The 2022 AMC 10 Papers A and B covered all five blocks — algebra, geometry, number theory, combinatorics and probability — with frequent factoring, permutation-combination and units-digit problems, and a geometry block stressing quick perimeter and area computation. Scan for the full papers and answer keys.
2022 AMC 10 A/B paper overview and exam highlights.
The 2022 AMC 10 was held in November 2022 in two papers (A and B), covering all five areas: algebra, geometry, number theory, combinatorics, and probability.
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 2022 paper set more problems on factoring, permutations and combinations, and units digits of powers, with geometry tilted toward quick perimeter and area computation.
2022 AMC 10 main topic areas, weights and emphasis.
Evaluation, Vieta, word and speed problems; about 27%.
Rectangle perimeter, circle area and circumference, triangles and cylinders; about 24%.
Divisibility, remainders, GCD and units digits of powers; about 17%.
Permutations, combinations and ordered counting; about 21%.
Classical probability and dice sums; about 11%.
2022 AMC 10-style mock questions (Basic · Medium · Hard) — submit to grade and view step-by-step solutions.
If x = 6, what is the value of x2 - 4x + 7?
Correct answer: C
Substitute x = 6: 62 - 4(6) + 7 = 36 - 24 + 7 = 19. Answer C. Key: direct substitution.The sum of three consecutive integers is 66. What is the largest?
Correct answer: D
Let the middle integer be n: 3n = 66, so n = 22 and the largest is 23. Answer D. Key: model consecutive integers by their middle.How many positive divisors does 36 have?
Correct answer: D
36 = 22×32, so the number of divisors is (2+1)(2+1) = 9. Answer D. Key: divisor-count formula.A rectangle has length 10 and width 4. What is its perimeter?
Correct answer: B
Perimeter = 2(10 + 4) = 28. Answer B. (40 is the area — do not confuse.) Key: rectangle perimeter formula.An item is marked up 30% above cost to a price of $91. What was the cost?
Correct answer: C
cost × 1.3 = 91, so cost = 91 / 1.3 = 70. Answer C. Key: price = cost × (1 + markup).A fair six-sided die is rolled once. What is the probability of rolling a prime number (2, 3, or 5)?
Correct answer: C
Prime outcomes are 2, 3, 5 (3 of 6), so the probability is 3/6 = 1/2. Answer C. Key: classical probability = favorable / total.In how many ways can 6 different books be arranged in a row?
Correct answer: C
Permutations of 6 distinct items: 6! = 6×5×4×3×2×1 = 720. Answer C. Key: n distinct items have n! arrangements.What is the remainder when 2022 is divided by 6?
Correct answer: A
6 × 337 = 2022, so the remainder is 0 — 2022 is divisible by 6. Answer A. Key: division with remainder.If 6x + 5 = 41, what is x?
Correct answer: D
6x = 41 - 5 = 36, so x = 6. Answer D. Key: isolate the variable.A circle has radius 21. What is its circumference? (Use π ≈ 22/7)
Correct answer: B
Circumference = 2πr = 2×(22/7)×21 = 44×3 = 132. Answer B. Key: circle circumference = 2πr.If x2 - 9x + 20 = 0, what is the sum of all possible values of x?
Correct answer: D
Factor: (x-4)(x-5) = 0, so x = 4 or 5, and the sum is 9. Answer D. Key: Vieta — sum of roots = -b/a = 9.What is the greatest common divisor of 54 and 90?
Correct answer: C
54 = 2×33 and 90 = 2×32×5, so GCD = 2×32 = 18. Answer C. Key: take the smallest power of each shared prime.A committee of 2 is chosen from 8 people. How many different committees are possible?
Correct answer: B
C(8,2) = (8×7)/(2×1) = 28. Answer B. Key: combinations are order-independent, C(n,k) = n!/(k!(n-k)!).In a triangle, two angles are 55° and 85°. What is the third angle?
Correct answer: C
Triangle angles sum to 180°, so the third angle = 180 - 55 - 85 = 40°. Answer C. Key: triangle angle-sum theorem.The average of 5 numbers is 22. After removing one number, the average of the remaining 4 is 20. What was the removed number?
Correct answer: C
Sum of 5 = 5×22 = 110; sum of 4 = 4×20 = 80; the removed number = 110 - 80 = 30. Answer C. Key: average = sum / count.What is the units digit of 42022?
Correct answer: C
The units digit of powers of 4 cycles as 4, 6 (period 2); even exponents give a units digit of 6. Since 2022 is even, the units digit is 6. Answer C. Key: cyclic units digits of powers.Two workers each need 8 hours alone to finish a job. How long do they need together?
Correct answer: B
Each rate is 1/8, so combined = 1/8 + 1/8 = 2/8 = 1/4 per hour, needing 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 20, what is the square side?
Correct answer: C
Triangle perimeter = 3×20 = 60, so the square side = 60 / 4 = 15. 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: B
Sums to 5: (1,4),(2,3),(3,2),(4,1) — 4 outcomes out of 36, so 4/36 = 1/9. Answer B. Key: enumerate ordered dice pairs.A car travels 150 km at 50 km/h and returns at 75 km/h. What is the average speed for the whole trip (km/h)?
Correct answer: B
Outbound time = 150/50 = 3 h; return = 150/75 = 2 h. Total distance 300 km over 5 h gives 300/5 = 60 km/h. Answer B. Key: average speed = total distance / total time, not the average of speeds.How many positive integers less than 100 are divisible by both 5 and 8?
Correct answer: B
Divisible by both 5 and 8 means divisible by LCM(5,8) = 40. The multiples of 40 below 100 are 40 and 80 — 2 of them. Answer B. Key: divisible by both ⟺ divisible by their LCM.Using the digits 1, 2, 3, 4, 5 (each at most once), how many two-digit numbers can be formed?
Correct answer: B
Tens digit 5 choices, units 4, giving 5×4 = 20. Answer B. Key: permutations P(5,2) = 5!/(5-2)!.A right cylinder has radius 2 and height 5. What is its total surface area? (in terms of π)
Correct answer: C
Surface area = 2πr2 + 2πrh = 2π(22) + 2π(2)(5) = 8π + 20π = 28π. Answer C. Key: cylinder surface = two bases + lateral area.Given x + y = 10 and xy = 24, what is x2 + y2?
Correct answer: C
x2 + y2 = (x+y)2 - 2xy = 102 - 2×24 = 100 - 48 = 52. Answer C. Key: identity linking sum of squares to sum and product.In how many ways can 13 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 = 13. For a=1: 6 ways — (1,1,11),(1,2,10),(1,3,9),(1,4,8),(1,5,7),(1,6,6); a=2: 4 ways — (2,2,9),(2,3,8),(2,4,7),(2,5,6); a=3: 3 ways — (3,3,7),(3,4,6),(3,5,5); a=4: 1 way — (4,4,5). Total 14. 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 2022 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 2022 AMC 10 A/B paper.
Finish all 25 within 75 minutes: do the types you trust first, flag the hard ones, and sweep back at the end.
Memorize the units-digit cycles of 2, 3, 4, 7, 8, 9; decide by the remainder in one step.
Tell permutation from combination, ordered from unordered, before applying a formula.
Keep rectangle perimeter, circle area/circumference, and cylinder surface area at hand; do not mix area with perimeter.
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 2022 AMC 10 papers and answers.
Scan to add the advisor for 2022 AMC 10 A/B past papers, answer keys and solutions, plus a custom prep plan.
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