algebra problem solving grade 9

Grade 9 Algebra Word Problems

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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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Grade 9 Math Lessons and Practice

• 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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Free Printable Math Worksheets for 9th Grade

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• Expressions and Equations
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Math worksheets for Grade 9 are an essential resource for teachers to help their students master the various mathematical concepts and skills required at this level. These worksheets cover a wide range of topics, including algebra, geometry, trigonometry, and statistics, providing ample practice for students to build a strong foundation in mathematics. Teachers can use these worksheets to supplement their lesson plans, assign as homework, or provide additional practice for struggling students. With a variety of question types and difficulty levels, Grade 9 math worksheets cater to the diverse learning needs of students, ensuring that they are well-prepared for the challenges of high school mathematics.

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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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9th Grade Math Worksheets: FREE & Printable

Looking for free printable 9th grade Math Worksheets and activities to help your student prepare for the 9th Grade math course? If so, then look no further!

Want to measure your 9th-grade student’s knowledge of Math concepts and assess their exam readiness? If so, then look no further.

Here is a comprehensive collection of FREE printable 9th-grade Math worksheets that would help students in 9th Grade Math preparation and practice.

Download our free Mathematics worksheets for 9th Grade Math.

Hope you enjoy it!

IMPORTANT: COPYRIGHT TERMS: Worksheets may not be uploaded to the internet, including classroom/personal websites or network drives. You can download the worksheets and print as many as you need. You can distribute the printed copies to your students, teachers, tutors, and friends. 

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The Absolute Best Book to Ace 9th Grade Math

Algebra I for Beginners The Ultimate Step by Step Guide to Acing Algebra I

9th grade math concepts.

• Translate Phrases into an Algebraic Statement
• Order of Operations
• Properties of Numbers
• The Distributive Property
• Scientific Notation

Expressions and Equations

• Simplifying Variable Expressions
• One–Step Equations
• Multi–Step Equations
• Finding Midpoint
• Finding Distance of Two Points
• Absolute Value Equations

Linear Functions

• Finding Slope
• Graphing Lines Using Line Equation
• Writing Linear Equations
• Graphing Linear Inequalities
• Slope and Rate of Change
• Find the Slope x–intercept and y–intercept
• Write an Equation from a Graph
• Slope –intercept Form and Point –slope Form
• Equations of Horizontal and Vertical Lines
• Equation of Parallel or Perpendicular Lines
• Graphing Absolute Value Equations
• Greatest Common Factor
• Least Common Multiple
• GCF of Monomials
• Factoring Quadratics
• Factoring by Grouping

Inequalities and System of Equations

• One–Step Inequalities
• Two–Step Linear Inequalities
• Advanced Linear Inequalities
• Solve Compound Inequalities
• Solve Absolute Value Inequalities
• Systems of Equations
• Systems of Equations Word Problems

Monomials Operations

• Add and Subtract Monomials
• Multiply and Divide Monomials
• Quadratic Equation
• Graphing Quadratic Functions
• Quadratic Equations
• Solve a Quadratic Equation by Factoring
• Quadratic Formula and Transformations of Quadratic Functions
• Quadratic Formula and the Discriminant

Polynomial Operations

• Simplifying Polynomials
• Adding and Subtracting Polynomials
• Multiplying a Polynomial and a Monomial
• Multiply Two Polynomials
• Multiply Two Binomials
• Operations with Polynomials
• Factor Polynomials
• Factoring Special Case Polynomials

Radical Expressions

• Simplifying Radical Expressions
• Multiplying Radical Expressions
• Simplifying Radical Expressions Involving Fractions
• Adding and Subtracting Radical Expressions
• Domain and Range of Radical Functions
• Solving Radical Equations

Rational Expressions

• Simplifying and Graphing Rational Expressions
• Adding and Subtracting Rational Expressions
• Multiplying and Dividing Rational Expressions
• Solving Rational Equations and Complex Fractions

 Statistics and Probabilities

• Probability Problems
• Combinations and Permutations

Statistics and Probabilities

9th grade math practice questions, fractions and decimals, real numbers and integers, proportions and ratios, algebraic expressions, equations and inequalities, polynomials, exponents and radicals, solid figures.

