Maths is that subject which is required at every step of life. A thorough understanding of the concept of basic calculations is required for a student to comprehend his mathematical skills. However, it is seen that children often execrate the subject owing to the various figures, formulas and calculations. Learning and teaching maths can at times become tiresome but here’s a solution to it. At AplusTopper, mathematics as a subject is made easy to learn and understand.

## Learn Basic Maths, Topics and Formulas for Mathematics

Maths concepts beginning from the number system, pre algebra, algebra, commercial arithmetic, geometry, trigonometry, arithmetic, statistics, calculus, probability and many more are explained with accuracy and in a simple manner to help the students enjoy learning maths. Solved Examples and Exercise Problems are also provided to help students learn with clarity and also test their understanding of the concepts.

### Pre-Algebra | Maths

#### Patterns

#### Big and Small Numbers

- What is the meaning of Place Value and Face Value in Maths?
- What is the Place Value Chart of an Indian and International System?
- What is a Decimal Value and Place Value of Decimals?
- How do you Round to the Nearest Ten Thousand
- What is the Definition of an Equivalent Decimal
- Converting To and From Scientific Notation
- What is the Difference between Ascending and Descending Order
- Addition and Subtraction of Decimals
- How do you Multiply and Divide Decimals?
- How do you Convert Fractions into Decimals and Vice Versa
- How do you Convert Unlike Decimals into Like Decimals

#### Handling Negative Numbers

Fundamental Operations on Integers

#### Doing Calculations

- Whole Numbers And Its Properties
- Hints for Remembering the Properties of Real Numbers
- What Are The Four Basic Operations In Mathematics
- Order of Operations and Evaluating Expressions
- Absolute Value
- Absolute Value Equations
- Absolute Value Inequalities
- Absolute Value of Complex Numbers

#### Using Inequalities (less than, greater than)

#### Using Exponents

#### Factors and Multiples

- Finding Factors and Multiples
- Common Factors
- How to Find The Prime Factors Using Factor Tree
- How To Find The HCF And LCM Using Prime Factorisation Method

#### Ratios and Proportions

#### Fractions and Percents

- What is Fraction and How many Types of Fractions are there
- Comparing and Ordering of Fractions
- Operations on Fractions
- What is an Equivalent Fraction
- Conversion of Fraction into Decimal
- Percents
- How do you Calculate Percentages?

#### Rational and Irrational Numbers

- What is a Rational Number?
- What Is Irrational Number
- Rational and Irrational Numbers
- Decimal Representation of Rational Numbers
- How to Convert Decimal Number into Rational Number?
- How do you Add and Subtract Rational Numbers?
- How do you Multiply and Divide Rational Numbers?

**How to Estimate Answers**

- Introduction to Estimation
- Estimation Tips and Tricks
- Visual Estimation
- Estimation Games

**Some Examples Using Pre-Algebra**

Here are some subjects of Mathswhere you can use your new skills:

- Celsius and Fahrenheit
- Interest

### Algebra 1 | Maths

#### The Basics

#### Exponents

#### Simplifying

- Adding Signed Numbers
- Multiplying Negatives
- Associative, Commutative and Distributive Laws
- Hints for Remembering the Properties of Real Numbers
- Proportions
- What is a Ratio and Proportion
- What is Fraction and How many Types of Fractions are there
- Comparing and Ordering of Fractions
- Operations on Fractions
- What is an Equivalent Fraction

#### Factoring

#### Logarithms

#### Polynomials

- What is a Polynomial?
- Types of Polynomials
- Monomials, Binomials, and Polynomials
- How do you determine the degree of a Polynomial?
- Zeros of a Polynomial Function
- Factors and Coefficients of a Polynomial
- Relationship Between Zeros and Coefficients of a Polynomial
- How to form a polynomial with the given zeroes
- Adding Polynomials
- Subtracting Polynomials
- Dividing Polynomials
- Multiplying Binomials
- Polynomial Long Multiplication

#### Linear Equations

- Equations of Straight Lines
- Point-Slope Equation of a Line
- Cartesian Coordinates
- What is the Cartesian Coordinate System
- Polar and Cartesian Coordinates

#### Quadratic Equations

- Quadratic Equations
- Nature of the Roots of a Quadratic Equation
- Solving Quadratic Equations with Complex Roots
- Factoring Quadratics
- Solving Quadratic Equations by Factoring
- Solving Factorable Quadratic Equations
- Completing the Square
- Solving Quadratic Equations by Completing the Square

#### Solving Word Questions

- Solving Word Questions
- Solving Inequality Word Questions

#### Functions

#### Sequences and Series

- Sequences and Series
- What is the pattern of numbers?
- Arithmetic Sequences and Series
- Geometric Sequences and Series
- What is Arithmetico–Geometric Sequence?
- Recursive Sequences

### Algebra 2 | Maths

**Sets**

**Numbers**

- The Evolution of Numbers
- Prime and Composite Numbers
- Fundamental Theorem of Arithmetic
- Whole Numbers and Integers
- Rational Numbers
- Irrational Numbers
- Rational Numbers and Irrational Numbers
- Real Numbers
- Imaginary Numbers
- Complex Numbers
- Adding and Subtracting Complex Numbers
- Multiplying and Dividing Complex Numbers
- Absolute Value of Complex Numbers
- The Complex Plane
- Common Number Sets

**Inequalities**

- Introduction to Inequalities
- Properties of Inequalities
- Solving Inequalities
- Absolute Value Inequalities
- Solving Rational Inequalities
- Solving Inequality Word Questions
- Intervals

