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Mathematics Notes for 9th Class Exercise 6 Rev

“Math” a compulsory subject for 9th class Science students. and Mathematics Notes for 9th Class Exercise 6 Rev or Math Notes Class 9 English Medium (Science Group) included in this book.

Class 9th Math Solution:

The whole Summary of all Chapter as follow:

• We learned to find the H.C.F. and L.C.M. of algebraic expressions by the methods of factorization and division.
• We established a relation between H.C.F. and L.C.M. of two polynomials p(x) and q(x) given by the formula
L .C.M. x H.C.F. = p(x) x q(x)
and used it to determine L.C.M. or H.C.F. etc.
• Any unknown expression may be found if three of them are known by using the relation
L.C.M x H.C.F = p(x) x q(x)
• H.C.F. and L.C.M. are used to simplify fractional expressions involving basic operations of +, – , x , ÷.
• Determination of square root of algebraic expression by factorization and division methods has been defined and explained.

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Math Ch#6, 09th Class

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1 / 17

L.C.M of $a^2+b^2$ and $a^4 - b^4$ is _________

$a^2+b^2$
$a^2-b^2$
$a^4-b^4$
$a-b$

(Choose Correct Option)

Option-III

Option-IV

Option-I

Option-II

2 / 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-IV

Option-I

Option-III

3 / 17

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

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

(Select Correct Option)

Option-1

Option-4

Option-3

Option-2

4 / 17

the Square Root of $a^2 - 2a + 1$ is __________

± (a + 1)

± (a - 1)

a + 1

a - 1

5 / 17

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

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

(Chose Correct Option)

Option-3

Option-4

Option-2

Option-1

6 / 17

H.C.F of $x^2 - 5x+6$ and $x^2 - x-6$ is _______

x+2

x-3

x-2

x+4

7 / 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-1

Option-3

Option-4

8 / 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-1

Option-2

Option-3

Option-4

9 / 17

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

Quotient

Sum

Product

Difference

10 / 17

L.C.M of $15x^2 , 45xy , 30xyz$ is __________

$90xyz$
$90x^2yz$
$15xyz$
$15x^2yz$

(Choose Correct Option)

Option-II

Option-IV

Option-III

Option-I

11 / 17

H.C.F of $a^2 - b^2$ and $a^3 - b^3$ is ________

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

(Choose Correct Option)

Option-III

Option-IV

Option-II

Option-I

12 / 17

What should be added to complete the square of $x^4 + 64$ _____

$8x^2$
$-8x^2$
$16x^2$
$4x^2$

Select Correct Option

Option-1

Option-4

Option-3

Option-2

13 / 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-1

Option-4

Option-2

14 / 17

H.C.F of $x^2 +3x+2$ , $x^2+4x+3$ and $x^2+5x+4$ is __________

(x+3)

(x+4)(x+1)

(x+1)

(x+1)(x+2)

15 / 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-III

Option-IV

16 / 17

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

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

(Select Correct Option)

Option-4

Option-1

Option-3

Option-2

17 / 17

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

$x^{2}+x-6$
$x+3$
$x-2$
$x+2$

(Chose Correct Option)

Option-2

Option-1

Option-3

Option-4

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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)

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Mathematics Notes for 9th Class Exercise 6 Rev

Class 9th Math Solution:

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Math Solution 9th Class (Science Group)

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