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.

Best Resources to Prepare for AMC 8

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

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

About Think Academy

Think Academy, a top math education brand under TAL Education Group, offers specialized training for the prestigious AMC 8 competition. In 2025, 672 Think Academy students earned national awards—65% of them placed on the Achievement, Honor, or Distinguished Honor Rolls. From 2022 to 2025, our results have grown rapidly, setting records in award counts and perfect scores. Backed by expert teachers and a proven curriculum, Think Academy prepares middle schoolers for lasting success in competitive math. Explore our AMC 8 courses and start your child’s winning journey.

Want more insights on math education and parenting tips? Subscribe to our newsletter for weekly expert advice and updates on the latest learning tools.