2012
2012 AMC8 Paper & Solutions Pick
25 questions with solutions, harder combinatorics, geometry focuses on area transformations.
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Download 2012 PDF 12 Sample Questions
40 Minutes
Max Score 25
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Exam Overview
Exam Overview
This exam emphasizes geometry, combinatorics, area calculations. Overall difficulty is moderate.
Difficulty
- EasyQ1-10
- MediumQ11-20
- HardQ21-25
Topics
- Algebra30%
- Geometry30%
- Number Theory20%
- Combinatorics20%
Awards
Distinguished Honor Roll
Distinguished Honor Roll (Top 1%)
22+
Honor Roll
Honor Roll (Top 5%)
18+
Achievement Roll
Grade 6 and below · 15+ points
15+
Sample Problems
2012 AMC8 Sample Problems (12 questions)
Sample reference problems by difficulty — click an option to check your answer
Q1EasyArithmetic
Calculate the value of 999 + 1001 + 1000.
Steps
999+1001=2000, +1000=3000
Answer: DAdding symmetric numbers
Q4EasyRate / Speed
Walking at a speed of 5 km/h, how many km can you walk in 30 minutes?
Steps
30 minutes = 0.5 hours
5×0.5=2.5 km
Answer: EDistance = speed × time
Q7EasyArea
A parallelogram has base 15 and height 8. What is its area?
Steps
Area=15×8=120
Answer: AArea of a parallelogram = base × height
Q10EasyConvert percentages to fractions
A number becomes 96 after increasing by 20%. What is the original number?
Steps
1.2x=96 → x=80
Answer: BIncreasing by 20% means multiplying by 1.2
Q11MediumPrime factor
Factor 210 into prime factors. What is the sum of all the distinct prime factors?
Steps
210=2×3×5×7
Sum=2+3+5+7=17
Answer: BStart prime factorization from the smallest prime
Q14MediumArea
Triangle ABC has area 60, and D is the point on BC that divides it into thirds (closer to B). Find the area of triangle ABD.
Steps
BD/BC=1/3
S(ABD)=S(ABC)×1/3=20
Answer: EFor triangles sharing a vertex, the ratio of areas equals the ratio of their bases
Q16MediumKey concept: equations
The ages of a father and son add up to 60 years, and the father's age is 3 times the son's age. How old is the father now?
Steps
Let the son be x years old and the father be 3x years old
x + 3x = 60 → 4x = 60 → x = 15
Father = 3×15 = 45
Answer: BSum-and-multiple problem: sum ÷ (multiple + 1) = smaller value
Q19MediumProbability
If you flip 3 coins, what is the probability of getting at least 2 heads?
Steps
P(2 heads)=C(3,2)/8=3/8
P(3 heads)=1/8
At least 2 heads = 3/8+1/8=1/2
Answer: CFor "at least" problems, split into cases and compute
Q21HardApply the relevant mathematical concept
From 1 to 100, how many times does the digit "7" appear?
Steps
7 in the ones place: 7,17,27,...,97 = 10 times
7 in the tens place: 70,71,...,79 = 10 times
20 times in total
Answer: DCount the ones place and the tens place separately
Q22HardArea
A square has side length 10. After cutting a small square of side length 2 from each of the four corners, it is folded into an open-top box. What is the volume?
Steps
Base=(10-4)×(10-4)=36
Height=2
Volume=36×2=72
Answer: DAfter cutting the corners, each side of the base shrinks by twice the corner length
Q24HardNumber Theory
Find the largest n such that 1+2+3+...+n < 100.
Steps
1n(n+1)/2 < 100
2n(n+1) < 200
313×14=182<200 ✓
14×15=210>200
Largest n=13
Answer: BSum formula for an arithmetic sequence
Q25HardCombinatorics
In how many ways can 8 people be seated around a round table?
Steps
Circular permutations = (n-1)!
7!=5040
Answer: BA circular arrangement has one fewer degree of freedom than a linear arrangement
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