Maths Formulas – Most of you might feel Maths as your biggest nightmare. But, it’s not and it can be quite interesting once you get to know the applications of it in real life. It’s all about connecting the dots and knowing which calculation to use. Maths Formulas are difficult to memorize and Learn Cram Experts have curated some of the List of Basic Mathematical Formulas that you may find useful in your way of preparation.
Students of Class 6 to 12 can utilise the Maths Formulas PDF and cover the entire syllabus. Revise these formulae thoroughly and identify your strengths and weaknesses in the subject and its formulae. Resolve your doubts while solving the problems by making use of these General Maths Formulas for Classes 6, 7, 8, 9, 10, 11, 12.
Maths Formulas for Class 6 to 12 PDF Free Download
Looking for some smart ways to remember the Mathematical Formulas? You can make use of the handy learning aids and develop an in-depth knowledge on the subject. Check out the Class 6 to 12 Maths Formulas available Chapter Wise as per the Latest CBSE Syllabus and score more marks in the exam.
These Maths Formulas act as a quick reference for Class 6 to Class 12 Students to solve problems easily. Students can get all basic mathematics formulas absolutely free from this page and can methodically revise and memorize them.
Comprehensive list of Maths Formulas for Classes 12, 11, 10, 9 8, 7, 6 to solve problems efficiently. Download Mathematics Formula PDF to complete the syllabus and excel in your exams.
Maths Formulas for Class 6
Maths Formulas for Class 7
Maths Formulas for Class 8
Maths Formulas for Class 9
Maths Formulas for Class 10
Maths Formulas for Class 12
List of Basic Maths Concepts
Sets and Relations
- Set
- Subset and Superset
- Venn Diagram
- Operations on Sets
- Ordered Pair
- Relation
- Composition of Relation
Functions and Binary Operations
- Functions
- Equal Functions
- Real-Valued and Real Functions
- Standard Real Functions and their Graphs
- Operations on Real Functions
- Compositions of Two Functions
- Even and Odd Functions
- Binary Operations
Complex Numbers
- Equality of Complex Numbers
- Algebra of Complex Numbers
- Argand Plane and Argument of a Complex Number
- Cube Roots of Unity
- nth Roots of Unity
- Geometry of Complex Numbers
Theory of Equations aad Inequations
- Polynomial
- Quadratic Equation
- Quadratic Expression
- Inequality
- Linear Inequality
- Solution Set
Sequences and Series
- Sequence
- Series
- Arithmetic Progression (AP)
- Geometric Progression (GP)
- Harmonic Progression (HP)
- Arithmetic-Geometric Progression
Permutations and Combinations
- Fundamental Principles of Counting
- Factorial
- Permutation Circular
- Permutation
- Combination
Binomial Theorem and Principle of Mathematical Induction
- Binomial Theorem for Positive Integer
- General Term in a Binomial Expansion
- Middle Term in a Binomial Expansion
- Greatest Term Multinomial Theorem
- R-f Factor Relations
- Binomial Theorem for Any Index
- Principle df Mathematical Induction
Matrices
- Matrix
- Algebra of Matrices
- Transpose of Matrix
- Symmetric and Skew- Symmetric Matrices
- Elementary Operations (Transfo r matio ns of a Matrix)
- Coniugate of a Matrix
- Rank of a Matrix
Determinants
