### Math / Contest Math Class Descriptions

**Online Classes: **2-hour weekly online classes via ZOOM. In addition, students are provided with reading assignment and handout with weekly homework problems to work on at beginning of week via Canvas.

**Classroom Class (CM201-CM701):** 2-hour class where 45-60 minutes of those are spent on lecturing. Rest of the time is reserved for problem solving. During the problem solving time, students are asked to work independently and/or with a partner. Students are also encouraged to share their solutions with the class.

### Math Kangaroo

Momentum Learning offers Math Kangaroo classes for future math enthusiasts. Students will not only learn arithmetic calculations but they will also be introduced to problem solving skills that will help them excel and build a strong foundation in math and science. Class will feature problems that inspires lateral thinking.

**Class will cover topics: **

- Comparing Numbers
- Skip – Counting
- Place Value
- Addition and Subtraction
- Multiplication
- Division
- Shapes
- Perimeter and Area
- Measurement
- Basic Number Theory*
- Exponents*
- Fractions*
- Decimals*
- Percent*
- Ratio and Rates*
- Statistics*
- Integers*
- Expressions and Equations*

Topics marked with start will only be covered in 3rd grade and up groups.

Our class will use materials from Beast Academy, Sunshine Math and Singapore Math.

### CM201 – Contest Math Level 2 (Beginner)

**Description:** This class is intended for students who are new to problem solving and math competitions. This class will help students to learn concepts and techniques beyond the school curriculum. Students who wish to enroll this class are expected to complete 5th grade curriculum and be familiar with operation with integers, basic operations with fractions, exponents and solve basic equations. CM 201 also helps students improve their scores on math contests such as AMC 8, MATHCOUNTS etc.

No placement test is required.

**Homework: **A 10-20 question problem set will be assigned by the end of each class. Students are expected to spend about 2 hours per week outside the class to finish the homework.

**What will be covered: **

**First Semester: **

**Algebra: **Arithmetic Properties (Operations with Rational Numbers, Exponents, Radicals), Algebraic Expressions, Solving Equations

**Number Theory**: Divisibility, Prime Factorization, Number of Divisors, LCM-GCF

**Combinatorics: **Basic Counting Techniques, Permutations, Combinations and Probability

**Second Semester:**

**Geometry:** Angles, Pythagorean Theorem, Special Right Triangles, Similarity, Area, Circles

**Algebra and Combinatorics Practice and Problems**

**Who should skip this course:** Students who scored 15+ on AMC 8

### CM301 – Contest Math Level 3 (Beginner)

**Description:** This class is intended for students who are new to problem solving and math competitions. This class will help students to learn concepts and techniques beyond the school curriculum. Students who wish to enroll this class are expected to be familiar with pre-algebra topics (operation with integers, fractions, exponents and solve basic equations) and/or have completed our CM201 course. CM 301 also helps students improve their scores on math contests such as AMC 8, Chapter MATHCOUNTS etc.

**Homework: **A 10-15 question problem set will be assigned by the end of each class. Students are expected to spend about 2 hours per week outside the class to finish the homework.

**What will be covered: **

**First Semester: **

**Algebra: **Divisibility, Prime Factorization, Number of Divisors

**Number Theory: **TBD

**Combinatorics: **Basic Counting Techniques, Permutations, Combinations and Probability

**Second Semester:**

**Geometry:** Angles, Pythagorean Theorem, Special Right Triangles, Similarity, Area, Circles

**Algebra and Combinatorics Practice and Problems**

**Who should skip this course:** Students who scored 20+ on 2016 AMC 8

### CM401 – Contest Math Level 4 (Intermediate)

**Description:** This class is intended for students who have been active in math competitions for a year or so. and are willing to improve their scores by learning more in depths topics and techniques. CM 401 also helps students improve their scores on AMC10/12 and on MATHCOUNTS.

**Who should take this course? **Students who wish to enroll this class are expected to have mid to high AMC 8 score **(2017 19+, 2016 20+, 2015 18+) **and/or have completed our CM301 course for both fall and spring semesters.

**Homework: **A 10-15 question problem set will be assigned by the end of each class. Students are expected to spend about 2 hours per week outside the class to finish the homework.

**What will be covered: **

**First Semester: **

**Algebra: **System of Equations, Word Problems, Algebraic Manipulations, Quadratic and cubic Polynomials, Vieata’s, Functions, Sequences and Series

**Combinatorics: **Permutations, Combinations, P.I.E., Binomial Theorem, Probability

**Second Semester:**

**Geometry:** Triangle Geometry (Similarity, Area, Parts of a Triangle), Quadrilaterals, Circle Geometry (Angle, Area and Length)

**Number Theory:** Number of Divisor, Prime Numbers, Modular Arithmetic, Diophantine Equations,

**Who should skip this course:** Students who scored 100+ on AMC 10

### CM501 – Contest Math Level 5 (Intermediate – Advanced)

**Description:** This class is intended for students who have been active in math competitions for a few years and are willing to improve their scores by learning more in depths topics and techniques. CM 501 helps students improve their scores on Mathcounts, AMC10/12 and AIME.

**Who should take this course? **Students who wish to enroll this class are expected to have **mid AMC 10 score (100+)** and/or have completed our CM401 course for both fall and spring semesters.

**Homework: **A 10-15 question problem set will be assigned by the end of each class. Students are expected to spend about 2 hours per week outside the class to finish the homework.