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Algebra II for Beginners The Ultimate Step by Step Guide to Acing Algebra II

Pre-algebra for beginners the ultimate step by step guide to preparing for the pre-algebra test, pre-algebra tutor everything you need to help achieve an excellent score.

by: Effortless Math Team about 4 years ago (category: Blog , Free Math Worksheets )

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9th Grade Algebra Worksheets

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Grade 9 math

IXL offers hundreds of grade 9 math skills to explore and learn! Not sure where to start? Go to your personalized Recommendations wall to find a skill that looks interesting, or select a skill plan that aligns to your textbook, provincial curriculum, or standardized test.

• 1 Classify numbers
• 2 Compare rational numbers
• 3 Put rational numbers in order
• 4 Number lines
• 5 Convert between decimals and fractions
• 6 Square roots of perfect squares
• 7 Square roots of fractions and decimals
• 8 Estimate square roots

B. Operations

• 1 Add, subtract, multiply and divide integers
• 2 Evaluate numerical expressions involving integers
• 3 Evaluate variable expressions involving integers
• 4 Add and subtract rational numbers
• 5 Add and subtract rational numbers: word problems
• 6 Multiply and divide rational numbers
• 7 Multiply and divide rational numbers: word problems
• 8 Evaluate numerical expressions involving rational numbers
• 9 Evaluate variable expressions involving rational numbers

C. Ratios, rates and proportions

• 1 Identify equivalent ratios
• 2 Write an equivalent ratio
• 3 Unit rates
• 4 Unit prices
• 5 Solve proportions
• 6 Solve proportions: word problems
• 7 Scale drawings: word problems

D. Percents

• 1 Convert between percents, fractions and decimals
• 2 Solve percent equations
• 3 Percent word problems
• 4 Percent of change
• 5 Percent of change: word problems

E. Geometry

• 1 Perimeter
• 3 Area of compound figures
• 4 Area between two shapes
• 6 Count lines of symmetry
• 7 Draw lines of symmetry
• 8 Interior angles of polygons
• 9 Transversal of parallel lines
• 10 Volume of prisms and pyramids
• 11 Volume of cones and cylinders
• 12 Volume of spheres
• 13 Nets of three-dimensional figures
• 14 Surface area of prisms and pyramids
• 15 Surface area of cones and cylinders
• 16 Surface area of spheres
• 17 Similar figures: side lengths and angle measures
• 18 Similar triangles and indirect measurement
• 19 Area and perimeter of similar figures
• 20 Similar solids
• 21 Volume and surface area of similar solids
• 22 Perimeter, area and volume: changes in scale
• 23 Identify reflections, rotations and translations
• 24 Reflections, rotations and translations: find the coordinates
• 25 Reflections, rotations and translations: graph the image
• 26 Dilations and scale factors
• 27 Pythagorean theorem
• 28 Pythagorean theorem: word problems
• 29 Converse of the Pythagorean theorem: is it a right triangle?
• 1 Parts of a circle
• 2 Circles: calculate area, circumference, radius and diameter
• 3 Circles: word problems
• 4 Central angles
• 5 Arc measure and arc length
• 6 Area of sectors
• 7 Circle measurements: mixed review
• 8 Arcs and chords
• 9 Tangent lines
• 10 Perimeter of polygons with an inscribed circle
• 11 Inscribed angles
• 12 Angles in inscribed right triangles
• 13 Angles in inscribed quadrilaterals I
• 14 Angles in inscribed quadrilaterals II

G. Coordinate plane

• 1 Coordinate plane review
• 2 Quadrants and axes
• 3 Distance between two points

H. Properties

• 1 Properties of addition and multiplication
• 2 Distributive property
• 3 Simplify variable expressions using properties
• 4 Properties of equality

