AMC stands for the American Mathematics Competitions, a series of examinations and curriculum materials aimed at fostering interest and strengthening problem-solving skills in mathematics. If you’re considering participating in the AMC 10, this article will provide a comparison of AMC 10 with both AMC 8 and in-school math, shedding light on the difficulty of AMC 10 through these analyses. 

AMC 10 vs. AMC 8

The AMC series comprises various levels, with the entry level being AMC 8 for students in grade 8 or below. To learn more about AMC 8 problems, you can refer to this article. Next in line is AMC 10, tailored for students in grade 10 or below. It is a 25-question, 75-minute, multiple-choice examination designed to promote the development and enhancement of problem-solving skills. In addition to AMC 8 and AMC 10, there are more advanced-level math competitions such as AMC 12, AIME, and USAMO/USAJMO.

To understand the difficulty of the AMC 10 compared to AMC 8, let’s examine three key aspects:

1. Exam Length and Scoring Rules

AMC 10 offers a longer duration of 75 minutes, in contrast to the 40 minutes provided for AMC 8. The scoring rules also differ between the two exams. While guessing is possible in AMC 8, with 1 point for a correct answer and 0 points for a wrong or unanswered question, AMC 10 encourages test-takers to refrain from answering questions they are uncertain about. AMC 10 awards 6 points for a correct response, 1.5 points for no answer, and 0 points for an incorrect answer. The AMC 10 scoring system emphasizes accuracy and allows candidates relatively ample time to ensure the correctness of their answers. 

2. Exam Content and Preparation

AMC 8 covers the Math Common Core curriculum up to grade 8, providing students with the opportunity to learn the necessary concepts before entering middle school. On the other hand, AMC 10 encompasses the entire content of Algebra 1 and Geometry, going deeper than AMC 8. As a result, the preparation period for AMC 10 is typically longer, ranging from 2 to 3 years compared to 1 to 1.5 years for AMC 8. Students who have not been exposed to the secondary school curriculum may face a disadvantage when preparing for AMC 10. 

3. Difficulty of Questions

The difficulty of the questions is a critical aspect when comparing the AMC 8 and AMC 10 exams. While the length of the AMC 8 exam can be a challenge, the primary obstacle in taking the AMC 10 lies in the complexity of the questions. Even if students have sufficient time to answer the questions, they may struggle to score high if they are not adequately prepared for the difficulty level.

The AMC 10 presents a higher level of difficulty than the AMC 8 in all aspects. It covers a broader range of mathematical modules, and its problems are significantly more challenging. The most complex problem on the AMC 8 is roughly equivalent in difficulty to the first 10 problems on the AMC 10. The AMC 10 exam typically features a mix of questions, with the first 10 questions being relatively easy, questions 11 to 17 falling into the medium difficulty range, and Questions 18 to 25 classified as challenging or difficult.

To illustrate this, let’s look at an example:

AMC 8

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AMC 10

As we can see, both problems test the area of similar triangles. The AMC 8 problem provides students with the diagram of similar triangles, making it relatively straightforward for students to calculate and obtain the result directly. However, the AMC 10 problem requires students to draw auxiliary lines themselves, and it provides fewer conditions than the one in AMC 8. Solving this AMC 10 problem demands a strong familiarity with the logic of solving such problems, requiring more thinking and careful consideration before proceeding with calculations.

AMC 10 vs. In-School Math

If you have already participated in the AMC exam, you likely understand the differences between AMC 8 and AMC 10. However, if you have not yet taken the AMC exam, it would be a good starting point to first understand the distinctions between AMC 10 and in-school math. The biggest disparity between in-school math and competition math is the depth of thinking and creativity required. This is why many students who can easily earn an A in their school’s fast-track math classes might struggle to score 60-70 on the AMC 10 without preparation.

To highlight the differences between AMC 10 and in-school math, let’s examine four problem types across various modules:

1. Algebra

In-School Math

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AMC 10

While school-level algebra tends to focus on computation, the AMC 10’s assessment of algebra leans more towards analysis and integrated application. It introduces equations with parameters, demanding additional critical thinking from students.

2. Geometry

In-School Math

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AMC 10

In school-level mathematics, geometry questions often test students’ understanding and memory of concepts without emphasizing problem-solving skills. However, in the AMC 10, geometry questions frequently assess multiple knowledge points simultaneously, requiring students to synthesize and apply these concepts effectively.

3. Number Theory

Number theory is rarely covered in school-level mathematics, but it appears in the AMC 10. As a result, students need to undertake additional study to master problem-solving techniques and basic conclusions. This preparation can significantly reduce the time consumed by the trial-and-error method.

This number theory question from the Think Academy 2023 AMC 10 preparation group serves as an excellent example to highlight the importance of problem-solving techniques:

2018 AMC 10B, Question 11

Student 1’s Solution

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Student 2’s Solution

The first student demonstrated a deep understanding of number theory, employing a common conclusion regarding perfect squares: when “p” is a prime number and not equal to 3, the remainder of the square of “p” divided by 3 is 1. Armed with this insightful knowledge, the student efficiently calculates the result within a mere 20 seconds.

The second student attempted to solve the problem through trial and error, which, while feasible for this relatively straightforward question, may prove cumbersome and inefficient for more challenging problems. In such cases, relying solely on trial and error would consume a significant amount of time, hindering the student’s ability to tackle other questions within the given time constraints.

4. Permutations, Combinations, and Probability

2018 AMC 10B, Question 9

In terms of permutations, combinations, and probability, students get a brief introduction when studying Algebra 1 and Algebra 2 in school, but the depth of these topics is far from what is required in the AMC 10. Many school teachers use the probability of the sum of two dice as an experimental question to facilitate student exploration. However, in the AMC 10, the number of dice can reach up to seven, far exceeding the scope of in-school mathematics. This requires students to learn to summarize and draw inferences from one example to others; otherwise, they might be completely at a loss when encountering such problems. 

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Understanding these distinctions between AMC 10 and in-school math is crucial for your successful preparation and approach to the exam. To support students in their journey, Think Academy offers specialized courses tailored for the AMC 10. These courses follow a systematic approach, covering essential questions, easy questions, and the final, more challenging questions. Don’t miss this opportunity to excel in the AMC 10 and boost your problem-solving skills in mathematics! 

For any inquiries or further information, you can contact Think Academy at info@thethinkacademy.com or call +1 (844) 844-6587.