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Mathematics Notes for 9th Class Exercise 6.3

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Mathematics Notes for 9th Class Exercise 6.3

“Math” a compulsory subject for 9th class Science students. and Mathematics Notes for 9th Class Exercise 6.3 or Math Notes Class 9 English Medium (Science Group) included in this book.

How to Find Square Root of Algebraic Expression:

As with numbers define the square root of given expression p(x) as another expression q(x) such that q(x) . q(x) = p(x). As 5 # 5 = 25, so square root of 25 is 5. It means we can find square root of the expression p(x) if it can be expressed as a perfect square.
In this section we shall find square root of an algebraic expression
(i) Square Root by factorization (ii) Square Root by division

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Math Ch#6, 09th Class

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1 / 17

the Square Root of is __________

a - 1

± (a - 1)

± (a + 1)

a + 1

2 / 17

H.C.F of $5x^{2}$ and $20 x^{3} y^{3}$ is ____________

$5x^{2}y^{2}$
$20x^{3}y^{3}$
$100x^{5}y^{5}$

(Select Correct Option)

Option-3

Option-1

Option-2

Option-4

3 / 17

L.C.M of and is _________

(Choose Correct Option)

Option-III

Option-II

Option-I

Option-IV

4 / 17

The Square Root of $x^4 + \frac{1}{x^4}+2$ is ___________

$\pm \left ( x + \frac{1}{x} \right )$
$\pm \left ( x^2 + \frac{1}{x^2} \right )$
$\pm \left ( x - \frac{1}{x} \right )$
$\pm \left ( x^2 - \frac{1}{x^2} \right )$

Select Correct Option

Option-2

Option-3

Option-4

Option-1

5 / 17

H.C.F of $a^{3}+b^{3}$ and $a^{2}-ab+b^{2}$ is ________

$a^{2}-ab+b^{2}$

(Chose Correct Option)

Option-4

Option-3

Option-1

Option-2

6 / 17

H. C. F of ( $p^{3}q-pq^{3}$ ) and ( $p^{5}q^{2}-p^{2}q^{5}$ ) is ___________

$pq(p^{2}-q^{2})$
$p^{2}q^{2} (p-q)$
$pq(p^{3}-q^{3})$

(Select Correct Option)

Option-1

Option-3

Option-4

Option-2

7 / 17

Simplify $\frac{a^3-b^3}{a^4-b^4} \div \frac{a^2+ab+b^2}{a^2+b^2}$ = ________

$\frac{1}{a+b}$
$\frac{1}{a-b}$
$\frac{a-b}{a^2+b^2}$
$\frac{a+b}{a^2+b^2}$

(Which option is Correct)

Option-3

Option-2

Option-4

Option-1

8 / 17

Simplify $\frac{a^2 +5a-14}{a^2 - 3a-18} \times \frac{a+3}{a-2}$ = _________

$\frac{a+7}{a-6}$
$\frac{a+7}{a-2}$
$\frac{a+3}{a-6}$
$\frac{a-2}{a+3}$

(Choose Correct Option)

Option-II

Option-I

Option-III

Option-IV

9 / 17

Simplify $\left ( \frac{2x+1}{x+y}-1 \right )\div \left ( 1-\frac{x}{x-y} \right )$ = __________

$\frac{x}{x+y}$
$\frac{y}{x+y}$
$\frac{y}{x}$
$\frac{x}{y}$

Which Option is Correct

Option-2

Option-4

Option-1

Option-3

10 / 17

H.C.F of and $x^{2}+x-6$ is ___________

$x^{2}+x-6$

(Chose Correct Option)

Option-3

Option-4

Option-2

Option-1

11 / 17

L.C.M of is __________

(Choose Correct Option)

Option-II

Option-III

Option-I

Option-IV

12 / 17

Simplify $\frac{a}{9a^2 - b^2} + \frac{1}{3a-b}$ = __________

$\frac{4a}{9a^2-b^2}$
$\frac{4a-b}{9a^2-b^2}$
$\frac{4a+b}{9a^2-b^2}$
$\frac{b}{9a^2-b^2}$

