## Competitive Math Contents

The lessons and problem set for this program are designed to prepare students for various math competitions. The lower level classes prepare and expose students to tackle problems which normally found in Math Olympiad, Math Challenge Tournament and Math Kangaroo. The upper level classes will focus on MathCounts, AMC 8, and Math Olympiad types of problems.

These classes are only available in the summer.

Warm-up/Mental Math

Lessons on Topic

Guided Problems

Independent Exercises and Class Discussion

Break

Group/Team Challenge

Group Discussion

Short Problems/Cool Down

No homework except for unfinished classwork

Below is a short description for each level along with sample problems from the curriculum.

These classes are only available in the summer.

**Typical Schedule (Class Format)**Warm-up/Mental Math

Lessons on Topic

Guided Problems

Independent Exercises and Class Discussion

Break

Group/Team Challenge

Group Discussion

Short Problems/Cool Down

No homework except for unfinished classwork

Below is a short description for each level along with sample problems from the curriculum.

**Introduction to Competitive Math****Contents covered in Track A**: Logic and Deductive Reasoning, Algebraic Thinking, Mystery Numbers, Patterns, Orders and Numbers, and Spatial.

**Contents covered in Track B**: Division and Patterns, Missing Digits and Operation Signs, Alphametics, Arrangements, Organized Lists, and Non-routines.

Sample Problems:

*Sal was the 11th person in line for face-painting. Nora was the second from the last person in line. If there were 15 people lined up for the face-painting, how many people were between Sal and Nora?*

**(Orders and Positions)**

**Competitive Math 1****Contents covered in Track A**: Digits and Numbers, Algebraic Thinking, Patterns, Systematic Listing, Geometry, Logical and Spatial.

**Contents covered in Track B**: Sequences, Summation, Averages, Number Patterns, Missing Numbers & Palindromes, and Alphametics.

Sample Problems:

*Study the figures in the sequence below. Find the number of dots in Figure 25.***(Pattern)***Place the number 1 to 8 into the circles so that the four calculations are correct?*

**(Missing Numbers)**

**Competitive Math 2****Contents covered in Track A**: Number Theory (Primes, Composites, Divisibility Rules), Patterns in Calendar, Arithmetic and Averages, Perimeters and Areas, More Geometry (Polygons, Angles, Sum of Angles), and Units Digit.

**Contents covered in Track B**: Number and Sequence, Rate and Speed, Counting and Probability, Ratios and Fractions, Measurements and Geometry, Algebraic Thinking and Logical Deduction.

Sample Problems:

*A number is a multiple of 9 and it’s larger than 1000. The number is divisible by both 5 and 7, and it is not divisible by 2. If the number is less than 2000, what is the number?*

**(Number Theory)****A committee of three is chosen from five counselors - Allen, Benjamin, Coby, Dahlia and Eshita. What is the probability Benjamin is on the committee?**

*(Counting and Probability)**Tom and Dima are designing a fort. They notice that if they increase the length of the floor by 2 feet then the floor area will increase by 12 square feet. If they increase the width by 3 feet, then the floor area will increase by 24 square feet. What are the dimensions of the floor in their design?*

**(Measurements)**

**Competitive Math 3****Contents covered in Track A**: Number Theory, Rate and Proportions, Speed and Movement, Geometry – Polygons and Circles, Counting and Probability, Permutations and Combinations.

**Contents covered in Track B**: Work and Rates, Arithmetic and Percent, Geometry – 3D, Geometry – Angles and Similarity, Logical Deduction, Mixed Word Problems.

Sample Problems:

**Abhinav, Bella, and Chandra were all born after 2000. Each of them was born in a year after 2000 that is divisible by exactly one of the prime numbers 2, 3 or 5. Each of these primes is a divisor of one of the birth years. What is the least possible sum of their birth years?**

*(Number Theory)***How many ounces of a 30% copper alloy must be melted with a 70% copper alloy in order to produce 20 ounces of a 46% copper alloy?**

*(Percent)***A box contains 26 slips of paper, each showing a different letter of the alphabet. If two slips of paper are drawn from the box at the same time, what is the probability that both letters appear in the word ALGEBRA? Express your answer as a common fraction. **

*(Counting and Probability)*

**Competitive Math 4****Contents covered in Track A**: Number Theory, Set Theory, Geometry – Pythagorean Theorem and Similar Figures, Exponent and Radicals, Functions and Operations, Counting and Probability.

**Contents covered in Track B**: Algebra Expressions and Equations, Exponents and Radicals, Geometry – Areas and Sectors, Number Bases, Modular Arithmetic, Mixed Word Problems.

Sample Problems:

**A book contains 30 stories, each starting on a new page. The lengths of these stories are 1, 2, 3,..., 30 pages, respectively. The first story starts on the first page. What is the largest number of stories that can start on an odd-numbered page?**

*(Number Theory)**A regular octagon with side length 1 unit has area 2+2√2 square units. The area of a regular octagon with side length 3 units can be expressed in simplest radical form as 𝑎(𝑏+√𝑐) square units. What is the value of a + b + c?*

**(Geometry)****Seventy-five bingo balls, each with a different positive integer from 1 through 75, are placed in a cage. A random ball is selected, its number is announced, and the ball is returned to the cage. This process occurs a total of 20 times. What is the probability that at least one ball is selected more than once? Express your answer as a decimal to the nearest hundredth.**

*(Counting and Probability)**A date is called weird if the number of its month and the number of its day have a greatest common factor of 1. For example, April 15th is weird because the greatest common factor of 4 and 15 is 1. What month has the fewest number of weird days and how many weird days are in that month?*

**(Mixed Word Problems)**