Topics
Sets
Sets and Functions
Unit 1: Sets and Functions
Sets
- Sets and Their Representations
- Empty Set (Null or Void Set)
- Finite and Infinite Sets
- Equal Sets
- Subsets
- Power Set
- Universal Set
- Venn Diagrams
- Union of Sets
- Intersection of Sets
- Difference of Sets
- Complement of a Set
- Properties of Complement of Sets
- Problems on Union and Intersection of Two and Three Sets.
Relations and Functions
- Ordered Pairs
- Concept of Relations
- Pictorial Diagrams
- Concept of Function
- Function as a Type of Mapping
- Types of Functions
- Some Functions and Their Graphs
- Exponential Function
- Sum, Difference, Product, Quotient of Functions
Trigonometry
- Magnitude of an Angle
- Angles and Their Measurement in Higher Mathematics
- Conversion from One Measure to Another
- Trigonometric Ratios
- Truth of the Identity
- Signs of Trigonometric Functions
- Domain and Range of Trigonometric Functions
- Expressing Sin (X±Y) and Cos (X±Y) in Terms of Sinx, Siny, Cosx and Cosy and Their Simple Applications
- Trigonometric Functions of Sum and Difference of Two Angles
- Trigonometric Equations
- Solution of Trigonometric Equations (Solution in the Specified Range)
- Graphs of Trigonometric Functions
- Trigonometric Functions of Multiple Angles
- Trigonometric Functions of Half Angles
- Convention of Sign of Angles
- The Relation S = rθ Where θ is in Radians
- Relation Among Trigonometric Ratios
- Periods of Trigonometric Functions
- Compound and Multiple Angles- Addition and Subtraction Formula
- Trigonometric Functions of All Angles
- Sum and Differences as Products
- Product to Sum Or Difference
- Trigonometric Equations
Relations and Functions
Unit 2: Algebra
Algebra1
Principle of Mathematical Induction
Complex Numbers
- Concept of Complex Numbers
- Conjugate of a Complex Number
- Properties of Conjugate, Modulus and Argument (or Amplitude) of Complex Numbers
- Argand Plane and Polar Representation
- Square Root of a Complex Number
- Cube Root of Unity
- Properties of Cube Roots of Unity
- Algebraic Properties of Complex Numbers
- Algebraic Operations of Complex Numbers
- Locus Questions on Complex Numbers.
- Triangle Inequality
Quadratic Equations
- Concept of Quadratic Equations
- Equations Reducible to Quadratic Equations
- Nature of Roots of a Quadratic Equation
- Quadratic Functions
- Sign of Quadratic
- Quadratic Inequalities
- Representation of Inequalities
- Graphical Solution of Linear Inequations
- Solution of System of Linear Inequalities in Two Variables
Permutations and Combinations
- Permutations
- Fundamental Principles of Counting
- Derivation of Formulae and Their Connections
- Simple Applications of Permutations and Combinations
- Circular Permutations
- Restricted Permutation
- Permutation - Certain Things Always Occur Together
- Permutation - Certain Things Never Occur
- Permutation - Formation of Numbers with Digits
- Permutation - Permutation of Alike Things
- Permutation - Permutation of Repeated Things
- Permutation - Word Building
- Combination
Binomial Theorem
- Introduction of Binomial Theorem
- Binomial Theorem for Positive Integral Indices
- General and Middle Terms
- Simple Applications of Binomial Theorem
Sequence and Series
- Sequence, Series, and Progression
- Arithmetic Progression (A.P.)
- Three or More Terms in Arithmetic Progression (A.P.)
- Inserting Two Or More Arithmetic Means Between Any Two Numbers
- Geometric Progression (G. P.)
- Three Terms in Geometric Progression (G.P.)
- Four Terms Are in Geometric Progression (G.P.)
- Geometric Mean
- Relationship Between A.M. and G.M.
