math problem solving 9th grade

9th GRADE MATH PRACTICE PROBLEMS

Problem 1 :

Simplify √20 - √225 + √80

Decompose  20, 225 and 80 into prime factors.

√20  =  √2  ⋅  2  ⋅  5  =  2√5

√225  =  √5  ⋅  5  ⋅  3  ⋅  3  =  5  ⋅  3  =  15

√225  =  √2  ⋅  2  ⋅  2  ⋅  2  ⋅  5  =  (2  ⋅  2)√5  =  4√5

Then, we have

√ 20 -  √ 225 +  √ 80  =   2√5 - 15 + 4√5

√ 20 -  √ 225 +  √ 80  =  6 √5 - 15

√ 20 -  √ 225 +  √ 80   =  6√5 - 15

√ 20 -  √ 225 +  √ 80   =  3(2√5 - 5)

Problem 2 :

The perimeter of the rhombus is 20 cm. One of the diagonals is of length 8 cm. Find the length of the other diagonal.

In a rhombus, the diagonals are intersecting at right angles.

Perimeter of rhombus  =  20 cm

4a  =  20

a  =  5 cm

Length of diagonal  =  8 cm

Half of diagonal  =  4

Let x be the half of the other diagonal.

5 2  =  4 2 + x 2

25  =  16 + x 2

x 2  =  25 - 16

x 2   =  9

x  =  3

Length of other diagonal  =  2(3)

  =  6 cm

Problem 3 :

Jerry and Silvia wanted to go from the southwest corner of a square field to the northeast corner. Jerry walked due east and then due north to reach the goal, but Silvia headed northeast and reached the goal walking in a straight line. How much shorter Silvia's trip was, compared to Jerry's trip? 

Let AB  =  1, BC  =  1

Then AC  =   √1 2 + 1 2

AC  =   √2

Distance covered by Jerry  =  1 + 1  ==> 2

Distance covered by Silvia  =   √2

Difference of distance covered  =  2 -  √2

  =  2 - 1.414

  =  0.586

  =  (0.586/ 2)  ⋅ 100%

  =  30%

So Silvia's trip is 30% shorter than the Jerry's trip.

Problem 4 :

Solve log 10 (2x + 50)  =  3

log 10  (2x + 50) = 3

2x + 50  =  10 3

2x  =  1000-50

2x  =  950

x  =  425

So, the value of x is 425.

Problem 5 :

A set has only one element is called ____________ set 

A set has only one element is called as singleton set.

Problem 6 :

Which of the following statement represents this Venn diagram?

In the given venn diagram, the common region for both A and B is not shaded, then the remaining part of B is shaded. So the correct statement is B-A.

Problem 7: 

If (x+p) (x+q) = x 2 -5x-300, find the value of p² + q²

(x+p) (x+q)   =   x 2 -5x-300

x 2 +(p+q)x+pq  =   x 2 -5x-300

p+q  =  -5 and pq  =  -300

p 2 +q 2   =  (p+q) 2 - 2pq

  =  (-5) 2 -2(-300)

  =  25 + 600

p 2 +q 2   =   625

Problem 8 :

The point of concurrence of the angle bisector of a triangle is called the _____________ of the triangle.

The point of concurrence of the angle bisector of a triangle is called the incenter of the triangle.   9

Problem 9 :

The angles are supplementary and larger angle is twice the smaller angle.Find the angles.

Let x be the smaller angle

2x  -  larger angle

2x+x  =  180

3x   180

x  =  60

So, the required angles are 60 and 120.

Problem 10 :

Find the distance between the points

A (-15,-3) and B (7, 1)

Distance between two points  =  √(7+15) 2 + (1+3) 2

  =  √(-22) 2  + 4 2

  =   √(484  + 16)

  =   √500

  =  10 √5

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Grade 9 Algebra Word Problems

Related Pages Grade 8 Algebra Word Problems Algebra Word Problems Solving Equations More Algebra Lessons

These lessons cover grade 9 algebra word problems involving age, distance, rate, time and coins with examples and step-by-step solutions. It includes various examples and solutions for algebra word problems that you will commonly encounter in 9th grade.

