##### NSF Pre-Mathcounts Coaching - Syllabus

###### NSF Pre-Mathcounts Coaching - Beginner Level

Goal: Introduction to basic MATHCOUNTS topics, teach fundamental concepts.

Recommended Criteria: Should meet the following criteria.

- Students must be in 3rd, 4th or 5th grade.

Classwork: New topic with 20 example problems per class.

- Number theory
- Algebra
- Geometry
- Probability

###### Beginner

Least Common Multiple and Greatest Common Factor

- Find the largest number which can exactly divide 513, 783 and 1107.
- Find the smallest number exactly divisible by 12, 15, 20, 27.
- The GCF of two numbers is 14 and the LCM is 11592. If one of the numbers is 504, find the other.
- The product of two numbers is 16184 and their LCM is 952. Find their GCF
- Find the largest number which can divide 1354, 1866 and 2762 leaving the same remainder of 10.
- Find the largest number which can divide 290, 460 and 552 leaving the remainders of 4, 5, and 6 respectively.
- Find the greatest possible length of a rope which can be used to measure exactly the lengths 7m, 3m 85cm and 12m 95cm.
- Three different containers contain different qualities of mixtures of milk and water whose measurements are 403 kg, 434 kg and 465 kg. What biggest measure must be there to measure all different qualities an exact number of times?
- Find the least number which when divided by 6, 9, 12, 15 and 18 leaves the same reminder 2 in each case.
- Find the greatest number of four digits which is exactly divisible by each one of the numbers 12, 18, 21 and 28?
- Find the least number of square tiles required to pave the ceiling of a room 15 m 17 cm long and 9 m 2 cm broad.
- Five bells toll at the station together and arrive respectively at intervals of 6, 7, 8, 9, 12 seconds.

###### NSF Pre-Mathcounts Coaching - Intermediate Level

Goal: Introduction to basic MATHCOUNTS topics, teach fundamental concepts.

Recommended Criteria: Should meet one of the first two criteria and the third one.

- Students must be in 4th or 5th grade

Classwork: New topic with 20 example problems per class + Additional 10 problems for homework.

- Number theory
- Algebra
- Geometry
- Probability

###### NSF Pre-Mathcounts Coaching - Advanced Level

Goal: Introduce more topics and then review on all topics from all levels. Primary goal is to help them to be ready for MATHCOUNTS preparation next year.

Recommended Criteria: Should meet the first criteria and one of the last two.

- Student must be in 5th grade or above
- Returning student from last year Pre-Mathcounts coaching
- New student (5th grade or above) who can handle the level of complexity of problems in next page. Student must know to solve single variable equations

Classwork: New topic with 20 example problems per class.

###### Advanced

- 3x + 2y = 11 x - y = 7
- 3p + 2q = 6 2p + 5q = -7
- 3x + y = 13 2x – 3y = 16
- 4x – 2y = 16 3x + 4y = 4
- 2x + 6y = 17 3x – 2y = 20
- The equations 5x + 2y = 48 and 3x + 2y = 32 represent the money collected from school concert tickets sales during two class periods. If x represents the cost for each adult ticket and y represents the cost for each student ticket, what is the cost for each adult ticket?
- Margie is responsible for buying a week's supply of food and medication for the dogs and cats at a local shelter. The food and medication for each dog costs twice as much as those supplies for a cat. She needs to feed 164 cats and 24 dogs. Her budget is $4240. How much can Margie spend on each dog for food and medication?
- Two small pitchers and one large pitcher can hold 8 cups of water. One large pitcher minus one small pitcher constitutes 2 cups of water. How many cups of water can each pitcher hold?
- A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?
- A landscaping company placed two orders with a nursery. The first order was for 13 bushes and 4 trees, and totalled $487. The second order was for 6 bushes and 2 trees, and totalled $232. The bills do not list the per-item price. What were the costs of one bush and of one tree?

###### Reference Materials used

Problems are taken from various sources.

- Singapore Math
- Math Olympiad
- Continental Math League
- Challenge Math
- MATHCOUNTS