10th Grade Math

10th grade math topics are planned and covered all the lessons in different segments. 10th grade math help is provided for the 10th grade students in all segments to cover all the math lesson plans which are categorized into Arithmetic, Algebra, Geometry, Mensuration and Trigonometry.

All types of solved examples on different topics are explained along with the step-by-step solutions so that students can attempt how to solve these problems quickly in your own convenient methods. 10th grade math practice sheets are presented in such a way that students can learn math while practicing math problems.

Keeping in mind the mental level of student in tenth 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 10th 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 10th grade math test or exams students need to learn problems ratio and proportion, profit & loss and interest (simple and compound), ratio, proportion and variation, inequation, surds, 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, theorems on circle, theorems on tangent to a circle, theorems on similarity, constructions and appendix, triangle theorems & proofs, properties of polygons, transformations, trigonometric ratios, trigonometric ratios of complementary angles, application of trigonometric ratios in practical problems and etc……

If student follow math-only-math they can improve their knowledge by practicing the worksheets for 10th graders which will help them to score in their exam.

Tenth Grade Math Lessons – Table of Contents

Commercial Mathematics

● Compound Interest

• Compound Interest Definition
• Compound Interest
• Compound Interest with Growing Principal
• Compound Interest with Periodic Deductions
• Compound Interest by Using Formula
• Compound Interest when Interest is Compounded Yearly
• Compound Interest when Interest is Compounded Half-Yearly
• Compound Interest when Interest is Compounded Quarterly
• Problems on Compound Interest
• Variable Rate of Compound Interest
• Difference of Compound Interest and Simple Interest
• Practice Test on Compound Interest
• Uniform Rate of Growth
• Uniform Rate of Depreciation
• Uniform Rate of Growth and Depreciation

● Sales Tax and Value Added Tax

• Calculation of Sales Tax
• Sales Tax in a Bill
• Mark-ups and Discounts Involving Sales Tax
• Profit Loss Involving Tax
• Value Added Tax
• Problems on Value Added Tax (VAT)
• Worksheet on Printed Price, Rate of Sales Tax and Selling Price
• Worksheet on Profit/Loss Involving Sales Tax
• Worksheet on Sales Tax and Value-added Tax
• Worksheet on Mark-ups and Discounts Involving Sales Tax

● Shares and Dividends

• Share and Value of Shares
• Dividend and Rate of Dividend
• Calculation of Income, Return and Number of Shares
• Problems on Income and Return from Shares
• Problems on Shares and Dividends
• Worksheet on Basic Concept on Shares and Dividends
• Worksheet on Income and Return from Shares
• Worksheet on Share and Dividend

Algebra/Linear Algebra

● Linear Inequations in One Variable (Unknown)

• Linear Inequation in One Variable
• Laws of Inequality
• Replacement Set and Solution Set in Set Notation
• Difference Between Equation and Inequation
  
• Solving a Linear Inequation Algebraically
• Problems on Law of Inequality
• Problems on Linear Inequation
• Worksheet on Laws of Inequality
• Worksheet on Solution of a Linear Inequation in One Variable

● 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

● Factorization

• Polynomial
• Polynomial Equation and its Roots
  
• Division Algorithm
  
• Remainder Theorem
  
• Problems on Remainder Theorem
  
• Factors of a Polynomial
  
• Worksheet on Remainder Theorem
  
• Factor Theorem
  
• Application of Factor Theorem

● Ratio and proportion

• Basic Concept of Ratios
• Important Properties of Ratios
• Ratio in Lowest Term
  
• Types of Ratios
• Comparing Ratios
• Arranging Ratios
  
• Dividing into a Given Ratio
  
• Divide a Number into Three Parts in a Given Ratio
• Dividing a Quantity into Three Parts in a Given Ratio
  
• Problems on Ratio
  
• Worksheet on Ratio in Lowest Term
  
• Worksheet on Types of Ratios
  
• Worksheet on Comparison on Ratios
• Worksheet on Ratio of Two or More Quantities
  