Age Word Problems

Age Problems with two unknowns or variables

Example: Taylor is five times as old as Spenser. The sum of their ages is eighteen. How old are Taylor and Spencer?

Solution: Let x represent Spenser’s age Therefore, Taylor’s age is 5x x + 5x = 18 6x = 18 x = 3 Therefore, Spenser is 3 years old and Taylor is 15 years old.

Grade 9 Algebra Word Problems - Age

Example 1: A mother is three times as old as her daughter. Six years ago, the mother’s age was six tines that of her daughter. How old are they now?

Solution: Let x represent the daughter’s age. Therefore, 3x is the mother’s age. 6(x - 6) = 3x - 6 6x - 6 = 3x - 6 3x = 30 x = 10 Therefore, the daughter’s is 10 years old and the mother is 30 years old.

Example 2: A father is now three times as old as his son. Eight years ago, the father was five times as old as his son. How old are they now?

Rate, Distance, Time Word Problems

Grade 9 Algebra Word Problems - Rate, Distance, Time

Example: A bus leaves the terminal and averages 40 km/hr. One hour late, a second bus leaves the same terminal and averages 50 km/hr. In how many hours will the second bus overtake the first?

Grade 9 Rate, Distance, Time Word Problems

Example 1: One motorist travels 5 km.hr faster than another. They leave from the same place and travel in opposite directions. What is the rate of each if they are 195 km apart after 3 hours?

Example 2: A pilot flew from airport A to airport B at a rate of 100 km/hr and flew back from airport B to airport A at 120 km/hr. The total time it took was 11 hours. How far is it from airport A to airport B?

Coin Word Problems

Grade 9 Algebra Word Problems - Coins

Example: A coin collection amounting to $25 consists of nickels and dimes. There are 3 times as many nickels and dimes. There are 3 times as many nickels as dimes. How many coins of each kind are there?

Solution: Let x = number of dimes 3x = number of nickels 10x + 5(3x) = 2500 25x = 2500 x = 100 Therefore, there are 100 dimes and 300 nickels.

Grade 9 Coin Algebra Word Problems

Example: Mr. Rogers has $4.62. He has 3 times as many dimes as nickels and 6 more pennies than dimes. How many coins of each kind does he have?

Coin Algebra Word Problems - Grade 9

Example: Bob has in his pocket a number of pennies, 5 times as many nickels as pennies and 5 more quarters than pennies. The coins amount to $2.27. Find the number of each kind of coin.

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Free Printable algebra Worksheets for 9th Grade

Algebra-focused math worksheets for Grade 9 students, created to help educators discover effective teaching tools. Explore our collection of free printable resources to enhance your lessons.

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Explore printable algebra worksheets for 9th Grade

Algebra worksheets for Grade 9 are essential resources for teachers who want to provide their students with a comprehensive understanding of algebraic concepts and applications. These worksheets cover a wide range of topics, including linear equations, quadratic functions, systems of equations, and polynomials, all of which are crucial for building a strong foundation in mathematics. Teachers can utilize these worksheets to supplement their lesson plans, provide additional practice for students who may be struggling with certain concepts, or even as a form of assessment to gauge students' progress throughout the school year. By incorporating algebra worksheets for Grade 9 into their curriculum, teachers can ensure that their students are well-prepared for the challenges of higher-level math courses.

Quizizz is an excellent platform for teachers to access a variety of algebra worksheets for Grade 9, as well as other math resources. This interactive platform allows educators to create engaging quizzes and activities that can be used in the classroom or assigned as homework. In addition to algebra worksheets, Quizizz offers a vast library of resources for other math topics, such as geometry, trigonometry, and calculus, making it a one-stop-shop for all of your math teaching needs. Furthermore, Quizizz provides teachers with valuable insights into their students' performance, allowing them to identify areas where additional support may be needed. By incorporating Quizizz into their teaching toolkit, educators can enhance their students' learning experience and ensure that they are well-equipped to tackle the challenges of Grade 9 math and beyond.