- Determinant
- Minor and Cofactors
- Adjoint of a Matrix
- Inve rse of a Matrix
- Homogeneous and Non- homogeneous System of Linear Equations
Probability
- Experiment
- Algebra of Events
- Bayes Theorem
- Random Variable
- Bernoulli Trials and Binomial Distribution
Trigonometric Functions, Identities and Equations
- Measurement of Angles
- Relation Between Degree and Radian
- Trigonometric Ratios For Acute Angle
- Trigonometric (or Circular) Functions
- Graph of Trigonometric Functions
- Fundamental Trigonometric Identities
- Trigonometric Functions of Compound Angles
- Transformation Formulae
- Trigonometric Functions of Multiple Angles
- Trigonometric Periodic Functions
- Trigonometric Equations
Solution of Triangles
- Basic Rules of Triangle
- Trigonometrical Ratios of Half of the Angles of Triangle
- Area of a Triangle
Heights and Distances
- Angie of Elevation
- Angle of Depression
Inverse Trigonometric Functions
- Domain and Range of Inverse Trigonometric Functions
- Graphs oflnverse Triginometric Functions
- Elementary Properties of Inverse Trigonometric Functions
- Inverse Hyperbolic Functions
Rectangular Axis
- Rectangular Axis
- Quadrants
- Distance Formulae
- Section Formulae
- Area of Triangle/ Quadrilateral
- Shifting of Origin/Rot at ion of Axes
- Equation of Locus
Straight Line
- Slope (Gradient) of a Line
- Angle between Two Lines
- Equation of a Straight Line
- Distance of a Point from a Line
- Equation of the Bisectors
- Pair of Lines
Circles
- Standard Equation of a Circle
- Equation of Circle Passing Through Three Points »
- Parametric Equation of Circle
- Equation of Tangent
- Equation of Normal
- Pair of Tangents
- Common Tangents of Two Circles
- Family of Circles
- Limiting Points
- Diameter of Circle
Parabola
- Conicsection
- general Equation of Conic
- Standard Forms of a Parabola and Related Terms
- Equation of Tangent
- Point of I ntersection of Two Tangents
- Equation of Normal
- Length of Tangent and Normal
- Equation of Diameter
- Pair of Tangents
- Chor of Contact
Ellipse
- Parametric Equation
- Equation of Tangent
- Equation of Normal
Hyperbola
- Hyperbola of the Form
- Conjugate Hyperbola
- Equation of Hyperbola in Different Forms
- Tangent Equation of Hyperbola
- Normal Equation of Hyperbola
- Asymptote
- Rectangular Hyperbola
limits, Continuity & Differentiability
- Limit
- Methods of Evaluating Limits
- Sandwich Theorem
- Continuity
- Differentiability
- Fundamental Theorems of Differentiability
Derivatives
- Derivatives of Standard Functions
- Fundamental Rules for Derivatives
- Derivatives of Different Types of Function
- Differentiation of a Determinant
- Successive Differentiations
- Partial Differentiations
Application of Derivatives
- Derivatives as the Rate of Change
- Tangents and Normals
- Rolle’s Theorem
- Lagrange’s Mean Value Theorem
- Approximations and Errors
- Increasing Function
- Maxima and Minima of Functions
Indefinite Integrals
- Some Standard Integral Formulae
- Properties of Integration
- Intergation by Substitution
- Integration by Parts
- Integration by Partial Fractions
- Integration of Irrational Algebraic Function
Definite Integrals
- Fundamental Theorem of Calculus
- Properties of Definite Integral
- Integral Function