I. Exponents

• 1 Understanding exponents
• 2 Powers with integer bases
• 3 Powers with decimal and fractional bases
• 4 Negative exponents
• 5 Multiplication with exponents - integral bases
• 6 Division with exponents - integral bases
• 7 Multiplication and division with exponents - integral bases
• 8 Power rule - integral bases
• 9 Multiplication with exponents - variable bases
• 10 Division with exponents - variable bases
• 11 Multiplication and division with exponents - variable bases
• 12 Power rule - variable bases
• 13 Evaluate expressions using properties of exponents
• 14 Identify equivalent expressions involving exponents

J. Scientific notation

• 1 Convert between standard and scientific notation
• 2 Compare numbers written in scientific notation
• 3 Multiply numbers written in scientific notation
• 4 Divide numbers written in scientific notation

K. Problem solving

• 1 Word problems: mixed review
• 2 Word problems with money
• 3 Consecutive integer problems
• 4 Rate of travel: word problems
• 5 Weighted averages: word problems

L. Number sequences

• 1 Identify arithmetic and geometric sequences
• 2 Arithmetic sequences
• 3 Geometric sequences
• 4 Evaluate variable expressions for number sequences
• 5 Write variable expressions for arithmetic sequences
• 6 Write variable expressions for geometric sequences
• 7 Number sequences: mixed review

M. Variable expressions and equations

• 1 Write variable expressions
• 2 Simplify variable expressions involving like terms and the distributive property
• 3 Identify equivalent linear expressions
• 4 Write variable equations
• 5 Does x satisfy the equation?
• 6 Solve equations using order of operations
• 7 Rearrange multi-variable equations

N. Solve equations

• 1 Model and solve equations using algebra tiles
• 2 Write and solve equations that represent diagrams
• 3 Solve one-step linear equations
• 4 Solve two-step linear equations
• 5 Solve advanced linear equations
• 6 Solve equations with variables on both sides
• 7 Solve equations: complete the solution
• 8 Find the number of solutions
• 9 Create equations with no solutions or infinitely many solutions
• 10 Solve linear equations: word problems
• 11 Solve linear equations: mixed review

O. Single-variable inequalities

• 1 Graph inequalities
• 2 Write inequalities from graphs
• 3 Identify solutions to inequalities
• 4 Solve one-step linear inequalities: addition and subtraction
• 5 Solve one-step linear inequalities: multiplication and division
• 6 Solve one-step linear inequalities
• 7 Graph solutions to one-step linear inequalities
• 8 Solve two-step linear inequalities
• 9 Graph solutions to two-step linear inequalities
• 10 Solve advanced linear inequalities
• 11 Graph solutions to advanced linear inequalities

P. Data and graphs

• 1 Interpret bar graphs, line graphs and histograms
• 2 Create bar graphs, line graphs and histograms
• 3 Interpret circle graphs
• 4 Interpret stem-and-leaf plots
• 5 Interpret box-and-whisker plots
• 6 Interpret a scatter plot
• 7 Scatter plots: line of best fit

Q. Relations and functions

• 1 Relations: convert between tables, graphs, mappings and lists of points
• 2 Identify independent and dependent variables
• 3 Identify functions
• 4 Identify functions: vertical line test
• 5 Find values using function graphs
• 6 Evaluate a function
• 7 Evaluate a function: plug in an expression
• 8 Complete a function table from a graph
• 9 Complete a function table from an equation
• 10 Interpret the graph of a function: word problems

R. Direct variation

• 1 Identify proportional relationships
• 2 Find the constant of variation
• 3 Graph a proportional relationship
• 4 Write direct variation equations
• 5 Write and solve direct variation equations

