2015 Mathcounts State/National Prep

Harder concepts from Mathcounts Mini :
Also try the follow-up problems with detailed solutions. Don't do every question. Just the ones you think is hard.

Geometry :
#27 : Area and Volume 

#30: Similar Triangles and Proportional Reasoning

#34: Circles and Right Triangles

#35: Using Similarity to Solve Geometry Problems

#41: Analytic Geometry : Center of Rotation

More questions to practice from my blog post. 

From Mathcounts Mini : Video tutorials on counting and probability for Mathcounts state/national prep concepts are in the of difficulty.

Counting the Number of Subsets of a Set

Constructive Counting

More Constructive Counting 

Probability and Counting

Probability with Geometry Representations  : Oh dear, the second half part is hilarious.

Probability with Geometry Representations : solution to the second half problem from previous video

Try this one from 1998 AIME #9. It's not too bad.

From Mathcounts Mink : Center of rotation, equal distance from a point to other two points or two lines, angle bisector (last problem on the follow-up worksheet)

Mathcounts Mini : #41 - Analytic Geometry

This Week's Work : Week 53 for Inquisitive Young Mathletes

For this week's work, review 1991 Mathcounts National sprint and target round questions you got wrong or not fast enough. Please try once more to see if you now can solve them at ease.

For this week's review, try the following Mathcounts Mini :

Similar Triangles and Proportional Reasoning

Try the follow-up problems

Detailed solutions

I'll send you notes/solutions/links to some of the hardest problems later.

Take care and happy problem solving !!

This Week's Work : Week 52 for Inquisitive Young Mathletes

Finish 2000 Mathcounts National sprint and target rounds according to the rules.
Check your e-mail.

E-mail me your scores + what questions you skip, couldn't solve fast, preferably with
the wrong answers put down so I can tell if you have some ideas.

Constructive Counting from Mathcounts Mini

Try some questions from the activity sheet till you fully understand the concepts.

Activity sheet solutions 

This Week's Work : Week 51 for Inquisitive Young Mathletes

For this week's work :

Try 2013 Mathworks Math Contest problems from Texas State University

Answer key and statistics can be viewed here. 

I'll send you detailed solutions once we finish all the problems.

Practice more "at least" problems :

2014 AMC-10 B problem 16 

Solution

From Mathcounts Mini : Video tutorials on counting and probability for Mathcounts state/national prep concepts are in order the of difficulty.

Counting the Number of Subsets of a Set

Constructive Counting

More Constructive Counting 

Probability and Counting

This Week's Work : Week 50 - for Inquisitive Young Mathletes

Counting Restrictions from Glyia

Very nice introductory level counting questions with restrictions.

from Mathcounts Mini : Counting the Number of Subsets of a Set

 from AoPS :

Counting with Restrictions Part 3  : This one is tricky. Make sure you understand the concepts well.

Try this question from 2011 AMC-8 # 23 :

How many 4-digit positive integers have four different digits, where the leading digit is not zero, the integer is a multiple of 5, and 5 is the largest digit?

Solutions from AoPS

Counting with Combinations Part 3

At our group lessons, we'll continue working on harder Mathcounts concepts, not just the accuracy, but speed.

Take care and happy problem solving !!

This Week's Work : Week 48 - for Inquisitive Young Mathletes

Tackling Problems with Vieta Section 10.4: Vieta for Quadratics Part 1 Section 10.4: Vieta for Quadratics Part 2 Section 10.4: Tackling Problems with Vieta Practicing Problems using Vieta's formula The Binomial Theorem

• Section 14.2: Introducing the Binomial Theorem   


• Section 14.4: Using the Binomial Theorem Part 1


• Section 14.4: Using the Binomial Theorem Part 2


• Section 14.4: Using the Binomial Theorem Part 3


• Section 14.5: Using the Binomial Theorem Part 4

Casework Counting Part I 

Casework Counting Part II 

This Week's Work : Week 47 - for Inquisitive Young Mathletes

This week, we'll continue discussing this year's Mathcounts state harder problems. Please try these problems before our lesson. Review sprint round questions we went over at last Sunday's lesson, especially #18 to see if you can get that question right and fast the first try. The technique used for this question is very similar to the first explanation from this episode of Mathcounts mini -- more construction counting. Review Binomial Theorem and see if you can use the following concepts solving this year's state sprint # 28. (You can also use modular arithmetic, or mod.) Chapter 14: The Binomial Theorem

• Section 14.2: Introducing the Binomial Theorem   
• Section 14.4: Using the Binomial Theorem Part 1
• Section 14.4: Using the Binomial Theorem Part 2
• Section 14.4: Using the Binomial Theorem Part 3
• Section 14.5: Using the Binomial Theorem Part 4

Have a calculator ready for target and team round questions.

Take care and happy problem solving !!

2014 Mathcounts State/National/AMC Prep : More Counting and Probability Problems from Mathcounts Mini / AoPS

From Mathcounts Mini : Video tutorials on counting and probability for Mathcounts state prep

Counting the Number of Subsets of a Set

Constructive Counting

More Constructive Counting 

Probability and Counting

Probability with Geometry Representations  : Oh dear, the second half part is hilarious.

Probability with Geometry Representations : solution to the second half problem from previous video

Try this one from 1998 AIME #9. It's not too bad.

This Week's Work : week 3 -- for Inquisitive Young Mathletes

Assignment 1: 
Watch and learn Simon's Favorite Factoring Trick.

Work on some of the problems as well to check your understanding.

Assignment 2: 
Just learn as much as you can.
We'll keep practicing counting and probability.

Counting Permutations : from Art of Problem Solving

With or Without Replacement : from Art of Problem Solving

Notes on Permutations from the Math Page

Permutations with Some Identical Elements