2006
2006 AMC8 Paper & Solutions Pick
25 questions with solutions, geometry focuses on circles and triangles, practical word problems.
Scan to get free 2006 PDF + solutions
12 Sample Questions
40 Minutes
Max Score 25
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Exam Overview
Exam Overview
This exam emphasizes geometry. Overall difficulty is moderate.
Difficulty
- EasyQ1-10
- MediumQ11-20
- HardQ21-25
Topics
- Algebra35%
- Geometry30%
- Number Theory15%
- Combinatorics20%
Awards
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
2006 AMC8 Sample Problems (12 questions)
Sample reference problems by difficulty — click an option to check your answer
Q1EasyArithmetic
Calculate the value of 345+655.
Steps
345+655=1000
Answer: EMake a round number
Q3EasyKey concept: fractions
What is 2/5 as a percentage?
Steps
2/5=0.4=40%
Answer: EConverting a fraction to a percentage
Q5EasyArea
What is the circumference of a circle with radius 3 cm? (π≈3.14)
Steps
2×3.14×3=18.84
Answer: DCircumference=2πr
Q8EasyApply the relevant mathematical concept
For the data 5, 3, 8, 3, 6, what is the sum of the mode and the mean?
Steps
Mode=3, Mean=(5+3+8+3+6)/5=5
3+5=8
Answer: BThe mode is the value that appears most often
Q11MediumKey concept: equations
A is 6 years older than B. Three years ago, A's age was twice B's age. How old is A now?
Steps
Let B be x and A be x+6
(x+3)=(2)(x-3)
x+3=2x-6→x=9
A=15
Answer: DThe age difference never changes
Q14MediumDivisibility
How many perfect squares are there from 1 to 50?
Steps
1, 4, 9, 16, 25, 36, 49 — 7 in total
Answer: C√50≈7.07
Q16MediumArea
An isosceles right triangle has a hypotenuse of 10. What is its area?
Steps
Leg=10/√2=5√2
Area=1/2×(5√2)²=25
Answer: CArea=hypotenuse²/4
Q19MediumProbability
A die is rolled 3 times. What is the probability that the sum of the three rolls is 3?
Steps
Only (1,1,1) works
Probability=1/216
Answer: CFor the three rolls to sum to 3, all must be 1
Q21HardNumber Theory
Find the value of 2006²-2005².
Steps
Difference of squares=(2006+2005)(2006-2005)=4011×1=4011
Answer: Aa²-b²=(a+b)(a-b)
Q22HardKey concept: permutations
A, B, C, D are arranged in a row with A and B not adjacent. How many arrangements are there?
Steps
Total 4!=24, A and B adjacent=3!×2=12
24-12=12
Answer: DNot adjacent = total minus adjacent
Q24HardGeometry
A trapezoid has top base 8, bottom base 16, and height 10. A diagonal divides the trapezoid into two triangles. What is the difference between their areas?
Steps
Lower triangle=1/2×16×10=80
Upper triangle=1/2×8×10=40
Difference=40
Answer: DA diagonal divides the trapezoid into two triangles with the same height
Q25HardCombinatorics
Choose 4 numbers from 1 to 12 so that their sum is even. How many ways are there?
Steps
From 1 to 12 there are 6 odd numbers and 6 even numbers
Three cases give an even sum: 4 even / 4 odd / 2 odd and 2 even
4 even C(6,4)=15, 4 odd C(6,4)=15
2 odd 2 even C(6,2)×C(6,2)=15×15=225
Total 15+15+225 = 255
Answer: BWhether the sum is odd or even is determined by the number of odd terms
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