2001 AMC 10 Papers & Solutions - Hanlin International Education

Overview

2001 AMC 10 Paper Overview

2001 AMC 10 paper overview and exam highlights.

The 2001 AMC 10 was held in November 2001, 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.

The 2001 paper set more problems on divisor counts, work rates, average speed, and combinatorial counting, combining formulas with careful reading.

Topics

2001 AMC 10 Key Topics Tested

2001 AMC 10 main topic areas, weights and emphasis.

Algebra28%

Evaluation, quadratics, word and speed problems; about 28%.

Geometry22%

Rectangle perimeter, triangle area, cylinder surface area; about 22%.

Number Theory18%

Divisibility, remainders, GCD and divisor counts; about 18%.

Combinatorics22%

Coin outcomes, combinations and ordered counting; about 22%.

Probability10%

Classical probability and dice sums; about 10%.

Practice

25 Online Practice Questions

2001 AMC 10-style mock questions (Basic · Medium · Hard) — submit to grade and view step-by-step solutions.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Basic · Q1–10

1Algebra

If x = 2, what is the value of 3x² + 5x + 1?

Correct answer: A

Substitute x = 2: 3(2)² + 5(2) + 1 = 3×4 + 10 + 1 = 12 + 10 + 1 = 23. Answer A. Key: direct substitution.

2Algebra

The sum of three consecutive integers is 138. What is the largest?

Correct answer: B

Let the middle integer be n: 3n = 138, so n = 46 and the largest is 47. Answer B. Key: model consecutive integers by their middle.

3Number Theory

How many positive divisors does 360 have?

Correct answer: C

360 = 2³×3²×5, so the number of divisors is (3+1)(2+1)(1+1) = 24. Answer C. Key: divisor-count formula.

4Geometry

A rectangle has length 7 and width 6. What is its perimeter?

Correct answer: D

Perimeter = 2(7 + 6) = 2×13 = 26. Answer D. (42 is the area — do not confuse.) Key: rectangle perimeter formula.

5Algebra

An item is marked up 10% above cost to a price of

21. What was the cost?

Correct answer: E

cost × 1.1 = 121, so cost = 121 / 1.1 = 110. Answer E. Key: price = cost × (1 + markup).

6Probability

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.

7Combinatorics

Eight coins are tossed at once. How many heads/tails outcomes are possible?

Correct answer: B

Each coin has 2 outcomes, so 8 coins give 2⁸ = 256. Answer B. Key: independent outcomes multiply.

8Number Theory

What is the remainder when 2001 is divided by 11?

Correct answer: C

11 × 181 = 1991, and 2001 - 1991 = 10, so the remainder is 10. Answer C. Key: division with remainder.

9Algebra

If 5x + 8 = 43, what is x?

Correct answer: D

5x = 43 - 8 = 35, so x = 7. Answer D. Key: isolate the variable.

10Geometry

A triangle has base 14 and height 9. What is its area?

Correct answer: E

Area = ½×14×9 = 126/2 = 63. Answer E. Key: triangle area formula.

Medium · Q11–20

11Algebra

If x² - 20x + 75 = 0, what is the sum of all possible values of x?

Correct answer: A

Factor: (x-5)(x-15) = 0, so x = 5 or 15, and the sum is 20. Answer A. Key: Vieta — sum of roots = -b/a = 20.

12Number Theory

What is the greatest common divisor of 72 and 108?

Correct answer: B

72 = 2³×3² and 108 = 2²×3³, so GCD = 2²×3² = 36. Answer B. Key: take the smallest power of each shared prime.

13Combinatorics

A committee of 2 is chosen from 30 people. How many different committees are possible?

Correct answer: C

C(30,2) = (30×29)/(2×1) = 435. Answer C. Key: combinations are order-independent, C(n,k) = n!/(k!(n-k)!).

14Geometry

In a triangle, two angles are 30° and 80°. What is the third angle?

Correct answer: D

Triangle angles sum to 180°, so the third angle = 180 - 30 - 80 = 70°. Answer D. Key: triangle angle-sum theorem.

15Algebra

The average of 8 numbers is 11. After removing one number, the average of the remaining 7 is 10. What was the removed number?

Correct answer: E

Sum of 8 = 8×11 = 88; sum of 7 = 7×10 = 70; the removed number = 88 - 70 = 18. Answer E. Key: average = sum / count.

16Number Theory

What is the units digit of 3²⁰⁰¹?

Correct answer: A

The units digit of powers of 3 cycles as 3, 9, 7, 1 (period 4). Since 2001 = 4×500 + 1, the remainder is 1, corresponding to the 1st value, so the units digit is 3. Answer A. Key: cyclic units digits of powers.

17Algebra

One worker can finish a job in 12 hours and another in 24 hours. How long does it take them together?

Correct answer: B

Rates: 1/12 + 1/24 = 2/24 + 1/24 = 3/24 = 1/8 per hour, so together they need 1 / (1/8) = 8 hours. Answer B. Key: combined rate = sum of individual rates.

18Geometry

A square and an equilateral triangle have the same perimeter. If the triangle side is 100, what is the square side?

Correct answer: C

Triangle perimeter = 3×100 = 300, so the square side = 300 / 4 = 75. Answer C. Key: equal perimeters split by side count.

19Probability

Two fair six-sided dice are rolled. What is the probability the sum is 8?

