2011

2011 AMC8 Paper & Solutions Pick

25 questions with solutions, number theory introduces congruence, algebra focuses on ratios.

Sample Problems Download PDF

Scan to get free 2011 PDF + solutions

12 Sample Questions

40 Minutes

Max Score 25

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Exam Overview

This exam emphasizes algebra, number theory, ratios. Overall difficulty is moderate.

DDifficulty

EasyQ1-10
MediumQ11-20
HardQ21-25

TTopics

Algebra35%

Geometry30%

Number Theory20%

Combinatorics15%

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

2011 AMC8 Sample Problems (12 questions)

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

Q2EasyProportion

On a map with a scale of 1:50000, how many meters does 3 cm on the map represent in reality?

A) 150

B) 1500

C) 15000

D) 150000

E) 1500000

Steps

3×50000=150000cm=1500m

Answer: BWatch the units when converting with a scale

Q4EasyArithmetic

Calculate the value of 1000-357.

A) 643

B) 633

C) 653

D) 663

E) 673

Steps

1000-357=643

Answer: ASubtraction with borrowing

Q6EasyArea

A circle has radius 5. What is its circumference approximately? (π≈3.14)

A) 15.7

B) 25.7

C) 78.5

D) 157

E) 31.4

Steps

circumference=2πr=2×3.14×5=31.4

Answer: ECircumference of a circle = 2πr

Q9EasyAverage

The average of 4 numbers is 25, and one of them is 40. What is the average of the other 3 numbers?

A) 15

B) 18

C) 22

D) 20

E) 25

Steps

total=100, after removing 40 the sum=60

60/3=20

Answer: DThe relationship between the average and the total

Q12MediumApply the relevant mathematical concept

Find the remainder when 3^15 is divided by 5.

A) 1

B) 3

C) 2

D) 4

E) 0

Steps

The powers of 3 mod 5 cycle: 3,4,2,1 (period 4)

15÷4=3 remainder 3

3^15≡3³=27≡2(mod 5)

Answer: CPowers are periodic under modular arithmetic

Q14MediumKey concept: equations

A and B together have 100 yuan. After A gives B 25 yuan, they have equal amounts. How much did A originally have?

A) 75

B) 50

C) 60

D) 70

E) 80

Steps

After giving, each has 50 yuan

A originally had 50+25=75

Answer: AA gives B 25 → A decreases by 25 and B increases by 25

Q16MediumArea

What is the measure of each interior angle of a hexagon?

A) 120

B) 90

C) 108

D) 135

E) 150

Steps

sum of interior angles=(6-2)×180=720

each=720/6=120

Answer: AEach interior angle of a regular n-gon = (n-2)×180/n

Q18MediumProbability

A bag contains 3 red, 2 blue, and 1 green ball. If 2 balls are drawn, what is the probability that they are the same color?

A) 1/5

B) 4/15

C) 2/5

D) 1/3

E) 7/15

Steps

total C(6,2)=15

same color: red C(3,2)=3, blue C(2,2)=1

probability=4/15

Answer: BCount the same-color draws case by case

Q21HardNumber Theory

How many numbers from 1 to 200 are the cube of some integer?

A) 4

B) 6

C) 5

D) 7

E) 8

Steps

1³=1, 2³=8, 3³=27, 4³=64, 5³=125

6³=216>200

5 in total

Answer: CCheck one by one by listing them out

Q22HardKey concept: permutations

Five people A, B, C, D, E line up in a row, with A to the left of B. How many arrangements are there?

A) 48

B) 72

C) 60

D) 80

E) 120

Steps

total permutations 5!=120

probability that A is to the left of B=1/2

120/2=60

Answer: CBy symmetry: A to the left of B = A to the right of B

Q24HardArea

A trapezoid has area 84, and the sum of its two parallel sides is 28. What is its height?

A) 6

B) 4

C) 5

D) 7

E) 8

Steps

84=1/2×28×h

84=14h → h=6

Answer: ASolve for the height from the trapezoid area formula

Q25HardCombinatorics

Choosing 3 different digits from 1 to 9 to form a three-digit number, how many of them are odd?

A) 200

B) 224

C) 280

D) 252

E) 320

Steps

odd → the last digit is odd (1,3,5,7,9), 5 choices

the hundreds and tens digits are arranged from the remaining 8 digits: P(8,2)=8×7=56

5×56 = 280 in total

Answer: CThe last digit determines parity, so fix the last digit first

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2011 AMC8 Paper & Solutions Pick

Scan to get free 2011 PDF + solutions

Exam Overview

DDifficulty

TTopics

AAwards

2011 AMC8 Sample Problems (12 questions)

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