2013
2013 AMC8 Paper & Solutions Pick
25 questions with solutions, strong algebra word problems, geometry covers Pythagorean theorem.
Free 2013 PDF Download
Download 2013 PDF 12 Sample Questions
40 Minutes
Max Score 25
No Calculator
Exam Overview
Exam Overview
This exam emphasizes algebra, geometry, word problems. Overall difficulty is moderate.
Difficulty
- EasyQ1-10
- MediumQ11-20
- HardQ21-25
Topics
- Algebra40%
- Geometry25%
- Number Theory15%
- Combinatorics20%
Awards
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
2013 AMC8 Sample Problems (12 questions)
Sample reference problems by difficulty — click an option to check your answer
Q1EasyArithmetic
Calculate the value of 2×3×4×5.
Steps
2×3=6, 6×4=24, 24×5=120
Answer: BMultiply step by step
Q3EasyConvert percentages to fractions
What is 15% of 200?
Steps
200×0.15=30
Answer: AConvert the percent to a decimal, then multiply
Q5EasyApply the relevant mathematical concept
What is the range of the data set 3, 7, 8, 12, 15?
Steps
Range = 15 - 3 = 12
Answer: ARange = maximum value - minimum value
Q8EasyKey concept: equations
Five times a number minus 8 equals 27. What is the number?
Steps
5x-8=27 → 5x=35 → x=7
Answer: DLinear equation in one variable
Q11MediumPythagorean Thm.
A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?
Steps
√(36+64)=√100=10
Answer: A6-8-10 is a multiple of 3-4-5
Q13MediumApply the relevant mathematical concept
A pool has two inlet pipes, A and B. Pipe A fills the pool in 6 hours, and pipe B fills it in 4 hours. If both pipes are opened together, how many hours does it take to fill the pool?
Steps
Rate of A = 1/6, rate of B = 1/4
Combined rate = 1/6 + 1/4 = 5/12
Time = 12/5 = 2.4 hours
Answer: BSolve work problems using rates
Q15MediumArea
A circle has a diameter of 14. Approximately what is its area? (π ≈ 3.14)
Steps
r=7, area = π×49 ≈ 153.86
Answer: EArea of a circle = πr²
Q18MediumNumber Theory
Find the value of LCM(12, 18, 30).
Steps
12=2²×3, 18=2×3², 30=2×3×5
LCM=2²×3²×5=180
Answer: EMultiply the highest power of each prime factor
Q21HardLogic
A says: "B is older than me." B says: "C is younger than me." C says: "I am older than A." Only one person is lying. Who is the oldest?
Steps
If A, B, and C all tell the truth: B>A, B>C, C>A → B>C>A
2Verify: A says B>A, B says CA, all three tell the truth
The oldest is B
Answer: ATest each assumption one by one
Q22HardKey concept: permutations
Four people A, B, C, D stand in a row, and A is not in the first position. How many arrangements are there?
Steps
Total arrangements 4!=24
A in the first position 3!=6
24-6=18
Answer: AFor restricted arrangements, subtract the invalid ones from the total
Q24HardNumber Theory
A number leaves a remainder of 3 when divided by 4, and a remainder of 5 when divided by 6. What is the smallest such number?
Steps
n≡3(mod 4) → 3,7,11,15,19...
n≡5(mod 6) → 5,11,17,23...
Smallest common value = 11
Answer: DList values step by step to find the smallest common value
Q25HardCombinatorics
From 5 boys and 4 girls, choose 3 people, with at least 1 girl. How many ways are there to choose?
Steps
Total C(9,3)=84
All boys C(5,3)=10
At least 1 girl = 84 - 10 = 74
Answer: AUse the complement method for "at least" problems
All Years
All Years Navigation
All AMC8 exam years from 1999-2026, click to view
202612 sample Q & Sol.
202512 sample Q & Sol.
202412 sample Q & Sol.
202312 sample Q & Sol.
202212 sample Q & Sol.
202112 sample Q & Sol.
202012 sample Q & Sol.
201912 sample Q & Sol.
201812 sample Q & Sol.
201712 sample Q & Sol.
201612 sample Q & Sol.
201512 sample Q & Sol.
201412 sample Q & Sol.
201312 sample Q & Sol.
201212 sample Q & Sol.
201112 sample Q & Sol.
201012 sample Q & Sol.
200912 sample Q & Sol.
200812 sample Q & Sol.
200712 sample Q & Sol.
200612 sample Q & Sol.
200512 sample Q & Sol.
200412 sample Q & Sol.
200312 sample Q & Sol.
200212 sample Q & Sol.
200112 sample Q & Sol.
200012 sample Q & Sol.
199912 sample Q & Sol.