In the visual area model, what type of parts are (a^2), (2ab), and (b^2)?
Correct answer: B
All these represent areas of squares or rectangles. Exam tip: understand identity terms as area parts.
View question detailsMathematics
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.
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Easy · Level 72 · area-terms,visual-meaning,concept
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- Only line lengths
- Area parts
- Only angles
- Only perimeter
Easy · Level 72 · square-identity,side-of-square,visual-model
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- (r+s)
- (r-s)
- (rs)
- (2r+s)
Easy · Level 72 · numeric-area,square-identity,visual-calculation
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- (81+9+1)
- (81+18+1)
- (81+1)
- (9+1)
Easy · Level 72 · constant-corner,rectangle-model,area-parts
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- In the rectangle ((x+3)(x+4))
- In the square ((x+12)^2)
- In the rectangle ((x+2)(x+5))
- In the square ((x+6)^2)
Easy · Level 72 · removed-square,difference-of-squares,visual-model
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- Square with side (4)
- Square with side (2)
- Square with side (x-2)
- Square with side (x+2)
Easy · Level 72 · small-square,middle-area,binomial-square
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- (7) and (14x)
- (49) and (7x)
- (49) and (14x)
- (14) and (49x)
Easy · Level 72 · difference-of-squares,numeric-model,fast-calculation
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- Perfect square identity
- Difference of squares identity
- Cube identity
- Equal side identity
Easy · Level 72 · algebraic identities,rectangle model,binomial multiplication,like terms,linear term
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- \(6x\)
- \(7x\)
- \(x\)
- \(5x\)
Easy · Level 72 · algebraic identities, visual models, square of sum, area model, class 9 mathematics
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- One a^2 square, one b^2 square, and two ab rectangles
- Two a^2 squares and one b^2 square
- One a^2 square, one b^2 square, and one ab rectangle
- One a^2 square and two b^2 squares
Easy · Level 72 · algebraic identities,visual models,area addition,rectangle area,polynomial expressions
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- \(x^2+8x\)
- \(x^2+64\)
- \(8x^2+x\)
- \(x+8\)
Easy · Level 72 · equal-rectangles,complete-square,visual-tiles
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- (20x)
- (10x)
- (100x)
- (5x)
Easy · Level 72 · difference-of-squares,visual-proof,rearrangement
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- Square with side (x+5)
- By removing a square of side (5) from a square of side (x)
- Rectangle with length (x) and breadth (5)
- Square with side (x-5)
Easy · Level 72 · algebraic identities,visual models,area partition,square model,binomial square
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- Two
- Three
- Four
- Five
Easy · Level 72 · algebraic identities,binomial square,visual models,polynomial expansion,class 9 mathematics
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- \(4x^2+12x+9\)
- \(2x^2+12x+9\)
- \(4x^2+6x+9\)
- \(4x^2+9\)
Easy · Level 72 · three-term-square,square-parts,visual-model
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- (a^2), (b^2), (c^2)
- (ab), (bc), (ca)
- (2ab), (2bc), (2ca)
- (a+b+c)
Easy · Level 72 · distributive-area,rectangle-model,visual-multiplication
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- (2x^2+5x)
- (2x^2+5)
- (x^2+10x)
- (2x+5x)
Easy · Level 72 · concept,visual-learning,algebraic-identities
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- It is only for memorising answers
- It shows algebraic terms as areas
- It shows only perimeter
- It removes multiplication
Easy · Level 72 · numeric-difference,area-rectangle,fast-calculation
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- (100)
- (110)
- (120)
- (121)
Easy · Level 72 · combined-parts,square-model,area-identity
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- (x^2+10x+25)
- (x^2+5x+25)
- (x^2+6x+5)
- (x^2+25)
Easy · Level 72 · same-area,visual-proof,identity-concept
View options
- Both expressions are equal
- Both expressions are always negative
- The area changes
- The figure disappears
If a square is read as (r^2), (2rs), and (s^2), what will be its side?
Correct answer: A
These terms come from the area model of ((r+s)^2). Exam tip: identify (2rs) from two equal rectangles.
View question detailsUsing the visual identity, the area of a square with side (9+1) equals which sum?
Correct answer: B
In ((9+1)^2), (9^2), two (9) rectangles, and (1^2) are added. Exam tip: do not forget the two equal rectangles.
View question detailsIn which situation will the small corner of the visual model be (12)?
