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Class 8 Exam  >  Class 8 Tests  >  Mathematics (Maths) Class 8  >  Olympiad Test: Algebraic Expressions And Identities - Class 8 MCQ

Olympiad Test: Algebraic Expressions And Identities - Class 8 MCQ


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20 Questions MCQ Test Mathematics (Maths) Class 8 - Olympiad Test: Algebraic Expressions And Identities

Olympiad Test: Algebraic Expressions And Identities for Class 8 2025 is part of Mathematics (Maths) Class 8 preparation. The Olympiad Test: Algebraic Expressions And Identities questions and answers have been prepared according to the Class 8 exam syllabus.The Olympiad Test: Algebraic Expressions And Identities MCQs are made for Class 8 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Olympiad Test: Algebraic Expressions And Identities below.
Solutions of Olympiad Test: Algebraic Expressions And Identities questions in English are available as part of our Mathematics (Maths) Class 8 for Class 8 & Olympiad Test: Algebraic Expressions And Identities solutions in Hindi for Mathematics (Maths) Class 8 course. Download more important topics, notes, lectures and mock test series for Class 8 Exam by signing up for free. Attempt Olympiad Test: Algebraic Expressions And Identities | 20 questions in 20 minutes | Mock test for Class 8 preparation | Free important questions MCQ to study Mathematics (Maths) Class 8 for Class 8 Exam | Download free PDF with solutions
Olympiad Test: Algebraic Expressions And Identities - Question 1
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Which of the following is an expression?

Detailed Solution for Olympiad Test: Algebraic Expressions And Identities - Question 1
(c) Becoz highest power of variable 'x' is not equal to zero . ..
Olympiad Test: Algebraic Expressions And Identities - Question 2
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Which of the following is a binomial?

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

An algebraic expression consisting of unlike terms is called a binomial. 

so, 2x+7 is a binomial as it contains two unlike terms i.e 2x and 7.

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Olympiad Test: Algebraic Expressions And Identities - Question 3
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Expressions consists of _____________ and _______________.

Detailed Solution for Olympiad Test: Algebraic Expressions And Identities - Question 3
Variables and constants .This is because an expression is made up of these only.
Olympiad Test: Algebraic Expressions And Identities - Question 4
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What degree does x3 - x2y2 - 8y2+ 2 have?
Detailed Solution for Olympiad Test: Algebraic Expressions And Identities - Question 4

 

Olympiad Test: Algebraic Expressions And Identities - Question 5
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When numbers/literals are added or subtracted, they are called _________.
Detailed Solution for Olympiad Test: Algebraic Expressions And Identities - Question 5
Each number or literal is referred to as a term in algebra. When these terms are combined through addition or subtraction, they form an expression. Thus, the correct answer is 'terms.'
Olympiad Test: Algebraic Expressions And Identities - Question 6
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Multiply (a + 7) and (b – 5).
Detailed Solution for Olympiad Test: Algebraic Expressions And Identities - Question 6

(a+7)(b-5) = a(b-5)+7(b-5) = ab-5a+7b-35

Olympiad Test: Algebraic Expressions And Identities - Question 7
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Simplify: (x + y) (2x – 3y + z) – (2x – 3y)z 
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Olympiad Test: Algebraic Expressions And Identities - Question 8
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If (x+1/x) = 6, find  x2+1/x2 
Detailed Solution for Olympiad Test: Algebraic Expressions And Identities - Question 8

x²+1/x² can be written as (x+1/x)²-2 on putting values we have 6²-2=34
(x+1/x)2 = x²+1/x²+2(x)(1/x)
(x+1/x)2 = x²+1/x²+2
(x+1/x)2-2 = x²+1/x²

