The 2018 AMC 10 Papers A and B were overall balanced in algebraic computation and geometric calculation, with triangle-area, units-digit (including the constant units digit of 6), permutation-combination and divisibility-counting problems concentrated in the back half, demanding computational steadiness. Scan for the full papers and answer keys.
2018 AMC 10 A/B paper overview and exam highlights.
The 2018 AMC 10 was held in November 2018 in two papers (A and B), balanced overall between algebra and computational geometry.
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 (Paper A).
The 2018 paper concentrated on triangle area, units digits of powers (including the fixed digit of 6), permutations/combinations, and divisibility counting.
2018 AMC 10 main topic areas, weights and emphasis.
Evaluation, Vieta, word and speed problems; about 28%.
Triangle area, circle circumference, rectangles and cylinders; about 26%.
Divisibility, remainders, GCD and units digits of powers; about 16%.
Permutations, combinations and ordered selection; about 20%.
Classical probability and dice sums; about 10%.
2018 AMC 10-style mock questions (Basic · Medium · Hard) — submit to grade and view step-by-step solutions.
If x = 5, what is the value of 3x2 - 2x - 1?
Correct answer: C
Substitute x = 5: 3(5)2 - 2(5) - 1 = 75 - 10 - 1 = 64. Answer C. Key: direct substitution.The sum of four consecutive integers is 110. What is the largest?
Correct answer: D
Let the smallest be n: n+(n+1)+(n+2)+(n+3) = 4n+6 = 110, so 4n = 104, n = 26, and the largest is 29. Answer D. Key: model a consecutive run by its first term.How many positive divisors does 64 have?
Correct answer: B
64 = 26, so the number of divisors is 6+1 = 7. Answer B. Key: divisor count of a prime power.A rectangle has length 14 and width 5. What is its perimeter?
Correct answer: B
Perimeter = 2(14 + 5) = 2×19 = 38. Answer B. (70 is the area — do not confuse.) Key: rectangle perimeter formula.An item is marked up 35% above cost to a price of $81. What was the cost?
Correct answer: C
cost × 1.35 = 81, so cost = 81 / 1.35 = 60. Answer C. Key: price = cost × (1 + markup).A fair six-sided die is rolled once. What is the probability of rolling exactly 3?
Correct answer: A
Only one face shows 3, so the probability is 1/6. Answer A. Key: classical probability = favorable / total.From A, B, C, D, choose 2 letters to form a two-letter code (no repeats). How many codes?
Correct answer: C
P(4,2) = 4×3 = 12. Answer C. Key: ordered selection uses permutations.What is the remainder when 2018 is divided by 9?
Correct answer: C
The digit sum is 2+0+1+8 = 11, and 11 mod 9 = 2, so the remainder is 2. Answer C. Key: digit-sum test for 9.If 8 - 3x = 2, what is x?
Correct answer: B
3x = 8 - 2 = 6, so x = 2. Answer B. Key: isolate the variable.A triangle has base 12 and height 7. What is its area?
Correct answer: B
Area = ½×12×7 = 6×7 = 42. Answer B. Key: triangle area formula.If x2 - 13x + 42 = 0, what is the sum of all possible values of x?
Correct answer: D
Factor: (x-6)(x-7) = 0, so x = 6 or 7, and the sum is 13. Answer D. Key: Vieta — sum of roots = -b/a = 13.What is the greatest common divisor of 66 and 88?
Correct answer: B
66 = 2×3×11 and 88 = 23×11, so GCD = 2×11 = 22. Answer B. Key: take the smallest power of each shared prime.A committee of 2 is chosen from 12 people. How many different committees are possible?
Correct answer: B
C(12,2) = (12×11)/(2×1) = 66. Answer B. Key: combinations are order-independent, C(n,k) = n!/(k!(n-k)!).In a triangle, two angles are 22° and 38°. What is the third angle?
Correct answer: C
Triangle angles sum to 180°, so the third angle = 180 - 22 - 38 = 120°. Answer C. Key: triangle angle-sum theorem.The average of 6 numbers is 17. After removing one number, the average of the remaining 5 is 15. What was the removed number?
Correct answer: D
Sum of 6 = 6×17 = 102; sum of 5 = 5×15 = 75; the removed number = 102 - 75 = 27. Answer D. Key: average = sum / count.What is the units digit of 62018?
Correct answer: D
Any positive power of 6 ends in 6 (61 = 6, 62 = 36, …). Answer D. Key: the units digit of powers of 6 is fixed.One worker can finish a job in 12 hours and another in 4 hours. How long does it take them together?
Correct answer: C
Rates: 1/12 + 1/4 = 1/12 + 3/12 = 4/12 = 1/3 per hour, so together they need 1 / (1/3) = 3 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 24, what is the square side?
Correct answer: C
Triangle perimeter = 3×24 = 72, so the square side = 72 / 4 = 18. Answer C. Key: equal perimeters split by side count.Two fair six-sided dice are rolled. What is the probability the sum is 12?
Correct answer: A
The only sum-12 outcome is (6,6) — 1 out of 36, so 1/36. Answer A. Key: enumerate ordered dice pairs.A car travels 60 km at 20 km/h and returns at 60 km/h. What is the average speed for the whole trip (km/h)?
Correct answer: B
Outbound time = 60/20 = 3 h; return = 60/60 = 1 h. Total distance 120 km over 4 h gives 120/4 = 30 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 7 and 14?
Correct answer: C
Divisible by both 7 and 14 means divisible by LCM(7,14) = 14. The multiples of 14 below 100 are 14, 28, 42, 56, 70, 84, 98 — 7 of them. Answer C. Key: divisible by both ⟺ divisible by their LCM.From 8 people, a captain and a vice captain are chosen (different people). How many ways?
Correct answer: C
Captain 8 choices, vice captain 7, giving P(8,2) = 8×7 = 56. Answer C. Key: ordered selection uses permutations.A right cylinder has radius 5 and height 1. What is its total surface area? (in terms of π)
Correct answer: C
Surface area = 2πr2 + 2πrh = 2π(52) + 2π(5)(1) = 50π + 10π = 60π. Answer C. Key: cylinder surface = two bases + lateral area.Given x + y = 14 and xy = 48, what is x2 + y2?
Correct answer: C
x2 + y2 = (x+y)2 - 2xy = 142 - 2×48 = 196 - 96 = 100. Answer C. Key: identity linking sum of squares to sum and product.In how many ways can 17 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 = 17. For a=1: 8 ways — (1,1,15) to (1,8,8); a=2: 6 ways — (2,2,13) to (2,7,8); a=3: 5 ways — (3,3,11),(3,4,10),(3,5,9),(3,6,8),(3,7,7); a=4: 3 ways — (4,4,9),(4,5,8),(4,6,7); a=5: 2 ways — (5,5,7),(5,6,6). Total 24. 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 2018 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 2018 AMC 10 A/B paper.
Finish all 25 within 75 minutes; skip hard ones and bank the solvable ones first.
Any power of 6 ends in 6; powers of 2, 3, 7, 8 cycle by period.
Keep triangle area = ½·base·height and rectangle area = length×width at hand.
Decide ordered first, then choose P or C; avoid extra factorials.
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 2018 AMC 10 papers and answers.
Scan to add the advisor for 2018 AMC 10 A/B past papers, answer keys and solutions, plus a custom prep plan.
Note: Name + School + Grade + Year
