# AMC 8

masterclass

## Sequence and greatest integer | AIME I, 2000 | Question 11

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2000 based on Sequence and greatest integer. Sequence and greatest integer - AIME I, 2000 Let S be the sum of all numbers of the form \(\frac{a}{b}\),where a and b are relatively...

## Arithmetic sequence | AMC 10A, 2015 | Problem 7

Try this beautiful problem from Algebra: Arithmetic sequence from AMC 10A, 2015, Problem. Arithmetic sequence - AMC-10A, 2015- Problem 7 How many terms are in the arithmetic sequence $13$, $16$, $19$, $\dotsc$, $70$, $73$? \(20\)\(21\)\(24\)\(60\)\(61\) Key Concepts...

## Series and sum | AIME I, 1999 | Question 11

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Series and sum. Series and sum - AIME I, 1999 given that \(\displaystyle\sum_{k=1}^{35}sin5k=tan\frac{m}{n}\) where angles are measured in degrees, m and n are...

## Inscribed circle and perimeter | AIME I, 1999 | Question 12

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Inscribed circle and perimeter. Inscribed circle and perimeter - AIME I, 1999 The inscribed circle of triangle ABC is tangent to AB at P, and its radius is 21...

## Problem based on Cylinder | AMC 10A, 2015 | Question 9

Try this beautiful problem from Mensuration: Problem based on Cylinder from AMC 10A, 2015. Cylinder - AMC-10A, 2015- Problem 9 Two right circular cylinders have the same volume. The radius of the second cylinder is $10 \%$ more than the radius of the first. What is...

## Cubic Equation | AMC-10A, 2010 | Problem 21

Try this beautiful problem based on Cubic Equation from AMC 10A, 2010. Cubic Equation - AMC-10A, 2010- Problem 21 The polynomial $x^{3}-a x^{2}+b x-2010$ has three positive integer roots. What is the smallest possible value of $a ?$ \(31\)\(78\)\(43\) Key Concepts...

## THIS WEEK

We will keep our focus on Number Theory**. **

*Competency to be mastered:* Number Theoretic Functions.

**Prelude: **Number theoretic functions are beautiful. They count number of divisors, number of co-prime residues, and a variety of other things for natural numbers. This week we will be mastering it, and try relevant AMC standard problems.

## Outstanding Mathematics *Personalized*

#### a personal mentor for every student

Each student is unique. We are keenly aware of this fact.

Cheenta mathematics olympiad program has a unique feature: a personal **one-on-one session** is assigned for every student, every week.

Add to this the group sessions, round-the-clock math support and **one-problem-a-day homework system**.

Join us for a truly engaging mathematics experience.

## Competency Framework for AMC 8

Competency

###### Number Theory

###### 21 competencies

###### Geometry

###### 12 competencies

###### Algebra

###### 16 competencies

###### Combinatorics

###### 7 competencies

It is simple.

Master one competency every week.

Use** Group session + one-on-one session + one-problem-a-day** to achieve this

### Cheenta is a home for outstanding mathematics since 2010

## Fall in love with maths

After all, we want to fall in love with mathematics. Cheenta faculty members are olympians and researchers from leading universities of the world. Take a sip from their river of passion for mathematics.