**What will be covered: **

**First Semester: **

**Algebra: **System of Equations, Algebraic Manipulations, Polynomials, Vieata`s, Functions, Trigonometry, Complex Numbers. Sequences and

Series

**Combinatorics: **Permutations, Combinations, P.I.E., Recursion, Binomial Theorem, Induction.

**Second Semester:**

**Geometry:** Triangle Geometry (Similarity, Area, Parts of a Triangle), Quadrilaterals, Circle Geometry (Angle, Power of a Point, Ptolemy’s)

**Number Theory:** Modular Arithmetic, Diophantine Equations, Fermat Little Theorem, Wilson`s Theorem, Chinese Remainder Theorem.

**Who should skip this course:** Students who scored 6+ on AIME

### CM601 – Contest Math Level 6 (Advanced)

**Description:** This class is intended for students who have been active in math competitions for a few years and are willing to improve their scores by learning more in depths topics and techniques. CM 601 helps students improve their scores on AMC 10/12 and AIME.

**Who should take this course? **Students who wish to enroll this class are expected to have **mid AIME score (6-10)** and/or have completed our CM501 course for both fall and spring semesters.

**Homework: **A 10-15 question problem set will be assigned by the end of each class. Students are expected to spend about 2 hours per week outside the class to finish the homework.

**What will be covered: **

**First Semester:**

**Geometry**: Area and Length in Triangles, Cyclic Quadrilaterals and Ptolemy, Power of a Point, Trigonometry, Law of Sines and Cosines, Cartesian Coordinates, Solid Geometry.

**Combinatorics**: Distributions, principle of inclusion and exclusion, counting on cycles, bijection, constructive expectation, recursion, Burnside Lemma

**Second Semester:**

**Algebra**: Polynomials and Vieta, Algebraic Manipulations, Systems of Equations, Complex numbers and DeMoivre formula, Sequences and Series.

**Number Theory**: Digits of Numbers, Modular Arithmetic, Euclidean Algorithm, Diophantine Equations, Fermat Little Theorem, Wilson’s Theorem, Chinese Remainder Theorem.

**Summer (Online Only): **Algebra

Week 1: Solving system of equations

Week 2: Functions review and special functions

No class on June 19.

Week 3: Exponents and logarithms

Week 4: Quadratic Equations and graphing parabola

Week 5: Polynomials I Division and Factor Theorem

Week 6: Polynomials II Vieta Formulas

Week 7: Complex Numbers and Roots of Unity

Week 8: Inequalities and Cauchy Schwarz Inequality

Week 9: Optimization: Maxima and minima

Week 10: Arithmetic and Geometric Sequences and Series

**Who should skip this course:** Students who scored 12+ on AIME

### CM700 – Introduction to Olympiad Geometry

**Description:**This class is intended for students who have been active in math competitions for a few years but are relatively new to Olympiad Math (proofs). Students will learn how to write proofs and learn more in depths topics and techniques to transition from AIME type of problems to USA(J)MO type of problems. In terms of difficulty of problems solved in class we will be focusing on and solving USA(J)MO-level Olympiad geometry problems and various competitions from around the world. CM700 helps students improve their USA(J)MO scores.

The main textbook is Evan Chen’s Euclidean Geometry for Mathematical Olympiads. In addition, we will use Lemmas in Euclidean Geometry by Andreescu et al.

**Who should take this course? **Students who wish to enroll this class are expected to **have qualified for the USA(J)MO in the past**.

**Homework: **2 Olympiad problems are assigned to each student to solve and upload on Canvas each week. Students are expected to spend about 5-6 hours per week outside the class to prepare for the online meeting and to finish the homework after the meeting.

**What will be covered: **

1. Angle Chasing and Cyclic Quadrilaterals

2. Orthic Triangle, Incenter Excenter Lemma, Phantom Points

3. Power of a point and radical axes/center

4. Extended Law of Sines, Collinearity/concurrency and Ceva/Menelaus theorems

5. Homothety and the Nine Point Circle

6. Simson Lines, Incircle and Excircles

7. Isogonal Conjugates and Symmedians

8. Curvilinear incircle and mixtilinear incircles

9. Computational Geometry I: Coordinates, Areas, and Trigonometry

10. Computational Geometry II: Coordinates, Areas, and Trigonometry

### CM701 – Contest Math Level 7 (Advanced – Olympiad Math)

**Description:** This class is intended for students who have been active in math competitions for a few years and are willing to improve their scores by learning more in depths topics and techniques. CM701 helps students improve their USA(J)MO scores.

**Who should take this course? **Students who wish to enroll this class are expected to **have qualified for the USA(J)MO in the past**.

**Homework: **2 Olympiad problems are assigned to each student to solve and upload on Canvas each week. Students are expected to spend about 5-6 hours per week outside the class to prepare for the online meeting and to finish the homework after the meeting.

**What will be covered: **

**First Semester: **

**Geometry**: Incenter-excenter lemma, radical axes, concurrency and collinearity through Ceva and Menelaus; homothety and the nine-point circle; isogonal conjugates, mixtilinear circles; inversion; projective geometry; Complete quadrilaterals

**Second Semester:**

**Algebra**: Algebraic inequalities (AM-GM, Cauchy-Schwarz); convexity and Jensen inequality; smoothing, and isolated fudging techniques. polynomials; functional equations.

**Combinatorics**: Algorithms; processes; games; counting in two ways; extremal combinatorics; the probabilistic method.

**Who should skip this course:** Students who are USAJMO Winners or who scored 28+ on USAMO