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9th Grade Algebra

Word problems.

Word problems are an essential part of any math curriculum, but they can be challenging for many students. Whether you're struggling with algebra, geometry, or calculus, word problems can leave you feeling frustrated and unsure of where to start. In this post, we'll take a closer look at word problems and provide some tips for solving them.

First, let's answer some common questions about word problems.

What are word problems?

Word problems are math problems that are presented in a real-world context. They require you to read and understand a situation or scenario and then apply mathematical concepts to solve the problem. Why are word problems important?

Word problems are important because they help you develop critical thinking skills and apply math concepts to real-world situations. They also help you prepare for standardized tests like the SAT and ACT, which often include word problems.

What math is freshman math?

Freshman math typically includes algebra, geometry, and sometimes trigonometry. Depending on your school and your level of math proficiency, you may take a more advanced course like pre-calculus or calculus. Now that we've answered some common questions, let's look at a specific example. Suppose you're working on your 9th grade algebra homework and come across this word problem:

A car rental company charges a flat fee of $30 per day plus $0.25 per mile driven. If a customer rents a car for 4 days and drives 200 miles, how much will the rental cost?

How do you solve this 9th grade math problem?

Step 1: Identify what you know and what you need to find. In this problem, you know the flat fee per day and the cost per mile driven. You also know the number of days and miles driven. You need to find the total cost of the rental.

Step 2: Set up an equation. To find the total cost of the rental, you can use the formula: Total cost = (flat fee per day x number of days) + (cost per mile x number of miles) Plugging in the given values, you get: Total cost = ($30 x 4) + ($0.25 x 200) Step 3: Simplify the equation. Multiplying and adding, you get: Total cost = $120 + $50 Total cost = $170 So, the rental will cost $170.

In conclusion, word problems may seem daunting at first, but with some practice and a systematic approach, you can master them. Remember to identify what you know and what you need to find, set up an equation, and simplify it to find the answer. With these tips, you'll be solving word problems like a pro in no time.

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

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• 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
• 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
• 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 ± b)^2
• Expansion of (a ± b ± c)^2
• Expansion of (x ± a)(x ± b)
• Express a^2 + b^2 + c^2 – ab – bc – ca as Sum of Squares
• Completing a Square
• Simplification of (a + b)(a – b)
• Application Problems on Expansion of Powers of Binomials and Trinomials
• Worksheet on Expansion of (a ± b)^2 and its Corollaries
• Worksheet on Expanding of (a ± b ± c)^2 and its Corollaries
• Worksheet on Expansion of (x ± a)(x ± b)
• Worksheet on Completing Square
• Worksheet on Simplification of (a + b)(a – b)
• Worksheet on Application Problems on Expansion of Powers of Binomials and Trinomials
• Expansion of (a ± b)^3
• Simplification of (a ± b)(a^2 ∓ ab + b^2)
• Simplification of (a + b + c)(a^2 + b^2 + c^2 – ab – bc – ca)
• Expansion of (x + a)(x + b)(x + c)
• Problems on Expanding of (a ± 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 – b^2
• Problems on Factorization Using a^2 – b^2 = (a + b)(a – 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 ≠ 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 – 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

• 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 angle 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, 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
• 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
• 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
• Pythagoras’ Theorem
• Converse of Pythagoras’ Theorem
• Applying Pythagoras’ Theorem
• Riders Based on Pythagoras’ Theorem
• 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 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 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

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

We at ccssmathanswers take every effort and utmost care so that your kid will grow. 9th Grade Students can find all the concepts as per the Common Core State Standards Curriculum. You can learn the Math Concepts in the comfort of your home. 9th Grade Math Topics will emphasize a conceptual understanding rather than repetitive drills.

In fact, our Grade 9 Math Worksheets help you test your knowledge and bridge the knowledge gap accordingly. Once you start solving the 9th Grade Textbook Solutions you will witness the Mathemagic happen. Simply click on the direct links available for corresponding topics and allot time to the areas you feel difficult.

