The 2019 AMC 10 Papers A and B kept a high share of algebra and combinatorial counting, with triangle-area, circle-circumference, units-digit and permutation-counting problems appearing frequently; the back half emphasized rigorous categorization and enumeration. Scan for the full papers and answer keys.
2019 AMC 10 A/B paper overview and exam highlights.
The 2019 AMC 10 was held in November 2019 in two papers (A and B), keeping a high share of algebra and combinatorial counting.
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 2019 paper set more problems on triangle area, circle circumference, units digits of powers, and permutation counting, with mid-to-late questions stressing rigorous casework.
2019 AMC 10 main topic areas, weights and emphasis.
Evaluation, Vieta, word and speed problems; about 29%.
Triangle area, circle circumference, rectangles and cylinders; about 25%.
Divisibility, remainders, GCD and units digits of powers; about 16%.
Permutations, combinations and circular counting; about 20%.
Classical probability and dice sums; about 10%.
2019 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 2x2 + x - 3?
Correct answer: C
Substitute x = 4: 2(4)2 + 4 - 3 = 32 + 4 - 3 = 33. Answer C. Key: direct substitution.The sum of three consecutive integers is 78. What is the largest?
Correct answer: C
Let the middle integer be n: 3n = 78, so n = 26 and the largest is 27. Answer C. Key: model consecutive integers by their middle.How many positive divisors does 72 have?
Correct answer: D
72 = 23×32, so the number of divisors is (3+1)(2+1) = 12. Answer D. Key: divisor-count formula.A rectangle has length 15 and width 2. What is its perimeter?
Correct answer: C
Perimeter = 2(15 + 2) = 2×17 = 34. Answer C. (30 is the area — do not confuse.) Key: rectangle perimeter formula.An item is marked up 40% above cost to a price of $84. What was the cost?
Correct answer: C
cost × 1.4 = 84, so cost = 84 / 1.4 = 60. Answer C. Key: price = cost × (1 + markup).A fair six-sided die is rolled once. What is the probability of rolling an odd number (1, 3, or 5)?
Correct answer: C
Odd outcomes are 1, 3, 5 (3 of 6), so the probability is 3/6 = 1/2. Answer C. Key: classical probability = favorable / total.From 6 different books, 4 are selected and arranged in a row. How many ways?
Correct answer: C
P(6,4) = 6×5×4×3 = 360. Answer C. Key: permutations P(n,k) = n!/(n-k)!.What is the remainder when 2019 is divided by 7?
Correct answer: D
7 × 288 = 2016, and 2019 - 2016 = 3, so the remainder is 3. Answer D. Key: division with remainder.If 5x - 2 = 23, what is x?
Correct answer: C
5x = 23 + 2 = 25, so x = 5. Answer C. Key: isolate the variable.A triangle has base 10 and height 7. What is its area?
Correct answer: B
Area = ½×base×height = ½×10×7 = 35. Answer B. Key: triangle area formula.If x2 - 10x + 21 = 0, what is the sum of all possible values of x?
Correct answer: D
Factor: (x-3)(x-7) = 0, so x = 3 or 7, and the sum is 10. Answer D. Key: Vieta — sum of roots = -b/a = 10.What is the greatest common divisor of 42 and 98?
Correct answer: B
42 = 2×3×7 and 98 = 2×72, so GCD = 2×7 = 14. Answer B. Key: take the smallest power of each shared prime.A committee of 2 is chosen from 11 people. How many different committees are possible?
Correct answer: B
C(11,2) = (11×10)/(2×1) = 55. Answer B. Key: combinations are order-independent, C(n,k) = n!/(k!(n-k)!).In a triangle, two angles are 33° and 47°. What is the third angle?
Correct answer: C
Triangle angles sum to 180°, so the third angle = 180 - 33 - 47 = 100°. Answer C. Key: triangle angle-sum theorem.The average of 5 numbers is 25. After removing one number, the average of the remaining 4 is 23. What was the removed number?
Correct answer: D
Sum of 5 = 5×25 = 125; sum of 4 = 4×23 = 92; the removed number = 125 - 92 = 33. Answer D. Key: average = sum / count.What is the units digit of 72019?
Correct answer: B
The units digit of powers of 7 cycles as 7, 9, 3, 1 (period 4). Since 2019 = 4×504 + 3, the remainder is 3, corresponding to the 3rd value, so the units digit is 3. Answer B. Key: cyclic units digits of powers.One worker can finish a job in 10 hours and another in 15 hours. How long does it take them together?
Correct answer: D
Rates: 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 per hour, so together they need 1 / (1/6) = 6 hours. Answer D. Key: combined rate = sum of individual rates.A square and an equilateral triangle have the same perimeter. If the triangle side is 32, what is the square side?
Correct answer: C
Triangle perimeter = 3×32 = 96, so the square side = 96 / 4 = 24. Answer C. Key: equal perimeters split by side count.Two fair six-sided dice are rolled. What is the probability the sum is 4?
Correct answer: B
Sums to 4: (1,3),(2,2),(3,1) — 3 outcomes out of 36, so 3/36 = 1/12. Answer B. Key: enumerate ordered dice pairs.A car travels 180 km at 60 km/h and returns at 120 km/h. What is the average speed for the whole trip (km/h)?
Correct answer: C
Outbound time = 180/60 = 3 h; return = 180/120 = 1.5 h. Total distance 360 km over 4.5 h gives 360/4.5 = 80 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 15?
Correct answer: B
Divisible by both 6 and 15 means divisible by LCM(6,15) = 30. The multiples of 30 below 100 are 30, 60, 90 — 3 of them. Answer B. Key: divisible by both ⟺ divisible by their LCM.In how many ways can 5 people sit around a circular table? (rotations are the same)
Correct answer: A
Circular arrangements of n people are (n-1)!, so (5-1)! = 4! = 24. Answer A. Key: fix one person, arrange the rest.A right cylinder has radius 4 and height 4. What is its total surface area? (in terms of π)
Correct answer: C
Surface area = 2πr2 + 2πrh = 2π(42) + 2π(4)(4) = 32π + 32π = 64π. Answer C. Key: cylinder surface = two bases + lateral area.Given x + y = 13 and xy = 42, what is x2 + y2?
Correct answer: C
x2 + y2 = (x+y)2 - 2xy = 132 - 2×42 = 169 - 84 = 85. Answer C. Key: identity linking sum of squares to sum and product.In how many ways can 16 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 = 16. For a=1: 7 ways — (1,1,14) to (1,7,8); a=2: 6 ways — (2,2,12) to (2,7,7); a=3: 4 ways — (3,3,10),(3,4,9),(3,5,8),(3,6,7); a=4: 3 ways — (4,4,8),(4,5,7),(4,6,6); a=5: 1 way — (5,5,6). Total 21. 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 2019 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 2019 AMC 10 A/B paper.
Finish all 25 within 75 minutes; jot a draft on hard ones but secure the basics first.
Keep triangle area = ½·base·height and circle area/circumference at hand to cut derivation.
n people around a table give (n-1)! arrangements; distinguish from n! in a line.
Units digits cycle by the base; locate the result with the exponent remainder.
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 2019 AMC 10 papers and answers.
Scan to add the advisor for 2019 AMC 10 A/B past papers, answer keys and solutions, plus a custom prep plan.
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