Mathematics
Chapter 1 – Real Numbers
Content
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Introduction.
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Euclid’s division algorithm.
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The Fundamental theorem of arithmetic.
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Revisiting irrational numbers.
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Revisiting rational numbers and their decimal expansions.
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Exercises- 1.1, 1.2 , 1.3 and 1.4.
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Summary.
Video Clip
Questions on the real numbers
Important questions :
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Use Euclid’s division algorithm to find the HCF of 135 and 225.
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Use Euclid’s division lemma to show that the square of any positive integer is either of the form of 3m or 3m + 1 for some integer m.
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Express 156 as a product of its prime factors.
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Find the HCF and LCM of 96 and 404 by prime factorisation method.
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Without actually performing the long division State whether the given rational number 13/3125 will have a terminating decimal expansion or not.
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Prove that square root of 5 is irrational.
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Use Euclid’s algorithm to find H CF of 135 and 225.
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Find the H CF and LCM of 510 and 92 by prime factorisation method.
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The H CF of two numbers is 145 and their LCM is 2175. If one of the number is 275 and the other.
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Find the largest number which divides 320 and 457 leaving remainder 5 and 7 respectively.
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Find the H CF of 81 and 237 and express it as a linear combination of 81 and 237.
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Show that one and only one out of n ,n+2 , n+4 Is divisible by 3, where n is a positive integer.
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State whether the following rational number will have a terminating or non terminating decimal expansion 15/1600
Chapter 2 - Polynomials
Content
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Introduction.
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Geometrical meaning of the series of a polynomial.
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Relationship between series and coefficients of a polynomial.
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Division algorithm for polynomials.
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Summary.
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Exercise problems
Video Clip
Questions from chapter 2 polynomials:
1) Find the zeroes of the quadratic polynomial x2 + 7x + 10, and verify the relationship between the zeroes and the coefficients.
2) Find a quadratic polynomial, the sum and product of whose zeroes are -3 and 2 respectively.
3) Find all the zeroes of 2x4 – 3x3 -3x2 +6x-2, if you know that two of its zeroes are √2 and -√2.
4) Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: x2 + 3x +1, 3x4 +5x3 – 7x2 + 2x +2.
5) Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder: P(x) =x4 – 5x +6, g(x) = 2-x2.
6) Divide 2x2 + 3x +1 by x+2.
7) Find the zeroes of the cubic polynomial 2x3 – 5x2 – 14x + 8, and verify the relationship between the zeroes and the coefficients
Chapter -1 Question Paper
Chapter -1 Question Paper
Chapter 3 : pair of linear equations in two variables.
Contents
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Introduction.
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Pair of linear equations in two variables.
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Graphical method of solution of a pair of linear equations.
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Algebraic methods of solving a pair of linear equations
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Substitution method , elimination method and cross multiplication method.
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Equations reducible to a pair of linear equations in two variables.
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Summary.
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Exercise problems and worked problems.