2000

2000 AMC8 Paper & Solutions Pick

25 questions with solutions, millennium exam, moderate difficulty.

Sample Problems Download PDF

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12 Sample Questions

40 Minutes

Max Score 25

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Exam Overview

This exam emphasizes multiple math topics. Overall difficulty is moderate.

DDifficulty

EasyQ1-10
MediumQ11-20
HardQ21-25

TTopics

Algebra35%

Geometry30%

Number Theory15%

Combinatorics20%

AAwards

Distinguished Honor Roll

Distinguished Honor Roll (Top 1%)

18+

Honor Roll

Honor Roll (Top 5%)

14+

Achievement Roll

Grade 6 and below · 15+ points

15+

Sample Problems

2000 AMC8 Sample Problems (12 questions)

Sample reference problems by difficulty — click an option to check your answer

Q1EasyArithmetic

Calculate the value of 2000-1.

A) 1000

B) 1001

C) 1099

D) 1900

E) 1999

Steps

2000-1=1999

Answer: EBasic subtraction

Q3EasyKey concept: ratios

Sugar and water are in the ratio 1:4, and there are 200 grams of sugar water. How much sugar is there?

A) 30

B) 40

C) 35

D) 45

E) 50

Steps

Each part = 200/5 = 40

Answer: BDividing in a given ratio

Q6EasyArea

What is the area of a triangle with base 6 and height 10?

A) 16

B) 24

C) 36

D) 60

E) 30

Steps

1/2×6×10=30

Answer: EArea of a triangle

Q9EasyAverage

What is the average of 10, 20, and 30?

A) 20

B) 15

C) 18

D) 22

E) 25

Steps

60/3=20

Answer: AAverage = sum ÷ count

Q11MediumKey concept: equations

A number is increased by 5 and then multiplied by 3 to give 39. What is the number?

A) 8

B) 6

C) 7

D) 9

E) 10

Steps

3(x+5)=39→x+5=13→x=8

Answer: AInverse operations

Q14MediumGeometry

A square has a perimeter of 48. What is its area?

A) 96

B) 120

C) 168

D) 144

E) 192

Steps

Side length = 12, area = 144

Answer: DPerimeter → side length → area

Q16MediumProbability

If two different numbers are chosen from 1 to 6, what is the probability that their sum is 7?

A) 2/5

B) 3/10

C) 1/3

D) 1/2

E) 1/5

Steps

C(6,2)=15 ways

Sum equals 7: (1,6)(2,5)(3,4) = 3 ways

3/15=1/5

Answer: EProbability with combinations

Q18MediumNumber Theory

How many positive divisors does 72 have?

A) 8

B) 12

C) 10

D) 14

E) 16

Steps

72=2³×3²

(3+1)(2+1)=12

Answer: BFormula for the number of divisors

Q21HardArea

A circle has an area of 314 (π≈3.14). What is its circumference?

A) 31.4

B) 62.8

C) 50

D) 100

E) 200

Steps

πr²=314→r=10

Circumference = 2πr = 62.8

Answer: BArea → radius → circumference

Q22HardKey concept: permutations

Three boys and three girls are arranged in a row so that boys and girls alternate. How many arrangements are there?

A) 72

B) 36

C) 48

D) 60

E) 96

Steps

Boy first: 3!×3!=36

Girl first: 3!×3!=36

Total 72

Answer: ASplit into two cases by whether a boy or a girl is first

Q24HardNumber Theory

Find the value of 2000²-1999².

A) 3999

B) 1999

C) 2000

D) 4000

E) 4001

Steps

(2000+1999)(2000-1999)=3999

Answer: ADifference of squares formula

Q25HardCombinatorics

Three people are chosen from 8, and person A must be included. How many ways are there?

A) 15

B) 20

C) 28

D) 35

E) 21

Steps

A is fixed, so choose 2 from the remaining 7 people

C(7,2)=21

Answer: EFix the required element first, then choose the rest

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2000 AMC8 Paper & Solutions Pick

Scan to get free 2000 PDF + solutions

Exam Overview

DDifficulty

TTopics

AAwards

2000 AMC8 Sample Problems (12 questions)

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