• Worksheet on Dividing a Quantity in a Given Ratio
• Word Problems on Ratio
  
• Proportion
  
• Definition of Continued Proportion
  
• Four Numbers in Proportion
• Mean and Third Proportional
  
• Word Problems on Proportion
  
• Worksheet on Proportion and Continued Proportion
  
• Worksheet on Mean Proportional
  
• Properties of Ratio and Proportion
  

● Matrix

• Definition of a Matrix
  
• Order of a Matrix
  
• Position of an Element in a Matrix
  
• Classification of Matrices
• Problems on Classification of Matrices
  
• Square Matrix
• Row Matrix
• Column Matrix
  
• Null Matrix
• Equal Matrices
  
• Identity (or Unit) Matrix
• Triangular Matrix
  
• Addition of Matrices
  
• Addition of Two Matrices
  
• Properties of Addition of Matrices
  
• Negative of a Matrix
  
• Subtraction of Matrices
  
• Subtraction of Two Matrices
  
• Scalar Multiplication of a Matrix
  
• Multiplication of a Matrix by a Number
  
• Properties of Scalar Multiplication of a Matrix
• Multiplication of Matrices
  
• Multiplication of Two Matrices
  
• Problems on Understanding Matrices
  
• Worksheet on Understanding Matrix
  
• Worksheet on Addition of Matrices
  
• Worksheet on Matrix Multiplication
  
• Worksheet on Matrix
  

Reflection and Coordinate Geometry

● Reflection

• Position of a Point in a Plane
• Reflection of a Point in a Line
• Reflection of a Point in the x-axis
• Reflection of a Point in the y-axis
• Reflection of a Point in the Origin
• Reflection of a Point in a Line Parallel to the x-axis
• Reflection of a Point in a Line Parallel to the y-axis
• Problems on Reflection in the x-axis or y-axis
• Invariant Points for Reflection in a Line
• Reflection in Lines Parallel to Axes
• Worksheet on Reflection in the Origin

● Distance and Section Formulae

• Distance Formula
• Distance Properties in some Geometrical Figures
• Conditions of Collinearity of Three Points
• Problems on Distance Formula
• Distance of a Point from the Origin
• Distance Formula in Geometry
• Section Formula
• Midpoint Formula
• Centroid of a Triangle
• Worksheet on Distance Formula
• Worksheet on Collinearity of Three Points
• Worksheet on Finding the Centroid of a Triangle
• Worksheet on Section Formula

● Equation of a Straight Line

• Inclination of a Line
• Slope of a Line
• Intercepts Made by a Straight Line on Axes
• Slope of the Line Joining Two Points
• Equation of a Straight Line
• Slope-intercept Form of a Straight Line
  
• Point-slope Form of a Line
• Two-point Form of a Line
• Equally Inclined Lines
• Slope and Y-intercept of a Line
• Condition of Perpendicularity of Two Straight Lines
• Condition of parallelism
• Problems on Condition of Perpendicularity
• Worksheet on Slope and Intercepts
• Worksheet on Slope Intercept Form
• Worksheet on Two-point Form
• Worksheet on Point-slope Form
• Worksheet on Collinearity of 3 Points
• Worksheet on Equation of a Straight Line

Geometry and Measurement

● Loci

• Concept of loci
• Theorems on Locus of a Point which is Equidistant from Two Fixed Points
  

● Properties of Tangents

• Secant and Tangent
• Common Tangents to Two Circles
  
• Tangent - Perpendicular to Radius
  
• Two Circles Touch each Other
  
• Two Tangents from an External Point
  
• Angles between the Tangent and the Chord
  
• Problems on Properties on Tangents
  
• Chord and Tangent Intersect Externally
  
• Direct Common Tangents
  
• Important Properties of Direct Common Tangents
• Transverse Common Tangents
  
• Important Properties of Transverse Common Tangents
  
• Examples of Loci Based on Circles Touching Straight Lines or Other Circles
  
• Circumcircle of a Triangle
  
• Incircle of a Triangle
  
• Circumcentre and Incentre of a Triangle
  
• Solved on the Basic Properties of Tangents
  
• Problems on Two Tangents to a Circle from an External Point
  
• Two Tangents are Drawn to a Circle from an External Point
  
• Two Parallel Tangents of a Circle Meet a Third Tangent
  
• Contact of Two Circles
  
• Tangent is Parallel to a Chord
  
• Measure of the Angles of the Cyclic Quadrilateral
  
• Problems on Relation Between Tangent and Secant
  
• Problems on Common Tangent to Two Circles

● Area and Perimeter of a Circle

• Area and Perimeter of a Circle
• Area and Perimeter of a Sector of a Circle
• Area and Perimeter of a Semicircle and Quadrant of a Circle
  
• Area of Combined Figures
  
• Area of the Shaded Region
  
• Find the Area of the Shaded Region
  
• Application Problems on Area of a Circle
  

Trigonometry

● Trigonometrical Ratios and Identities

• Basic Trigonometric Ratios: Learn the determination of trigonometrical ratios and their names.