Olympiad Test: Algebraic Expressions And Identities - Question 9
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Olympiad Test: Algebraic Expressions And Identities - Question 10
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Which of the following is an expression?
Detailed Solution for Olympiad Test: Algebraic Expressions And Identities - Question 10
Option C is correct bcuz, an expression consists of at least one variable like :- x, y, z as well as a number. An expression can also be like this :- 2xy, 3y², 5xy+8, 6z²-3, etc
Olympiad Test: Algebraic Expressions And Identities - Question 11
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Which of the following is a trinomial?
Detailed Solution for Olympiad Test: Algebraic Expressions And Identities - Question 11
Because monomial 1 term binomial, 2 terms and trinomial 3 terms therefor 7_3x+4y trinomial.
Olympiad Test: Algebraic Expressions And Identities - Question 12
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Which of the following is like term as 3xy2?
Detailed Solution for Olympiad Test: Algebraic Expressions And Identities - Question 12
To determine which option is a like term to 3xy2, we need to identify terms that have the same variables raised to the same powers. - Option A: 7xy - The variable part is xy, but in the given term, it's xy2. Since the exponents of y differ, these are not like terms. - Option B: 7xy2 - The variable part is xy2, which matches exactly with the given term. Therefore, this is a like term. - Option C: 7x - The variable part is x, but in the given term, it's xy2. Since the variables are different, these are not like terms. - Option D: 7y2 - The variable part is y2, but in the given term, it's xy2. Since one includes x and the other does not, they are not like terms. Thus, the correct answer is B because 7xy2 has the same variables with the same exponents as 3xy2, making them like terms.
Olympiad Test: Algebraic Expressions And Identities - Question 13
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Subtract 3x (x – 4y + 5z) from 4x (2x – 3y + 10z).
Detailed Solution for Olympiad Test: Algebraic Expressions And Identities - Question 13

Correct option is D.

Olympiad Test: Algebraic Expressions And Identities - Question 14
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n (4 + m) = 4n + ___ 
Detailed Solution for Olympiad Test: Algebraic Expressions And Identities - Question 14
N(4+m) = 4n + ___Here , n is multiplied by 4 which is added to n multiplied by m.so, n×4= 4n n×m= nm so the answer is 4n + nm.
Olympiad Test: Algebraic Expressions And Identities - Question 15
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Using identity evaluate 297 × 303.
Detailed Solution for Olympiad Test: Algebraic Expressions And Identities - Question 15
297×303
(300-3)(300+3)
(300)whole square (3)whole square
90000-9
89991. identity 
{a-b} {a+b} ={a square} - {b square}
Olympiad Test: Algebraic Expressions And Identities - Question 16
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Simplify: (1.5x – 4y)(1.5x + 4y +3) – 4.5x +12y 
Detailed Solution for Olympiad Test: Algebraic Expressions And Identities - Question 16
(1.5x - 4y) (1.5x + 4y + 3) - 4.5x + 12y
= 1.5x(1.5x + 4y +3) - 4y(1.5x + 4y +3) - 4.5x +12y
= (1.5x X 1.5x) + (1.5x X 4y) + (1.5x X 3) - (4y X 1.5x) - (4y X 4y) - (4y x 3) - 4.5x +12y

= 2.25x^2 + 6xy + 4.5x - 6xy - 16y^2 - 12y - 4.5x + 12y
= 2.25x^2 + ( 6 - 6)xy + (4.5 - 4.5)x - 16y^2 + (12 - 12)y
= 2.25x^2  + 0 + 0 - 16y^2 + 0
= 2.25x^2 - 16y^2
Olympiad Test: Algebraic Expressions And Identities - Question 17
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If x + y = 12 and xy = 32, find the value of x2+ y2.
Detailed Solution for Olympiad Test: Algebraic Expressions And Identities - Question 17
x=8 or 4 and y=4 or 8 so,x^2+y^2=64 +16 or 16 +64 =80 and that is option A.
Olympiad Test: Algebraic Expressions And Identities - Question 18
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(x – a) (x + a) = ?
Detailed Solution for Olympiad Test: Algebraic Expressions And Identities - Question 18
(a-b)(a+b) = a^2 - b^2(x-a)(x+a) = x (x+a) -a (x+a) = x^2 + ax -ax -a^2 = x^2 - a ^2
Olympiad Test: Algebraic Expressions And Identities - Question 19
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Which of the following is a trinomial?
Detailed Solution for Olympiad Test: Algebraic Expressions And Identities - Question 19
A trinomial is a polynomial consisting of exactly three terms. - Option A, 3a + 4b + 5, contains three distinct terms: 3a, 4b, and 5. - Options B, C, and D have fewer than three terms (binomials or monomials) and thus are not trinomials. Therefore, the correct answer is option A.
Olympiad Test: Algebraic Expressions And Identities - Question 20
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If x = 3 is solution of x² + kx + 15, value of k is
Detailed Solution for Olympiad Test: Algebraic Expressions And Identities - Question 20

Since solution is x=3, this means the equation is equal to 0 when x=3, substituting the values gives k=-8

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