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| matric:9th_science [2021/03/25 18:00] – Administrator | matric:9th_science [2023/03/08 18:04] (current) – Dr. Atiq ur Rehman | ||
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| ====== Mathematics 9 (Science Group) ====== | ====== Mathematics 9 (Science Group) ====== | ||
| - | + | ~~NOTOC~~ | |
| - | Mathematics 9 is written by Dr. Karamat H. Dar and Prof. Irfan-ul-Haq and this book is published by Carvan Book House, Lahore, Pakistan. This book consist of 302 pages and there are 17 units. Notes of Unit 1 and 3 are provided by **[[: | + | {{ : |
| + | Mathematics 9 is written by Dr. Karamat H. Dar and Prof. Irfan-ul-Haq and this book is published by Carvan Book House, Lahore, Pakistan. This book consist of 302 pages and there are 17 units. Notes of Unit 1 and 3 are provided by **[[: | ||
| ====== Definitions ====== | ====== Definitions ====== | ||
| - | * Definitions by Amir Shehzad | {{ : | + | * Definitions by Amir Shehzad | {{ : |
| * Definitions by Bahadar Ali Khan | {{ matric: | * Definitions by Bahadar Ali Khan | {{ matric: | ||
| Line 19: | Line 20: | ||
| ===== Unit 02: Real and Complex Numbers ===== | ===== Unit 02: Real and Complex Numbers ===== | ||
| The following MCQs was send by [[people: | The following MCQs was send by [[people: | ||
| + | |||
| + | * Solutions | {{ : | ||
| * MCQs | {{ : | * MCQs | {{ : | ||
| Line 29: | Line 32: | ||
| * MCQs | {{ : | * MCQs | {{ : | ||
| - | =====Unit 04 :Algebraic Expressions and Algebraic Formulas===== | + | =====Unit 04: Algebraic Expressions and Algebraic Formulas===== |
| In this unit, following topics has been covered: | In this unit, following topics has been covered: | ||
| * Algebraic Expressions | * Algebraic Expressions | ||
| Line 37: | Line 40: | ||
| The following notes of this chapter are provided by Mr. Adil Aslam | The following notes of this chapter are provided by Mr. Adil Aslam | ||
| - | * **Unit 4** | VIEW [[: | + | * **Unit 04** | VIEW [[: |
| + | =====Unit 05: Factorization===== | ||
| + | In this unit, following topics has been covered: | ||
| + | After studying this unit , the students will be able to: | ||
| + | * Recall factorization of expressions of the following types. | ||
| + | * $ka + kb + kc$ | ||
| + | * $ac + ad + bc + bd$ | ||
| + | * $a^2 + 2ab + b^2$ | ||
| + | * $a^2 – b^2$ | ||
| + | * $a^2 + 2ab + b^2 – c^2$ | ||
| + | * Factorize the expressions of the following types. | ||
| + | * Type I: $a^4 + a^2b^2 + b^4$ or $a^4 + 4b^4$ | ||
| + | * Type II: $x^2 + px + q$ | ||
| + | * Type III: $ax^2 + bx + c$ | ||
| + | * Type IV: $(ax^2 + bx + c) (ax2 + bx + d) + k$\\ $(x + a) (x + b) (x + c) (x + d) + k$\\ $(x + a) (x + b) (x + c) (x + d) + kx^2$ | ||
| + | * Type V: $a^3 + 3a^2b + 3ab^2 + b^3$\\ $a^3 − 3a^2b + 3ab^2 − b^3$ | ||
| + | * Type VI: $a^3 + b^3$ | ||
| + | * State and prove remainder theorem and explain through examples. | ||
| + | * Find Remainder (without dividing) when a polynomial is divided by a linear polynomial. | ||
| + | * Define zeros of a polynomial. | ||
| + | * State and prove Factor theorem. | ||
| + | * Use Factor theorem to factorize a cubic polynomial. | ||
| + | |||
| + | The following notes of this chapter are provided by Mr. Adil Aslam | ||
| + | * **Unit 05** | VIEW [[: | ||
| =====Unit 06: Algebraic Manipulation===== | =====Unit 06: Algebraic Manipulation===== | ||
| In this unit, following topics has been covered: | In this unit, following topics has been covered: | ||
| Line 70: | Line 97: | ||
| * Exercise 7.3 | VIEW [[: | * Exercise 7.3 | VIEW [[: | ||
| + | |||
| + | ===== Unit 08: Linear Graph and their Application ===== | ||
| + | Notes of this unit are available at the following page: https:// | ||
| ===== Unit 09: Introduction to Coordinate Geometry ===== | ===== Unit 09: Introduction to Coordinate Geometry ===== | ||
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| No notes available yet | No notes available yet | ||
| + | ===== Unit 10: Congruent Triangles ===== | ||
| + | |||
| + | After studying this unit, the students will be able to: | ||
| + | * Prove that in any correspondence of two triangles, if one side and any two angles of one triangle are congruent to the corresponding side and angles of the other, then the triangles are congruent. | ||
| + | * Prove that if two angles of a triangle are congruent, then the sides opposite to them are also congruent. | ||
| + | * Prove that in a correspondence of two triangles, if three sides of one triangle are congruent to the corresponding three sides of the other, the two triangles are congruent. | ||
| + | * Prove that if in the correspondence of two right-angled triangles, the hypotenuse and one side of one are congruent to the hypotenuses and the corresponding side of the other, then the triangles are congruent. | ||
| + | |||
| + | * Exercise 10.1 | {{ : | ||
| + | |||
| + | * Exercise 10.2 | {{ : | ||
| + | |||
| + | * Exercise 10.3 | {{ : | ||
| + | | ||
| + | * Exercise 10.4 | {{ : | ||
| + | | ||
| + | * Review Exercise 10 | {{ : | ||
| + | |||
| + | * [[matric: | ||
| ===== Unit 12: Line Bisectors and Angle Bisectors ===== | ===== Unit 12: Line Bisectors and Angle Bisectors ===== | ||