CBSE ADDA

CBSE MATH STUDY: Factor and reminder theorem :Polynomial class IX :  Proof of this factor theorem Let  p ( x ) be a polynomial of degree greater than or equal to one and  a   be  areal number such that  p ( a... Proof of this factor theorem Let  p ( x ) be a polynomial of degree greater than or equal to one and  a   be  areal number such that  p ( a ) = 0. Then, we have to show that ( x  –  a ) is a factor of  p ( x ). Let  q ( x ) be the quotient when  p ( x ) is divided by  ( x – a ). By remainder theorem, Dividend  = Divisor x Quotient + Remainder p ( x ) = ( x – a ) x  q ( x ) +  p ( a ) [Remainder theorem] ⇒   p ( x ) = ( x – a ) x  q ( x ) [ p ( a ) = 0] ⇒  ( x – a ) is a factor of  p ( x ) Conversely, let ( x – a ) be a factor of  p ( x ). Then we have to prove that  p ( a ) = 0 Now,     ( x – a ) is a factor of  p ( x ) ⇒   p ( x ), when divided by ( x – a ) gives remainder zero.  But, by the remainder theorem,  p ( x ) when divided by ( x – a ) gives the remainde

Drop an altitude of length h to the side of length c. Then A = (1/2)cxh, So, A2 = (c2 h2)/ 4. Use the Pythagorean Theorem to obtain the following system: (1) x2 + h2 = a2 (2) y2 + h2 = b2 (3) x + y = c Substitute y = c - x into (2) and simplify.Then subtract the result from (1). You will find that 2cx = a2 - b2 + c2. From (1), 4c2 h2  = 4a2 c2 - 4c2 x2 = (2ac + 2cx) (2ac - 2cx) = (2ac + a2 - b2 + c2)(2ac - a2 + b2 -c2) = ((a+c)2 - b2) (b2 - (a-c)2) = (a+c+b)(a+c-b)(b+a-c)(b-a+c) = (2s)(2s-2b)(2s-2c)(2s-2a) = 16s(s-a)(s-b)(s-c)

Chapter 2 Polynomials class9  Practice Questions Paper Important Identities : - 1. ( x + y )2 = x2 + 2xy +y2 2. ( x – y)2 = x2 – 2xy + y2 3. (x + y)(x – y) = x2 – y2 4. (x + a)(x + b) = x2 +(a + b)x + ab 5. (x + y)3  = x3 + 3x2y + 3xy2 + y3  = x3 + y3 +3xy(x +y) 6. (x - y)3 = x3 - 3x2y + 3xy2 - y3  = x3+ y3 -3xy(x -y) 7. (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx 8. x3 + y3 = (x + y)(x2 – xy + y2) x3 - y3 = (x - y)(x2 + xy + y2) 9. x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz – zx) 10. If x + y + z = 0 , then x3 + y3 + z3 = 3xyz 1. Classify the following as monomials, binomials and trinomials : (a)x3          b) 2y2 – 4y + 3  c) t2 – 4  d) √2 e) x3 + 4x2 + 5x f) u7 + u2 – 4. 2. Write the coefficients of x2 in each of the following : a) 3x^2 – 4y  b) x + x^2 + 7y  c) 3x + 4y – 5z d) x^2 + 2xy + 3y^2 3.

9 CBSE Maths chapter  9th Quadrilaterals Prove that followings: 1. A diagonal of a parallelogram divides it into two congruent triangles. 2 In a parallelogram, opposite sides and angle are equal. 3. If each pair of opposite sides of quadrilateral is equal, then it is a parallelogram. 4. If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. 5. The diagonals of a parallelogram bisect each other. 6. If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. 7. A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel. 8. The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side. 9. The line segment joining the mid- points of the two sides of a triangle is parallel to the third side. 10. Show that each angle of a rectangle is a right angle. 11. Show that the diagonal of a rhombus are perpendicular to each other. 12. Show that the bisectors of the ang

Linear Equation in Two Variables Class 09 Maths CBSE Practice Test paper 1. Find four different solutions of the equation x+2y=6. 2. Find two solutions for each of the following equations: (i) 4x + 3y = 12 (ii) 2x + 5y = 0 (iii) 3y + 4=0 3. Write four solutions for each of the following equations: (i) 2x + y = 7 (ii) πx + y = 9 (iii) x = 4y. 4. Given the point (1, 2), find the equation of the line on which it lies. How many such equations are there? 5.Draw the graph of the equations (i) x + y = 7 (ii) 2y + 3 = 9 (iii) y - x = 2 (iv) 3x - 2y = 4 (v) x + y - 3 = 0 6.Draw the graph of each of the following linear equations in two variables: (i) x + y = 4 (ii) y = 3x (iii) 3 = 2x + y (iv) x - 2 = 0 (v) 2x + 4 = 3x + 1. 7. If the point (3, 4) lies on the graph of the equation 3y=ax+7, find the value of ‘a’. 8. Solve the equations 2x + 1 = x - 3, and represent the solution(s) on  (i) the number line,  (ii) the Cartesian plane. 9. Draw a graph of the line x - 2y = 3. From the gr