Correct answer: D

Sums to 8: (2,6),(3,5),(4,4),(5,3),(6,2) — 5 outcomes out of 36, so 5/36. Answer D. Key: enumerate ordered dice pairs.

20Algebra

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: E

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 E. Key: average speed = total distance / total time, not the average of speeds.

Hard · Q21–25

21Number Theory

How many positive integers less than 100 are divisible by both 5 and 15?

Correct answer: A

Divisible by both 5 and 15 means divisible by LCM(5,15) = 15. The multiples of 15 below 100 are 15, 30, 45, 60, 75, 90 — 6 of them. Answer A. Key: divisible by both ⟺ divisible by their LCM.

22Combinatorics

A committee of 3 is chosen from 14 people. How many different committees are possible?

Correct answer: B

C(14,3) = (14×13×12)/(3×2×1) = 2184/6 = 364. Answer B. Key: combinations are order-independent, C(n,k) = n!/(k!(n-k)!).

23Geometry

A right cylinder has radius 3 and height 9. What is its total surface area? (in terms of π)

Correct answer: C

Surface area = 2πr² + 2πrh = 2π(3²) + 2π(3)(9) = 18π + 54π = 72π. Answer C. Key: cylinder surface = two bases + lateral area.

24Algebra

Given x + y = 34 and xy = 285, what is x² + y²?

Correct answer: D

x² + y² = (x+y)² - 2xy = 34² - 2×285 = 1156 - 570 = 586. Answer D. Key: identity linking sum of squares to sum and product.

25Combinatorics

In how many ways can 34 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 = 34. For a=1: 16 ways — (1,1,32) to (1,16,17); a=2: 15 ways — (2,2,30) to (2,16,16); a=3: 13 ways — (3,3,28) to (3,15,16); a=4: 12 ways — (4,4,26) to (4,15,15); a=5: 10 ways — (5,5,24) to (5,14,15); a=6: 9 ways — (6,6,22) to (6,14,14); a=7: 7 ways — (7,7,20) to (7,13,14); a=8: 6 ways — (8,8,18) to (8,13,13); a=9: 4 ways — (9,9,16) to (9,12,13); a=10: 3 ways — (10,10,14) to (10,12,12); a=11: 1 way — (11,11,12). Total 96. Answer E. Key: ordered enumeration to avoid duplicates.

Specs

2001 AMC 10 Format

Unified AMC 10 specs, consistent across years.

Questions & Scoring25 multiple-choice; +6 correct, +1.5 blank, 0 wrong; max 150

Duration75 minutes

Papers2001 has a single paper (Papers A/B added from 2002)

EligibilityGrade 10 and below; under 17.5 on test day

AdvancementMeeting the cut-off qualifies for AIME

Papers A & B

2001 has a single paper; AMC 10 added Papers A and B from 2002, when students may take either or both and keep the higher score.

How to Use

How to Use This Page

Four steps · Overview / Topics / Practice / Prep

1

Paper Overview

Read the 2001 AMC 10 overview and format specs to grasp the year’s style.

2

Find Topics

Review the key topics and weights, and locate your weak areas.

3

Take the Quiz

Complete the 25 mock questions (75-minute limit); submit for auto-grading and right/wrong marks.

4

Review & Prep

Open the step-by-step solutions, learn from mistakes, and scan for full papers to push for AIME.

Scan for Full Papers

Prep

2001 AMC 10 Prep Guide

Prep tips and score-boosting advice for the 2001 AMC 10 paper.

1

Timed Mock Exams

Finish all 25 within 75 minutes; skip when stuck, bank the solvable ones, and return to the hard ones.

2

Divisor Counts

Factor N into prime powers; the divisor count is the product of (exponent + 1).

3

Average Speed

Average speed = total distance / total time — never the arithmetic mean of the two speeds.

4

Combined Work Rates

Combined rate = sum of individual rates; time = 1 / combined rate.

5

Push for AIME

Aiming above 100? Lock the basics and medium questions, then take the last 5 step by step; scan for full papers and a plan.

FAQ

2001 AMC 10 Past Paper FAQ

Frequent questions about the 2001 AMC 10 papers and answers.

Where can I download the 2001 AMC 10 past paper? +

This page archives the 2001 AMC 10 paper entries. Paper and answer files are placeholders — scan to consult the advisor for full materials.

When are 2001 AMC 10 answers released? +

Papers and answer keys are compiled after the exam. The answer entry on this page is a placeholder — scan to get the answer key and step-by-step solutions first.

What is the difference between AMC 10 Papers A and B? +

The two papers are comparable in difficulty and scope, differing only in date and specific questions. You may take either or both; the higher score is used for awards and AIME qualification.

How should I prepare for the 2001 AMC 10? +

Practice past papers under time limits, drill by topic, and review mistakes against the answer key. To reach the AIME cut-off, consider 1-on-1 coaching — scan for a custom plan.

2001 AMC 10 Past Papers

2001 AMC 10 Paper Overview

2001 AMC 10 Key Topics Tested

25 Online Practice Questions

Basic · Q1–10

Medium · Q11–20

Hard · Q21–25

2001 AMC 10 Format

Papers A & B

How to Use This Page

Paper Overview

Find Topics

Take the Quiz

Review & Prep

2001 AMC 10 Prep Guide

Timed Mock Exams

Divisor Counts

Average Speed

Combined Work Rates

Push for AIME

2001 AMC 10 Past Paper FAQ

Other Years

Start 2001 AMC 10 Prep

Scan for Papers