- Arithmetico Geometric Series
Coordinate Geometry1
Unit 3: Coordinate Geometry
Trigonometry
Straight Lines
- Brief Recall of Two Dimensional Geometry from Earlier Classes
- Shifting of Origin
- Concept of Slope (or, gradient)
- Various Forms of the Equation of a Line
- Equations of Line in Different Forms
- Equation of Family of Lines Passing Through the Point of Intersection of Two Lines
- Distance in Lines (Point & Parallel Lines)
- Equations of Bisectors of Angle Between Two Lines
- Family & Concurrent Lines
- Foundation of Coordinate Geometry
- Locus
Circles
- Equations of a Circle in Standard Form
- Equations of a Circle in Diameter Form
- Equations of a Circle in General Form
- Equations of a Circle in Parametric Form
- Focus-directrix Property
- Given the Equation of a Circle, to Find the Centre and the Radius
- Finding the Equation of a Circle
- Equation of Tangent and Condition of Tangency
Calculus1
Logarithms
Unit 4: Calculus
Limits and Derivatives
- Derivative Introduced as Rate of Change Both as that of Distance Function and Geometrically
- Introduction of Limits
- Limits of Polynomials and Rational Functions
- Limits of Exponential Functions
- Limits of Logarithmic Functions
- Limits of Trigonometric Functions
- Limits of Algebraic Functions
- Fundamental Theorem on Limits
- Introduction of Derivatives
- Derivative of Slope of Tangent of the Curve
- Derivative of Algebraic Functions
- Differentiation Or Derivative Using First Principles
- Algebra of Derivative of Functions
- Derivative of Polynomials and Trigonometric Functions
Complex Numbers
Statistics and Probability
Unit 5: Statistics and Probability
Statistics - 1
- Measures of Central Tendency for Different Data Types
- Mean Deviation
- Standard Deviation
- Standard Deviation - by Direct Method
- Standard Deviation - by Step Deviation Method"
- Introduction of Variance and Standard Deviation
- Comparison of Two Frequency Distributions with Same Mean
- Quartiles and Range in Statistics
Probability
- Concept of Probability
- Elementary Types of Events and Properties of Probability
- Addition Theorem – for Any Two Events a and B, Result on Complementary Events
- Occurrence of an Event
- Axiomatic Approach to Probability
- Probability of 'Not', 'And' and 'Or' Events
Quadratic Equations
Unit 6: Mathematical Reasoning
Conic Section
- Sections of a Cone
- Conics as a Section of a Cone
- Definition of Foci, Directrix, Latus Rectum
- Parabola and its types
- Latus Rectum
- Ellipse and its Types
- Latus Rectum
- Hyperbola and its Types
- Transverse and Conjugate Axes
- Coordinates of Vertices
- Foci and Centre
- Equations of the Directrices and the Axes
- General Second Degree Equation
- Equation of Tangent and Condition of Tangency
- Point of Contact and Locus Problems
Introduction to Three-dimensional Geometry
Linear and Quadratic Inequalities
Unit 7: Financial Mathematics
Permutations and Combinations
Mathematical Reasoning
- Mathematically Acceptable Statements
- New Statements from Old
- Special Words Or Phrases
- Consolidating the Understanding
- Introduction of Validating Statements
- Validation by Contradiction
- Difference Between Contradiction, Converse and Contrapositive
- Contrapositive and Converse
Statistics - 2
- Combined Mean and Standard Deviation
- Measures of Central Tendency for Different Data Types
- Deciles
- Percentiles
Binomial Theorem
Correlation Analysis
- Definition and Meaning of Covariance
- Karl Pearson’s Coefficient of Correlation
- Rank Correlation by Spearman’s
Sequences and Series
Basic Concepts of Points and Their Coordinates
Index Numbers and Moving Averages
Index Numbers
- Price Index Number
- Simple Aggregate Method
- Weighted Aggregate Method
- Simple Average of Price Relatives
- Weighted Average of Price Relatives
Moving Averages
- Meaning and Purpose of the Moving Averages
- Calculation of Moving Averages with the Given Periodicity and Plotting Them on a Graph
- If the Period is Even, Then the Centered Moving Average is to Be Found Out and Plotted
Straight Lines
Circles and Parabola
Limits and Derivatives
Statistics
Probability
Mathematical Reasoning
Simple Interest and Compound Interest
Annuity
Taxation
Utility Bills
Video Tutorials
Shaalaa.com | Correlation Formula Derivation, Karl Pearson's Coefficient Part 1
Related QuestionsVIEW ALL [14]
A sample of 5 items is taken from the production of a firm. Length and weight of the five items arc given below :
| Length (cm) | 3 | 4 | 6 | 7 | 10 |
| Weight (gm) | 9 | 11 | 14 | 15 | 16 |
Calculate Karl Pearson's coefficient of correlation between the length and weight and interpret the result.
A train travelled between two stations. The distance and time were recorded as below:
| Distance (Km) | 80 | 120 | 160 | 200 | 240 |
| Time (Hr) | 2 | 3 | 4 | 5 | 6 |
Draw scatter diagram and identify the type of correlation.
Calculate from `e_0^0,e_1^0,e_2^0` from the following data :
| Age x | 0 | 1 | 2 |
| `l_x` | 1000 | 900 | 700 |
| `T_x` | - | - | 11500 |
Find Karl Pearson's correlation coefficient for the following data :
| X | 3 | 2 | 1 | 5 | 4 |
| Y | 8 | 4 | 10 | 2 | 6 |
Related concepts
- Concepts of Statistics - Comparison of Two Frequency Distributions with Same Mean
- Concepts of Statistics - Co-efficient of Variation
- Concepts of Statistics - Effect of Change of Origin and Scale on Variance and Standard Deviation
- Concepts of Statistics - Combined Variance and Standard Deviation
