2018 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 2018 AMC 8
• Five representative real questions with solutions and common mistakes
• Best resources to prepare for AMC 8

2018 AMC 8 Topic Distribution

The 2018 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, 4, 5, 9, 11, 15, 24	area / coordinate geometry / composite shapes / circle area reasoning / visual spatial reasoning
Word Problems / Arithmetic	1, 6, 10, 12, 14, 17, 18	ratios, rates, mean, travel time, remainder, average score manipulation
Number Theory / Algebra	3, 7, 8, 13, 20, 21, 25	divisibility, sequences, harmonic mean, modular arithmetic, exponential / cubes count
Combinatorics & Logic	16, 19, 22	arrangements, sign rules, geometry puzzle with midpoint
Probability & Statistics	23	probability from polygon vertex random selection

Real Questions and Solutions Explained

Geometry Example – Problem 4

Question:

The twelve-sided figure shown has been drawn on 1 cm × 1 cm graph paper. What is the area of the figure in cm²?

(A) 12  (B) 12.5  (C) 13  (D) 13.5  (E) 14

Solution:

There are (3\times3 = 9) whole unit squares in the center.

There are also 8 small right triangles around the outside.
Every 2 of these triangles form 1 whole square, giving 4 more squares.

\[
9 + 4 = 13
\]

Answer: (C)

Common Mistakes:

• Only counting the inner 9 unit squares and forgetting the corner triangles.
• Mis-pairing the 8 triangles (they must be paired 2→1 full square).
• Trying to apply polygon area formulas instead of simple square counting.

Word Problem Example – Problem 12

Question:

The clock in Sri’s car, which is not accurate, gains time at a constant rate. One day as he begins shopping, he notes that his car clock and his watch (which is accurate) both say 12:00 noon. When he is done shopping, his watch says 12:30 and his car clock says 12:35. Later that day, Sri loses his watch. He looks at his car clock and it says 7:00. What is the actual time?

(A) 5:50  (B) 6:00  (C) 6:30  (D) 6:55  (E) 8:10

Solution:

In 30 real minutes, the car clock advanced 35 minutes.
So the car clock runs (\frac{35}{30}) times as fast as the real clock.

From 12:00 to when the car clock reads 7:00 → it gained 7 hours.

Real elapsed time:

\[
7\text{ hours}\times\frac{30}{35}=6\text{ hours}
\]

So the real time is:

12:00 + 6 hours = 6:00

Answer: (B)

Common Mistakes:

• Using 35–30 = 5 as linear gain per hour (wrong logic).
• Comparing minutes and hours inconsistently.
• Forgetting to convert proportion before applying to total hours.

Number Theory Example – Problem 21

Question:

How many positive three-digit integers have a remainder of 2 when divided by 6, a remainder of 5 when divided by 9, and a remainder of 7 when divided by 11?

(A) 1  (B) 2  (C) 3  (D) 4  (E) 5

Solution:

We want a number that is 4 less than a multiple of 6, 9, and 11 (because (11-7=4), (9-5=4), (6-2=4)).

LCM of 6, 9, 11 is:

\[
\text{LCM}=11\times3^2\times2=198
\]

So numbers that satisfy the condition can be written as:

\[
198k – 4
\]

For three-digit integers, (k=1,2,3,4,5) → (194, 392, 590, 788, 986)

There are 5 valid numbers.

Answer: (E)

Common Mistakes:

• Trying to brute force instead of modular pattern shifting.
• Forgetting that the remainders differ by exactly 4.
• Miscalculating LCM of 6, 9, and 11.

Combinatorics Example – Problem 19

Question:

Question:
In a sign pyramid a cell gets a “+” if the two cells below it have the same sign, and it gets a “−” if the two cells below it have different signs. The diagram below illustrates a sign pyramid with four levels. How many possible ways are there to fill the four cells in the bottom row to produce a “+” at the top of the pyramid?

(A) 2  (B) 4  (C) 8  (D) 12  (E) 16

Solution:

List the sign patterns in the bottom row that generate a “+” at the top.
There are exactly 8 possible patterns that result in a final top “+”.

Answer: (C)

Common Mistakes:

• Counting every possible fill and dividing randomly.
• Assuming symmetry halves the count.
• Misinterpreting the “different sign → negative” rule.

Probability Example – Problem 23

Question:

From a regular octagon, a triangle is formed by connecting three randomly chosen vertices of the octagon. What is the probability that at least one of the sides of the triangle is also a side of the octagon?

(A) \(\frac{2}{7}\)  (B) \(\frac{5}{42}\)  (C) \(\frac{11}{14}\)  (D) \(\frac{5}{7}\)  (E) \(\frac{6}{7}\)

Solution:

Choose side “lengths” (a,b,c) representing how many vertices are skipped along each side of the triangle.
The valid configurations where at least one side skips exactly 1 vertex account for \(\frac{5}{7}\) of all possible triangles.

Answer: (D)

Common Mistakes :

• Counting all selections equally without side-length structure.
• Ignoring skip-length equivalence classes in the octagon.
• Overcounting symmetric orderings of same-length sides.

Free Download: 2018 AMC 8 Problems & Solutions

Check the full step-by-step worked solutions.

Download AMC 8 Mock Exams & Daily Practice Pack

Targeted AMC 8 preparation requires both daily skill-building and timed mock exam training. Download high-frequency practice problems and full-length mock exams — all adapted from real AMC 8 trends to ensure efficient, focused prep.

• Daily Practice: Covers key AMC 8 topics like number theory, algebra, geometry, and word problems — great for building speed, accuracy, and confidence over time.
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For more detailed module resources, please visit the All-in-one AMC8 Resource Hub, featuring module practice, mock tests, and biweekly updates.

Recommended Reading

• 2019 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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