Applications of Integrals
- Area of Curves Given by Polar Equations
- Area of Curves Given by Parametric Curves
- Curve Sketching
- Volume and Surface Area
Differential
- Equations
- Order and Degree of a Differential Equation
- Linear and Non-Linear Differential Equations
- Solution of Differential Equations
- Formation of Differential Equations
Vectors
- Types of Vectors
- Addition of Vectors Differences (Subtraction) of Vectors
- Multiplication of a Vector by a Scalar
- Components of a Vector
- Vector joining Two Points
- Section Formulae
- Scalar or Dot Product of Two Vectors
- Vector or Cross Product of Two Vectors
- Scalar Triple Product Vector Triple Product
Three Dimensional Geometry
- Coordinate System
- Direction Cosines
- Line in Space
- Plane
- Angle Between Two Planes
- Parallelism and Perpendicularity of Two Planes
Statistics
- Graphical Representation of Frequency Distributions
- Measures of Central Tendency
- Arithmetic Mean
- Geometric Mean
- Harmonic Mean
- Median
- Mode
- Covariance
- Rank Correlation (Spearman’s)
- Regression
Mathematical Reasoning
- Statement (Proposition)
- Elementary Logical Connectives or Logical Operators
- Truth Value and Truth Table
- Quantifiers
- Validity of Statements
Linear Programming Problem (LPP)
- Objective Function
- Constraints
- Non-negative Restrictions
- Optimal Value
- Solution of Simultaneous Linear Inequations
- Graphical Method of Solving a Linear Programming Problem
- Different Types of Linear Programming Problems
Elementary Arithmetic-I
- Types of Number System
- ClassificationofNumbcrsin Decimal Number System
- Test of Divisibility of a Natural Number
- Rule of Determine the Digit at Unit Place
- Rational Numbers
- Irrational Number
- Real Number
- Complex Numbers
- Fraction
- Ascending/Descending Orders in Fraction
- Power of Index
- Surds
- HCF and LCM
- Simplification
- Average
- Ratio and Proportion
- Proportion
Elementary Arithmetic-II
- Fundamental Formula
- Speed, Time and Distance
- Problem Based on Trains
- Boats and Streams
- Pipes and Cisterns
- Clock
- Calendar
Elementary Arithmetic- lll
- Percentage
- Profit, Loss and Discount
- Simple Interest
- Compound Interest
- Growth and Depriciation
- Partnership
- Share and Debenture
- Alligation or Mixture
Elementary Algebra
- Polynomial
- Synthetic Division Method (Horners Method)
- Remainder Theorem
- Linear Equations Rational Expression
logarithms
- Types of Logarithms
- Anti Logarithm
Geometry
- Triangles
- Congruency of Triangles
- Quadrilaterals
- Polygon
Mensuration
- Perimeter and Area of Plane Figure
- Surface Area and Volume of Solid Figure
Quadratic Equation Formulas
1. Quadratic Expression
A polynomial of degree two of the form ax^{2} + bx + c (a ≠ 0) is called a quadratic expression in x.
2. The Quadratic Equation
ax^{2} + bx + c = 0 (a ≠ 0) has two roots, given by
α = \(\frac{-b+\sqrt{b^{2}-4 a c}}{2 a}\) and β = \(\frac{-b-\sqrt{b^{2}-4 a c}}{2 a}\)
3. Nature of roots
The term b^{2} – 4ac is called discriminant of the equation. It is denoted by ∆ or D.
(A) Suppose a, b, c ∈ R and a ≠ 0 then
- If D > 0 ⇒ roots are real and unequal
- If D = 0 ⇒ roots are real and equal and each equal to -b/2a
- If D < 0 ⇒ roots are imaginary and unequal or complex conjugate.
