FOUNDATION GRADUATES
MODULE 1 : HIGH SCHOOL MATHEMATICS

Arithmetic

Evolution of every number under the Real number set and all major six operators.

Properties of each number type on the four basic operators.

Knowing more about a number through prime factorization and divisibility tests.

Application of Prime factorization for HCF and LCM.

Ratios and Percentages

Direct and Indirect variation.


Algebra

Introduction to the evolution and hence purpose of algebra through early civilizations, a formalization by Islamic scholars around 800 AD, and further developments during the Renaissance and also the concept of Coordinate geometry.

Algebraic expressions, Polynomials, and Polynomials in one variable.

System of linear equations in two variables and study of nature of solutions.

Quadratic equations in one variable and discriminant method for solutions and the type of solutions depending on the discriminant.

Inequations

Word problems based on all these equations taken specifically and in detail.


Geometry

Geometry in Early Civilisations to Euclid’s Elements in Greece during 300BC.

A highly systematic introduction to Euclid's work on Geometry, which was a compilation of all geometry known at that time, more than his contribution.

Starting from defining basic elements that go on to make objects and how they interact with others.

The first few proofs are based on just lines intersecting in different ways, without considering polygons.

Next, three lines intersect to form triangles and hence we study on congruency and similarity of triangles.


Next. four lines intersecting to form quadrilaterals and studying specific theorems for various standard quadrilaterals from trapezium to square.

Finally, a polygon with an infinite number of sides, a Circle. Interaction of circles with chords, tangents, and secants.

After understanding all the important theorems, the problemsolving sessions have to teach how a student can solve a new problem.

Mensuration

Areas and Perimeters of all types of triangles and quadrilaterals

Areas and Perimeters of Circles, Sectors of a Circle and Segments of a Circle.

Surface area and Volumes of cubes, cuboids, cylinders, cones and spheres.


Statistics

Introduction the a relatively new branch of mathematics and its relation with Probability.

Measures of Central Tendency: Mean, Median, and Mode.

Measures of Dispersion: Standard deviation & Variance.


Probability

Concept of Probability through coins, dice, and cards.

Introduction to counting tools, Permutation and Combination, and solving problems that cannot be solved using simple counting.

Compliment of an event, Conditional Probability, and Circular Probability.