• Relations Between the Trigonometric Ratios: Learn how the trigonometric ratios related between each other.

• Properties of Trigonometrical Ratios: Learn how to prove the properties of basic formula of trigonometrical ratios.
• Problems on Trigonometric Ratios:
• Reciprocal Relations of Trigonometric Ratios:
• Trigonometrical Identity:
• Problems on Trigonometric Identities:
• Elimination of Trigonometric Ratios:
• Eliminate Theta between the equations:
• Problems on Eliminate Theta:
• Trig Ratio Problems:
• Proving Trigonometric Ratios:
• Trig Ratios Proving Problems:
• Verify Trigonometric Identities:
• Trigonometric Identities
  
• Elimination of Unknown Angles
  
• Finding the Unknown Angle
  
• Worksheet on Trigonometric Identities
  
• Worksheet on Evaluation Using Trigonometric Identities
  
• Worksheet on Establishing Conditional Results
  
• Worksheet on Elimination of Unknown Angle(s)
  
• Worksheet on Finding the Unknown Angle

• Problems on Relation between the Rations: Learn how to solve the problems based on the relation between the trigonometrical ratios.

● Trigonometric Ratios of Complementary Angles

• Complementary Angles and their Trigonometric Ratios
• Worksheet on Evaluation using Trigonometric Ratios of Complementary Angles
  
• Worksheet on Establishing Equality using Trigonometric Ratios of Complementary Angles
  
• Worksheet on Establishing Identities and Simplification Using Trigonometric Ratios of Complementary Angles
  

● Height and Distance

• Angle of Elevation
  
• Angle of Depression
  
• Height and Distance with Two Angles of Elevation
  
• Finding sin Value from Trigonometric Table
  
• Finding cos Value from Trigonometric Table
  
• Finding tan Value from Trigonometric Table
  
• Worksheet on Heights and Distances
  

Statistics and Probability 

● Graphical Representation

• Histogram
  
• Frequency Polygon
  
• Method of Constructing a Frequency Polygon with the Help of a Histogram
  
• Method of Constructing Frequency Polygon with the Help of Class Marks
  
• Cumulative-Frequency Curve
  
• Problems on Histogram
• Problems on Frequency Polygon
  
• Problems on Cumulative-Frequency Curve

● Measures of Central Tendency

• Mean of Ungrouped Data
  
• Problems on Mean of Ungrouped Data
  
• Mean of Grouped Data
  
• Mean of Classified Data
  
• Step-deviation Method
  
• Finding the Mean from Graphical Representation
  
• Worksheet on Finding the Mean of Raw Data
  
• Worksheet on Finding the Mean of Arrayed Data
  
• Worksheet on Finding the Mean of Arrayed Data
  
• Median of Raw Data
  
• Problems on Median of Raw Data
  
• Finding the Median of Grouped Data
  
• Lower Quartile and the Method of Finding it for Raw Data
  
• Upper Quartile and the Method of Finding it for Raw Data
  
• Find the Quartiles for Arrayed Data
  
• Range and Interquartile Range
  
• Median Class
  
• Estimate Median, Quartiles from Ogive
  
• Worksheet on Finding the Median of Raw Data
  
• Worksheet on Finding the Median of Arrayed Data
  
• Worksheet on Finding the Quartiles & Interquartile Range of Raw Data
  
• Worksheet on Estimating Median and the Quartiles using Ogive
  

● Probability

• Probability
  
• Definition of 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 Rolling a Die
  
• Probability for Rolling Two Dice
• Probability for Rolling Three Dice
• Solved Probability Problems
• Probability Questions Answers
  
• Coin Toss Probability Worksheet
• Worksheet on Playing Cards
  
• 10th Grade Worksheet on Probability
  

Pre-calculus

Mathematical Models with Applications

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