(B) Suppose a, b, c ∈ Q, a ≠ 0 then
- If D > 0 & D is perfect square ⇒ roots are unequal & rational
- If D > 0 & D is not perfect square ⇒ roots are irrational & unequal
4. Conjugate roots
1. If D < 0 →
One root:
α + iβ
Other root:
α – iβ
then
2. D > 0 →
One root:
α + \(\sqrt{\beta}\)
Other root:
α – \(\sqrt{\beta}\)
5. Sum of roots
S = α + β = \(\frac{-b}{a}=-\frac{\text { Coefficient of } x}{\text { cofficient of } x^{2}}\)
6. Product of roots
P = αβ = \(\frac{c}{a}=\frac{\text { Constant term }}{\text { coefficient of } x^{2}}\)
7. Formation of an equation with given roots
x^{2} – Sx + P = 0
8. Relation between roots-and coefficients
If roots of quadratic equation ax^{2} + bx + c = 0 (a ≠ 0) are α and β then
- (α – β) = \(\sqrt{(\alpha+\beta)^{2}-4 \alpha \beta}\) = ± \(\frac{\sqrt{b^{2}-4 a c}}{a}=\frac{\pm \sqrt{D}}{a}\)
- α^{2} + β^{2} = (α + β)^{2} – 2αβ = \(\frac{b^{2}-2 a c}{a^{2}}\)
- α^{2} – β^{2} = (α + β)\(\sqrt{(\alpha+\beta)^{2}-4 \alpha \beta}\) = – \(\frac{b \sqrt{b^{2}-4 a c}}{a^{2}}=\frac{\pm \sqrt{D}}{a}\)
- α^{3} + β^{3} = (α + β)^{3} – 3αβ(α + β) = – \(\frac{b\left(b^{2}-3 a c\right)}{a^{3}}\)
- α^{3} – β^{3} = (α – β)^{3} – 3αβ(α – β)\(\sqrt{(\alpha+\beta)^{2}-4 \alpha \beta}\) {(α + β)^{2} – αβ} = \(\frac{\left(b^{2}-a c\right) \sqrt{b^{2}-4 a c}}{a^{3}}\)
- α^{4} + β^{4} = {(α + β)^{2} – 2αβ}^{2} – 2α^{2}β^{2} = \(\left(\frac{b^{2}-2 a c}{a^{2}}\right)^{2}-2 \frac{c^{2}}{a^{2}}\)
- α^{4} – β^{4} = (α^{2} – β^{2})(α^{2} + β^{2}) \(=\frac{\pm b\left(b^{2}-2 a c\right) \sqrt{b^{2}-4 a c}}{a^{4}}\)
- α^{2} + αβ + β^{2} = (α + β)^{2} – αβ
- \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^{2}+\beta^{2}}{\alpha \beta}=\frac{(\alpha+\beta)^{2}-2 \alpha \beta}{\alpha \beta}\)
- α^{2}β + β^{2}α = αβ(α + β)
- \(\left(\frac{\alpha}{\beta}\right)^{2}+\left(\frac{\beta}{\alpha}\right)^{2}=\frac{\alpha^{4}+\beta^{4}}{\alpha^{2} \beta^{2}}=\frac{\left(\alpha^{2}+\beta^{2}\right)^{2}-2 \alpha^{2} \beta^{2}}{\alpha^{2} \beta^{2}}\)
(xii) nb^{2} = ac(1 + n)^{2} when one root is n times of another
9. Roots under particular cases
For the quadratic equation ax^{2} + bx + c = 0
- If b = 0 ⇒ roots are of equal magnitude but of opposite sign
- If c = 0 ⇒ one root is zero other is – b/a
- If b = c = 0 ⇒ both roots are zero
- If a = c ⇒ roots are reciprocal to each other
- If \(\left.\begin{array}{ll}
a>0 & c<0 \\
a<0 & c>0
\end{array}\right\}\) ⇒ both roots are of opposite signs
- If \(\left.\begin{array}{l}
\mathrm{a}>0, \mathrm{b}>0, \mathrm{c}>0 \\
\mathrm{a}<0, \mathrm{b}<0, \mathrm{c}<0 \end{array}\right\}\) ⇒ both roots are negative
- If \(\left.\begin{array}{l} \mathrm{a}>0, \mathrm{b}<0, \mathrm{c}>0 \\
\mathrm{a}<0, \mathrm{b}>0, \mathrm{c}<0
\end{array}\right\}\) ⇒ both roots are positive
10. Condition for common roots
Let quadratic equations are a_{1}x^{2} + b_{1}x + c_{1} = 0 and a_{2}x^{2} + b_{2}x + c_{2} = 0
(i) If only one root is common:
\(\frac{\alpha^{2}}{\mathrm{b}_{1} \mathrm{c}_{2}-\mathrm{b}_{2} \mathrm{c}_{1}}=\frac{\alpha}{\mathrm{a}_{2} \mathrm{c}_{1}-\mathrm{a}_{1} \mathrm{c}_{2}}=\frac{1}{\mathrm{a}_{1} \mathrm{b}_{2}-\mathrm{a}_{2} \mathrm{b}_{1}}\)
(ii) If both roots are common: \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\)
11. Nature of the factors of the Quadrate Expression
- Real and different, if b^{2} – 4ac > 0.
