and return to them.
Master the tests for 2, 3, 4, 5, 6, 8, 9, and 11 to count multiples quickly.
A three-digit number cannot start with 0; count by place value to avoid omissions.
Keep cylinder surface area and the sum-of-squares identity at hand and substitute to save time.
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 2020 AMC 10 papers and answers.
Scan to add the advisor for 2020 AMC 10 A/B past papers, answer keys and solutions, plus a custom prep plan.
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