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## Ninth Grade Math Lessons, Practice Test, Worksheets, Textbook Questions and Answer Key

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### Arithmetic

#### Rational Numbers

- Rational Numbers
- Decimal Representation of Rational Numbers
- Rational Numbers in Terminating and Non-Terminating Decimals
- Recurring Decimals as Rational Numbers
- Laws of Algebra for Rational Numbers
- Comparison between Two Rational Numbers
- Rational Numbers Between Two Unequal Rational Numbers
- Representation of Rational Numbers on Number Line
- Problems on Rational numbers as Decimal Numbers
- Problems Based On Recurring Decimals as Rational Numbers
- Problems on Comparison Between Rational Numbers
- Problems on Representation of Rational Numbers on Number Line
- Worksheet on Rational Number as Decimal Numbers
- Worksheet on Recurring Decimals as Rational Numbers
- Worksheet on Comparison between Rational Numbers
- Worksheet on Representation of Rational Numbers on the Number Line

#### Irrational Numbers

- Irrational Numbers
- Definition of Irrational Numbers
- Decimal Representation of Irrational Number
- Representation of Irrational Numbers on The Number Line
- Comparison between Two Irrational Numbers
- Comparison between Rational and Irrational Numbers
- Real number between Two Unequal Real Numbers
- Rationalization
- Problems on Irrational Numbers
- Problems on Rationalizing the Denominator
- Worksheet on Irrational Numbers

#### Profit and Loss

- Cost Price, Selling Price, and Rates of Profit and Loss
- Problems on Cost Price, Selling Price and Rates of Profit and Loss
- Understanding Overheads Expenses
- Worksheet on Cost Price, Selling Price and Rates of Profit and Loss
- Understanding Discount and Mark Up
- Successive Discount
- Worksheet on Discount and Markup
- Worksheet on the application of overhead Expenses
- Worksheet on Successive Discounts

#### Compound Interest

- Compound Interest
- Introduction to Compound Interest
- Compound Interest as Repeated Simple Interest
- Formulae for Compound Interest
- Comparison between Simple Interest and Compound Interest
- Worksheet on Compound Interest as Repeated Simple Interest
- Worksheet on Use of Formula for Compound Interest

### Algebra/Linear Algebra

#### Expansion of Powers of Binomials and Trinomials

- Expansion of (a Â± b)^2
- Expansion of (a Â± b Â± c)^2
- Expansion of (x Â± a)(x Â± b)
- Express a^2 + b^2 + c^2 â€“ ab â€“ bc â€“ ca as Sum of Squares
- Completing a Square
- Simplification of (a + b)(a â€“ b)
- Application Problems on Expansion of Powers of Binomials and Trinomials
- Worksheet on Expansion of (a Â± b)^2 and its Corollaries
- Worksheet on Expanding of (a Â± b Â± c)^2 and its Corollaries
- Worksheet on Expansion of (x Â± a)(x Â± b)
- Worksheet on Completing Square
- Worksheet on Simplification of (a + b)(a â€“ b)
- Worksheet on Application Problems on Expansion of Powers of Binomials and Trinomials
- Expansion of (a Â± b)^3
- Simplification of (a Â± b)(a^2 âˆ“ ab + b^2)
- Simplification of (a + b + c)(a^2 + b^2 + c^2 â€“ ab â€“ bc â€“ ca)
- Expansion of (x + a)(x + b)(x + c)
- Problems on Expanding of (a Â± b)^3 and its Corollaries

#### Factorization

- Introduction to Factorization
- Problems on Factorization by Grouping of Terms
- Problems on Factorization of Expressions of the Form a^2 â€“ b^2
- Problems on Factorization Using a^2 â€“ b^2 = (a + b)(a â€“ b)
- Factorization of a Perfect-square Trinomial
- Factorization of Expressions of the Form x^2 + (a + b)x + ab
- Factorization of Expressions of the Form ax^2 + bx + c, a â‰ 1
- Problems on Factorization of Expressions of the Form x^2 +(a + b)x +ab
- Worksheet on Factorization of the Trinomial ax^2 + bx + c
- Factorization of Expressions of the Form a^3 + b^3
- Factorization of Expressions of the Form a^3 – b^3
- Factorization of expressions of the Form a^3 + b^3 + c^3 â€“ 3abc
- Factorization of Expressions of the Form a^3 + b^3 + c^3, a + b + c = 0
- Miscellaneous Problems on Factorization
- Worksheet on Factorization

