2025 AMC 8 Real Questions and Analysis

In this article, you’ll find:

• A concise topic distribution (with a pie chart)
• The core concepts typically tested in each module
• A module-to-question mapping table for the 2025 AMC 8
• Five representative real questions with solutions and common mistakes
• Best resources to prepare for AMC 8

2025 AMC 8 Topic Distribution

The 2025 AMC 8 contains 25 multiple-choice questions completed in 40 minutes, emphasizing logical reasoning and conceptual understanding.

Learn more about AMC 8 Format and Scoring Here: AMC 8 FAQs: The Ultimate Guide for First-Time Test Takers

Detailed Module Analysis

Module	Question Numbers	What It Tests (Brief)
Geometry	1, 5, 8, 10, 11, 12, 15, 18, 24	Area/perimeter, similarity & transformations, angle & length relations, coordinate/diagram reasoning
Word Problems	3, 4, 7, 16, 19, 20	D=RT, proportional reasoning, mixtures, unit consistency, multi-step translation to algebra
Number Theory	2, 6, 13, 22, 23	Divisibility, remainders, modular arithmetic, prime factor patterns
Combinatorics	21, 25	Counting paths/casework, symmetry/binomial coefficients
Probability & Statistics	9, 14, 17	Mean/median/mode, visual data interpretation, basic probability

Real Questions and Solutions Explained

Geometry Example – Problem 1

Question:

The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire 4 × 4 grid is covered by the star?

(A) 40 (B) 50 (C) 60 (D) 75 (E) 80

Solution:
By symmetry, divide the 4 × 4 grid into four congruent 2 × 2 quadrants. Each quadrant has identical coverage by the star.
Focus on one quadrant: using a sliding / reconfiguration argument, you can show that exactly half of that quadrant is covered (by rearranging triangular pieces).

Coverage per quadrant:
\[\frac{1}{2}\]

Total coverage across four quadrants:
\[4 \times \frac{1}{2} = 2\]

Overall fraction of the grid:
\[\frac{2}{4} = \frac{1}{2}\]

Therefore, 50% of the grid is covered.
Answer (B)

Common Mistakes:

• Computing many small triangle areas individually (prone to arithmetic errors).
• Ignoring symmetry or quadrant division.
• Sliding triangles incorrectly (overlaps or gaps).
• Forgetting to scale results to all four quadrants.

Word Problem Example – Problem 19

Question:

Two towns 𝐴 and 𝐵 are connected by a straight road 15 miles long. Traveling from 𝐴 to 𝐵, the speed limit changes every 5 miles: first 25 mph, then 40 mph, then 20 mph. Two cars start at the same time from 𝐴 and 𝐵, traveling exactly at the speed limits each segment. Where (how many miles from 𝐴) will they meet?

(A) 7.75 (B) 8.0 (C) 8.25 (D) 8.5 (E) 8.75

Solution:

Divide the 15-mile road into three 5-mile segments with limits 25 / 40 / 20 mph.  

Car 𝐴 takes 5 ÷ 25 = 0.2 h to finish its first segment.  

Car 𝐵 takes 5 ÷ 20 = 0.25 h for its first segment.  

At 0.25 h, car 𝐴 has traveled an extra 0.05 h into the second segment:  

40 × 0.05 = 2 miles, so it is 5 + 2 = 7 miles from 𝐴.  

The remaining gap between them is 5 − 2 = 3 miles.  

Relative speed = 40 + 40 = 80 mph.  

Time to meet = \[\frac{3}{80}\] h = 0.0375 h ≈ 2.25 min.  

Car 𝐴 travels 40 × 0.0375 = 1.5 mi more.  

Meeting point = 7 + 1.5 = 8.5 mi from 𝐴.  

Answer (D)

Common Mistakes :

• Assuming both cars drive at identical speeds in each zone.
• Ignoring the 0.05 h time offset before both enter the same segment.
• Misconverting units (hours ↔ minutes).
• Forgetting to add car 𝐴’s extra distance in the middle segment.

Number Theory Example – Problem 6

Question:

Sekou writes the numbers 15, 16, 17, 18, 19. After he erases one of them, the sum of the remaining four numbers is a multiple of 4. Which number did he erase?

(A) 15 (B) 16 (C) 17 (D) 18 (E) 19

Solution:

Total sum = 15 + 16 + 17 + 18 + 19 = 85.
Since 85 mod 4 = 1, let the erased number be 𝑥.
We want 85 − 𝑥 ≡ 0 (mod 4) ⇒ −𝑥 ≡ −1 (mod 4) ⇒ 𝑥 ≡ 1 (mod 4).

Compute each mod 4: 15 ≡ 3, 16 ≡ 0, 17 ≡ 1, 18 ≡ 2, 19 ≡ 3.
Thus 𝑥 = 17.

Answer (C)

Common Mistakes :

• Forgetting to take the total sum mod 4.
• Arithmetic errors when finding remainders.
• Mishandling the negative sign in congruences.
• Not verifying which single value satisfies the condition.

Combinatorics Example – Problem 25

Question:

Makayla finds all possible paths in a 5 × 5 diamond-shaped grid. Each path starts at the bottom and ends at the top, always moving one unit northeast or northwest. She computes the area between each path and the right side of the grid. What is the sum of the areas determined by all possible paths?

(A) 2520 (B) 3150 (C) 3840 (D) 4730 (E) 5050

Solution:

Each path has 10 moves (5 NE + 5 NW). The number of such paths is \[\frac{10!}{5!\,5!}=252\]

Let the total area to the right be 𝑋. By symmetry, the total to the left is also 𝑋. For any single path, the sum “area to right + area to left” equals 25, so \[2𝑋=25\times252\] and thus \[𝑋=\frac{25\times252}{2}=3150\]

Answer (B)

Common Mistakes :

• Trying to list every path and compute areas individually.
• Missing the key insight that left + right area is constant.
• Miscounting paths.
• Using symmetry without explicit reasoning.

Probability Example – Problem 14

Question:

A number 𝑁 is inserted into the list 2, 6, 7, 7, 28. The mean (average) of the new list of six numbers is twice the median of that list. What is 𝑁?

(A) 7 (B) 14 (C) 20 (D) 28 (E) 34

Solution:
Original sum = 2 + 6 + 7 + 7 + 28 = 50. After adding 𝑁, there are 6 numbers. The median = average of the 3rd and 4th numbers. Because 𝑁 ≥ 7, the middle two values are both 7, so the median = 7.

The mean is \[\frac{50 + N}{6}\].
Given that mean = 2 × median = 14, we have \[\frac{50 + N}{6} = 14\]
This gives \(50 + N = 84 \Rightarrow N = 34\)

Answer (E)

Common Mistakes :

• Misplacing 𝑁 when determining the median.
• Forgetting that for even data, the median is the average of the two middle numbers.
• Arithmetic slips when solving \[\frac{50 + N}{6} = 14\]
• Assuming 𝑁 affects the median when it does not.

2025 AMC 8 Answer Key

Question	Answer
1	B
2	B
3	C
4	B
5	C
6	C
7	D
8	A
9	B
10	D
11	C
12	C
13	A
14	E
15	C
16	C
17	D
18	B
19	D
20	A
21	A
22	D
23	B
24	E
25	B

Best Resources to Prepare for AMC 8

Visit All-in-one AMC8 Resource Hub: past papers, mock tests, and expert walkthroughs

Recommended Reading

• How to Prepare for AMC 8 Math Competition
• All About 2026 AMC 8: Dates, Registration, Scores and Prep Tips
• AMC 8 FAQs: The Ultimate Guide for First-Time Test Takers

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