The 2003 AMC 10 Papers A and B emphasized algebraic evaluation and number-theory divisibility, with dense coverage of factor-counting, work-rate, average-speed and combinatorial-counting problems that raised the bar for accuracy and formula discrimination in the back half. Scan for the full papers and answer keys.
2003 AMC 10 A/B paper overview and exam highlights.
The 2003 AMC 10 was held in November 2003 in two papers (A and B), with algebraic evaluation and divisibility in number theory standing out.
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 2003 paper set more problems on divisor counts, work rates, average speed, and combinatorial counting, combining formulas with careful reading.
2003 AMC 10 main topic areas, weights and emphasis.
Evaluation, quadratics, word and speed problems; about 30%.
Rectangle perimeter, triangle area, cylinder surface area; about 22%.
Divisibility, remainders, GCD and divisor counts; about 18%.
Coin outcomes, combinations and ordered counting; about 20%.
Classical probability and dice sums; about 10%.
2003 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 + 1?
Correct answer: A
Substitute x = 4: 3(4)2 - 2(4) + 1 = 3×16 - 8 + 1 = 48 - 8 + 1 = 41. Answer A. Key: direct substitution.The sum of three consecutive integers is 132. What is the largest?
Correct answer: B
Let the middle integer be n: 3n = 132, so n = 44 and the largest is 45. Answer B. Key: model consecutive integers by their middle.How many positive divisors does 240 have?
Correct answer: C
240 = 24×3×5, so the number of divisors is (4+1)(1+1)(1+1) = 20. Answer C. Key: divisor-count formula.A rectangle has length 12 and width 2. What is its perimeter?
Correct answer: D
Perimeter = 2(12 + 2) = 2×14 = 28. Answer D. (24 is length + width — 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: E
cost × 1.35 = 81, so cost = 81 / 1.35 = 60. Answer E. 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: A
Odd values are 1, 3, 5 (3 of 6), so the probability is 3/6 = 1/2. Answer A. Key: classical probability = favorable / total.Five coins are tossed at once. How many heads/tails outcomes are possible?
Correct answer: B
Each coin has 2 outcomes, so 5 coins give 25 = 32. Answer B. Key: independent outcomes multiply.What is the remainder when 2003 is divided by 9?
Correct answer: C
9 × 222 = 1998, and 2003 - 1998 = 5, so the remainder is 5. Answer C. Key: division with remainder.If 4x + 9 = 33, what is x?
Correct answer: D
4x = 33 - 9 = 24, so x = 6. Answer D. Key: isolate the variable.A triangle has base 14 and height 5. What is its area?
Correct answer: E
Area = ½×14×5 = 70/2 = 35. Answer E. Key: triangle area formula.If x2 - 10x + 24 = 0, what is the sum of all possible values of x?
Correct answer: A
Factor: (x-4)(x-6) = 0, so x = 4 or 6, and the sum is 10. Answer A. Key: Vieta — sum of roots = -b/a = 10.What is the greatest common divisor of 48 and 64?
Correct answer: B
48 = 24×3 and 64 = 26, so GCD = 24 = 16. Answer B. Key: take the smallest power of each shared prime.A committee of 2 is chosen from 27 people. How many different committees are possible?
Correct answer: C
C(27,2) = (27×26)/(2×1) = 351. Answer C. Key: combinations are order-independent, C(n,k) = n!/(k!(n-k)!).In a triangle, two angles are 30° and 70°. What is the third angle?
Correct answer: D
Triangle angles sum to 180°, so the third angle = 180 - 30 - 70 = 80°. Answer D. Key: triangle angle-sum theorem.The average of 8 numbers is 15. After removing one number, the average of the remaining 7 is 13. What was the removed number?
Correct answer: E
Sum of 8 = 8×15 = 120; sum of 7 = 7×13 = 91; the removed number = 120 - 91 = 29. Answer E. Key: average = sum / count.What is the units digit of 72003?
Correct answer: A
The units digit of powers of 7 cycles as 7, 9, 3, 1 (period 4). Since 2003 = 4×500 + 3, the remainder is 3, corresponding to the 3rd value, so the units digit is 3. Answer A. Key: cyclic units digits of powers.One worker can finish a job in 12 hours and another in 36 hours. How long does it take them together?
Correct answer: B
Rates: 1/12 + 1/36 = 3/36 + 1/36 = 4/36 = 1/9 per hour, so together they need 1 / (1/9) = 9 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 84, what is the square side?
Correct answer: C
Triangle perimeter = 3×84 = 252, so the square side = 252 / 4 = 63. Answer C. Key: equal perimeters split by side count.Two fair six-sided dice are rolled. What is the probability the sum is 11?
Correct answer: D
Sums to 11: (5,6),(6,5) — 2 outcomes out of 36, so 2/36 = 1/18. Answer D. Key: enumerate ordered dice pairs.A car travels 60 km at 20 km/h and returns at 30 km/h. What is the average speed for the whole trip (km/h)?
Correct answer: E
Outbound time = 60/20 = 3 h; return = 60/30 = 2 h. Total distance 120 km over 5 h gives 120/5 = 24 km/h. Answer E. 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: A
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 A. Key: divisible by both ⟺ divisible by their LCM.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)!).A right cylinder has radius 5 and height 5. What is its total surface area? (in terms of π)
Correct answer: C
Surface area = 2πr2 + 2πrh = 2π(52) + 2π(5)(5) = 50π + 50π = 100π. Answer C. Key: cylinder surface = two bases + lateral area.Given x + y = 31 and xy = 240, what is x2 + y2?
Correct answer: D
x2 + y2 = (x+y)2 - 2xy = 312 - 2×240 = 961 - 480 = 481. Answer D. Key: identity linking sum of squares to sum and product.In how many ways can 32 be written as a sum of three positive integers, where order does not matter?
Correct answer: E
Let a ≤ b ≤ c with a+b+c = 32. For a=1: 15 ways — (1,1,30) to (1,15,16); a=2: 14 ways — (2,2,28) to (2,15,15); a=3: 12 ways — (3,3,26) to (3,14,15); a=4: 11 ways — (4,4,24) to (4,14,14); a=5: 9 ways — (5,5,22) to (5,13,14); a=6: 8 ways — (6,6,20) to (6,13,13); a=7: 6 ways — (7,7,18) to (7,12,13); a=8: 5 ways — (8,8,16) to (8,12,12); a=9: 3 ways — (9,9,14) to (9,11,12); a=10: 2 ways — (10,10,12) to (10,11,11). Total 85. Answer E. 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 2003 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 2003 AMC 10 A/B paper.
Finish all 25 within 75 minutes; skip when stuck, bank the solvable ones, and return to the hard ones.
Factor N into prime powers; the divisor count is the product of (exponent + 1).
Combined rate = sum of individual rates; time = 1 / combined rate.
Average speed = total distance / total time — never the arithmetic mean of the two speeds.
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 2003 AMC 10 papers and answers.
Scan to add the advisor for 2003 AMC 10 A/B past papers, answer keys and solutions, plus a custom prep plan.
Note: Name + School + Grade + Year
