2004

2004 AMC8 Paper & Solutions Pick

25 questions with solutions, combinatorics features recursive methods.

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 combinatorics. Overall difficulty is moderate.

DDifficulty

EasyQ1-10
MediumQ11-20
HardQ21-25

TTopics

Algebra35%

Geometry25%

Number Theory15%

Combinatorics25%

AAwards

Distinguished Honor Roll

Distinguished Honor Roll (Top 1%)

20+

Honor Roll

Honor Roll (Top 5%)

16+

Achievement Roll

Grade 6 and below · 15+ points

15+

Sample Problems

2004 AMC8 Sample Problems (12 questions)

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

Q1EasyArithmetic

Calculate the value of 1000÷25.

A) 20

B) 30

C) 50

D) 40

E) 60

Steps

1000÷25=40

Answer: DBasic division

Q4EasyKey concept: fractions

Express 0.375 as a fraction in lowest terms.

A) 1/4

B) 2/5

C) 3/7

D) 5/8

E) 3/8

Steps

0.375=375/1000=3/8

Answer: EConvert the decimal to a fraction, then reduce

Q6EasyArea

What is the area of a parallelogram with base 9 and height 6?

A) 54

B) 27

C) 36

D) 45

E) 63

Steps

9×6=54

Answer: AArea of a parallelogram = base × height

Q9EasyAverage

Seven numbers have an average of 12. After removing one number, the remaining six numbers have an average of 14. What is the number that was removed?

A) 2

B) 4

C) 6

D) 0

E) 8

Steps

Total sum=84, sum after removal=84

Removed number=84-84=0

Answer: DThe difference of the sums is the removed number

Q12MediumKey concept: equations

A father and son's ages sum to 56, and the father's age is 3 times the son's age. How old is the father?

A) 36

B) 38

C) 40

D) 42

E) 44

Steps

x+3x=56→4x=56→x=14

Father=42

Answer: DLinear equation in one variable

Q14MediumArea

A triangle has area 48 and base 12. What is its height?

A) 4

B) 6

C) 10

D) 12

E) 8

Steps

48=1/2×12×h→h=8

Answer: ESolve backward for the height

Q16MediumProbability

What is the probability that the sum of two thrown dice is even?

A) 1/4

B) 1/3

C) 1/2

D) 2/3

E) 3/4

Steps

Both odd or both even, 9 ways each

18/36=1/2

Answer: CParity of the sum

Q18MediumFind the recursive pattern

What is the 8th term of the sequence 1, 1, 2, 3, 5, 8, ...?

A) 13

B) 18

C) 26

D) 21

E) 34

Steps

1, 1, 2, 3, 5, 8, 13, 21

8th term=21

Answer: DFibonacci sequence

Q21HardArea

A square has area 64. What is the area of the square formed by connecting the midpoints of its four sides?

A) 16

B) 24

C) 40

D) 32

E) 48

Steps

Original side length 8, midpoint square side length=8/√2=4√2

Area=32

Answer: DThe midpoint square's area is half the original area

Q22HardNumber Theory

Find the value of 1+2+3+...+50.

A) 1225

B) 1275

C) 1250

D) 1300

E) 1325

Steps

50×51/2=1275

Answer: BSum of an arithmetic sequence

Q24HardKey concept: permutations

Using the digits 1-5 to form five-digit numbers with no repeated digits, how many of them are even?

A) 24

B) 48

C) 36

D) 60

E) 72

Steps

Even last digit (2 or 4): 2 ways

The remaining 4 positions: 4!=24

2×24=48

Answer: BThe last digit determines parity

Q25HardCombinatorics

Given 8 points in a plane with no three collinear, how many line segments can be drawn?

A) 20

B) 24

C) 28

D) 32

E) 36

Steps

C(8,2)=28

Answer: CCombinations

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2004 AMC8 Paper & Solutions Pick

Scan to get free 2004 PDF + solutions

Exam Overview

DDifficulty

TTopics

AAwards

2004 AMC8 Sample Problems (12 questions)

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