AMC 8 Math Competition Test — Questions and Answers

Question 1: A rectangle has perimeter 24 and length 8. What is its area?

16
64
48
32 (Correct answer)

Correct answer: 32

Using P = 2(l + w): 24 = 2(8 + w), so w = 4, and area = 8 × 4 = 32.

Question 2: A class of 10 boys has an average score of 75, and a class of 15 girls has an average score of 80. What is the combined class average?

78 (Correct answer)
77
77.5
78.5

Correct answer: 78

Combined average = (10×75 + 15×80)/(10+15) = (750+1200)/25 = 1950/25 = 78.

Question 3: How many positive factors does 36 have?

9 (Correct answer)
7
8
6

Correct answer: 9

36 = 2² × 3² has (2+1)(2+1) = 9 factors: 1, 2, 3, 4, 6, 9, 12, 18, 36.

Question 4: Simplify: 3(2x + 4) − 2(x − 1).

4x + 10
4x + 6
4x + 14 (Correct answer)
8x + 10

Correct answer: 4x + 14

6x + 12 − 2x + 2 = 4x + 14.

Question 5: What is the prime factorization of 120?

2² × 3 × 5
2³ × 3² × 5
2 × 3 × 5²
2³ × 3 × 5 (Correct answer)

Correct answer: 2³ × 3 × 5

120 = 8 × 15 = 2³ × 3 × 5.

Question 6: There are 5 boys and 4 girls. In how many ways can a team of 3 boys and 2 girls be selected?

120
240
80
60 (Correct answer)

Correct answer: 60

C(5,3) × C(4,2) = 10 × 6 = 60.

Question 7: Scores of 60, 70, 80, and 90 in a frequency table have frequencies of 2, 5, 8, and 5. What is the mode?

75
90
70
80 (Correct answer)

Correct answer: 80

The mode is 80 because it has the highest frequency of 8 occurrences.

Question 8: From a group of 5 students, in how many ways can 2 students be chosen for a committee?

10 (Correct answer)
5
20
8

Correct answer: 10

C(5,2) = 5!/(2! × 3!) = 10.

Question 9: A student scored 18 out of 24 on a test. What percentage did they score?

65%
72%
75% (Correct answer)
70%

Correct answer: 75%

18/24 = 3/4 = 75%.

Question 10: What digit d makes the three-digit number 4d2 divisible by 3?

1
5
0 (Correct answer)
7

Correct answer: 0

For divisibility by 3, the digit sum 4+0+2 = 6 is divisible by 3, so d = 0 works.

Question 11: What is the sum of the first 10 positive integers?

60
50
45
55 (Correct answer)

Correct answer: 55

Using Gauss's formula: n(n+1)/2 = 10 × 11/2 = 55.

Question 12: How many lines of symmetry does a regular pentagon have?

5 (Correct answer)
3
6
4

Correct answer: 5

A regular pentagon has 5 lines of symmetry, one through each vertex and the midpoint of the opposite side.

Question 13: What is the volume of a rectangular box with dimensions 3 × 4 × 5?

80
47
94
60 (Correct answer)

Correct answer: 60

Volume = length × width × height = 3 × 4 × 5 = 60 cubic units.

Question 14: What is the units digit of 7²⁰?

7
1 (Correct answer)
9
3

Correct answer: 1

The units digits of powers of 7 cycle as 7, 9, 3, 1 (period 4); since 20 is divisible by 4, 7²⁰ ends in 1.

Question 15: A rectangle's length is increased by 20% and its width is decreased by 10%. By what percent does the area change?

10% decrease
8% decrease
8% increase (Correct answer)
10% increase

Correct answer: 8% increase

New area = 1.2 × l × 0.9 × w = 1.08lw, which is an 8% increase.

Question 16: What is the smallest positive integer n such that n² is divisible by 12?

2
6 (Correct answer)
4
12

Correct answer: 6

Since 12 = 2² × 3, for 12 | n², n must be divisible by both 2 and 3; the smallest such n is 6, and 6² = 36 = 12 × 3.

Question 17: A tank is 1/3 full. After adding 20 gallons it is 1/2 full. What is the tank's total capacity?

120 (Correct answer)
60
90
100

Correct answer: 120

The 20 gallons fills 1/2 − 1/3 = 1/6 of the tank, so the total capacity = 20 × 6 = 120 gallons.

Question 18: What is the value of 3a − 2b when a = 4 and b = −1?

10
12
14 (Correct answer)
16

Correct answer: 14

3(4) − 2(−1) = 12 + 2 = 14.

Question 19: What is 7/8 − 1/3?

11/24
13/24 (Correct answer)
17/24
6/5

Correct answer: 13/24

7/8 − 1/3 = 21/24 − 8/24 = 13/24.

Question 20: How many 2-digit numbers can be formed using digits 1, 3, 5, 7 if repetition is allowed?

16 (Correct answer)
12
20
8

Correct answer: 16

Each of the two digit positions has 4 choices, so there are 4 × 4 = 16 two-digit numbers.

Question 21: What is 40% of 40% of 100?

32
8
16 (Correct answer)
64

Correct answer: 16

40% of 100 = 40, and 40% of 40 = 16.

Question 22: A price increases from $40 to $50. What is the percent increase?

20%
25% (Correct answer)
10%
30%

Correct answer: 25%

Percent increase = (change / original) × 100% = (10/40) × 100% = 25%.

Question 23: A box has 6 red and 4 blue balls. Two balls are drawn without replacement. What is the probability both are red?

1/4
1/3 (Correct answer)
3/10
9/25

Correct answer: 1/3

P = (6/10) × (5/9) = 30/90 = 1/3.

Question 24: Five friends split a restaurant bill equally. If each pays $13.40, what is the total bill?

$65.00
$67.00 (Correct answer)
$70.00
$60.00

Correct answer: $67.00

Total = 5 × $13.40 = $67.00.

AMC 8 Math Competition Test

The AMC 8 is a 25-question, 40-minute multiple-choice math competition for students in grade 8 and below, covering number theory, geometry, algebra, probability, and problem-solving skills.

Questions

40 min

Time Limit

72%

To Pass

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Exam Rules

You can skip questions and return to them later
Flag questions for review before submitting
No feedback shown until you submit the entire exam
Unanswered questions count as wrong — answer everything
10 pretest questions are mixed in and don't affect your score
Timer auto-submits when time runs out
Your progress is auto-saved every 30 seconds