In our previous blog article, we analyzed the AMC 10A exam for 2023. In this installment, we will continue our analysis by delving into the content of the AMC 10B, encompassing an overall examination of the AMC competition, module analysis, common pitfalls, and novel question types. Embark with us on this cerebral voyage as we apply analytical acuity and mathematical mastery to navigate through the twists and turns of the 2023 AMC 10B exam.

Overall Difficulty Levels

The 2023 AMC 10B maintains a difficulty similar to past years, slightly surpassing the 10A but remaining easier than last year’s paper. Basic questions emphasize algebra for easier problems, while more challenging ones span probability, geometry, and algebra. Notably, the exam minimizes text descriptions, focusing on assessing students’ mastery of algebraic skills and intuitive understanding of geometric shapes.

A key aspect is the absence of extremely obscure topics, particularly in the first half, featuring conventional questions. This structure benefits students with a solid foundation or quick problem-solving skills. However, a significant difficulty spike in questions 12, 13, and 14 poses a challenge for those encountering similar problems for the first time.

Overall, achieving very high or very low scores on this exam is relatively challenging. It evaluates profound knowledge and problem-solving abilities, offering a balanced assessment of overall skills.

Module-Specific Breakdown

Algebra: A Polarized Challenge

• The 2023 AMC 10B exam featured 7 algebra questions, with a focus on the initial 10 and final 5 questions.
• Among the first 10 questions, 5 were dedicated to algebra, while the remaining 2 were positioned in the last 5.
• Interestingly, there were no algebra questions in the 11-20 question range.
• The difficulty of algebra questions exhibited distinct polarization, covering conventional topics but lacking questions on arithmetic progression.

Geometry: Increased Emphasis and Strategic Placement

• The geometry section comprised 10 questions, with a notable increase compared to previous years.
• Six geometry questions were concentrated in the 11-20 question range, making it a prominent category.
• Two geometry questions were present among the first 10 and last 10 questions.
• All geometry questions were moderately challenging, covering topics like area, tangency, regular polygons, and the Pythagorean theorem.
• Notably, the exam did not touch upon cylinders and cones.
• Three questions touched on solid geometry. Familiarity with these concepts simplified problem-solving:
  • Question 6: Relationship between points, lines, and faces in a cube.
  • Question 18: Euler’s theorem in spatial geometry.
  • Question 25: Properties of a regular icosahedron in spatial geometry.

Combinatorics: A Mix of Familiarity and Challenges

• The examination of combinations followed the usual pattern, primarily focusing on counting and probability.
• Out of the six combination questions, five were related to counting and probability.
• Three questions were probability-based, two involved counting, and one related to a sports competition.
• The final question in this section assessed students’ understanding of spatial geometry, emphasizing knowledge of a three-dimensional figure for a quick solution.
• Questions in counting and probability incorporated various additional knowledge points and tested their application in different contexts.

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

Question number	Answer	Module	Key Knowledge Area	Difficulty level *
1	C	Algebra	Average (Mean) Problems	1
2	B	Algebra	Percentage Application Problems	1
3	D	Geometry	Right triangle	1.5
4	C	Geometry	Unit conversion	1
5	A	Algebra	Application Problems	1
6	E	Algebra	Number Sequence	2
7	B	Geometry	Rotation of Geometric Figures	2.5
8	A	Number theory	Remainder	2
9	B	Algebra	Difference of two squares	2.5
10	C	Combinatorics	Covering Problems	2
11	B	Combinatorics	Partitioning Problems	2.5
12	C	Algebra	Graphs of Polynomials	3
13	B	Algebra	Absolute value inequality	3.5
14	C	Algebra	Integer Solutions of Algebraic Expressions	2.5
15	C	Number theory	Square number	3
16	E	Combinatorics	Rising Numbers and Falling Numbers	3.5
17	D	Geometry	Rectangular cuboid	3
18	E	Number theory	Greatest common divisor	3
19	B	Combinatorics	Geometric Models of Probability	4
20	A	Geometry	Ball	3
21	E	Combinatorics	The Classical Probability	3.5
22	B	Algebra	Quadratic Equations in Gaussian Form	3.5
23	B	Algebra	Number Sequence	4
24	E	Geometry	Analyzing Parametric Equations	4.5
25	B	Geometry	Pentagon	5

Strategies for Tackling Error-Prone and Tricky Questions

Error-Prone Questions and Answering Strategies

Question 13: This problem entails solving an absolute value inequality for the range of xy, which can be challenging. Graphing on a Cartesian plane often leads to mistakes due to the intricacies of the hollow shape, creating a subtle trap and making it error-prone.

Question 14: Positioned as the 14th question, this problem can stump students, widening the gap between high and average performers. While the correct method ensures a quick resolution, an incorrect approach can consume considerable time without guaranteed accuracy. Effective estimation techniques are valuable for tackling this problem.

Tricky Questions and Answering Strategies

Question 10: This question is quite innovative, both in its formulation and solution approach. Such problems, involving placing and covering haven’t appeared in previous years. The solution involves a unique strategy of coloring the regions with black and white, resembling a chessboard pattern. Recognizing that there are 5 black and 4 white regions, the minimum required moves can be determined to be 4.

Question 20: The tennis ball-shaped problem appears complex initially but transforms into a plane geometry problem involving the largest square formed by the four centers of circles inside the sphere.

Question 24: This problem involves a parameterized equation, a question type rarely encountered in the AMC10. Directly plotting the parameterized values on a normal two-dimensional plane is crucial for solving this particular problem.

We hope you’ll find this analysis beneficial. Get ready for a journey of valuable insights, strategies, and in-depth analyses to enhance your understanding and performance in the AMC Series. Subscribe to our newsletter for ongoing updates on educational insights and the latest trends.

Related Article: 2023 AMC 10A Exam Analysis: Difficulty, Structure, And Strategies