2007
2007 AMC8 Paper & Solutions Pick
25 questions with solutions, significant number theory and geometry weight.
Scan to get free 2007 PDF + solutions
12 Sample Questions
40 Minutes
Max Score 25
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Exam Overview
Exam Overview
This exam emphasizes geometry, number theory. Overall difficulty is moderate.
Difficulty
- EasyQ1-10
- MediumQ11-20
- HardQ21-25
Topics
- Algebra30%
- Geometry35%
- Number Theory20%
- Combinatorics15%
Awards
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
2007 AMC8 Sample Problems (12 questions)
Sample reference problems by difficulty — click an option to check your answer
Q2EasyArithmetic
Calculate the value of 7×8-15.
Steps
56-15=41
Answer: BMultiply before subtracting.
Q4EasyArea
What is the approximate area of a circle with diameter 10? (π≈3.14)
Steps
r=5, area=π×25≈78.5
Answer: BArea of a circle = πr²
Q6EasyKey concept: equations
3x=27, x=?
Steps
x=27/3=9
Answer: ABasic equation.
Q9EasyProbability
If you pick one number at random from 1 to 10, what is the probability of getting a prime number?
Steps
The primes 2, 3, 5, 7 give 4 numbers in total.
4/10=2/5
Answer: A1 is not a prime number.
Q11MediumNumber Theory
What is the greatest common divisor of 84 and 60?
Steps
84=2²×3×7, 60=2²×3×5
GCD=2²×3=12
Answer: DTake the lowest power of each common prime factor.
Q13MediumGeometry
A right triangle has hypotenuse 13 and one leg 5. What is the other leg?
Steps
√(169-25)=√144=12
Answer: A5-12-13 is a Pythagorean triple.
Q15MediumKey concept: equations
A two-digit number has digits that sum to 12. When the digits are swapped, the new number is 18 greater than the original. What is the original number?
Steps
Let the tens digit be a and the units digit be b, so a+b=12.
(10b+a)-(10a+b)=18 → 9(b-a)=18 → b-a=2
a=5, b=7, so the original number is 57.
Answer: EUse algebra for digit-swapping problems.
Q18MediumArea
A rhombus has side length 5 and one diagonal of length 6. What is its area?
Steps
Half of that diagonal is 3, and the other half-diagonal = √(25-9)=4.
The other diagonal = 8.
Area=1/2×6×8=24
Answer: CThe diagonals of a rhombus are perpendicular bisectors of each other.
Q21HardNumber Theory
What is the product of the largest prime number under 100 and the smallest prime number?
Steps
The largest is 97 and the smallest is 2.
97×2=194
Answer: ARemember that 1 is not a prime number.
Q22HardKey concept: permutations
Five people A, B, C, D, E are arranged in a row, with A and B next to each other. How many arrangements are there?
Steps
Treat them as a bundle: 4!×2=48
Answer: DUse the bundling method for adjacency.
Q24HardGeometry
A regular hexagon has side length 4. What is its approximate area? (√3≈1.73)
Steps
6 equilateral triangles = (√3/4)×16×6=24√3≈41.57
Answer: CA regular hexagon equals 6 equilateral triangles.
Q25HardCombinatorics
Choose 3 people from 8, where person A and person B are not both selected. How many ways are there?
Steps
Total ways C(8,3)=56
Both A and B selected: choose 1 more from the remaining 6 = C(6,1)=6
Not both selected = 56 − 6 = 50
Answer: AWhen direct counting is hard, count the complement instead.
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