Mathematics
Visual models of identities
सर्वसमिकाओं के दृश्य मॉडल
In Class 9 Mathematics, under the chapter Exploring Algebraic Identities, students use geometric diagrams and area-based representations to understand algebraic identities visually. They relate squares and rectangles formed from algebraic expressions to expansions such as binomial products, helping them see why both sides of an identity are equal rather than merely memorising formulas.
Practice questions
A square of side (5) is removed from a large square of side (z) and the remaining area is rearranged as a rectangle. What can be the sides of the rectangle?MediumLevel 67In a rectangle model the length is (x+2) and the breadth is (x+7). What is the sum of the four parts?MediumLevel 67In a rectangular tile model the sides are (t+3) and (t-4). What is the simplified area?MediumLevel 67In a visual model the square (k^2) and total strip area (12k) are shown. If the small square is (36) then the whole square is of what side?MediumLevel 67If a square of side (a+b) has two equal rectangles besides (a^2) and (b^2) then what is the combined contribution of those rectangles?MediumLevel 67A square of side (10) cm is split into (7) cm and (3) cm parts to show ((7+3)^2). What is the total area of the two rectangles?MediumLevel 67A visual model of area difference is made by removing a square of side (5) from a square of side (12). What is the remaining area?MediumLevel 67What is the visual area expression of a square with side (n-2)?MediumLevel 67In a rectangle model (x^2+11x+30) is shown in four parts. What are the possible sides?MediumLevel 67A square model has area (s^2-14s+49). What is the side of the small cut part?MediumLevel 67If a square with side (2x+3) is expanded visually then what is its area?MediumLevel 67In an area model the sides are (3a-2) and (3a-2). What will be the total area?MediumLevel 67A rectangle model shows area (4x^2-9). Which factor form is obtained using the difference of squares model?MediumLevel 67In a square of side (x+4) the total area of two edge strips is (8x). What is the area of the small corner square?MediumLevel 67In a tile model (a^2-b^2) must be changed into a rectangle. Which step is correct?MediumLevel 67If a visual model shows (x^2+10x+25) then it is an example of which identity?MediumLevel 67A rectangle model has sides (x+9) and (x-1). Which area is correct?MediumLevel 67In the visual expansion of a square with side (a+b+c) which rectangle terms appear along with (a^2) (b^2) and (c^2)?MediumLevel 67If a visual model shows (p^2+q^2) with only one (pq) rectangle then what is missing to complete ((p+q)^2)?MediumLevel 67In the model of a square with side (x-6) two strips are removed from (x^2). What is the area of each strip?MediumLevel 67