Mathematics Practice Material

 SI UNITS, SIGNS, SYMBOLS AND ABBREVIATIONS (1) Agreed conventions (a) Units may be written in full or using the agreed symbols, but no other abbreviation may be used. (b) The letter ‘s’ is never added to symbols to indicate the plural form. (c) A full stop is not written after symbols for units unless it occurs at the end of a sentence. (d) When unit symbols are combined as a quotient, e.g., metre per second, it is recommended that it should be written as m/s, or as m s -1 . (e) Three decimal signs are in common international use: the full point, the mid-point and the comma. Since the full point is sometimes used for multiplication and the comma for spacing digits in large numbers, it is recommended that the mid-point be used for decimals. (2) Names and symbols  

 INTERNAL ASSESSMENT The minimum number of assignments: Two assignments as prescribed by the teacher. Suggested Assignments Comparative newspaper coverage of different items. Survey of various types of Bank accounts, rates of interest offered. Planning a home budget. Conduct a survey in your locality to study the mode of conveyance / Price of various essential commodities / favourite sports. Represent the data using a bar graph / histogram and estimate the mode. To use a newspaper to study and report on shares and dividends. Set up a dropper with ink in it vertical at a height say 20 cm above a horizontally placed sheet of plain paper. Release one ink drop; observe the pattern, if any, on the paper. Vary the vertical distance and repeat. Discover any pattern of relationship between the vertical height and the ink drop observed. You are provided (or you construct a model as shown) - three vertical sticks (size of a pencil) stuck to a horizontal board. You should also have discs of v...

2.1 Introduction 2.2 Geometrical Meaning of the Zeroes of a Polynomial Example 1-i : Look at the graph in Fig.  given below. It is the graph of y = p(x), where p(x) is a polynomial. For  the graph, find the number of zeroes of p(x).   Example 1-ii  : Look at the graph in Fig.  given below. It is the graph of y = p(x), where p(x) is a polynomial. For  the graph, find the number of zeroes of p(x).   Example 1-iii  : Look at the graph in Fig.  given below. It is the graph of y = p(x), where p(x) is a polynomial. For  the graph, find the number of zeroes of p(x).    Example 1-iv : Look at the graph in Fig.  given below. It is the graph of y = p(x), where p(x) is a polynomial. For  the graph, find the number of zeroes of p(x).    Example 1-v : Look at the graph in Fig.  given below. It is the graph of y = p(x), where p(x) is a polynomial. For  the graph, find the number of zeroes of p(x).   Exampl...

1.1.Introduction 1.2.The Fundamental Theorem of Arithmetic   Theorem 1.1 (Fundamental Theorem of Arithmetic) : Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur. Applications of FTA 1. To determine the unit's or one's digit of a number given in exponential form. 2.To find LCM/HCF  of two or more numbers.  HCF = Product of the smallest power of each common prime factor in the numbers ( when written in Prime Factorization form ) LCM = Product of the greatest power of each prime factor, involved in the numbers ( when written in Prime Factorization form ) Example 1 : Consider the numbers 4n , where n is a natural number. Check whether there is any value of n for which 4ⁿ ends with the digit zero. Example 2 : Find the LCM and HCF of 6 and 20 by the prime factorisation method.    [ AP SQP-2025  ] Example 3: Find the HCF of 96 and 404 by the...