**Exponents**

- Exponents
- Variables with Exponents
- Using Exponents in Algebra
- Squares and Square Roots
- Squares and Square Roots in Algebra
- nth Root
- Fractional Exponents
- Laws of Exponents
- Exponents of Negative Numbers

**Polynomials**

- What is a Polynomial?
- Types of Polynomials
- Monomials, Binomials, and Polynomials
- Adding Polynomials
- Subtracting Polynomials
- Dividing Polynomials
- Multiplying Binomials
- Polynomials – Long Division
- Degree (of an Expression)
- Special Binomial Products
- Multiplying Binomials
- Difference of Two Cubes
- Polynomial Remainder Theorem
- Factoring in Algebra
- Factorization of Polynomials Using Factor Theorem
- How do you use the factor theorem?
- How to factorise a polynomial by splitting the middle term?
- Review Factoring Polynomials
- Zeros of a Polynomial Function
- Factors and Coefficients of a Polynomial
- Roots of Polynomials: Sums and Products
- Rational Expressions
- Using Rational Expressions
- Review Factoring Polynomials
- Solving Polynomial Equations of Higher Degree
- Examining Graphs of Polynomial Equations of Higher Degree

**Graphing Polynomials**

- How Polynomials Behave
- Polynomials: The Rule of Signs
- Polynomials: Bounds on Zeros

**Equations**

- Equations and Formulas
- Solving Equations
- Simplify
- Solving Word Questions
- Zero Product Property
- Implication and Iff
- Theorems, Corollaries, Lemmas

**Graphs**

- Cartesian Coordinates
- Pythagoras’ Theorem
- Distance Between 2 Points
- Graph of an Equation
- Finding Intercepts From an Equation
- Symmetry in Equations

**Linear Equations**

- Equation of a Straight Line
- Linear Equations
- Point-Slope Equation of a Line
- Equation of a Line from 2 Points
- Midpoint of a Line Segment
- Parallel and Perpendicular Lines

**Functions**

- What is a Function?
- Domain, Range and Codomain
- Evaluating Functions
- Increasing and Decreasing Functions
- Maxima and Minima of Functions
- Even and Odd Functions
- Set-Builder Notation
- Common Functions Reference:
- Square Function
- Square Root Function
- Cube Function
- Reciprocal Function
- Absolute Value Function
- Floor and Ceiling Function

- Function Transformations
- Operations with Functions
- Composition of Functions
- Finding Domains of Composite Functions
- Inverse Functions

**Equations of Second Degree**

- Quadratic Equations
- Factoring Quadratics
- Solving A Quadratic Equation By Factoring
- Completing the Square
- Solving a Quadratic Equation by Completing the Square
- Derivation of Quadratic Formula
- Graphing Quadratic Equations
- A Summary of the Methods of Solving Quadratic Equations
- Quadratic Equations in the Real World
- Circle Equations

**Solving**

- Mathematical Models and Mathematical Models 2
- Approximate Solutions
- Intermediate Value Theorem
- Solving Radical Equations
- Change of Variables
- Algebra Mistakes

**Solving Inequalities**

- Solving Inequalities
- Graphing Linear Inequalities
- Inequality Grapher
- Solving Quadratic Inequalities
- Solving Rational Inequalities
- Absolute Value in Algebra
- Absolute Value Equations

**Exponents and Logarithms**

- Introduction to Logarithms
- Exponents, Roots and Logarithms
- Working with Exponents and Logarithms
- Logarithmic Equations
- Exponential Function
- Logarithmic Function
- Exponential Growth and Decay

**Systems of Linear Equations**

- Systems of Linear Equations
- Solving Systems Of Equations By Elimination Method
- Solving Systems Of Equations By Substitution Method
- Cross Multiplication Method For Solving Equations
- Graphical Method Of Solving Linear Equations In Two Variables
- Matrices
- Special Types of Matrices
- Scalar, Vector, Matrix and Vectors
- Dot Product
- Cross Product
- How to Multiply Matrices
- Determinant of a Matrix
- Inverse of a Matrix:
- Using Elementary Row Operations (Gauss-Jordan)
- Using Minors, Cofactors and Adjugate

- Solving Systems of Linear Equations Using Matrices
- Solving Linear Quadratic Systems Algebraically
- Solving Linear Systems Algebraically Using Substitution
- Solving a Linear Quadratic System Graphically
- Solving Linear Systems Graphically

**Probability**

- Probability
- Probability – Types of Events
- The Basic Counting Principle
- Probability and Permutations
- Combinations and Permutations

**Sequences, Series and Partial Sums**

**Finally**

These last few subjects use what you have learned above.

- Partial Fractions
- Mathematical Induction
- Pascal’s Triangle
- Binomial Theorem
- Binomial Theorem for any Index

### Calculus | Maths

**Limits**

- Introduction to Limits
- Limits and Infinity
- Evaluating Limits
- Limits (Formal Definition)
- Continuous Functions

**Derivatives (Differential Calculus)**

- Introduction to Derivatives
- Slope of a Function at a Point (Interactive)
- Derivatives as dy/dx
- Derivative Plotter (Interactive)
- Derivative Rules
- Power Rule
- Second Derivative
- Partial Derivatives
- Differentiable
- Finding Maxima and Minima using Derivatives
- Concave Upwards and Downwards and Inflection Points
- Implicit Differentiation
- Taylor Series (uses derivatives)

**Integration (Integral Calculus)**

- Introduction to Integration
- Integration Rules
- Integration by Parts
- Integration by Substitution
- Definite Integrals
- Arc Length
- Integral Approximations
- Solids of Revolution by Disks and Washers

**Differential Equations**

- Introduction to Differential Equations
- Separation of Variables
- Solution of First Order Linear Differential Equations
- Homogeneous Differential Equations

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