#### Linear Equations

- Linear Equation in One Variable
- Solution of a Linear Equation in One Variable
- Laws of Equality
- Method of Solving a Linear Equation in One Variable
- Problems on Application of Linear Equations
- Different Types of Problems in Linear Equation in One Variable
- Worksheet on Linear Equation in One Variable
- Worksheet on Forming of Linear Equations in One Variable
- Worksheet on Solving a Word Problem by using Linear Equation in One Unknown

#### Changing the Subject of a Formula

- Establishing an Equation
- Subject of a Formula
- Change of Subject of Formula
- Evaluation of Subject by Substitution
- Problem on Change the Subject of a Formula
- Worksheet on Framing a Formula
- Worksheet on Change of Subject

#### Simultaneous Linear equations

- Solution of a Linear Equation in Two Variables
- Method of Elimination
- Method of Substitution
- Method of Cross Multiplication

#### Exponents/Indices

- Power of a Number
- Laws of Indices
- nth Root of a

#### Quadratic Equation

- Introduction to Quadratic Equation
- Formation of Quadratic Equation in One Variable
- Solving Quadratic Equations
- General Properties of Quadratic Equation
- Methods of Solving Quadratic Equations
- Roots of a Quadratic Equation
- Examine the Roots of a Quadratic Equation
- Problems on Quadratic Equations
- Quadratic Equations by Factoring
- Word Problems Using Quadratic Formula
- Examples on Quadratic Equations
- Word Problems on Quadratic Equations by Factoring
- Worksheet on Formation of Quadratic Equation in One Variable
- Worksheet on Quadratic Formula
- Worksheet on Nature of the Roots of a Quadratic Equation
- Worksheet on Word Problems on Quadratic Equations by Factoring

### Geometry and Measurement

- Triangles
- Classification of Triangles on the Basis of Their Sides and Angles
- Medians and Altitudes of a Triangle
- Geometrical Property of Altitudes
- Properties of Angles of a Triangle
- Congruency of Triangles
- Criteria for Congruency
- Problems on Congruency of Triangles
- Any point on the bisector of an angleÂ is equidistant from the arms of that angle
- An Altitude of an Equilateral Triangle is also a Median
- Bisectors of the Angles of a Triangle Meet at a Point
- Application of Congruency of Triangles
- Angles Opposite to Equal Sides of an Isosceles Triangle are Equal
- Equal Sides of an Isosceles Triangle are Produced,Â the Exterior Angles angles are equal.
- The Three Angles of an Equilateral Triangle are Equal.
- Sides Opposite to the Equal Angles of a Triangle are Equal
- Problems on Properties of Isosceles Triangles
- Problem on Two Isosceles Triangles on the Same Base
- Lines Joining the Extremities of the Base of an Isosceles Triangle
- Points on the Base of an Isosceles Triangle
- Theorem on Isosceles Triangle

#### Inequalities in Triangles

- Greater Side has the Greater Angle Opposite to It
- Greater Angle has the Greater Side Opposite to It
- The Sum of any Two Sides of a Triangle is Greater than the Third Side
- Perpendicular is the Shortest Theorem
- Comparison of Sides and Angles in a Triangle
- Problem on Inequalities in Triangle
- Sum Of Any Two Sides Is Greater Than Twice The Median
- Sum of the Four Sides of a Quadrilateral Exceeds the Sum of the Diagonals

