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Olympiad Test: Algebraic Expressions And Their Identities - 1 - Class 8 MCQ


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20 Questions MCQ Test Mathematical Olympiad Class 8 - Olympiad Test: Algebraic Expressions And Their Identities - 1

Olympiad Test: Algebraic Expressions And Their Identities - 1 for Class 8 2024 is part of Mathematical Olympiad Class 8 preparation. The Olympiad Test: Algebraic Expressions And Their Identities - 1 questions and answers have been prepared according to the Class 8 exam syllabus.The Olympiad Test: Algebraic Expressions And Their Identities - 1 MCQs are made for Class 8 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Olympiad Test: Algebraic Expressions And Their Identities - 1 below.
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Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 1

What are the factors of the expression ab – a - b + 1?

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 1
- To factor the expression ab - a - b + 1, start by grouping terms.
- Rewrite it as ab - a - b + 1 = a(b - 1) - 1(b - 1).
- Notice that both terms contain (b - 1).
- Factor out (b - 1): (b - 1)(a - 1).
- This shows that the expression can be represented as the product of (a - 1) and (b - 1).
- Therefore, the correct answer is (a - 1)(b - 1).
Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 2

If (2x - 3) is a factor of 6x2 – 7x – 3, then what is the other factor?

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 2

6x2 – 7x – 3

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Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 3

What are the factors of (g + h)2 - 4gh ?

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 3

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 4

If one of the factor of 25(x + y)2 – 36 (x – 2y)2 is (17y – x), then what is the other factor?

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 4

25 (x + y)2 – 36 (x – 2y)2

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 5

Find the value of (a + 1) (a – 1) (a2 + 1).

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 5

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 6

If x + y = 12 and xy = 14 then what is the value of x2 + y2?

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 6

(x + y)2 = x2 + y2 + 2xy

                = 116

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 7

​If  then what is the value of 

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 7

 = 

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 8

If x + y = 10 and xy = 9, what is the value of x2 – y2?

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 8

( x + y) 2 = x2 + y2+ 2xy


∴ 

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 9

If   then find the value of .

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 9



Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 10

The perimeter of a triangle is 6m2 – 4m + 9 and two of the sides are m2 – 2m + 1 and 2m2 + 3m + 5. What is the third side?

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 10

Third side = 6m2 – 4m + 9 – (m2 – 2m + 1 + 2m2 + 3m + 5)

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 11

What is the remainder when 7 + 15x – 13x2 + 5x3 is divided by 4 – 3x + x2?

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 11


Clearly (x - 1) is remainder.

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 12

What is the quotient if x4 – 2x3 + 2x2 + x + 4 is divided by x2 + x + 1?

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 12


∴ Quotient = x2 - 3x + 4

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 13

What is the quotient if 5x3 – 4x2 + 3x + 18 is divided by 3 – 2x + x2?

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 13

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 14

​If  then what is the value of 

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 14


Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 15

 8a2 b3 ÷ (-2ab)?

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 15

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 16

What is the value of 

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 16

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 17

What is the numerical coefficient in the product of 2abc, - 16a2bc and 3ab2c2?

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 17

(2abc) (- 16 a2 bc) (3a b2 c2)
= - 96 a4 b4 c3

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 18

​If  what is the value of ?

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 18


Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 19

What is the value of 

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 19


 

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 20

What is the remainder when 6x2 – 11x + 15 is divided by 2x – 5?

Detailed Solution for Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 20

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