The 2024 AMC 10 Papers A and B continued comprehensive coverage of algebraic computation, geometric intuition and combinatorial construction, with frequent number-theory divisibility and units-digit, probability and average-speed word problems; the back half demanded computational accuracy. Scan for the full papers and answer keys.
2024 AMC 10 A/B paper overview and exam highlights.
The 2024 AMC 10 was held in November 2024 in two papers (A and B), continuing a blend of algebraic computation, geometric intuition, and combinatorial construction.
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 cut-off has recently been around 105 (Paper A) and 100 (Paper B).
The 2024 paper set more problems on divisibility, units digits of powers, probability, and average-speed word problems, with mid-to-late questions demanding computational accuracy.
2024 AMC 10 main topic areas, weights and emphasis.
Evaluation, simplification, word and speed problems; about 28%.
Rectangle and circle perimeter/area, triangles and cylinders; about 26%.
Divisibility, remainders, GCD and units digits of powers; about 16%.
Permutations, combinations and ordered counting; about 19%.
Classical probability and dice sums; about 11%.
2024 AMC 10-style mock questions (Basic · Medium · Hard) — submit to grade and view step-by-step solutions.
If x = 4, what is the value of 3x2 - 2x + 5?
Correct answer: D
Substitute x = 4: 3(4)2 - 2(4) + 5 = 48 - 8 + 5 = 45. Answer D. Key: direct substitution.The sum of four consecutive integers is 70. What is the largest?
Correct answer: D
Let the smallest be n: n+(n+1)+(n+2)+(n+3) = 4n+6 = 70, so 4n = 64, n = 16, and the largest is 19. Answer D. Key: model a consecutive run by its first term.How many positive divisors does 30 have?
Correct answer: C
30 = 2×3×5, so the number of divisors is (1+1)(1+1)(1+1) = 8 (namely 1,2,3,5,6,10,15,30). Answer C. Key: divisor-count formula.A rectangle has length 7 and width 4. What is its perimeter?
Correct answer: B
Perimeter = 2(length + width) = 2(7 + 4) = 22. Answer B. (28 is the area — do not confuse.) Key: rectangle perimeter formula.An item is marked up 25% above cost to a price of $75. What was the cost?
Correct answer: C
cost × 1.25 = 75, so cost = 75 / 1.25 = 60. Answer C. Key: price = cost × (1 + markup).A fair six-sided die is rolled once. What is the probability of rolling an even number?
Correct answer: C
Even outcomes are 2, 4, 6 (3 of 6), so the probability is 3/6 = 1/2. Answer C. Key: classical probability = favorable / total.In how many ways can 4 different books be arranged in a row?
Correct answer: D
Permutations of 4 distinct items: 4! = 4×3×2×1 = 24. Answer D. Key: n distinct items have n! arrangements.What is the remainder when 2024 is divided by 8?
Correct answer: A
8 × 253 = 2024, so the remainder is 0 — 2024 is divisible by 8. Answer A. Key: division with remainder.If 2x + 7 = 19, what is x?
Correct answer: D
2x = 19 - 7 = 12, so x = 6. Answer D. Key: isolate the variable.A circle has diameter 14. What is its circumference? (Use π ≈ 22/7)
Correct answer: B
Circumference = π × diameter = (22/7) × 14 = 22 × 2 = 44. Answer B. Key: circle circumference = πd.If x2 - 7x + 12 = 0, what is the sum of all possible values of x?
Correct answer: D
Factor: (x-3)(x-4) = 0, so x = 3 or 4, and the sum is 7. Answer D. Key: Vieta — sum of roots = -b/a = 7.What is the greatest common divisor of 60 and 90?
Correct answer: D
60 = 22×3×5 and 90 = 2×32×5, so GCD = 2×3×5 = 30. Answer D. Key: take the smallest power of each shared prime.A committee of 2 is chosen from 6 people. How many different committees are possible?
