====== Mathematics 9 (Science Group) ====== ~~NOTOC~~ {{ :matric:9th-science-ptb.jpg?nolink|Mathematics 9 (Science Group)}} 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 **[[:people:moin]]**. We are very thankful to him for providing these notes. The soft form of this book can be downloaded from PITB webiste from [[https://pctb.punjab.gov.pk/E-Book%202022|HERE]] ====== Definitions ====== * Definitions by Amir Shehzad | {{ :matric:definition-9th-science-amir-shehzad.pdf |Download PDF}} * Definitions by Bahadar Ali Khan | {{ matric:9th_science:definition-9th-science-bahadar-ali-khan.pdf |Download PDF}} ===== Unit 01: Matrix ===== These notes are prepared by Mr. [[:people:moin]]. * Solutions | {{ :matric:9th_science:ch01-matric-science.pdf |Download PDF}} * MCQs | {{ :matric:9th_science:9th-science-unit-01-mcqs-ptb.pdf |Download PDF}} ===== Unit 02: Real and Complex Numbers ===== The following MCQs was send by [[people:amir]]. We are very thankful to him for sending these notes. * Solutions | {{ :matric:9th-science-unit02-ptb-amir-shehzad.pdf |Download PDF}} NEW * MCQs | {{ :matric:9th_science:9th-science-unit-02-mcqs-ptb.pdf |Download PDF}} ===== Unit 03: Logarithms ===== These notes are prepared by [[:people:moin]]. MCQs are made by Mr. [[:people:amir]] * Solutions | {{ :matric:9th_science:ch03-matric-science-moin-latif.pdf |Download PDF}} * MCQs | {{ :matric:9th_science:9th-science-unit-03-mcqs-ptb.pdf |Download PDF}} =====Unit 04: Algebraic Expressions and Algebraic Formulas===== In this unit, following topics has been covered: * Algebraic Expressions * Algebraic Formulas * Surds and their Application * Rationalization The following notes of this chapter are provided by Mr. Adil Aslam * **Unit 04** | VIEW [[:matric:9th_science:unit_04:viewer?f=9th-science-ch-9-adil-aslam-ptb|View Online]] | {{ :matric:9th_science:9th-science-ch-9-adil-aslam-ptb.pdf |Download PDF}} =====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 [[:matric:9th_science:unit_05:viewer?f=unit05-matric-science-adil-aslam-ptb|View Online]] | {{ :matric:9th_science:unit05-matric-science-adil-aslam-ptb.pdf |Download PDF}} =====Unit 06: Algebraic Manipulation===== In this unit, following topics has been covered: * Highest common factor and least common multiples * Basic operations on algebraic fractions * Square root of algebraic expression There are total four exercises in unit 6. Notes of this chapter will be added soon. ===== Unit 07: Linear Equations and Inequalities ===== These notes are send by Mr. **Malik Faisal Rafiq**. We are very thankful to him for sending these notes. **Linear Equations:** A linear equation is one unknown variable $x$ is an equation of the form $ax+b=0$, where $a,b\in \mathbb{R}$ and $a\neq 0$. **Radical Equations:** When the variable in an equation occurs under a radical, the equation is called radical equation. **Equation Involving Absolute Value:** The absolute value of real number $a$ denoted by $|a|$ is defined as $$ |a|=\left\{\begin{matrix} a & \text{if } a\geq 0, \\ -a & \text{if } a<0. \end{matrix}\right. $$ e.g. $|6|=6$, $|0|=0$, $|-3|=3$. **Defining inequalities:** Let $a,b$ be real numbers. Then $a$ is greater than $b$ if the difference $a-b>0$ and we denote this order relation by the inequality $a>b$. An equivalent statement is that $b$ is less than $a$, symbolized by $bMatric 9th(Science) Amir_Shehzad}} =====Important Questions===== The following file was send by Ms. Maryam Jabeen. * {{ :matric:9th-science-importent-questions-theorem-exercises-unit10-16.pdf |Important Questions from Theorem Exercises Unit 10-16}} The MCQs of full book are send by [[:people:amir]] * {{ :matric:9th-science-mcqs-ptb.pdf |MCQs of Full Book, Matric 9th (Science)}} NEW {{tag>Matric 9th(Science) Amir_Shehzad Moin_Latif Maryam_Jabeen Bahadar_Ali_Khan}}