## Pakistan Best Smart Syllabus Exam Prep Program

Take the program now to ace your Grade 9 & 10 board examinations!

## KPK Smart Syllabus - Grade 09

 Date Topic Lesson Lesson Object

## 18

KPK Smart Syllabus PDF

## 25

Introduction to Matrices

Types of Matrices

Properties of Addition and Subtraction of Matrices

Multiplicative Inverse of Matrix

Multiplicative Inverse of Matrix

Solution of Simultaneous Linear Equations

## 1

Real Numbers

Properties of Real Numbers

Base, Exponent, and Value

Laws of Exponents/ Indices

Complex Numbers

Basic Operation on Complex Numbers

## 8

Scientific Notation

Introduction to Logarithms

Characteristic and Mantissa of a Common Log of a Number

Log of a Number

Anti-log of a Number

Product Law of Logarithms

Quotient Law of Logarithms

Power Law of Logarithms

Change of Base Law of Logarithms

Application of the Laws of Logarithms

## 15

Rational Expressions and Polynomials

Reduce an Algebraic Expression to its Lowest Form

Sum, Difference, and Product of Rational Expressions

Division of Rational Expressions

Value of an Algebraic Expression at Some Particular Real Number

Formula: or

Formula:

Formula:

Formula:

Multiplication and Division of Surds

Rationalize the Denominators and Evaluate Second Order Surds

Rationalize Complex Denominators

## 22

Factorise

Factorise

Factorise

Factorise

Factorise

Factorise or

Factorise

Factorise

Factorise or or

Factorise

Factorise

Remainder Theorem

Use Factor Theorem to Factorise a Cubic Polynomial

## 1

HCF by Factorisation

LCM by Factorisation

HCF by Division

Relationship Between HCF and LCM

Use HCF and LCM to Reduce Fractional Expressions

Square Root of Algebraic Expressions

## 8

Solution of Linear Equations in One Variable

Solution of Linear Equations Involving Absolute Value

Solution of Linear Inequalities with Rational Coefficients

## 15

Cartesian Plane and Linear Graphs

Drawing Graphs

-

## 22

Distance Formula

Collinear and Non-Collinear Points - Triangles

Collinear and Non-Collinear Points - Rectangle

Collinear and Non-Collinear Points - Parallelogram

Midpoint Formula

Application of Distance and Midpoint Formulae

## 29

In a Triangle, Sides Opposite to Congruent Angles Are Congruent

Congruency of Two Triangles Based on HL

## 5

Prove Properties of Parallelograms

Prove that a Quadrilateral Is a Parallelogram

Prove Triangle Mid-Point Properties

## 12

Any Point on the Right Bisector of a Line Segment Is Equidistant From Its End Points

Any Point Equidistant From the End Points of a Line Segment Is on the Right Bisector of It

The Right Bisectors of the Sides of a Triangle Are Concurrent

Any Point on the Bisector of an Angle Is Equidistant From Its Arms

Any Point Inside an Angle, Equidistant From Its Arms, Is on the Bisector of It

The Bisectors of the Angles of a Triangle Are Concurrent

## 19

In a Triangle, the Longer Side Has an Angle of Greater Measure Opposite to It

In a Triangle, the Side Opposite to the Greater Angle Is Longer Than the Other Sides

The Sum of the Lengths of Any Two Sides of a Triangle Is Greater Than the Third

The Perpendicular Is the Shortest Distance From Any Point to the Line

## 26

If Two Triangles Are Similar, the Length of Their Corresponding Sides Are Proportional

## 3

In a Right-Angled Triangle, the Square of the Length of Hypotenuse Is Equal to the Sum of the Squares of the Lengths of the Other Two Sides

If the Square of One Side of a Triangle Is Equal to the Sum of the Squares of the Other Two Sides, Then the Triangle Is a Right-Angled Triangle

## 10

Parallelograms on the Same Base and Between the Same Parallel Lines Are Equal in Area

## 17

Construction of Triangles

Draw Angle Bisectors, Altitudes, Perpendicular Bisectors, and Medians in Triangles

## Learn Smart Pakistan is Pakistan's Premier Online Study Aid.

Use this schedule for your weekly exam prep fix, or register on Learn Smart Pakistan for assessments, videos, past papers, cheat sheets, and more.

Learn Smart is the smart way to master the Smart Syllabus!