#### Midpoint Theorem

- Midpoint Theorem
- Converse of Midpoint Theorem
- Four Triangles which are Congruent to One Another
- Straight Line Drawn from the Vertex of a Triangle to the Base
- Midpoint Theorem on Trapezium
- Midsegment Theorem on Trapezium
- Midpoint Theorem on Right-angled Triangle
- Collinear Points Proved by Midpoint Theorem
- Equal Intercepts Theorem
- Problems on Equal Intercepts Theorem
- Midpoint Theorem by using the Equal Intercepts Theorem
- Proof By the Equal Intercepts Theorem

#### Similarity

- Similarity
- Enlargement Transformation
- Reduction Transformation
- Properties of Size Transformation
- Similar Triangles
- Criteria of Similarity between Triangles
- AA Criterion of Similarity
- Basic Proportionality Theorem
- Converse of Basic Proportionality Theorem
- Application of Basic Proportionality Theorem
- Greater segment of the Hypotenuse is Equal to the Smaller Side of the Triangle
- AA Criterion of Similarly on Quadrilateral
- Pythagorasâ€™ Theorem
- Converse of Pythagorasâ€™ Theorem
- Applying Pythagorasâ€™ Theorem
- Riders Based on Pythagorasâ€™ Theorem

#### Rectilinear Figures

- Rectilinear Figures
- Sum of the Interior Angles of an n-sided Polygon
- Sum of the Exterior Angles of an n-sided Polygon

#### Parallelogram

- Concept of Parallelogram
- Opposite Sides of a Parallelogram are Equal
- Opposite Angles of a Parallelogram are Equal
- Diagonals of a Parallelogram Bisect Each Other
- A Quadrilateral is a Parallelogram if its Diagonals Bisect Each Other
- Pair of Opposite Sides of a Parallelogram are Equal and Parallel
- A Rhombus is a Parallelogram whose Diagonals Meet at Right Angles
- A Parallelogram whose Diagonals Intersect at Right Angles is a Rhombus
- In a Rectangle the Diagonals are of Equal Lengths
- A Parallelogram, whose Diagonals are of Equal Length, is a Rectangle
- Diagonals of a Square are Equal in Length & they Meet at Right Angles
- Diagonals of a Parallelogram are Equal & Intersect at Right Angles
- Conditions for Classification of Quadrilaterals and Parallelograms
- Bisectors of the Angles of a Parallelogram form a Rectangle

#### Area

- Area of a Closed Figure
- Base and Height (Altitude) in a Triangle and a Parallelogram
- Every Diagonal of a Parallelogram Divides it into Two Triangles of Equal Area
- Parallelogram on the Same Base and Between the Same Parallel Lines are Equal in Area
- Area of a Parallelogram is Equal to that of a Rectangle Between the Same Parallel Lines
- Area of a Triangle is Half that of a Parallelogram on the Same Base and between the Same Parallels
- Triangles on the Same Base and between the Same Parallels are Equal in Area
- Triangles with Equal Areas on the Same Base have Equal Corresponding Altitudes
- Problems on Finding Area of Triangle and Parallelogram
- Area of the Triangle formed by Joining the Middle Points of the Sides of a Triangle is Equal to One-fourth Area of the given Triangle
- The Area of a Rhombus is Equal to Half the Product of its Diagonals
- If Each Diagonal of a Quadrilateral Divides it in Two Triangles of Equal Area then Prove that the Quadrilateral is a Parallelogram

#### Statistics

- Statistics and Statistical Data
- Representation of Data
- Statistical Variable
- Range of the Statistical Data
- Frequency of the Statistical Data
- Mean of Ungrouped Data
- Arithmetic Mean
- Word Problems on Arithmetic Mean
- Properties of Arithmetic Mean
- Problems Based on Average
- Problems on Mean of Ungrouped Data
- Properties Questions on Arithmetic Mean
- Median of Raw Data
- Problems on Median of Ungrouped Data
- Worksheet on Mean of Ungrouped Data
- Worksheet on Median of Ungrouped Data
- Frequency Distribution
- Class Interval
- Tally Marks
- Constructing Frequency Distribution Tables
- Class Limits
- Class Boundaries
- Nonoverlapping Class Intervals into Overlapping Class Intervals
- Cumulative Frequency

