2023 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 2023 AMC 8
• Five representative real questions with solutions and common mistakes
• Best resources to prepare for AMC 8

2023 AMC 8 Topic Distribution

The 2023 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	2, 7, 12, 17, 19, 24	Folding & cutting, coordinate and similar triangles, area/ratio reasoning
Word Problems	1, 5, 10, 11, 13, 15, 18	Contextual arithmetic, rates, proportions, multi-step logic and unit conversion
Number Theory	3, 4, 6, 16, 22, 25	Defined operations, primes, remainder patterns, inequalities and sequences
Combinatorics & Logic	8, 14, 20, 21	Arrangements, max/min construction, enumeration logic
Probability & Statistics	9, 23	Probability, data interpretation and graph reading

Real Questions and Solutions Explained

Geometry Example – Problem 12

Question:

The figure below shows a large white circle with a number of smaller white and shaded circles in its interior. What fraction of the interior of the large white circle is shaded?

(A) \(\frac{1}{4}\)  (B) \(\frac{11}{36}\)  (C) \(\frac{1}{3}\)  (D) \(\frac{19}{36}\)  (E) \(\frac{5}{9}\)

Solution:

Let the grid unit be 1. The large circle has radius 3, so its area is \(A_{big}=9\pi.\)

The middle gray circle has radius 2, and two unit white circles (radius 1) are removed, so \(A_{center}=4\pi-2\pi=2\pi.\)

On the right, there are two shaded small disks with radius 0.5, plus one half of such a disk: \(A_{right}=2\times(0.5)^2\pi+\frac{1}{2}(0.5)^2\pi=\frac{5}{8}\pi.\)

By symmetry, the small gray crescent on the left equals another half of a radius-0.5 disk: \(A_{left}=\frac{1}{8}\pi.\)

Total shaded area \(A_{shaded}=2\pi+\frac{5}{8}\pi+\frac{1}{8}\pi=\frac{11}{4}\pi.\)

Shaded fraction \(\frac{A_{shaded}}{A_{big}}=\frac{\frac{11}{4}\pi}{9\pi}=\frac{11}{36}.\)

Answer: (B)

Common Mistakes:

• Not subtracting the two unit white disks from the radius-2 disk.
• Counting the rightmost little circle as a full disk instead of a half disk.
• Missing the left gray crescent, which contributes another half of a small disk.

Word Problem Example – Problem 11

Question:

NASA’s Perseverance Rover was launched on July 30, 2020. After traveling 292,526,838 miles, it landed on Mars in Jezero Crater about 6.5 months later. Which of the following is closest to the Rover’s average interplanetary speed in miles per hour?

(A) 6,000  (B) 12,000  (C) 60,000  (D) 120,000  (E) 600,000

Solution:

Take 1 month ≈ 30 days. So \(6.5\times30=195\text{ days}=195\times24=4680\text{ hours}.\)

Average speed \(\frac{292,526,838}{4680}\approx62,500\text{ mph},\) closest to 60,000.

Answer: (C)

Common Mistakes:

• Using days instead of hours in the denominator.
• Over-refining month length (31 vs. 30) unnecessarily.
• Rounding too early.

Number Theory Example – Problem 6

Question:

The digits 2, 0, 2, and 3 are placed in the expression below, one digit per box. What is the maximum possible value of the expression?

(A) 0  (B) 8  (C) 9  (D) 16  (E) 18

Solution:

We maximize \((a^{b})(c^{d})\) using {2,0,2,3}.

Using 0 as base → product 0; using 0 as exponent → 1.

Pair largest base with largest exponent: \(3^2=9\); \(2^0=1\). Thus \(9\times1=9.\)

Any other arrangement gives at most \(2^3\times2^0=8.\)

Answer: (C)

Common Mistakes:

• Using 0 as a base (product 0).
• Miscomputing \(2^3\times2^0=8\) as 16.
• Reusing digits incorrectly.

Combinatorics Example – Problem 14

Question:

Nicolas is planning to send a package to his friend Anton, who is a stamp collector. To pay for the postage, Nicolas would like to cover the package with a large number of stamps. Suppose he has a collection of 5-cent, 10-cent, and 25-cent stamps, with exactly 20 of each type. What is the greatest number of stamps Nicolas can use to make exactly $7.10 in postage? (Note: The amount $7.10 corresponds to 7 dollars and 10 cents. One dollar is worth 100 cents.)

(A) 45  (B) 46  (C) 51  (D) 54  (E) 55

Solution:

Let’s use the most stamps to make 7.10. We have 20 of each stamp — 5-cent, 10-cent, and 25-cent stamps.

If we want the highest number of stamps, we should use the smaller value stamps first. Using 20 of the 5-cent stamps and 20 of the 10-cent stamps gives us 3.00 dollars in postage. So we still need 7.10 − 3.00 = 4.10 dollars.

However, when we try to use 25-cent stamps, 25 cents does not divide evenly into 4.10, so we need to “give back” 15 cents to make the total become 4.25 dollars. The most efficient way is to remove one 10-cent stamp and one 5-cent stamp.

Now we have 38 stamps used so far. Next, we use \(\frac{425}{25} = 17\) more stamps of 25 cents to complete the postage.

Total stamps used = 38 + 17 = 55

Answer: (E)

Common Mistakes:

• Thinking “20 of each” means you MUST use all 20 of each type instead of “at most 20”.
• Starting with quarters first instead of maximizing smaller stamps first.
• Forgetting to check if the remaining amount is divisible by 25.
• Not knowing that removing stamps strategically (like 15 cents) can increase the total stamp count.

Probability Example – Problem 9

Question:

Malaika is skiing on a mountain. The graph below shows her elevation, in meters, above the base of the mountain as she skis along a trail. In total, how many seconds does she spend at an elevation between 4 and 7 meters?

(A) 6  (B) 8  (C) 10  (D) 12  (E) 14

Solution:

From the graph, elevation 4 ≤ 𝑦 ≤ 7 occurs in three segments. Their total horizontal lengths add to \(2+6+4=12\text{ seconds}.\)

Answer: (D)

Common Mistakes :

• Measuring vertical distance instead of time.
• Missing one of the three segments.
• Not including the endpoints.

2023 AMC 8 Answer Key

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

Best Resources to Prepare for AMC 8

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

Recommended Reading

• 2024 AMC 8 Real Questions and Analysis
• 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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