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Mathematics Notes for 9th Class Exercise 6.1

“Math” a compulsory subject for 9th class Science students. and Mathematics Notes for 9th Class Exercise 6.1 or Math Notes Class 9 English Medium (Science Group) included in this book.

The Question is How to Finding H.C.F. ?
We can find H. C. F. of given expressions by the following two methods.
(i) By Factorization (ii) By Division
Sometimes it is difficult to find factors of given expressions. In that case, method of division can be used to find H. C. F. We consider some examples to explain these two methods.
(i) H.C.F. by Factorization
Example: Find the H. C. F. of the following polynomials. x2 – 4, x2 + 4x + 4, 2×2 + x – 6
Solution by factorization:

x2 – 4 = (x + 2) (x – 2)
x2 + 4x + 4 = (x + 2)2
2×2 + x – 6 = 2×2 + 4x – 3x – 6 = 2x(x + 2) – 3(x + 2)
= (x + 2) (2x – 3)
Hence, H. C. F. = x + 2

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Math Ch#6, 09th Class

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1 / 17

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

  • 8x^2
  • -8x^2
  • 16x^2
  • 4x^2

Select Correct Option

2 / 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)

3 / 17

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

  1. a+b
  2. a^{2}-ab+b^{2}
  3. (a-b)^2
  4. a^2+b^2

(Chose Correct Option)

4 / 17

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

  1. \frac{4a}{9a^2-b^2}
  2. \frac{4a-b}{9a^2-b^2}
  3. \frac{4a+b}{9a^2-b^2}
  4. \frac{b}{9a^2-b^2}

(Choose Correct Option)

5 / 17

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

6 / 17

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

7 / 17

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

8 / 17

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

  1. a^2+b^2
  2. a^2-b^2
  3. a^4-b^4
  4. a-b

(Choose Correct Option)

9 / 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)

10 / 17

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

  1. x^{2}+x-6
  2. x+3
  3. x-2
  4. x+2

(Chose Correct Option)

11 / 17

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

12 / 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)

13 / 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)

14 / 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

15 / 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

16 / 17

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

  1. 90xyz
  2. 90x^2yz
  3. 15xyz
  4. 15x^2yz

(Choose Correct Option)

17 / 17

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

  1. a -b
  2. a+b
  3. a^2 + ab+ b^2
  4. a^2 - ab+b^2

(Choose Correct Option)

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Math Solution 9th Class (Science Group)

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

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)


Online Practice/ Test - MCQs & Short Questions

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)


Online Practice/ Test - MCQs & Short Questions

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)


Online Practice/ Test - MCQs & Short Questions

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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Exercise 6.1           (English)            (Urdu)


Exercise 6.2           (English)            (Urdu)


Exercise 6.3           (English)            (Urdu)


Exercise 6-Rev      (English)            (Urdu)


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Exercise 7.1           (English)            (Urdu)


Exercise 7.2           (English)            (Urdu)


Exercise 7.3           (English)            (Urdu)


Exercise 7-Rev      (English)            (Urdu)


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Exercise 8.1           (English)            (Urdu)


Exercise 8.2           (English)            (Urdu)


Exercise 8.3           (English)            (Urdu)


Exercise 8-Rev      (English)            (Urdu)


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Exercise 9.1           (English)            (Urdu)


Exercise 9.2           (English)            (Urdu)


Exercise 9.3           (English)            (Urdu)


Exercise 9-Rev      (English)            (Urdu)


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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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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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Exercise 12.1           (English)            (Urdu)


Exercise 12.2           (English)            (Urdu)


Exercise 12.3           (English)            (Urdu)


Exercise 12-Rev      (English)            (Urdu)


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Exercise 13.1           (English)            (Urdu)


Exercise 13.2           (English)            (Urdu)


Exercise 13-Rev      (English)            (Urdu)


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Exercise 14.1           (English)            (Urdu)


Exercise 14.2           (English)            (Urdu)


Exercise 14-Rev      (English)            (Urdu)


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Exercise 15           (English)            (Urdu)


Exercise 15-Rev   (English)            (Urdu)


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Exercise 16.1           (English)            (Urdu)


Exercise 16.2           (English)            (Urdu)


Exercise 16-Rev      (English)            (Urdu)


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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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9th Math Science Group (English Medium)


9th Math Science Group (Urdu Medium)


9th Math Arts Group (Urdu Medium)



Mathematics Notes for 9th:

How to find L.C.M. by Factorization:

Working Rule to find L.C.M. of given Algebraic Expressions 
(i) Factorize the given expressions completely i.e., to simplest form.
(ii) Then the L.C.M. is obtained by taking the product of each factor appearing in any of the given expressions, raised to the highest power with which that factor appears.

Example: Find the L.C.M. of p(x) = 12(x3 – y3) and q(x) = 8(x3 – xy2)
Solution: By prime factorization of the given expressions, we have
p(x) = 12(x3 – y3) = 22 x 3 x (x – y) (x2 + xy + y2)
and q(x) = 8(x3 – xy2) = 8x(x2 – y2) = 23x(x + y) (x – y)
Hence L.C.M. of p(x) and q(x),
23 x 3 x x(x + y) (x – y) (x2 + xy + y2) = 24x (x + y) (x3 – y3)

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:

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