Grade-7 a Consolidation of the Basics Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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(1) in Each Question, Write Out the Expression Which Gives Us the Nth Term of the Series

(a)

(b)

(2) in Each Question, Write Out the Expression Which Gives Us the Nth Term of the Series

(a)

(3) Write Out the Expression Which Gives Us the Nth Term of the Series

(a)

(4) Manisha Have 450 Pen. She Gave Z Number of Pen to Her Friend Nilam

(a) How many pen remained with Manisha?

(b) If she gave another y number of pen to her friend Yogesh then, how many pen remain with her?

(c) Is Manisha gave 25 pen to Nilam and 75 pen to Yogesh, Then how many pen remain with Manisha?

(5) Substitute the Values of a, B, C in the Expression 5a + 2b - 4c. Then Write Out the Answer in the Box Given

(a)

(b)

(6) Each Question Contains an Algebraic Expression. Write Out the Numerical Coefficients and the Constant Terms in Each of Them. Then Find the Value of the Expression when a = 3 and B = – 5

Table Supporting: 6_Each_question_contains_an_algebraic_expression_Write_out_the_numerical_coefficients_and_the_constant_terms_in_each_of_them_Then_find_the_value_of_the_expression_when_a________3_and_b________5
ExpressionNumerical CoefficientsConstant termValue for

a = 3 and b = – 5

(a)
(b)

(7) Each Question Contains an Algebraic Expression. Write Out the Numerical Coefficients and the Constant Terms in Each of Them. Then Find the Value of the Expression when a = 2 and B = – 4

Table Supporting: 7_Each_question_contains_an_algebraic_expression_Write_out_the_numerical_coefficients_and_the_constant_terms_in_each_of_them_Then_find_the_value_of_the_expression_when_a________2_and_b________4
ExpressionNumerical CoefficientsConstant termValue for

a = 3 and b = – 5

(a)
(b)

(8) Circle All the Algebraic Expressions in the Right That Are β€˜Like’ the Expression in the Left

Table Supporting: 8_Circle_all_the_algebraic_expressions_in_the_right_that_are_like_the_expression_in_the_left
(a)
(b)
(c)
(d)
(e)

(9) Simplify the Following Equations

(a)

(10) Simplify the Following Equations

(a)

(11) If Determine the expression obtained by simplifying.

(a)

(12) If Determine the expression obtained by simplifying.

(a)

Answers and Explanations

Answer 1 (A)

  • Given series:
  • Difference (d) between two consecutive term:

  • Here Difference between two consecutive terms remain same (unchanged) , means we can get next term by adding 5 to the previous term.
  • Now formula to find out nth term of series is;

Where;

  • Therefore nth term of given series:

Answer 1 (B)

  • Given series:
  • Difference (d) between two consecutive term:

  • Here Difference between two consecutive terms remain same (unchanged) , means we can get next term by adding 4 to the previous term.
  • Now formula to find out nth term of series is;

Where;

  • Therefore nth term of given series:

Answer 2 (A)

  • Given series:
  • Difference (D) between two consecutive term:

  • Here Difference between two consecutive terms will not remain same (changed from one difference between two consecutive terms to second one difference between two consecutive terms)
Illustration 2 for Answers_and_Explanations
  • From above we can say that if we write a difference between two consecutive terms of main series, than difference terms itself form a series

  • Difference (d) between two consecutive term:

  • Here difference between two consecutive terms of difference series remain same (unchanged) , means we can get next term of difference series by adding 3 to the previous term.
  • Now, if difference of two consecutive terms itself forms a series than nth term of main series must be quadratic.
  • And for the quadratic function;

  • Where
  • Here function represent the nth term of series so,

  • Now, When

  • Now Second term of main series is 3 so,

  • Now, Third term of main series is 8 so,

  • Now, to solve equation-1 and equation -2, multiply equation -1 by 2 and then substitute from equation-2.

  • Put the value of in equation-1

  • Now put the value of in main function.

  • Therefore nth term of series.

Answer 3 (A)

  • Given series:
  • Difference (d) between two consecutive term:

  • Here Difference between two consecutive terms remain same (unchanged) , means we can get next term by adding 6 to the previous term.
  • Now formula to find out nth term of series is;

Where;

  • Therefore nth term of given series:

Answer 4 (A)

  • Manisha have 450 number of pen.
  • She gave z number of pen to Nilam than pen remained with Manisha

  • Therefore After giving z number of pen to Nilam; Manisha have

Number of pen remain with her

Answer 4 (B)

Manisha gave another y number of pen to her friend Yogesh.