S. Linear functions

• 1 Identify linear functions
• 2 Find the slope of a graph
• 3 Find the slope from two points
• 4 Find a missing coordinate using slope
• 5 Slope-intercept form: find the slope and y-intercept
• 6 Slope-intercept form: graph an equation
• 7 Slope-intercept form: write an equation from a graph
• 8 Slope-intercept form: write an equation
• 9 Slope-intercept form: write an equation from a table
• 10 Slope-intercept form: write an equation from a word problem
• 11 Linear equations: solve for y
• 12 Write linear functions to solve word problems
• 13 Complete a table and graph a linear function
• 14 Compare linear functions: graphs, tables and equations
• 15 Write equations in standard form
• 16 Standard form: find x- and y-intercepts
• 17 Standard form: graph an equation
• 18 Equations of horizontal and vertical lines
• 19 Graph a horizontal or vertical line
• 20 Point-slope form: graph an equation
• 21 Point-slope form: write an equation
• 22 Point-slope form: write an equation from a graph
• 23 Slopes of parallel and perpendicular lines
• 24 Write an equation for a parallel or perpendicular line
• 25 Transformations of linear functions

T. Systems of linear equations

• 1 Is (x, y) a solution to the system of equations?
• 2 Solve a system of equations by graphing
• 3 Solve a system of equations by graphing: word problems
• 4 Find the number of solutions to a system of equations by graphing

U. Monomials

• 1 Identify monomials
• 2 Multiply monomials
• 3 Multiply monomials to find area
• 4 Divide monomials
• 5 Multiply and divide monomials
• 6 Powers of monomials

V. Polynomials

• 1 Polynomial vocabulary
• 2 Model polynomials with algebra tiles
• 3 Add and subtract polynomials using algebra tiles
• 4 Add and subtract polynomials
• 5 Add polynomials to find perimeter
• 6 Multiply a polynomial by a monomial
• 7 Multiply polynomials to find area
• 8 Divide a polynomial by a monomial
• 1 Identify hypotheses and conclusions
• 2 Counterexamples

X. Probability

• 1 Theoretical probability
• 2 Experimental probability
• 3 Compound events: find the number of outcomes
• 4 Identify independent and dependent events
• 5 Probability of independent and dependent events

Y. Statistics

• 1 Calculate mean, median, mode and range
• 2 Interpret charts to find mean, median, mode and range
• 3 Mean, median, mode and range: find the missing number
• 4 Quartiles
• 5 Identify biased samples

Grade 9 Algebra Quiz Questions And Answers

Hey, if you're looking for some new and unique algebra quiz questions and answers for grade 9th students, you've come to the right place. The below quiz is designed to test your understanding of the topics covered. Algebra is considered the most challenging subject by most people in grade nine, but this is essentially not true as all that one needs to understand to practice after covering every topic. Do you need some help with Algebra? Start by taking this quiz and watch out. Good luck!

The sum of 2 numbers is 46. One number is 12 more than the other. What are the numbers?

Rate this question:

Evaluate this equation for the given value of a and b.  a 2  + b 2  , for a = 2 and b = 2

The sum of 3 consecutive whole numbers is 108. what are the numbers, jack is 5 years older than mary. in four years the sum of their age is 33 years old. what are their ages.

Mary is 10 years old, Jack is 15 years old

Mary is 9 years old, Jack is 19 years old

Mary is 12 years old, Jack is 17 years old

Mary is 8 years old, Jack is 19 years old

A basketball court is a rectangle with dimensions 29m by 16m. What is the length of a diagonal to the nearest meter?

Approximately 29

Approximately 30

Approximately 33

Approximately 32

Large pizzas cost $12.50 and small pizzas cost $9.00. The pizza parlor sold 38 pizzas with a total value of $415.50. How many of each type did the pizza parlor sell?

20 large, 17 small

22 large, 18 small

21 large, 17 small

23 large, 18 small

Find the value of x in this equation:  (x - 4) / (- 6) = 3

Simplify this equation:  (-5x - 10) / (x + 2), what are the x and y intercepts of the line 2x−3y+6=0, what will be the slope of the line with equation  y - 4 = 10 .

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