2010

2010 AMC8 Paper & Solutions Pick

25 questions with solutions, easier difficulty, good for foundational practice.

Sample Problems Download PDF

Scan to get free 2010 PDF + solutions

12 Sample Questions

40 Minutes

Max Score 25

No Calculator

Exam Overview

This exam emphasizes multiple math topics. Overall difficulty is relatively basic.

DDifficulty

EasyQ1-10
MediumQ11-20
HardQ21-25

TTopics

Algebra35%

Geometry30%

Number Theory15%

Combinatorics20%

AAwards

Distinguished Honor Roll

Distinguished Honor Roll (Top 1%)

19+

Honor Roll

Honor Roll (Top 5%)

15+

Achievement Roll

Grade 6 and below · 15+ points

15+

Sample Problems

2010 AMC8 Sample Problems (12 questions)

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

Q1EasyArithmetic

Calculate the value of 56 ÷ 8 + 3.

A) 7

B) 10

C) 8

D) 9

E) 11

Steps

7+3=10

Answer: BDivide before adding

Q3EasyRatio

The ratio of boys to girls is 4:5, and there are 36 students in the whole class. How many boys are there?

A) 14

B) 15

C) 16

D) 18

E) 20

Steps

Each part = 36/9 = 4, boys = 4×4 = 16

Answer: CDistribute according to the ratio

Q5EasyApply the relevant mathematical concept

The scores on 5 tests are 80, 85, 90, 85, 95. What is the mode?

A) 80

B) 85

C) 87

D) 90

E) 95

Steps

85 appears twice, the most

Answer: BThe mode is the value that appears most often

Q8EasyArea

A triangle has a base of 10 and a height of 7. What is its area?

A) 25

B) 35

C) 30

D) 40

E) 70

Steps

1/2×10×7=35

Answer: BFormula for the area of a triangle

Q11MediumKey concept: equations

Three times a number plus 5 equals five times that number minus 7. What is the number?

A) 4

B) 5

C) 7

D) 8

E) 6

Steps

3x+5=5x-7 → 12=2x → x=6

Answer: EMove terms and combine

Q13MediumArea

If the radius of a circle is doubled, by how many times does the area increase?

A) 2

B) 3

C) 6

D) 8

E) 4

Steps

Area = πr², if r becomes 2r then area = π(2r)² = 4πr²

It increases by a factor of 4

Answer: EThe area is proportional to the square of the radius

Q15MediumProbability

When tossing two coins, what is the probability of getting exactly one head and one tail?

A) 1/4

B) 1/3

C) 2/3

D) 3/4

E) 1/2

Steps

(head, tail) and (tail, head): 2 outcomes / 4 total

Probability = 1/2

Answer: EList all equally likely outcomes

Q17MediumNumber Theory

How many prime numbers are there from 1 to 30?

A) 10

B) 8

C) 9

D) 11

E) 12

Steps

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

10 in total

Answer: A1 is not a prime number

Q21HardLogic

Four people are in a race. A says, "I am not first." B says, "I am faster than A." C says, "I am last." D says, "B is not first." Only one person is lying. Who is first?

A) A

B) B

C) D

D) C

E) Cannot be determined

Steps

Assume D is first and check: A is not first ✓, and that B is faster than A needs to be verified

Test each assumption one by one; when D is first, exactly one person is lying

Answer: CMethod of testing each assumption one by one

Q22HardArea

The largest possible circle is drawn inside a square with side length 6. What is the area inside the square but outside the circle? (π ≈ 3.14)

A) 5.16

B) 7.74

C) 6.44

D) 8.28

E) 9.42

Steps

Area of the square = 36

Area of the circle = π×9 ≈ 28.26

Difference = 36 - 28.26 = 7.74

Answer: BSubtract the inscribed circle from the square

Q24HardKey concept: permutations

How many three-digit even numbers with no repeated digits can be formed using 0, 1, 2, 3, 4?

A) 30

B) 20

C) 24

D) 28

E) 36

Steps

Even units digit: 0, 2, 4

Units digit 0: 4 choices for the hundreds digit × 3 choices for the tens digit = 12

Units digit 2: 3 choices for the hundreds digit (1, 3, 4) × 3 choices for the tens digit = 9

Units digit 4: same as 2 = 9

Total = 12 + 9 + 9 = 30

Answer: ACase analysis where the leading digit cannot be 0

Q25HardCombinatorics

Ten balls are numbered 1-10. Three balls are drawn so that the sum of their numbers is even. How many ways are there?

A) 50

B) 55

C) 65

D) 60

E) 70

Steps

5 odd and 5 even

All even: C(5,3)=10; two odd and one even: C(5,2)×C(5,1)=50

10+50=60

Answer: DSum is even: either all even or two odd and one even

Get Full 2010 AMC8 Exam + Solutions

Scan the QR code below to get free 2010 PDF + solutions

2010 AMC8 Paper & Solutions Pick

Scan to get free 2010 PDF + solutions

Exam Overview

DDifficulty

TTopics

AAwards

2010 AMC8 Sample Problems (12 questions)

Steps

Steps

Steps

Steps

Steps

Steps

Steps

Steps

Steps

Steps

Steps

Steps

Get Full 2010 AMC8 Exam + Solutions

All Years Navigation

Contact Us