In this comprehensive analysis, Think Academy‘s math experts delve into the recently concluded 2023 AMC 10A competition, exploring overall difficulty levels and question structures. From the initial set of relatively basic questions to the concentration of geometry in the moderate difficulty range, and finally, to the last five particularly challenging questions, our analysis unveils patterns and nuances that shape the examination landscape. Our module-specific breakdown sheds light on the varying levels of difficulty and the knowledge proficiency required in each area. Additionally, we identify error-prone questions and tricky questions,  providing effective answering strategies. Read on! 

Overall Difficulty Levels

The question difficulty is relatively moderate, and the final questions are less complex than anticipated.

1.  Easy questions start from a basic level, but none are absolute giveaways. Unlike prior years where the first question was a straightforward calculation, this year’s initial question involved a problem-solving scenario, not difficult but requiring multiple steps, without offering complete free points. Additionally, within the first 10 questions, the 7th and 9th questions are prone to errors, challenging students’ mindset when placed at the beginning.

2. Moderate-difficulty questions focus primarily on geometry. While the tested geometry knowledge areas are similar to previous years, there are no exceptionally difficult or time-consuming questions. Many questions can be solved with a clear approach, and the 16th question, the most challenging in geometry, requires an analysis combining some number theory knowledge.

3. The last 5 questions do not present particularly challenging situations, and familiarity with core concepts is generally sufficient for quick resolution.

Overall, this exam assesses students’ attention to detail in various aspects. Meticulous students are likely to score significantly higher, leading to overall scores that could be either very high or very low.

Module-Specific Breakdown

Exam Structure and Module Distribution

Module	Question Numbers	Total Count
Algebra	1，2，5，8，10，21，23	7
Geometry	4，6，11，13，15，17，18，19，22，24	10
Combinatorics	7，9，14，16，20，25	7
Number theory	3，12	2

Algebra: Varied Difficulty Levels

• Algebra questions encompassed 7 problems.
• Concentration is observed in the initial 10 and final 5 questions.
• Surprisingly, no algebra questions were found in the 11-20 range.
• A distinct polarization in difficulty is evident.
• Topics covered include basic operations, fractions, mean, exponentiation, polynomials, and algebraic expressions with integer solutions.
• Notably, the customary examination of arithmetic progression is omitted.

Geometry: The Key to High Scores

• Geometry consisted of 10 questions.
• Six geometry questions were concentrated in the 11-20 range.
• Two geometry questions were present in both the initial and final 10 questions.
• There is a lack of exceptional difficulty in geometry questions.
• Covered topics encompass square/triangle/circle areas, tangency of circles, regular polygons, and the Pythagorean theorem.
• Adherence to standard planar geometry concepts is evident.
• Proficiency in geometry correlates with higher scores.
• Solid Geometry:
  • Three questions touched on the topic.
  • There was no delve into pure solid geometry concepts.
  • Question 6 focused on cube geometry.
  • Question 18 explored Euler’s theorem.
  • Question 25 addressed a polyhedron’s properties.
  • The absence of topics like cylinders and cones raises curiosity about their potential inclusion in subsequent sections.

Combinatorics: Emphasis on Counting Principles and Probability

• The examination’s approach to combinatorics remains consistent, focusing on counting principles and probability.
• Among the six combinatorial questions, five were centered on counting principles and probability (3 probability + 2 counting).
• An additional question delved into the realm of sports competitions.
• The last question on counting and probability exhibited a distinctive characteristic, testing students’ understanding of spatial geometry.
  • Knowing the properties of a specific geometric shape facilitated a quick solution.
  • Lack of familiarity with the three-dimensional figure made the question considerably challenging.
• The other counting and probability questions intricately interwove various knowledge domains, extending beyond the realms of pure combinatorics.

Answers, Key Knowledge Areas, and Difficulty Levels for Each Question

Question number	Answer	Module	Key Knowledge Area	Difficulty Level *
1	E	Algebra	Traveling itinerary problem	1
2	A	Algebra	Fraction word problems	1.5
3	A	Number theory	Perfect square	1
4	D	Geometry	Quadrilateral side relationships	1
5	E	Algebra	Exponential calculation	1
6	D	Geometry	Fundamental knowledge of a cube	2
7	B	Combinatorics	Dice probability	2.5
8	D	Algebra	Applications of Linear Functions	2
9	E	Combinatorics	Counting Numbers	2.5
10	D	Algebra	Average (Mean) Problems	2
11	C	Geometry	Area of Square and Triangle	2
12	B	Number theory	Division	2
13	C	Geometry	Inscribed angle	2.5
14	B	Combinatorics	Probability	3.5
15	E	Geometry	Area of Circle	2
16	B	Combinatorics	Sports Competition	3.5
17	A	Geometry	Pythagorean theorem	3
18	D	Combinatorics	Euler’s theorem	3
19	E	Geometry	Geometric Rotation	3
20	D	Combinatorics	Counting Numbers	3.5
21	D	Algebra	Factor theorem	4
22	D	Geometry	Tangent Circles	3.5
23	C	Algebra+Number theory	Solving Integer Solutions for Algebraic Expressions	4.5
24	C	Geometry	Regular polygon	3
25	A	Combinatorics	Probability (Regular Icosahedron)	5

Strategies for Tackling Error-Prone and Tricky Questions

Error-Prone Questions and Answering Strategies

Question 9: This falls within the realm of counting problems and is particularly prone to undercounting issues during enumeration. Additionally, it involves considerations related to months and dates, making it unsuitable for the direct application of addition, multiplication principles, or permutation and combination formulas.

Question 19: This problem entails the rotation of geometric figures in a coordinate system. Many students may mistakenly interpret it as the intersection of lines AB and A’B”, but, in reality, it represents the intersection point of the perpendicular bisector lines.

Tricky Questions and Answering Strategies

Question 7: Probability problems involving the dynamic sum of dice points are relatively rare in the AMC10. The wording of the question may pose a challenge during the reading process, leading to a significant investment of time in comprehension. However, once the question is fully understood, the difficulty in solving it is not substantial.

Question 13: This is a geometric angle problem that essentially involves the sine theorem. In the context of the AMC10, the concept of central angles can be utilized to solve it. This approach provides a significant advantage for students in the Think program. We will instruct students on how to construct the diagram for this problem.

Question 18: This problem is, in fact, an examination of Euler’s theorem. While many students are familiar with Euler’s theorem and may use it to validate certain geometrical properties, there are instances during problem-solving where they might struggle to apply it. Knowing Euler’s theorem makes this particular question straightforward and quickly solvable.

We hope you find this analysis useful. We’re excited to share valuable insights, strategies, and thorough analyses to boost your understanding and performance in the AMC Series. Subscribe to our newsletter for continuous updates on educational insights and the latest trends.

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