The 2025 AMC 10 Papers A and B continued recent trends, emphasizing flexible use of algebra and combinatorics plus computation speed, with function-and-equation, geometric computation, number-theory divisibility and combinatorial-counting problems; some items featured clever categorization and construction. Scan for the full papers and answer keys.
2025 AMC 10 A/B paper overview and exam highlights.
The 2025 AMC 10 was held in November 2025 in two papers (A and B), continuing the recent style with emphasis on flexible use of algebra and combinatorics, plus speed and accuracy.
The format is unchanged: 25 multiple-choice questions, 75 minutes, 150 points max; a blank answer earns 1.5 points and a wrong answer earns 0. The AIME qualification cut-off has recently been around 105 (Paper A) and 99 (Paper B).
The 2025 paper continues to test functions and equations, computational geometry, divisibility in number theory, and combinatorial counting, with several problems requiring careful casework and construction.
2025 AMC 10 main topic areas, weights and emphasis.
Functions and equations, simplification, word problems; about 30%.
Triangles, circles, coordinate geometry, area and volume; about 25%.
Divisibility, divisor counts, modular arithmetic and digit cycles; about 15%.
Permutations and combinations, counting and construction, casework; about 20%.
Classical probability, dice and expectation; about 10%.
2025 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 2x2 - 5x + 1?
Correct answer: A
Substitute x = 3: 2(3)2 - 5(3) + 1 = 18 - 15 + 1 = 4. Answer A. Key: direct substitution.The sum of three consecutive integers is 72. What is the largest?
Correct answer: C
Let the middle integer be n: (n-1) + n + (n+1) = 3n = 72, so n = 24 and the largest is 25. Answer C. Key: model consecutive integers by their middle.How many positive divisors does 12 have?
Correct answer: C
12 = 22 × 3, so the number of divisors is (2+1)(1+1) = 6 (namely 1,2,3,4,6,12). Answer C. Key: divisor-count formula.A rectangle has length 8 and width 5. What is its perimeter?
Correct answer: B
Perimeter = 2(length + width) = 2(8 + 5) = 26. Answer B. (40 is the area — do not confuse.) Key: rectangle perimeter formula.A shirt is marked up 20% above cost to a price of $60. What was the cost?
Correct answer: C
cost × 1.2 = 60, so cost = 60 / 1.2 = 50. Answer C. Key: price = cost × (1 + markup).A fair six-sided die is rolled once. What is the probability of rolling a number greater than 4?
Correct answer: B
Outcomes greater than 4 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 3 different books be arranged in a row?
Correct answer: B
Permutations of 3 distinct items: 3! = 3×2×1 = 6. Answer B. Key: n distinct items have n! arrangements.What is the remainder when 2025 is divided by 7?
Correct answer: C
7 × 289 = 2023, and 2025 - 2023 = 2, so the remainder is 2. Answer C. Key: division with remainder.If 3x + 2 = 17, what is x?
Correct answer: C
3x = 17 - 2 = 15, so x = 5. Answer C. Key: isolate the variable.A circle has radius 7. What is its area? (Use π ≈ 22/7)
Correct answer: C
Area = πr2 = (22/7) × 72 = (22/7) × 49 = 22 × 7 = 154. Answer C. Key: circle area formula.If x2 - 5x + 6 = 0, what is the sum of all possible values of x?
Correct answer: D
Factor: (x-2)(x-3) = 0, so x = 2 or 3, and the sum is 5. Answer D. Key: Vieta — sum of roots = -b/a = 5.What is the greatest common divisor of 84 and 126?
Correct answer: D
84 = 22×3×7 and 126 = 2×32×7, so GCD = 2×3×7 = 42. Answer D. Key: take the smallest power of each shared prime.A committee of 2 is chosen from 5 people. How many different committees are possible?
Correct answer: A
C(5,2) = (5×4)/(2×1) = 10. Answer A. Key: combinations are order-independent, C(n,k) = n!/(k!(n-k)!).In a triangle, two angles are 40° and 75°. What is the third angle?