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.

Why Choose our Grade 9 Math Curriculum?

Master the concepts of Grade 9 Math Lessons and learn the benefits of following the Ninth Grade Math Curriculum. They are as under

• 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.
• Our Learning Material Provided engages the students irrespective of the learning methods adopted.

GE3172 – English Laboratory Syllabus

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• 9th Grade Math

9th grade math lessons are planned and introduce in different activities. 9th grade math help is provided for the 9th grade students in all segments to cover all the math lesson plans which are categorized into Arithmetic, Algebra, Geometry and Mensuration.

All types of solved examples on different topics are explained along with the step-by-step solutions. 9th grade math practice sheets are arranged in such a way that students can learn math while practicing math problems.

Keeping in mind the mental level of student in ninth grade, every efforts has been made to introduce new concepts in a simple and easy language, so that the students can understand the problems easily.

The difficulty level of the 9th grade math problems has emphasized the theoretical as well as the numerical aspects of the mathematics course. Each topic contains a large number of examples to understand the applications of concepts.

To get prepared for 9th grade math test or exams students need to learn graphing lines on the coordinate plane, solving literal equations, compound inequalities, graphing inequalities in two variables, multiplying binomials, polynomials, factoring techniques for trinomials, solving systems of equations, algebra word problems, variation, rational expressions, rational equations, graphs & functions, circles, construction, triangle theorems & proofs, properties of polygons, transformations, trigonometry and etc……

If student follow math-only-math they can improve their knowledge by practicing the worksheets for 9th graders which will help them to score in their exam.

Ninth Grade Math Lessons – Table of Contents

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

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

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 ± b)^2

Expansion of (a ± b ± c)^2

Expansion of (x ± a)(x ± b)

Express a^2 + b^2 + c^2 – ab – bc – ca as Sum of Squares

Completing a Square

Simplification of (a + b)(a – b)

Application Problems on Expansion of Powers of Binomials and Trinomials

Worksheet on Expansion of (a ± b)^2 and its Corollaries

Worksheet on Expanding of (a ± b ± c)^2 and its Corollaries

Worksheet on Expansion of (x ± a)(x ± b)

Worksheet on Completing Square

Worksheet on Simplification of (a + b)(a – b)

Worksheet on Application Problems on Expansion of Powers of Binomials and Trinomials

Expansion of (a ± b)^3

Simplification of (a ± b)(a^2 ∓ ab + b^2)

Simplification of (a + b + c)(a^2 + b^2 + c^2 – ab – bc – ca)

Expansion of (x + a)(x + b)(x + c)

Problems on Expanding of (a ± 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 – b^2

Problems on Factorization Using a^2 – b^2 = (a + b)(a – 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 ≠ 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 – 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

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

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 angle 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 , 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

Three Angles of an Equilateral 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

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

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

Pythagoras’ Theorem

Converse of Pythagoras’ Theorem

Applying Pythagoras’ Theorem

Riders Based on Pythagoras’ Theorem

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 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 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

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

Cross Section

Right Circular Cylinder

Hollow Cylinder

Problems on Right Circular Cylinder

• 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 : Beginning of trigonometry and invention of trigonometry and how and why trigonometry is important.

Measurement of Trigonometric Angles : In trigonometry learn about the measurement of angles.

Different systems of measurement of angles and their units.

Sexagesimal System : Concept on understanding Sexagesimal System, problems on Sexagesimal System.

Circular System : Concept on understanding Circular System, problems on Circular System.

Radian is a Constant Angle : Proof that radian is a constant angle.

Relation between Sexagesimal and Circular : Learn about the relation between the units of the two systems.

Conversion from Sexagesimal to Circular System : Learn how to convert or express Sexagesimal to Circular System.

Conversion from Circular to Sexagesimal System : Learn how to convert or express Circular to Sexagesimal Systemm.

Co-ordinate 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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