Mathematics G-10: Module 1

Dear students, In our daily life, we come across many patterns that characterize relations with brothers and sisters, mother and daughters, father and sons, teachers and students etc. In mathematics also, we come across many relations such as number 𝑚 is greater than number 𝑛; line 𝑛 is perpendicular to line 𝑚 etc... Function is defined as a special type of relation. In the present unit, we shall discuss Cartesian coordinates, conditions for a relation to be a function, different types of functions and their properties.

Dear students, in unit one of this module, you saw functions of the form 𝑦 = 𝑏, 𝑦=𝑎𝑥 + 𝑏 and 𝑎𝑥2 + 𝑏𝑥 + 𝑐. These functions are parts of a large class of functions called polynomial functions. Polynomial functions are functions that involve only one variable x, consisting of the sum of several terms; each term is a product of two factors; the first being a real number coefficient (constant) and the second being x (variable) raised to some non-negative integer power. In this unit, you will be looking at the different components of polynomial functions like degree, leading coefficient, zeros of a polynomial function, theorems on polynomial functions and properties of graphs of polynomial function.

The word ‘trigonometry’ is derived from the Greek word ‘trigon’ and ‘metron’ and it means ‘measuring the sides of a triangle’. The subject was originally developed to solve geometric problems involving triangles. It was studied by sea captains for navigation, surveyors for mapping out the new lands and engineers for other purposes. Currently, trigonometry is used in many areas such as seismology, designing electric circuits, describing the state of an atom, predicting the heights of tides in the ocean, analyzing a musical tone and in many other areas. Of a right-angled triangle. In this unit, we will study the trigonometric identities and application of trigonometric ratios in solving the problems and generalize the concept of trigonometric ratios to trigonometric functions and study their properties.