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

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(a)

(b)

(a)

(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?

(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

 Expression Numerical Coefficients Constant term Value fora = 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

 Expression Numerical Coefficients Constant term Value fora = 3 and b = – 5 (a) (b)

## (8) Circle All the Algebraic Expressions in the Right That Are ‘Like’ the Expression in the Left

 (a) (b) (c) (d) (e)

(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)

• 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:

• 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:

• 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)
• 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.

• 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:

• 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

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

• 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

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

• After putting the value of in expression: answer

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

• After putting the value of in expression: answer

• 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,
 Expression Numerical Coefficients Constant term Value fora = 3 and b = – 5 (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,
 Expression Numerical Coefficients Constant term Value fora = 3 and b = – 5 (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,
 Expression Numerical Coefficients Constant term Value fora = 2 and b = – 4 (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,
 Expression Numerical Coefficients Constant term Value fora = 2 and b = – 4 (b)

• 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,

• 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,

• 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,

• 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,

• 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,

• Given expression

• Therefore;

• Given expression;

• Therefore

• Given that:
• Now,

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