Grade 8 Consolidation of the Basic Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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(1) Identify the Constants and Variables in Each Expression

Table Supporting: 1_Identify_the_constants_and_variables_in_each_expression
ExpressionNumerical constantVariables
(a)
(b)

(2) Write Out the Coefficients and the Variables of Each Term of the Algebraic Expression

(a)

(b)

(3) Write in How Many Terms Each Expression Has After Simplification. Tick โ€˜Mโ€™ if the Expression is a Monomial, โ€˜Bโ€™ if It is a Binomial and โ€˜Tโ€™ if It is a Trinomial

Table Supporting: 3_Write_in_how_many_terms_each_expression_has_after_simplification_Tick_M_if_the_expression_is_a_monomial_B_if_it_is_a_binomial_and_T_if_it_is_a_trinomial
ExpressionNumber of terms after simplificationMonomial/binomial/trinomial
(a)

(b)

(4) Match Each Polynomial in Column a to Its โ€œTypeโ€ in Column B

Table Supporting: 4_Match_each_polynomial_in_Column_A_to_its_type_in_Column_B
Column-AColumn-B
(a) (a) Linear polynomial
(b) (b) quadratic polynomial
(c) (c) cubic polynomial
(d) (d) quartic polynomial
(e)
(f)

(5) Answer the Following Questions

(a) Add

(b) Subtract from

(6) is subtract from . The difference is added to the sum of and 3 times write out the resulting algebraic expression.

(7) Answer the Following Questions

(a)

(b)

(c)

(8) Answer the Following Questions

(a)

(b)

(c)

(9) Answer the Following Questions

(a)

(b)

(c)

(10) Answer the Following Questions

(a)

(b)

(11) Answer the Following Questions

(a)

(b)

Answers and Explanations

Answer 1 (A)

  • Expression equation is as below,

  • Numerical constant in algebraic expression is a fixed number as its value is fixed.
  • Here in given expression numerical constant is
  • Variables is a latter that is used in place of a number which value is not fixed and was find out with the help of related expression.
  • Here in given expression variables are
Table Supporting: Answers_and_Explanations
ExpressionNumerical constantVariables
(a)

Answer 1 (B)

  • Expression equation is as below,

  • Numerical constant in algebraic expression is a fixed number as its value is fixed.
  • Here in given expression numerical constant is
  • Variables is a latter that is used in place of a number which value is not fixed and was find out with the help of related expression.
  • Here in given expression variables are
Table Supporting: Answers_and_Explanations
ExpressionNumerical constantVariables
(b)

Answer 2 (A)

  • Coefficient is a constant number that stand beside the variable means in multiplication with variable.
  • Coefficient in given expression are
  • Variables is a latter that is used in place of a number which value is not fixed and was find out with the help of related expression.
  • Here in given expression variables are
Table Supporting: Answers_and_Explanations
ExpressionNumerical constantVariables
(a)

Answer 2 (B)

  • Coefficient is a constant number that stand beside the variable means in multiplication with variable.
  • Coefficient in given expression are
  • Variables is a latter that is used in place of a number which value is not fixed and was find out with the help of related expression.
  • Here in given expression variables are
Table Supporting: Answers_and_Explanations
ExpressionNumerical constantVariables
(a)

Answer 3 (A)

  • Given expression is already in its simplest form we cannot do any process in this expression to simplify it,
  • Hence simple form of given equation is
  • itีšs clear from simplest form that expression have three (3) term;
Illustration 2 for Answers_and_Explanations
Table Supporting: Answers_and_Explanations
ExpressionNumber of terms after simplificationMonomial/binomial/trinomial
(a)3

Answer 3 (B)

  • The simplest form of given equation is written as below,

  • Hence simple form of given equation is
  • itีšs clear from simplest form that expression have three (2) term;
Illustration 3 for Answers_and_Explanations
Table Supporting: Answers_and_Explanations
ExpressionNumber of terms after simplificationMonomial/binomial/trinomial
(b)2

Answer 4

  • Linear polynomial: A polynomial whose degree is 1 after simplificationof polynomial is named as a linear polynomial.
  • For example;
  • Quadratic polynomial: A polynomial whose degree is 2 after simplificationof polynomial is named as a Quadratic polynomial.
  • For example;
  • Cubic polynomial: A polynomial whose degree is 3after simplification of polynomial is named as a Cubic polynomial.
  • For example;
  • Quartic polynomial: A polynomial whose degree is 4after simplification of polynomial is named as a Cubic polynomial.
  • For example;
  • Hence
Illustration 4 for Answers_and_Explanations

Answer 5 (A)

  • Adding the given terms we have,

  • Hence,

Answer 5 (B)

  • Subtract from

  • Hence,

Answer 6

  • Here first is subtract from
  • Hence,

  • Sum of, and 3 times

  • Now, is subtracting from .
  • The difference is added to the sum of and 3 times

  • Hence the resulting algebraic expression is

Answer 7 (A)

  • Given equation,

  • Therefore, the answer will be

Answer 7 (B)

  • Given equation,

  • Hence, the answer will be

Answer 7 (C)

  • Given equation,

  • Therefore, the answer will be

Answer 8 (A)

  • Given equation,

  • Hence, the answer is

Answer 8 (B)

  • Given equation,

  • Hence, the answer is

Answer 8 (C)

  • Given equation,

  • Hence, the answer is

Answer 9 (A)

  • Here,

  • Hence, the answer is

Answer 9 (B)

  • Here,

  • Hence, the answer is

Answer 9 (C)

  • Here,

  • Hence, the answer is

Answer 10 (A)

  • Hence, the answer is

Answer 10 (B)

  • Hence, the answer is

Answer 11 (A)

  • Hence, the answer is

Answer 11 (B)

  • Hence, the answer is

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