(Choose Correct Option)

Option-II

Option-I

Option-IV

Option-III

13 / 17

H.C.F of , and is __________

(x+3)

(x+1)(x+2)

(x+1)

(x+4)(x+1)

14 / 17

What should be added to complete the square of _____

Select Correct Option

Option-4

Option-2

Option-1

Option-3

15 / 17

The product of two Algebraic expressions is equal to the ______ of their H.C.F and L.C.M

Quotient

Product

Sum

Difference

16 / 17

H.C.F of and is _______

x+4

x+2

x-2

x-3

17 / 17

H.C.F of and is ________

(Choose Correct Option)

Option-IV

Option-II

Option-III

Option-I

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Math Solution 9th Class (Science Group)

Chapter 01 - MATRICES AND DETERMINANTS

Exercise 1.1 (English) (Urdu)

Exercise 1.2 (English) (Urdu)

Exercise 1.3 (English) (Urdu)

Exercise 1.4 (English) (Urdu)

Exercise 1.5 (English) (Urdu)

Exercise 1.6 (English) (Urdu)

Exercise 1-Rev (English) (Urdu)

Online Practice/ Test - MCQs & Short Questions

Chapter 02 - REAL AND COMPLEX NUMBERS

Exercise 2.1 (English) (Urdu)

Exercise 2.2 (English) (Urdu)

Exercise 2.3 (English) (Urdu)

Exercise 2.4 (English) (Urdu)

Exercise 2.5 (English) (Urdu)

Exercise 2.6 (English) (Urdu)

Exercise 2-Rev (English) (Urdu)

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Chapter 03 - LOGARITHMS

Exercise 3.1 (English) (Urdu)

Exercise 3.2 (English) (Urdu)

Exercise 3.3 (English) (Urdu)

Exercise 3.4 (English) (Urdu)

Exercise 3-Rev (English) (Urdu)

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Chapter 04 - ALGEBRIC EXPRESSIONS & ALGEBRIC FORMULAS

Exercise 4.1 (English) (Urdu)

Exercise 4.2 (English) (Urdu)

Exercise 4.3 (English) (Urdu)

Exercise 4.4 (English) (Urdu)

Exercise 4-Rev (English) (Urdu)

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Chapter 05 - FACTORIZATION

Exercise 5.1 (English) (Urdu)

Exercise 5.2 (English) (Urdu)

Exercise 5.3 (English) (Urdu)

Exercise 5.4 (English) (Urdu)

Exercise 5-Rev (English) (Urdu)

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Chapter 06 - ALGEBRAIC MANIPULATION

Exercise 6.1 (English) (Urdu)

Exercise 6.2 (English) (Urdu)

Exercise 6.3 (English) (Urdu)

Exercise 6-Rev (English) (Urdu)

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Chapter 07 - LINEAR EQUATIONS AND INEQUALITIES

Exercise 7.1 (English) (Urdu)

Exercise 7.2 (English) (Urdu)

Exercise 7.3 (English) (Urdu)

Exercise 7-Rev (English) (Urdu)

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Chapter 08 - LINEAR GRAPHS & THEIR APPLICATION

Exercise 8.1 (English) (Urdu)

Exercise 8.2 (English) (Urdu)

Exercise 8.3 (English) (Urdu)

Exercise 8-Rev (English) (Urdu)

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Chapter 09 - INTRODUCTION TO COORDINATE GEOMETRY

Exercise 9.1 (English) (Urdu)

Exercise 9.2 (English) (Urdu)

Exercise 9.3 (English) (Urdu)

Exercise 9-Rev (English) (Urdu)

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Chapter 10 - CONGRUENT TRIANGLES

Exercise 10.1 (English) (Urdu)

Exercise 10.2 (English) (Urdu)