### Mensuration

#### Plane Figures

- Perimeter and Area of Plane Figures
- Perimeter and Area of a Rectangle
- Geometrical Properties of a Square
- Perimeter and Area of a Triangle
- Perimeter and Area of Mixed Figures
- Perimeter and Area of Rhombus
- Perimeter and Area of Parallelogram
- Perimeter and Area of Irregular Figures
- Perimeter and Area of Regular Hexagon
- Area and Circumference of a Circle
- Area of a Circular Ring
- Area and Perimeter of a Semicircle
- Area and Perimeter of Combined Figures

#### Solid Figures

**Cube and Cuboid**

- Solid Figures
- Volume and Surface Area of Cuboid
- Volume and Surface Area of Cube
- Volume and Surface Area of Cube and Cuboid
- Volume of Cuboid
- Volume of Cube
- Lateral Surface Area of a Cuboid

**Cylinder**

- Cross Section
- Cylinder
- Right Circular Cylinder
- Hollow Cylinder
- Problems on Right Circular Cylinder

**Probability**

- Probability
- Random Experiments
- Experimental Probability
- Events in Probability
- Empirical Probability
- Coin Toss Probability
- Probability of Tossing Two Coins
- Probability of Tossing Three Coins
- Complimentary Events
- Mutually Exclusive Events
- Mutually Non-Exclusive Events
- Conditional Probability
- Theoretical Probability
- Odds and Probability
- Playing Cards Probability
- Probability and Playing Cards
- Probability for Rolling Two Dice
- Solved Probability Problems
- Probability for Rolling Three Dice

### Pre-Calculus

#### Mathematical Models with Applications

**Basic Trigonometry**

- Trigonometry
- Measurement of Trigonometric Angles
- Sexagesimal System
- Circular System
- Radian is a Constant Angle
- Relation between Sexagesimal and Circular
- Conversion from Sexagesimal to Circular System
- Conversion from Circular to Sexagesimal System

**Coordinate Geometry**

- Independent Variables and Dependent Variables
- Coordinates of a Point
- Rectangular Cartesian Coordinates of a Point
- Quadrants and Convention for Signs of Coordinates
- Plotting a Point in Cartesian Plane
- Coordinate Geometry Graph
- Graph of Standard Linear Relations Between x, y
- Slope of the Graph of y = mx + c
- y-intercept of the Graph of y = mx + c
- Drawing Graph of y = mx + c Using Slope and y-intercept
- Problems on Plotting Points in the x-y Plane
- Problems on Slope and Y-intercept
- Worksheet on Plotting Points in the Coordinate Plane
- Worksheet on Graph of Linear Relations in x, y
- Worksheet on Slope and Y-intercept

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### Goals & Objectives of Ninth Grade Math Curriculum

The comprehensive collection of Ninth Grade Math Topics listed here focuses on the below areas. They are as such

- 9th Grade Math Concepts focuses on Algebra 1 and includes advanced mathematical concepts such as Geometry, Pre Calculus, Trigonometry, etc.
- Children must be able to Rearrange and Solve Basic Algebraic Equations.
- Ninth Graders must understand concepts completely before moving on so that they don’t feel lost and confused.
- Develops strong fundamentals that are useful for High School.
- Clear Cut Explanations provided for all the Problems makes it easy for you to grasp the techniques and formulas quickly.

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- Lesson Plans, Assessment Tests, help you master the concepts and achieve learning targets easily.
- Ninth Grade Math Worksheets, Lessons, etc. created helps your child achieve success in Mathematics.
- Practice Tests of Grade 9 help you remediate the knowledge gap and provides a Standardized Test Environment.
- All the 9th Standard Math Concepts, Pages explained are as per the latest syllabus guidelines.
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Must Read:

GE3172 – English Laboratory Syllabus

### Conclusion

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