# 9th Class Math Notes With Solutions For Federal Board (PDF)

Are you a student of class 9th and looking for the 9th Class Maths notes with solutions for the complete book? The notes dedicated to the FBISE students are here. Here is your Class 9 Maths solved Notes with Example Solutions For Federal Board in PDF free.

Most Pakistani students consider mathematics a difficult subject because they don’t take this subject with the other subjects. Rather having a firm belief in “parrot fashioning (Ratta’lization).” So, such a subject that fits differently in your study must have a special administration also. For that purpose, fasten your belts tighter because you will fly in a mathematics airplane whose sky hardly suits your atmosphere.

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Revising every day makes sense. When you memorize a topic the next day, about 20 to 30% fades away from your mind, especially in maths, where a lot of practice is required.

**See also:** 9th Class Chemistry Notes with Solved Examples

Doesn’t it take a lot of time? Nope! It is not! When you revise a topic every day, the topic takes less time. Your eyes remember the pattern and the words written in the book. According to them, many students seriously no idea why maths is being taught because it does not know, as is the case with Biology, Chemistry, and Physics. The science subjects mentioned above provide you insight into the inner and outer world.

Biology tells you about living things, and Physics shows you where an airplane flies in the sky. But maths? It enhances your rational and logical thinking normally considered in the test like DMCAT, CSS, SAT, and NTS in the future. You can think great, and you can solve a problem of your life well just by using a little brain.

### CHAPTER 1: MATRICES AND DETERMINANTS

Topics that chapter 1 includes are:

- Matrix:
- In elementary school, we learn how to multiply numbers. In algebra, we know how to multiply variables. In high school, we first see matrices, just variables with multiple indexes, like x2,3, or a13. Even though we don’t know what they are, at least we have a notation for talking about them.
- Matrices aren’t just things you multiply; they’re things that operate on other things. When you reach linear algebra, you get told what those matrices represent: linear transformations. You start the course thinking of matrices as abstractions and end it realizing they are concrete objects in the world.
- You can imagine a similar progression in programming languages. At first, you have arrays, like matrices with only one index. Then you have structs, which are arrays with multiple indexes—except, unlike matrices, they tend to be called by name rather than by position; and unlike in math, there is no single standard way to refer to the elements of a struct. Finally, objects in the object-oriented sense are collections of data fields plus methods that operate on those fields.
- Types of Matrices
- Addition and Subtraction of Matrices
- Multiplication of Matrices
- Multiplicative Inverse of a Matrix
- Solution of Simultaneous Linear Equations

### CHAPTER 2: REAL AND COMPLEX NUMBERS

Topics that chapter 2 includes are:

- Real Numbers
- Properties of Real Numbers
- Radicals and Radicands
- Laws of Exponents/Indices
- Complex Numbers
- Basic Operations on Complex Numbers

### CHAPTER 3: LOGARITHMS

Topics that chapter 3 includes are:

1. Scientific Notation 2. Logarithm 3. Common Logarithm and Natural Logarithm 4. Laws of Logarithm 5. Application of Laws of Logarithm in Calculations

### CHAPTER 4: ALGEBRAIC EXPRESSIONS AND ALGEBRAIC

Topics that chapter 4 includes are:

- Algebraic Expressions
- Algebraic Formula
- Surds and their Application
- Rationalization of Surds

### CHAPTER 5: FACTORIZATION

Topics that chapter 5 includes are:

- Factorization
- Remainder Theorem and Factor Theorem
- Factorization of a Cubic Polynomial

### CHAPTER 6: ALGEBRAIC MANIPULATION

Topics that chapter 6 includes are:

- Highest Common Factor & Least Common
- Basic Operations on Algebraic Fractions
- Square Root of Algebraic Expression

### CHAPTER 7: LINEAR EQUATIONS AND INEQUALITIES

Topics that chapter 7 includes are:

- Linear Equations
- Equations Involving Absolute Value
- Linear Inequalities
- Solving Linear Inequalities

### CHAPTER 8: LINEAR GRAPHS & THEIR APPLICATION

Topics that chapter 8 includes are:

- Cartesian Plane and Linear Graphs
- Conversion Graphs
- Graphically Solving 2 Variable Linear

### CHAPTER 9: INTRODUCTION TO COORDINATE GEOMETRY

Topics that chapter 9 includes are:

- Distance Formula
- Collinear Points
- Mid-Point Formula