2008

2008 AMC8 Paper & Solutions Pick

25 questions with solutions, algebra focuses on functions and graphs, challenging combinatorics.

Sample Problems Download PDF

Scan to get free 2008 PDF + solutions

12 Sample Questions

40 Minutes

Max Score 25

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Exam Overview

This exam emphasizes algebra, combinatorics. Overall difficulty is moderate.

DDifficulty

EasyQ1-10
MediumQ11-20
HardQ21-25

TTopics

Algebra35%

Geometry25%

Number Theory20%

Combinatorics20%

AAwards

Distinguished Honor Roll

Distinguished Honor Roll (Top 1%)

21+

Honor Roll

Honor Roll (Top 5%)

17+

Achievement Roll

Grade 6 and below · 15+ points

15+

Sample Problems

2008 AMC8 Sample Problems (12 questions)

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

Q1EasyArithmetic

Calculate the value of (8+12)÷4.

A) 3

B) 4

C) 5

D) 6

E) 8

Steps

20÷4=5

Answer: CCompute the parentheses first

Q3EasyRate / Speed

Riding at a speed of 15 km/h for 2 hours, how many km do you travel?

A) 30

B) 25

C) 28

D) 35

E) 40

Steps

15×2=30

Answer: ADistance = speed × time

Q6EasyPrime Numbers

What is the largest prime number less than 30?

A) 29

B) 23

C) 27

D) 28

E) 30

Steps

29 is prime, but 30 is not

Answer: ACheck each number one by one

Q9EasyArea

What is the area of a triangle with base 7 and height 12?

A) 42

B) 48

C) 56

D) 60

E) 84

Steps

1/2×7×12=42

Answer: ATriangle area formula

Q11MediumKey concept: functions

If f(x)=2x+1, what is f(5)?

A) 9

B) 10

C) 11

D) 12

E) 13

Steps

2(5)+1=11

Answer: CSubstitute and evaluate

Q13MediumArea

A trapezoid has top base 6, bottom base 10, and height 5. What is its area?

A) 30

B) 40

C) 35

D) 45

E) 50

Steps

1/2×(6+10)×5=40

Answer: BTrapezoid area formula

Q16MediumProbability

What is the probability of rolling a die and getting an even number greater than 3?

A) 1/3

B) 1/6

C) 1/4

D) 1/2

E) 2/3

Steps

Numbers that are even and greater than 3: 4 and 6, for a total of 2

Probability = 2/6 = 1/3

Answer: AWhen several conditions must hold at once, take their intersection

Q18MediumNumber Theory

What is the sum of all distinct prime factors of 60?

A) 8

B) 12

C) 10

D) 15

E) 18

Steps

60=2²×3×5

Distinct prime factors 2+3+5=10

Answer: CFactor into primes, then add

Q21HardCombinatorics

From 7 people, 4 are chosen to form a team, and persons A and B must be included. How many ways are there?

A) 10

B) 6

C) 15

D) 20

E) 35

Steps

With A and B already chosen, pick 2 more from the remaining 5 people

C(5,2)=10

Answer: AFix the required members first, then choose the rest

Q22HardKey concept: functions

If f(x)=x²-3x+2, what are the values of x when f(x)=0?

A) -12

B) 13

C) 12

D) -13

E) 23

Steps

x²-3x+2=(x-1)(x-2)=0

x=1 or x=2

Answer: CFactor to find the roots

Q24HardArea

An equilateral triangle is inscribed in a circle of radius 6. What is the area of the triangle? (√3≈1.73)

A) 36√3

B) 27√3

C) 18√3

D) 54

E) 72

Steps

Side length = r√3 = 6√3

Area = (√3/4)(6√3)² = (√3/4)×108 = 27√3

Answer: BFor an equilateral triangle inscribed in a circle, the side length = r√3

Q25HardLogic

Among 100 people, 70 can swim and 50 can ride a bike, and 30 can do both. How many can do neither?

A) 5

B) 8

C) 10

D) 12

E) 15

Steps

Can do at least one = 70+50-30 = 90

Can do neither = 100-90 = 10

Answer: CInclusion-exclusion principle

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2008 AMC8 Paper & Solutions Pick

Scan to get free 2008 PDF + solutions

Exam Overview

DDifficulty

TTopics

AAwards

2008 AMC8 Sample Problems (12 questions)

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