Correct answer: C
C(6,2) = (6×5)/(2×1) = 15. Answer C. Key: combinations are order-independent, C(n,k) = n!/(k!(n-k)!).In a triangle, two angles are 35° and 65°. What is the third angle?
Correct answer: C
Triangle angles sum to 180°, so the third angle = 180 - 35 - 65 = 80°. Answer C. Key: triangle angle-sum theorem.The average of 6 numbers is 20. After removing one number, the average of the remaining 5 is 19. What was the removed number?
Correct answer: C
Sum of 6 = 6×20 = 120; sum of 5 = 5×19 = 95; the removed number = 120 - 95 = 25. Answer C. Key: average = sum / count.What is the units digit of 32024?
Correct answer: A
The units digit of powers of 3 cycles as 3, 9, 7, 1 (period 4). Since 2024 = 4×506, the remainder is 0, corresponding to the 4th value, so the units digit is 1. Answer A. Key: cyclic units digits of powers.One worker can finish a job in 4 hours and another in 12 hours. How long does it take them together?
Correct answer: B
Rates: 1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3 per hour, so together they need 1 / (1/3) = 3 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 8, what is the square side?
Correct answer: B
Triangle perimeter = 3×8 = 24, so the square side = 24 / 4 = 6. Answer B. Key: equal perimeters split by side count.Two fair six-sided dice are rolled. What is the probability the sum is 7?
Correct answer: C
Sums to 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) — 6 outcomes out of 36, so 6/36 = 1/6. Answer C. Key: enumerate ordered dice pairs.A car travels 60 km at 30 km/h and returns at 60 km/h. What is the average speed for the whole trip (km/h)?
Correct answer: B
Outbound time = 60/30 = 2 h; return = 60/60 = 1 h. Total distance 120 km over 3 h gives 120/3 = 40 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 4 and 6?
Correct answer: C
Divisible by both 4 and 6 means divisible by LCM(4,6) = 12. The multiples of 12 below 100 are 12, 24, 36, 48, 60, 72, 84, 96 — 8 of them. Answer C. Key: divisible by both ⟺ divisible by their LCM.Using the digits 1, 2, 3, 4 (each at most once), how many three-digit numbers can be formed?
Correct answer: C
Hundreds digit 4 choices, tens 3, units 2, giving 4×3×2 = 24. Answer C. Key: permutations P(4,3) = 4!/(4-3)!.A right cylinder has radius 3 and height 8. What is its total surface area? (in terms of π)
Correct answer: B
Surface area = 2πr2 + 2πrh = 2π(32) + 2π(3)(8) = 18π + 48π = 66π. Answer B. Key: cylinder surface = two bases + lateral area.Given x + y = 8 and xy = 15, what is x2 + y2?
Correct answer: B
x2 + y2 = (x+y)2 - 2xy = 82 - 2×15 = 64 - 30 = 34. Answer B. Key: identity linking sum of squares to sum and product.In how many ways can 11 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 = 11. For a=1: 5 ways — (1,1,9),(1,2,8),(1,3,7),(1,4,6),(1,5,5); a=2: 3 ways — (2,2,7),(2,3,6),(2,4,5); a=3: 2 ways — (3,3,5),(3,4,4). Total 10. 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 2024 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 2024 AMC 10 A/B paper.
Finish all 25 within 75 minutes: go fast first, then steady, and reserve time to recheck the computations of the first 20.
Units digits of powers, divisibility tests, and average speed are error-prone — write each step to limit slips.
File errors by algebra / geometry / number theory / combinatorics / probability and target the weakest module.
Use these mock questions as a warm-up; scan for official past papers to match the real format and difficulty.
Aiming to qualify? Make zero mistakes on basics, a high pass rate on medium, then attack the last 5 step by step.
Frequent questions about the 2024 AMC 10 papers and answers.
Scan to add the advisor for 2024 AMC 10 A/B past papers, answer keys and solutions, plus a custom prep plan.
Note: Name + School + Grade + Year