Correct answer: C
Triangle angles sum to 180°, so the third angle = 180 - 40 - 75 = 65°. Answer C. Key: triangle angle-sum theorem.The average of 5 numbers is 18. After removing one number, the average of the remaining 4 is 16. What was the removed number?
Correct answer: D
Sum of 5 = 5×18 = 90; sum of 4 = 4×16 = 64; the removed number = 90 - 64 = 26. Answer D. Key: average = sum / count.What is the units digit of 72025?
Correct answer: C
The units digit of powers of 7 cycles as 7, 9, 3, 1 (period 4). Since 2025 = 4×506 + 1, the remainder is 1, so the units digit is 7. Answer C. Key: cyclic units digits of powers.One worker can finish a job in 6 hours and another in 3 hours. How long does it take them together?
Correct answer: C
Rates: 1/6 + 1/3 = 1/2 per hour, so together they need 1 / (1/2) = 2 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 12, what is the square side?
Correct answer: C
Triangle perimeter = 3×12 = 36, so the square side = 36 / 4 = 9. Answer C. Key: equal perimeters split by side count.Two fair six-sided dice are rolled. What is the probability the sum is 8?
Correct answer: B
Sums to 8: (2,6),(3,5),(4,4),(5,3),(6,2) — 5 outcomes out of 36, so 5/36. Answer B. Key: enumerate ordered dice pairs.A car travels 120 km at 60 km/h and returns at 40 km/h. What is the average speed for the whole trip (km/h)?
Correct answer: A
Outbound time = 120/60 = 2 h; return = 120/40 = 3 h. Total distance 240 km over 5 h gives 240/5 = 48 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 8?
Correct answer: A
Divisible by both 6 and 8 means divisible by LCM(6,8) = 24. The multiples of 24 below 100 are 24, 48, 72, 96 — 4 of them. Answer A. Key: divisible by both ⟺ divisible by their LCM.How many 3-digit positive integers have all digits distinct and in strictly increasing order (e.g. 257)?
Correct answer: A
Strictly increasing means digits come only from 1-9 (0 cannot appear, or it would lead the number). Choose any 3 of {1,…,9}: C(9,3) = 84, and each set has exactly one increasing order. Answer A. Key: increasing arrangements correspond 1-to-1 with 3-element subsets.A right cylinder has radius 4 and height 6. What is its total surface area? (in terms of π)
Correct answer: B
Surface area = 2πr2 + 2πrh = 2π(42) + 2π(4)(6) = 32π + 48π = 80π. Answer B. Key: cylinder surface = two bases + lateral area.Given x + y = 7 and xy = 11, what is x2 + y2?
Correct answer: A
x2 + y2 = (x+y)2 - 2xy = 72 - 2×11 = 49 - 22 = 27. Answer A. Key: identity linking sum of squares to sum and product.In how many ways can 10 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 = 10. For a=1: 4 ways — (1,1,8),(1,2,7),(1,3,6),(1,4,5); a=2: 3 ways — (2,2,6),(2,3,5),(2,4,4); a=3: 1 way — (3,3,4). Total 8. 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 2025 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 2025 AMC 10 A/B paper.
Complete all 25 questions within 75 minutes to train pacing and time management, avoiding spending too long on any single problem.
Use the topic breakdown and your quiz results to find weak areas in algebra, geometry, and number theory, then focus there.
Medium and hard problems often need casework and construction; drill enumeration that is complete and non-overlapping.
Open the solution for every wrong answer, grasp the reasoning and key concept, and revisit regularly to avoid repeats.
Aiming above 105? Secure all basic and most medium questions first, then tackle the last 5; scan for full papers and 1-on-1 coaching.
Frequent questions about the 2025 AMC 10 papers and answers.
Scan to add the advisor for 2025 AMC 10 A/B past papers, answer keys and solutions, plus a custom prep plan.
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