Correct answer: A
The small corner is formed by (3\times4=12). Exam tip: connect the constant term with the corner in a rectangle model.
View question detailsIf (x^2-4) is viewed visually, which small square has been removed?
Correct answer: B
Since (4=2^2), a small square of side (2) has been removed. Exam tip: find the side of the subtracted square.
View question detailsIn a square with side (x+7), what are the small square area and total area of the two rectangles?
Correct answer: C
The small square is (7^2=49), and the two rectangles total (2\times7x=14x). Exam tip: use the constant part in both square and rectangles.
View question detailsWhich visual identity can solve (12^2-8^2) without long multiplication?
Correct answer: B
(12^2-8^2=(12+8)(12-8)) gives the area quickly. Exam tip: when a difference appears, multiply sum and difference.
View question detailsIn the rectangle model of ((x+1)(x+6)), what will be the total (x)-term?
Correct answer: B
In the rectangle model for
\((x+1)(x+6)\), the two linear parts are
\(6x\) and
\(x\). Therefore, the total
\(x\)-term is
\(6x+x=7x\).
\(6x\) is only one part, not the complete linear term. Exam tip: add all like parts in a rectangle model before writing the result.
In the visual model of a square with side a+b , which partition correctly represents a^2+2ab+b^2 ?
Correct answer: A
Dividing each side of the large square into lengths
a
and
b
forms one
a^2
square, one
b^2
square, and two
ab
rectangles. Their areas add to
a^2+2ab+b^2
. Exam tip: count both
ab
rectangles.
What area is formed by joining an (x) by (x) square and an (x) by (8) rectangle?
Correct answer: A
The area of the square is \(x\times x=x^2\), and the area of the rectangle is \(x\times 8=8x\). Therefore, the total area of the joined figure is \(x^2+8x\). In \(x^2+64\), the 8 has incorrectly been squared. Exam tip: for a composite figure, add the areas of all its parts.
View question detailsIf (x^2+20x+100) is made with square tiles, what is the area of each of the two equal rectangles?
Correct answer: B
The total middle term is (20x), so each rectangle has area (10x). Exam tip: split the middle term into two equal parts.
View question detailsIn which model can (x^2-25=(x+5)(x-5)) be seen most clearly?
Correct answer: B
This is the visual construction of difference of squares. Exam tip: after removing the square, the remaining part forms a rectangle.
View question detailsHow many main parts are formed in the square model of side (a+b)?
Correct answer: C
When a square of side \((a+b)\) is divided into lengths a and b, it forms four regions: \(a^2\), \(ab\), \(ab\), and \(b^2\). Therefore, the correct answer is four. \(2ab\) is the combined area of the two separate \(ab\) regions, not one individual part. Exam tip: count each rectangle or square region separately in the diagram.
View question detailsIf ((2x+3)(2x+3)) is viewed as a square, what is it equal to?
Correct answer: A
This is \((2x+3)^2\). Using \((a+b)^2=a^2+2ab+b^2\), with \(a=2x\) and \(b=3\), gives \(4x^2+12x+9\). Option C uses only \(ab\) instead of the required middle term \(2ab\). Exam tip: always check the middle term as \(2ab\) when expanding a square.
View question detailsIn the visual model of ((a+b+c)^2), which are the square parts?
Correct answer: A
Each of the three side parts forms its own square. Exam tip: distinguish square parts and rectangular parts.
View question detailsIf a rectangle has length (2x+5) and breadth (x), what will the area model give?
Correct answer: A
Multiplying (x) by (2x) and (5) gives (2x^2+5x). Exam tip: multiply the breadth by both parts.
View question detailsWhich statement is correct for a visual model?
Correct answer: B
In a visual model, squares and rectangles explain the meaning of algebraic terms. Exam tip: connect the diagram with the formula.
View question detailsIf (11^2-1^2) is changed into a rectangle, what will be the area?
Correct answer: C
(11^2-1^2=(11+1)(11-1)=12\times10=120). Exam tip: solve quickly using difference of squares.
View question detailsIf a square with side (x+2+3) is first viewed as (x+5), what area will be obtained?
Correct answer: A
Since (2+3=5), the side becomes (x+5), and the area is (x^2+10x+25). Exam tip: simplify side parts first.
View question detailsIn an area model, what is the main conclusion of writing the area of the same figure in two ways?
Correct answer: A
The area of the same figure does not change, so both forms are equal. Exam tip: this idea is the basis of an algebraic identity.
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