Skip Navigation Links

Class Syllabus - AMC 10 (高中数学竞赛） by Dr. Dan Li

Syllabus ID: 1535

Semester:

Fall 2025

Class （班级）:

AMC 10 (高中数学竞赛）

Teacher (教师):

Dr. Dan Li

Phone:

na

Email:

danli091981@gmail.com

Class Time:

2:45 - 4:15 PM

Classroom:

BSN-2201

Course Description (课程介绍):

This AMC 10 preparation course develops mastery of algebra and related topics through the Art of Problem Solving – Introduction to Algebra curriculum. Students build strong conceptual foundations, learn multiple problem‑solving strategies, and apply them to AMC 10‑level contest problems. Weekly lessons, targeted practice, and timed mock exams cultivate precision, flexibility, and confidence for math competitions and beyond.


Prerequisite:

A solid understanding of prealgebra topics (fractions, decimals, ratios, percentages)
Familiarity with basic algebra concepts (variables, expressions, linear equations)
Comfort with problem‑solving and logical reasoning
Willingness to tackle challenging, multi‑step problems independently

Age recommendations (学生年龄段):

ages 13–16, grades 8–10

Textbooks (教材):

AoPS Introduction to Algebra

References (参考资料):

Objectives (教学目标):


By the end of this course, students should be able to:

1. Apply algebraic techniques (equations, inequalities, polynomials, functions) to AMC 10–level problems.

2. Translate complex word problems into solvable mathematical expressions.

3. Confidently graph and analyze relationships between variables.

4. Employ multiple strategies to tackle a variety of algebra-based contest questions.


Teaching Methods (教学方法):

This course uses a concept‑driven, problem‑solving–focused approach that blends:
- Interactive instruction to explain and deepen understanding of key algebraic concepts.
- Guided practice with worked examples and step‑by‑step reasoning.
- Collaborative problem solving to share strategies and build critical thinking skills.
- Contest‑style drills to develop speed, accuracy, and flexible thinking under timed conditions.
- Regular feedback and error analysis to strengthen understanding and refine techniques.


Student/Parent Responsibilities (学生，家长责任义务):


**Students:**

- Complete assigned work before class and try challenging problems independently first.

- Bring all required materials (textbook, notebook, calculator if allowed).

- Participate actively in discussions and contest problem reviews.



**Parents:**

- Encourage at least 3–4 hours of AMC problem practice weekly.

- Monitor student engagement and timely homework submission.

- Communicate with the instructor regarding significant challenges.

Required Supplies (文具要求):

Grading (评分标准):

Homework & Problem Sets (40%) – Accuracy, thoroughness, and consistency in weekly assignments.
Class Participation (20%) – Engagement in discussions, strategy sharing, and group problem‑solving.
Timed AMC 10 Practice Tests (30%) – Performance on mock contests and review sessions.
Challenge/Enrichment Problems (10%) – Extra‑credit problems that push beyond the standard syllabus.

Calendar (教学进度表):

**Weeks 1–2: Algebraic Foundations & Linear Equations**
- Properties of real numbers, order of operations
- Variables, expressions, evaluating & simplifying expressions
- Solving basic linear equations & inequalities
- Translating real-world problems into linear models
- AMC 10 problem practice on fundamentals

**Weeks 3–4: Ratios, Percents & Systems of Equations**
- Ratios, rates, proportions, percent applications
- Solving systems via substitution and elimination
- Word problem applications in contest problems

**Weeks 5–6: Quadratics – Factoring, Formula & Graphing**
- Factoring quadratic expressions & solving quadratics
- Quadratic formula and discriminant analysis
- Completing the square & graphing parabolas
- Connecting algebraic and graphical representations

**Weeks 7–8: Absolute Value, Exponents & Radicals**
- Absolute value equations & inequalities
- Laws of exponents, simplifying radicals, rational exponents
- Complex AMC 10-style exponent/radical problems

**Weeks 9–10: Polynomials, Special Factoring & Symmetry**
- Polynomial operations and degree
- Special products (difference of squares, sum/difference of cubes)
- Polynomial identities, symmetry, Vieta’s formulas
- Factor & Remainder Theorems

**Weeks 11–12: Functions, Graphs & Sequences**
- Function notation, evaluation, transformations, and inverses
- Arithmetic & geometric sequences
- Summation notation and series applications

**Weeks 13–14: Advanced Equations & AMC 10 Word Problems**
- Rational/fractional equations
- Introduction to functional equations in contests
- Mixture, work, and motion problems
- Translating complex problems into equations and solving systematically

**Week 15: Review & Mock Exam**
- Full AMC 10 algebra-focused practice test under timed conditions
- Review and group discussion of solutions
- Error analysis & final exam strategies

Additional Notes (其它):