## Screening test for the admission to Olympiad Level 1 lecture series

### Purpose of screening test:

- Knowledge of topics taught in Algebra, Combinatorics, Geometry and Number Theory as part of the
*â€śFoundation of Mathematics and Introduction to Olympiad Mathsâ€ť*program is a prerequisite for the topics that will be taught during the*â€śOlympiad Level 1â€ť*program. - Essentially, the
*â€śOlympiad Level 1*â€ť program is a continuation of the*â€śFoundation of Mathematics and Introduction to Olympiad Mathsâ€ť*program i.e. it starts off from the point where the latter program ends. - It has been observed that many students who do not fulfill this prerequisite find it very tough to understand the topics taught in the Olympiad Level 1 program and hence lose interest/drop off from the program after a few weeks.
- Hence from this year onwards, a screening test will be taken for all students who wish to enroll in the Olympiad Level 1 program. The only purpose of this test is to gauge whether these students have indeed understood the topics taught in the Foundation batch.
- The test will be an open-book one â€“ so there is no need for students to memorise anything.

Interested students should send email to both the following email ids:The instructions and the question sets will be sent to them as a reply to the student's mail.

### Number Theory

- Natural numbers, composite and prime numbers, integers, addition and multiplication operations, commutative and associative properties of these two operations, closure property of integers under addition and multiplication, distributive property, exponentiation and factorial notations, exponentiation properties, absolute value (modulus).
- Well Ordering Principle
- Mathematical Induction
- Divisibility of integers and various divisibility properties
- Division Algorithm and Addition/Multiplication Properties of Remainders
- Greatest Common Divisor, Linear Combinations of Integers and BĂ©zout's identity
- Relatively Prime integers, necessary and sufficient condition for relatively prime integers, divisibility properties related to relatively prime integers, Euclidâ€™s Lemma
- Euclidean Algorithm, Extended Euclidean Algorithm, Least Common Multiple
- Linear Diophantine Equations in two unknowns

**Tip: **** **Students should also be acquainted with the proofs of the various results/theorems/properties mentioned above â€“ since the techniques used therein are useful to solve non-numerical problems as well.

### Combinatorics

- Factorial notation
- Basic counting principles, addition principle and multiplication principle
- Arrangement of n distinct objects, arrangement of r out of n distinct objects â€“ with and without repetition.
- Selection of r objects out of n objects
- Permutations and combinations
- nPr and nCr notations; simple results/properties related to these notations
- Circular arrangement of n objects

### Algebra

- Simultaneous Linear Equations.
- Quadratic Equations. Basics.
- Arithmetic and Geometric Progression.
- Polynomials degree, and operations addition,subtraction,multiplication and division of polynomials.

### Geometry

- Angle properties related to circles: inscribed angle theorem, tangent-secant theorem, cyclic quadrilaterals, etc.
- Angle properties related to parallel lines: corresponding and alternate angles
- Other misc. angle properties: vertex opposite angles, exterior angle theorem etc.
- Congruence and similarity of triangles, basic proportionality theorem, midpoint theorem
- Pythagorus theorem, its extension to acute/obtuse triangles, Apolloniusâ€™ theorem
- Simple area formulae (with proof) for triangles, parallelograms, trapeziums etc.
- Concept of locus, for simple examples such as perpendicular bisector and angle bisector
- Constructions using ruler and compass, based on triangle congruence tests (SSS, ASA, RHS etc.)