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1999

1999 AMC8 Paper & Solutions Pick

AMC8 inaugural exam, 25 questions with solutions, classic problems for foundational practice.

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12 Sample Questions
40 Minutes
Max Score 25
No Calculator
Exam Overview

Exam Overview

AMC8, .

DDifficulty

  • EasyQ1-10
  • MediumQ11-20
  • HardQ21-25

TTopics

  • Algebra35%
  • Geometry30%
  • Number Theory15%
  • Combinatorics20%

AAwards

Distinguished Honor Roll
Distinguished Honor Roll (Top 1%)
18+
Honor Roll
Honor Roll (Top 5%)
14+
Achievement Roll
Grade 6 and below · 15+ points
15+
Sample Problems

1999 AMC8 Sample Problems (12 questions)

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

Q1EasyArithmetic
Calculate the value of 1999+1.
A) 1990
B) 2000
C) 1999
D) 2001
E) 2010

Steps

1999+1=2000
Answer: BBasic addition
Q3EasyKey concept: ratios
What is 2/3 of 12?
A) 4
B) 8
C) 6
D) 9
E) 10

Steps

12×2/3=8
Answer: BFraction multiplication
Q5EasyArea
What is the area of a rectangle with length 10 and width 6?
A) 16
B) 30
C) 40
D) 50
E) 60

Steps

10×6=60
Answer: EArea of a rectangle
Q8EasyApply the relevant mathematical concept
What is the mode of the data 4, 6, 8, 6, 4, 6?
A) 4
B) 5
C) 7
D) 6
E) 8

Steps

6 appears 3 times, the most
Answer: DDefinition of mode
Q11MediumKey concept: equations
If 5x-3=2x+9, what is x?
A) 2
B) 4
C) 3
D) 5
E) 6

Steps

3x=12 → x=4
Answer: BMove terms and combine
Q14MediumArea
A circle has radius 4. What is its area? (π≈3.14)
A) 25.12
B) 50.24
C) 37.68
D) 62.80
E) 100.48

Steps

π×16≈50.24
Answer: BArea formula of a circle
Q16MediumProbability
What is the probability of rolling an odd number on a die?
A) 1/6
B) 1/4
C) 1/2
D) 1/3
E) 2/3

Steps

The odd numbers 1, 3, 5 give 3 outcomes
3/6=1/2
Answer: CClassical probability
Q18MediumNumber Theory
What is the least common multiple of 18 and 24?
A) 36
B) 48
C) 72
D) 54
E) 96

Steps

18=2×3², 24=2³×3
LCM=2³×3²=72
Answer: CFor the LCM, take the highest power of each prime
Q21HardArea
A rhombus has diagonals 12 and 16. What is its perimeter?
A) 28
B) 40
C) 36
D) 44
E) 48

Steps

Half-diagonals 6 and 8
Side length=√(36+64)=10
Perimeter=40
Answer: BThe diagonals are perpendicular bisectors of each other
Q22HardKey concept: permutations
Four people A, B, C, D stand in a row with A and B not adjacent. How many arrangements are there?
A) 6
B) 8
C) 12
D) 10
E) 14

Steps

Total 4!=24, A and B adjacent=3!×2=12
24-12=12
Answer: CTotal minus adjacent
Q24HardNumber Theory
How many perfect squares are there from 1 to 100?
A) 8
B) 9
C) 11
D) 10
E) 12

Steps

1² to 10², which is 10 of them
√100=10
Answer: DCounting perfect squares
Q25HardCombinatorics
How many ways are there to choose 2 people from 5 to form a team?
A) 5
B) 8
C) 15
D) 10
E) 20

Steps

C(5,2)=10
Answer: DCombination formula

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