Class 10 Maths Chapter 4 Notes

Important full class 10 maths chapter 4 notes in 10th Class Mathematics Urdu Medium by Mr. Tasneem Haider. These computerized notes are very helpful in the preparation of class 10 maths chapter 4 notes for students of the 10th class Mathematics and these are according to the paper patterns of all Punjab boards.

• Important class 10 maths chapter 4 notes pdf for all students of Punjab  Textbook Board.
• Multiple Choice Questions. Four possible answers are given for the following questions. Tick the correct answer.
• (i). The identity (5x + 4)² = 25x² + 40x + 16 is true for:  (A) one value of x  (B) all values of x  (C) two values of x  (D) none of these
• Important class 10 maths notes chapter 4 for all students of Punjab  Textbook Board.
• (ii). A function of the form f (x) = N(x) / D(x) with D(x) ≠ 0, where N(x) and D(x) are polynomials in x is called:  (A) an identity  (B) an equation  (C) a fraction  (D) none of these
• (iii). A fraction in which the degree of the numerator is greater or equal to the degree of denominator is called:  (A) a proper fraction  (B) an improper fraction  (C) an equation  (D) algebraic relation
• Important class 10th maths chapter 4 notes for all students of Punjab  Textbook Board.
• (iv). A fraction in which the degree of numerator is less than the degree of the denominator is called:  (A) an equation  (B) an improper fraction  (C) an identity  (D) a proper fraction
• (v). 2x+1 / (x+1) (x-1) is:  (A) an improper fraction  (B) an equation  (C) a proper fraction  (D) none of these
• Important math class 10 chapter 4 notes for all students of Punjab  Textbook Board.
• Define proper, improper and rational fraction.
• Resolve an algebraic fraction into partial fractions when its denominator consists of: (i) non-repeated linear factors, repeated linear factors,  (ii) non-repeated quadratic factors,  (iii) repeated quadratic factors.
• Important maths class 10 notes chapter 4 for all students of Punjab  Textbook Board.
• Fraction: The quotient of two numbers or algebraic expressions is called a fraction. The quotient is indicated by a bar (--). We write, the dividend above the bar and the divisor below the bar. For example,  x²+2 / x -2 is a fraction with x - 20 ≠ 0. If x - 20 = 0, then the fraction is not defined because x - 2 = 0 , x = 2 which makes the denominator of the fraction zero.
• Important 10th class math chapter 4 notes for all students of Punjab  Textbook Board.
• Rational Fraction: An expression of the form N(x) / D(x) with D(x) ≠ 0 and N(x) and D(x) are polynomials in D(x) x with real  coefficients, is called a rational fraction. Every fractional expression can be expressed as a quotient of two polynomials. For example, x² + 3 / (x+1)² (x + 2) and 2x / (x-1) (x+2) are rational fractions.
• Important chapter 4 maths class 10 notes for all students of Punjab  Textbook Board.
• Proper Fraction: A rational fraction N(x) / D(x) with D(x) ≠ 0 is called a proper fraction if degree of the polynomial N(x), in the numerator is less than the degree of the polynomial D(x), in the denominator. For example, 2 / x + 1 , 2x - 3 / x²+4 and 3x² / x^3+1 are proper fractions.
• Partial fractions: Decomposition of resultant fraction N(x) / D(x) with D(x) ≠ 0, when  (a) D(x) consists of non-repeated linear factors.  (b) D(x) consists of repeated linear factors.  (c) D(x) consists of non-repeated irreducible quadratic factors.  (d) D(x) consists of repeated irreducible quadratic factors.
• Improper Fraction: A rational fraction N(x) / D(x) with D(x) ≠ 0 is called an improper fraction if degree of D(x) the polynomial N(x) is greater or equal to the degree of the polynomial D(x). For example,  5x / x + 2 , 3x² + 2 / x² + 7x + 12 , 6x^4 / x^3 + 1 are improper fractions.
• Every improper fraction can be reduced by division to the sum of a polynomial and a proper fraction. This means that if degree of the numerator is greater or equal to the degree of the denominator, then we can divide N(x) by D(x) obtaining a quotient polynomial Q(x) and a remainder polynomial R(x), whose degree is less than the degree of D(x). Thus N(x) / D(x) = Q(x) + R(x) / D(x) with D(x) ≠ 0.