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
In a square of side (b+6), if (b^2) is the large part, what is the total area of the two rectangles?MediumLevel 66A visual model has a (c^2) square, two (9c) strips and an (81) corner. What is the side of the whole square?MediumLevel 66If a (4x^2) square has total strips (14x) and corner (49), what is the side of the square?MediumLevel 66A student took only one (3x) strip in the model of ( (x+3)^2 ). What is the mistake?MediumLevel 66If \(x>y\), which product represents the remaining area in a visual model after a square of side \(y\) is removed from a square of side \(x\)?MediumLevel 66Why is the small (b^2) square added in the visual model of ( (a-b)^2 )?MediumLevel 66In the rectangle model of ( (x+2)(x+7) ), which set of four parts is correct?MediumLevel 66When making the area model of ( (2x+1)(x+4) ), what will be the total (x) term?MediumLevel 66In a rectangle model, the sides are (3y+2) and (y+5). Choose the correct total area.MediumLevel 66In the grid model of ( (4p+3)(p+2) ), what will be the constant corner?MediumLevel 66In a visual square model of an algebraic identity, if there is one region of area \(a^2\), one region of area \(b^2\), and two equal rectangular regions of area \(ab\), which identity does it represent?MediumLevel 66If in a square of side (x-6), two strips are removed from the large square (x^2), what is the total area of the removed strips?MediumLevel 66What is the final expansion in the model of a square with side (2x-5)?MediumLevel 66If ( (x+8)^2-(x-8)^2 ) is viewed as the visual difference of two squares, what is the result?MediumLevel 66A model divides a square of side (a+b+c) into parts. Which term must appear in the total area?MediumLevel 66In a square of side (a+b+c), what will be the areas of the small squares?MediumLevel 66A visual model shows both ( (m+n)^2 ) and ( (m-n)^2 ). What will be the difference of their areas?MediumLevel 66Which part is common in the square model of ( (x+3)^2 ) and the rectangle model of ( (x+3)(x+4) )?MediumLevel 66A rectangle is made with sides (x+5) and (x+5). If it is treated as a square model, which special fact is correct?MediumLevel 66A teacher showed ( (a+4)(a-4) ) using tiles. If the (a^2) tile remains and the (16) tile is removed, what is the correct identity?MediumLevel 66