AMC 8 Math Competition Test — Questions and Answers

Question 1: A circle has radius 7. What is its area? (Use π ≈ 22/7)

308
44
616
154 (Correct answer)

Correct answer: 154

Area = π × r² = (22/7) × 49 = 22 × 7 = 154.

Question 2: What is the smallest positive integer n such that n² is divisible by 12?

12
6 (Correct answer)
4
2

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 3: What is the prime factorization of 120?

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

Correct answer: 2³ × 3 × 5

120 = 8 × 15 = 2³ × 3 × 5.

Question 4: A card is drawn from a standard 52-card deck. What is the probability it is a face card (J, Q, or K)?

3/13 (Correct answer)
1/4
1/13
3/52

Correct answer: 3/13

There are 12 face cards (4 Jacks + 4 Queens + 4 Kings), so P = 12/52 = 3/13.

Question 5: What is the units digit of 7²⁰?

3
9
1 (Correct answer)
7

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 6: A number increased by 20% equals 60. What is the original number?

40
48
52
50 (Correct answer)

Correct answer: 50

1.2 × n = 60, so n = 60 ÷ 1.2 = 50.

Question 7: A fair coin is tossed twice. What is the probability of getting two heads?

1/2
2/3
1/3
1/4 (Correct answer)

Correct answer: 1/4

P(HH) = (1/2) × (1/2) = 1/4.

Question 8: What is 3.6 ÷ 0.4?

90
0.09
9 (Correct answer)
0.9

Correct answer: 9

3.6 ÷ 0.4 = 36 ÷ 4 = 9.

Question 9: What is the greatest common factor (GCF) of 48 and 36?

12 (Correct answer)
18
9
6

Correct answer: 12

The GCF of 48 and 36 is 12, since 12 divides both and no larger number does.

Question 10: In a class of 30 students, 18 play soccer and 14 play basketball, and 6 play both. How many students play neither sport?

2
8
4 (Correct answer)
6

Correct answer: 4

By inclusion-exclusion, 18 + 14 − 6 = 26 play at least one sport, so 30 − 26 = 4 play neither.

Question 11: Evaluate (2x − 3)² when x = 4.

15
30
25 (Correct answer)
20

Correct answer: 25

2(4) − 3 = 5, and 5² = 25.

Question 12: If 8 workers can build a wall in 6 days, how many days will 4 workers take to build the same wall?

8
12 (Correct answer)
14
10

Correct answer: 12

Total work = 8 × 6 = 48 worker-days; with 4 workers, time = 48 ÷ 4 = 12 days.

Question 13: A cylinder has radius 3 and height 7. What is its volume? (Use π ≈ 3.14)

131.88
197.82 (Correct answer)
263.76
65.94

Correct answer: 197.82

Volume = π × r² × h = 3.14 × 9 × 7 = 197.82 cubic units.

Question 14: The sum of three consecutive integers is 75. What is the largest of the three?

26 (Correct answer)
27
25
24

Correct answer: 26

With integers n, n+1, n+2: 3n + 3 = 75 gives n = 24, so the largest is 26.

Question 15: In a box plot, Q1 = 20, median = 30, Q3 = 40, minimum = 10, maximum = 60. What is the interquartile range (IQR)?

30
20 (Correct answer)
25
15

Correct answer: 20

IQR = Q3 − Q1 = 40 − 20 = 20.

Question 16: A histogram has intervals with frequencies: 0–10: 3, 10–20: 8, 20–30: 12, 30–40: 5. In which interval does the median fall?

20–30 (Correct answer)
10–20
30–40
0–10

Correct answer: 20–30

Total = 28 values; the 14th and 15th values fall in the 20–30 interval (cumulative through 20 is 11).

Question 17: In how many ways can 4 books be arranged on a shelf?

12
24 (Correct answer)
8
16

Correct answer: 24

4 distinct books can be arranged in 4! = 4 × 3 × 2 × 1 = 24 ways.

Question 18: How many 2-digit numbers can be formed using digits 1, 3, 5, 7 if repetition is allowed?

16 (Correct answer)
8
12
20

Correct answer: 16

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

Question 19: Express 0.625 as a fraction in lowest terms.

7/11
3/5
6/9
5/8 (Correct answer)

Correct answer: 5/8

0.625 = 625/1000 = 5/8 after dividing numerator and denominator by 125.

Question 20: What is the next term in the sequence: 2, 5, 10, 17, 26, …?

33
37 (Correct answer)
35
39

Correct answer: 37

The differences between terms are 3, 5, 7, 9 (increasing by 2), so the next difference is 11 and 26 + 11 = 37.

Question 21: A trapezoid has parallel bases of length 6 and 10, and a height of 4. What is its area?

24
64
40
32 (Correct answer)

Correct answer: 32

Area = ½ × (b₁ + b₂) × h = ½ × (6 + 10) × 4 = 32.

Question 22: What is the reciprocal of 2/5?

2/5
5/10
5/2 (Correct answer)
2/10

Correct answer: 5/2

The reciprocal of 2/5 is 5/2, obtained by swapping numerator and denominator.

Question 23: How many three-digit numbers have digits that are strictly increasing from left to right (each digit greater than the one before)?

56
210
84 (Correct answer)
120

Correct answer: 84

Each set of 3 distinct digits from 1–9 arranged in increasing order forms exactly one such number, giving C(9,3) = 84.

Question 24: A car travels at 50 mph for 2 hours and then at 70 mph for 3 hours. What is the total distance traveled?

250
310 (Correct answer)
300
280

Correct answer: 310

Distance = 50 × 2 + 70 × 3 = 100 + 210 = 310 miles.

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
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Unanswered questions count as wrong — answer everything
10 pretest questions are mixed in and don't affect your score
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