2009

2009 AMC8 Paper & Solutions Pick

25 questions with solutions, geometry covers 3D surface area.

Sample Problems Download PDF

Scan to get free 2009 PDF + solutions

12 Sample Questions

40 Minutes

Max Score 25

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Exam Overview

This exam emphasizes geometry, area calculations. Overall difficulty is moderate.

DDifficulty

EasyQ1-10
MediumQ11-20
HardQ21-25

TTopics

Algebra30%

Geometry35%

Number Theory15%

Combinatorics20%

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

2009 AMC8 Sample Problems (12 questions)

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

Q1EasyArithmetic

Calculate the value of 125+375+500.

A) 900

B) 950

C) 1000

D) 1050

E) 1100

Steps

125+375=500, 500+500=1000

Answer: CCombine numbers to make round figures

Q4EasyKey concept: fractions

What is 1/4 + 3/8?

A) 1/2

B) 3/4

C) 5/8

D) 7/8

E) 1

Steps

2/8+3/8=5/8

Answer: CFind a common denominator, then add

Q7EasyArea

What is the area of a square with side length 8?

A) 64

B) 24

C) 32

D) 48

E) 56

Steps

8²=64

Answer: AArea of a square = side²

Q9EasyKey concept: sequence

What is the 10th term of the sequence 2, 5, 8, 11, ...?

A) 26

B) 27

C) 28

D) 30

E) 29

Steps

Arithmetic sequence: a₁₀=2+(10-1)×3=29

Answer: EGeneral term of an arithmetic sequence: aₙ=a₁+(n-1)d

Q12MediumArea

A rectangular box has length 5, width 4, and height 3. What is its surface area?

A) 94

B) 60

C) 84

D) 108

E) 120

Steps

2(5×4+5×3+4×3)=2(20+15+12)=94

Answer: ASurface area of a rectangular box = 2(lw+lh+wh)

Q14MediumProbability

If you draw one card from a standard 52-card deck, what is the probability that it is a heart?

A) 1/2

B) 1/3

C) 1/13

D) 1/52

E) 1/4

Steps

13 hearts / 52 cards = 1/4

Answer: EClassical probability

Q16MediumKey concept: equations

The sum of two consecutive even numbers is 62. What is the larger number?

A) 28

B) 30

C) 34

D) 36

E) 32

Steps

x+(x+2)=62 → x=30

Larger = 32

Answer: EConsecutive even numbers differ by 2

Q19MediumArea

An equilateral triangle has side length 6. What is its area, approximately? (√3≈1.73)

A) 12.47

B) 14.72

C) 15.57

D) 18

E) 20.76

Steps

Area=(√3/4)×36=9√3≈15.57

Answer: CArea of an equilateral triangle = (√3/4)×a²

Q21HardNumber Theory

Find the value of 2^10 + 2^11 + 2^12.

A) 4096

B) 6144

C) 7168

D) 8192

E) 12288

Steps

=1024+2048+4096=7168

Or =2^10(1+2+4)=7×1024=7168

Answer: CFactor out the common factor to simplify

Q22HardKey concept: permutations

Five people stand in a row. Person A is not first and person B is not last. How many arrangements are there?

A) 60

B) 66

C) 72

D) 78

E) 84

Steps

Total 5!=120

A first: 4!=24; B last: 4!=24

A first and B last: 3!=6

120-24-24+6=78

Answer: DInclusion-exclusion principle

Q24HardGeometry

A square has a diagonal of length 10. What is its area?

A) 25

B) 36

C) 64

D) 50

E) 100

Steps

Side = 10/√2 = 5√2

Area = (5√2)² = 50

Or diagonal²/2 = 50

Answer: DArea of a square = diagonal²/2

Q25HardCombinatorics

From 6 people, you choose a team of at least 2. How many ways are there to do this?

A) 42

B) 57

C) 50

D) 56

E) 62

Steps

Total 2⁶=64

Choosing 0 people: 1 way; choosing 1 person: 6 ways

At least 2 people = 64-1-6=57

Answer: BSubtract the cases that don't meet the condition from the total number of subsets

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2009 AMC8 Paper & Solutions Pick

Scan to get free 2009 PDF + solutions

Exam Overview

DDifficulty

TTopics

AAwards

2009 AMC8 Sample Problems (12 questions)

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