So, now Manisha have

  • Therefore After giving y number of pen to Yogesh; Manisha have

Number of pen remain with her

Answer 4 (C)

  • Given that if Manisha gave 25 pen to Nilam and 75 pen to Yogesh then.

  • Now put this value in

  • Therefore Manisha have remain;

  • Therefore after giving 25 pen to Nilam and 75 pen to Yogesh, Manisha remain of pen with her

Answer 5 (A)

  • Given expression:
  • Now put the value of in above expression than,

  • After putting the value of in expression: answer

Answer 5 (B)

  • Given expression:
  • Now put the value of in above expression than,

  • After putting the value of in expression: answer

Answer 6 (A)

  • Numerical coefficient means the number beside the variable term. For example in expression 4a; 4 is numerical coefficient.
  • Constant term means the number which remain unchanged and not given in multiplication form of any variable; for example in given expression 4a + 3,4 is numerical coefficient and 3 is constant term
  • Now for given expression:

  • Numerical coefficient of term
  • Numerical coefficient of term
  • Numerical coefficient of term
  • So, Numerical coefficient of given expression is
  • Constant term of given expression is
  • Now, put the value of in given expression,

  • Therefore,
Table Supporting: Answers_and_Explanations
ExpressionNumerical CoefficientsConstant termValue for

a = 3 and b = – 5

(a)

Answer 6 (B)

  • Given expression:

  • Numerical coefficient of term
  • Numerical coefficient of term
  • Numerical coefficient of term
  • So, Numerical coefficient of given expression is
  • Constant term of given expression is
  • Now, put the value of in given expression,

  • Therefore,
Table Supporting: Answers_and_Explanations
ExpressionNumerical CoefficientsConstant termValue for

a = 3 and b = – 5

(b)

Answer 7 (A)

  • Given expression:

  • Numerical coefficient of term
  • Numerical coefficient of term
  • Numerical coefficient of term
  • So, Numerical coefficient of given expression is
  • Constant term of given expression is
  • Now, put the value of in given expression,

  • Therefore,
Table Supporting: Answers_and_Explanations
ExpressionNumerical CoefficientsConstant termValue for

a = 2 and b = – 4

(a)

Answer 7 (B)

  • Given expression:

  • Numerical coefficient of term
  • Numerical coefficient of term
  • Numerical coefficient of term
  • So, Numerical coefficient of given expression is
  • Constant term of given expression is
  • Now, put the value of in given expression,

  • Therefore,
Table Supporting: Answers_and_Explanations
ExpressionNumerical CoefficientsConstant termValue for

a = 2 and b = – 4

(b)

Answer 8 (A)

  • The expression that given in the left side is:
  • Means variable a have exponent 5 and variable b have exponent 3.
  • The likely to be same expression given on the right side also have, a have exponent 5 and variable b have exponent 3.
  • So,
Illustration 3 for Answers_and_Explanations

Answer 8 (B)

  • The expression that given in the left side is:
  • Means variable a have exponent 1 and variable b have exponent 2.
  • The likely to be same expression given on the right side also have, a have exponent 1 and variable b have exponent 2.
  • So,
Illustration 4 for Answers_and_Explanations

Answer 8 (C)

  • The expression that given in the left side is: 8
  • Means variable a have exponent 8 and variable b have exponent 4.
  • The likely to be same expression given on the right side also have, a have exponent 8 and variable b have exponent 4.
  • So,
Illustration 5 for Answers_and_Explanations

Answer 8 (D)

  • The expression that given in the left side is:
  • Means variable a have exponent 4 and variable b have exponent -3.
  • The likely to be same expression given on the right side also have, a have exponent 4 and variable b have exponent -3.
  • So,
Illustration 6 for Answers_and_Explanations

Answer 8 (E)

  • The expression that given in the left side is:
  • Means variable a have exponent 7 and variable b have exponent 3.
  • The likely to be same expression given on the right side also have, a have exponent 7 and variable b have exponent 3.
  • So,
Illustration 7 for Answers_and_Explanations

Answer 9 (A)

  • Given expression

  • Therefore;

Answer 10 (A)

  • Given expression;

  • Therefore

Answer (11)

  • Given that:
  • Now,

  • Put the value of A, B and C in above equation.

Answer (12)

  • Given that:
  • Now,

  • Put the value of A, B and C in above equation.

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