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Exploring Algebraic Identities — Practice Quiz

CBSE · Class 9 · Mathematics

Try a 4-question quiz on Exploring Algebraic Identities for CBSE Class 9 Mathematics: tap an answer to check it and see why.

168 questions70 flashcards13 formulas & key relations5 concepts

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Quick Quiz: Exploring Algebraic Identities

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1

Find the length and breadth of the rectangle whose area is x² + 8x + 15 square units.

2

A rectangular pool has breadth 4 m less than its length and area 96 m². Find the length and breadth of the pool.

3

Simplify the rational expression (x² - 7x + 12) / (5x² + 5x - 100), assuming the denominator is not zero.

4

Find the square of 119 using the trinomial square identity.

168 Questions·
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Sample Questions

1multiple choice
3 marks

Find the side of the cube whose volume is p³ + 6p²q + 12pq² + 8q³ cubic units.

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p + 2q units

Compare p³ + 6p²q + 12pq² + 8q³ with a³ + 3a²b + 3ab² + b³. Here a = p and b = 2q. So the expression becomes (p + 2q)³. Therefore the side is p + 2q units.

2multiple choice
3 marks

Rewrite 8n³ - 60n²m + 150nm² - 125m³ as a cube of a binomial.

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(2n - 5m)³

Compare 8n³ - 60n²m + 150nm² - 125m³ with a³ - 3a²b + 3ab² - b³. Take a = 2n and b = 5m. Then the expression becomes (2n - 5m)³.

3multiple choice
3 marks

Find the sum of cubes of three numbers whose sum is 10, product is 25, and sum of squares is 38.

Show answer

145

Use x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - xz - yz). First find xy + xz + yz using (x + y + z)² = x² + y² + z² + 2xy + 2xz + 2yz. So 100 = 38 + 2(xy + xz + yz), giving xy + xz + yz = 31. Then x³ + y³ + z³ - 75 = 10(38 - 31) = 70, so x³ + y³ + z³ = 145.

4multiple choice
3 marks

Find the factors of x² + 11x + 30.

Show answer

(x + 5)(x + 6)

Find two numbers whose sum is 11 and product is 30. The pair 5 and 6 works because 5 + 6 = 11 and 5 × 6 = 30. So x² + 11x + 30 = (x + 5)(x + 6).

+164 more questions on Exploring Algebraic Identities (CBSE Class 9 Mathematics)

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Frequently Asked Questions

What are the important topics in Exploring Algebraic Identities for CBSE Class 9 Mathematics?
Key topics in Exploring Algebraic Identities include Identity and Equation, Square of a Sum and Square of a Difference, Square of a Trinomial, Product of Binomials and Factorisation. Study these first, then practise questions on each for Class 9 exams.
How many practice questions are there for Exploring Algebraic Identities?
There are 168 questions on Exploring Algebraic Identities. Try the 4-question sample quiz on this page first; each answer shows an explanation when you tap it.

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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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