Exercise 10.3 (English) (Urdu)

Exercise 10.4 (English) (Urdu)

Exercise 10-Rev (English) (Urdu)

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Chapter 11 - PARALLELOGRAMS AND TRIANGLES

Exercise 11.1 (English) (Urdu)

Exercise 11.2 (English) (Urdu)

Exercise 11.3 (English) (Urdu)

Exercise 11.4 (English) (Urdu)

Exercise 11.5 (English) (Urdu)

Exercise 11-Rev (English) (Urdu)

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Chapter 12 - LINE BISECTORS AND ANGLE BISECTORS

Exercise 12.1 (English) (Urdu)

Exercise 12.2 (English) (Urdu)

Exercise 12.3 (English) (Urdu)

Exercise 12-Rev (English) (Urdu)

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Chapter 13 - SIDES AND ANGLES OF A TRIANGLE

Exercise 13.1 (English) (Urdu)

Exercise 13.2 (English) (Urdu)

Exercise 13-Rev (English) (Urdu)

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Chapter 14 - RATIO AND PROPORTION

Exercise 14.1 (English) (Urdu)

Exercise 14.2 (English) (Urdu)

Exercise 14-Rev (English) (Urdu)

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Chapter 15 - PYTHAGORAS’ THEOREM

Exercise 15 (English) (Urdu)

Exercise 15-Rev (English) (Urdu)

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Chapter 16 - THEOREMS RELATED WITH AREA

Exercise 16.1 (English) (Urdu)

Exercise 16.2 (English) (Urdu)

Exercise 16-Rev (English) (Urdu)

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Chapter 17 - PRACTICAL GEOMETRY -TRIANGLES

Exercise 17.1 (English) (Urdu)

Exercise 17.2 (English) (Urdu)

Exercise 17.3 (English) (Urdu)

Exercise 17.4 (English) (Urdu)

Exercise 17.5 (English) (Urdu)

Exercise 17-Rev (English) (Urdu)

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Math Past Papers

Math Text Books

9th Math Science Group (English Medium)

9th Math Science Group (Urdu Medium)

9th Math Arts Group (Urdu Medium)

Other Math Notes

10th Class Math Science Group (English Medium)

10th Class Math Science Group (Urdu Medium)

10th Math Past Papers (Science Group)

10th Math Past Papers (Arts Group)

9th Class Math Science Group (English Medium)

9th Class Math Science Group (Urdu Medium)

9th Class Math Arts Group (Urdu Medium)

9th Class Math Past Papers (Science Group)

9th Class Math Past Papers (Arts Group)

Mathematics Notes for 9th Chapter # 06:

(i) By Factorization:

First we seen how find the square root by factorization.

(ii) By Division:

we have also seen the division method, when it is difficult to convert the given expression into a perfect square by factorization, we use the method of actual division to find its square root. The method is similar to the division method of finding square root of numbers.

There are Seventeen chapters in Mathematics 9th Class for Punjab Textbook Board, Lahore. Solutions of all the chapters are given below. Anyone can download the PDF file of the notes. Note that, you can view these notes only if you have PDF reader software/ App on your device. However online view of the notes is also available on eStudent.pk . You can find all solution along with 9th Class Math Notes in Urdu (Science Group), Math MCQs Class 9.

Math Notes Class 9:

9^th class math notes chapter 6, 9^th class math solution chapter 6 pdf, math notes class 9 chapter 6, Math Notes Class 9 Exercise 6.3, exercise 6.3 class 9, exercise 6.3 class 9 then this post is specially for you and your future. All Boards of Intermediate & Secondary Educations in Punjab, Federal Board of Intermediate and Secondary Education, kpd board, Sindh board, Agha Khan Board and also Allama Iqbal Open University are taking examination according to Mathematics 9th Class. 9th Class Math key book pdf in English, Notes of 9th Class Math, Mathematics Notes for 9th Class Exercise 6.3.