- Rational and different, if b^{2} – 4ac is a perfect square.
- Real and equal, if b^{2} – 4ac = 0.
12. Position for roots of a quadratic equation ax^{2} + bx + c = 0
(A) Condition for both the roots will be greater than k.
(i) D ≥ 0 (ii) k < –\(\frac{b}{2 a}\) (iii) af(k) > 0
(B) Condition for both the roots will be less than k
(i) D ≥ 0 (ii) k > –\(\frac{b}{2 a}\) (iii) af(k) > 0
(C) Condition for k lie between the roots
(i) D > 0 (ii) af(k) < 0
(D) Condition for exactly one root lie in the interval (k_{1}, k_{2}) where k_{1} < k_{2}
(i) f(k_{1}) f(k_{2}) < 0 (ii) D > 0
(E) When both roots lie in the interval (k_{1}, k_{2}) where k_{1} < k_{2}
(i) D > 0 (ii) f(k_{1}) . f(k_{2}) > 0
(F) Any algebraic expression f(x) = 0 in interval [a, b] if
(i) sign of f(a) and f(b) are of same then either no roots or even no. of roots exist.
(ii) sing of f(a) and f(b) are opposite then f(x) = 0 has at least one real root or odd no. of roots.
13. Maximum & Minimum value of Quadratic Expression
In a quadratic expression ax^{2} + bx + c
- If a > 0, quadratic expression has least value at x = –\(\frac{b}{2 a}\). This least value is given by \(\frac{4 a c-b^{2}}{4 a}=-\frac{D}{4 a}\)
- If a < 0, quadratic expression has greatest value at x = –\(\frac{b}{2 a}\). This
greatest value is given by \(\frac{4 a c-b^{2}}{4 a}=-\frac{D}{4 a}\)
14. Quadratic expression in two variables
The general form of a quadratic expression in two variables x & y is ax^{2} + 2hxy + by^{2} + 2gx + 2fy + c. The condition that this expression may be resolved into two linear rational factors is
∆ = \(\left|\begin{array}{lll}
a & h & g \\
h & b & f \\
g & f & c
\end{array}\right|\) = 0 ⇒ abc + 2 fgh – af^{2} – bg^{2} – ch^{2} = 0 and h^{2} – ab > 0
This expression is called discriminant of the above quadratic expression.
FAQs on Maths Formulas
1. Where can I get all Mathematical Formulas?
You can get all Mathematical Formulas arranged in an organized manner as per the Chapters for various classes from here.
2. What are the types of mathematical formulas?
There are many types in maths as far as formulas are concerned. Have a glance at some of the types of Mathematical Formulas.
- Linear equation
- Quadratic equation
- Cubic equation
- First-order Differential equations
- Integral equations
- Trigonometric equations, Matrix equations, 2nd order differentials, Fourier transforms, Laplace transforms, Hamiltonians and much more.
3. Where can I find Maths Formulas for Class 6 to Class 12 in PDF Format?
You can find Maths Formulas for Classes 12, 11, 10, 9, 8, 7, 6 in PDF Format for various concepts in a structured way by referring to our page. Make the most out of these and score better grades in the exam.
4. How to download Class 6 to 12 Mathematics Formulas PDF?
All you have to do is just click on the direct links available for Mathematics Formulas and you will be directed to a new page. You can see a download button there and click on that and save the handy Maths Formulae PDF for future reference.
Summary
We hope the details prevailing above regarding the Maths Formulas for Class 12, 11, 10, 9, 8, 7, 6 will make it easy for you in your preparation. Solve the maths problems like never before with the curated list of simple Maths Formulas here. Bookmark our site for the latest information on Mathematical Formulas.