Class 10 Maths Chapter 1 Notes

Complete Notes of class 10 maths chapter 1 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 1 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 1 notes pdf for all students of Punjab  Textbook Board.
• Define quadratic equation.
• Solve a quadratic equation in one variable by factorization.
• Important class 10 maths chapter 1 notes pdf download for all students of Punjab  Textbook Board.
• Solve a quadratic equation in one variable by completing square.
• Derive quadratic formula by using method of completing square.
• Important class 10 maths notes chapter 1 for all students of Punjab  Textbook Board.
• Solve a quadratic equation by using quadratic formula.
• Solve the equations of the type ax^4 + bx^2 + c = 0 by reducing it to the quadratic form.
• Important class 10 notes maths chapter 1 for all students of Punjab  Textbook Board.
• Solve the equations of the type a p(x) + b / p(x) = c.
• Solve reciprocal equations of the type a ( x^2 + 1 / x^2 ) + b ( x + 1 / x ) + c = 0.
• Important class 10th chapter 1 maths notes for all students of Punjab  Textbook Board.
• Solve exponential equations involving variables in exponents.
• Solve equations of the type ( x + a ) ( x + b ) ( x + c ) ( x + d ) = k where a + b = c + d.
• Important class 10th maths chapter 1 notes for all students of Punjab  Textbook Board.
• Solve radical equations of the types (i). √ax + b = cx + d,  (ii). √x + a + √x + b = x+c,  (iii). √x² + px + m + √x² + px + n = q.
• Quadratic Equation: An equation, which contains the square of the unknown (variable) quantity, but no higher power, is called a quadratic equation or an equation of the second degree. 
• Important 10th maths 1st chapter notes for all students of Punjab  Textbook Board.
• A second degree equation in one variable x of the form   ax² + bx + c = 0 where a ≠ 0 and a, b, c are real numbers, is called the general or standard form of a quadratic equation. 
• Important math class 10 chapter 1 notes for all students of Punjab  Textbook Board.
• Here a is the co-efficient of x², b is the co-efficient of x and constant term is c.
• Remember that: If a = 0 in ax² + bx + c = 0, then it reduces to a linear equation bx + c = 0.
• Important maths class 10 notes chapter 1 for all students of Punjab  Textbook Board.
• The equations x² - 7x + 6 = 0 and 3x² + 4x = 5 are the examples of quadratic equations. x² - 7x + 6 = 0 is in standard form but 3x² + 4x = 5 is not in standard form. If b = 0 in a quadratic equation ax² + bx + c = 0, then it is called a pure quadratic equation. For example x² - 16 = 0 and 4x² = 7 are the pure quadratic equations.
• Important maths notes class 10 chapter 1 for all students of Punjab  Textbook Board.
• Solution of quadratic equations: To find solution set of a quadratic equation, following methods are used:
• (i) factorization  ,  (ii) completing square
• Important notes class 10 maths chapter 1 for all students of Punjab  Textbook Board.
• (i) Solution by factorization: In this method, write the quadratic equation in the standard form as ax² + bx + c = 0 , If two numbers r and s can be found for equation (i) such that r + s = b and rs = ac, then ax² + bx + c can be factorized into two linear factors. The procedure is explained in the following examples.
• Important notes for class 10 maths chapter 1 for all students of Punjab  Textbook Board.
• Example: Solve the quadratic equation 3x² - 6x = x + 20 by factorization.
• Solution: The standard form of 3x² - 7x - 20 = 0 ------)  (i)
• Important notes of class 10 maths chapter 1 for all students of Punjab  Textbook Board.
• Here As a = 3 , b = - 7, c = - 20  and ac = 3 x -20 = - 60 , As - 12 + 5 = - 7 and - 12 × 5 = - 60 so the equation (i) can be written as 
• 3x² - 12x + 5x - 20 = 0 , or 3x ( x - 4 ) + 5 ( x - 4 ) = 0 ,  ( x - 4 ) ( 3x + 5 ) = 0
• Important notes of maths class 10 chapter 1 for all students of Punjab  Textbook Board.
• Either x - 4 = 0 or 3x + 5 = 0, that is,
• Important 10th class math chapter 1 notes for all students of Punjab  Textbook Board.