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Home
Class 10
Real Numbers
The Fundamental Theorem of Arithmetic
Class 10 NCERT (CBSE and ICSE)
The Fundamental Theorem of Arithmetic
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Master this topic as part of
Real Numbers
Class 10
1.
Real Numbers
1.1.
Euclid's Division Lemma
1.2.
The Fundamental Theorem of Arithmetic
1.3.
Revisiting Irrational Numbers
2.
Polynomials
2.1.
Zeros of a Quadratic Polynomial and Relation Between Its Zeroes and Coefficients
2.2.
Zeros of a Cubic Polynomial and Relation Between Its Zeroes and Coefficients
2.3.
Division Algorithm for Polynomials
3.
Pair of Linear Equations in Two Variables
3.1.
Forming Linear Equations Under the Given Conditions
3.2.
Solutions of a Linear Equation
3.3.
Solving a System of Simultaneous Linear Equations
3.3.1.
Solving Simultaneous Linear Equations by Graphical Method
3.3.2.
Solving Simultaneous Linear Equations by Algebraic Method
3.3.2.1.
Substitution Method
3.3.2.2.
Elimination Method
3.3.2.3.
Cross Multiplication Method
3.4.
Conditions for Solvability of a System of Linear Equations
3.4.1.
System of Equations with Unique Solution
3.4.2.
System of Equations with Infinitely Many Solutions
3.4.3.
System of Equations with No Solution
3.4.4.
To Identify the Number of Solutions of a System of Simultaneous Linear Equations
3.4.5.
To Find the Value of the Unknown Variable When the Equation of the Two Lines is Given and their Graph is Described
3.4.6.
Graph of Consistent and Inconsistent System of Linear Equations
3.4.7.
Homogeneous System of Equations
3.5.
Word Problems on Linear Equations in two variables
4.
Quadratic Equations
4.1.
Identify Quadratic Equations
4.2.
Verify Solutions of a Quadratic Equation
4.3.
Solve Quadratic Equations by Factorization
4.4.
Solve Quadratic Equations by Completing the Square
4.5.
Solve Quadratic Equations by Using Quadratic Formula
4.6.
Nature of Roots of a Quadratic Equation
4.7.
Word Problems on Quadratic Equations
5.
Arithmetic Progressions
5.1.
Tell if a Progression is an Arithmetic Progression (AP)
5.2.
Find the First Term, Common Difference or the Next Term in an Arithmetic Progression (AP)
5.3.
Find the Unknown Variable(s) in an Arithmetic Progression (AP)
5.4.
Find the Numbers in AP Under Specified Conditions
5.5.
General Term (
n
th
Term) of an Arithmetic Progression (AP)
5.5.1.
Find the General Term of an Arithmetic Progression (AP)
5.5.2.
Find the Number of Terms in an Arithmetic Progression (AP)
5.5.3.
Find the Middle Term of an Arithmetic Progression
5.5.4.
Find the Position of the Term of an Arithmetic Progression under Different Conditions (AP)
5.6.
General Term (
n
th
Term) from the End of an Arithmetic Progression (AP)
5.7.
Arithmetic Mean
5.8.
Sum of
n
Terms of an Arithmetic Progression (AP)
5.8.1.
Find the General Term of an Arithmetic Progression When the Sum of
n
Terms is Given (AP)
5.8.2.
Find the Common Difference when the Sum of the Series is Given (AP) and the First and the Last Term is Given
5.8.3.
Find the Number of Terms in an Arithmetic Progression (AP) When the Sum of the Series is Given
5.8.4.
Find the Sum of an AP Under Different Conditions
5.9.
Word Problems on Arithmetic Progressions (AP)
6.
Triangles
6.1.
Basic Proportionality Theorem (Thales's Theorem) and its Applications
6.2.
Angle-Bisector Theorem and its Applications
6.3.
Similar Triangles
6.3.1.
Theorems and Problems Related to Similar Triangles
6.3.2.
Ratio of the Areas of Two Similar Triangles
6.4.
Pythagoras Theorem, Related Results and Problems
7.
Coordinate Geometry
7.1.
Distance Between Two Points
7.1.1.
Find the Distance of the Given Point from the Origin
7.1.2.
Find the Distance Between Two Given Points
7.1.3.
Find the Coordinates of a Point Which is at a Fixed Distance from Another Point
7.1.4.
Find a Point Equidistant from Two Given Points and Solve Related Problems
7.1.5.
Find if the Given Points are Collinear and Solve Related Problems
7.2.
Section Formula and Midpoint Formula
7.3.
Centroid of a Triangle
7.4.
Area of a Triangle
7.5.
Area of a Parallelogram
8.
Introduction to Trigonometry
8.1.
Trigonometric Ratios
8.1.1.
Trigonometric Ratios of an Acute Angle of a Right-Triangle
8.1.2.
Reciprocal Relation Between Trigonometric Ratios
8.1.3.
Quotient Relation of Trigonometric Ratios
8.1.4.
If One Trigonometric Ratio (or evident) is known for an Angle, Find Other Trigonometric Ratios of that Angle
8.1.5.
If One Trigonometric Ratio (or evident) is known for an Angle, Find Other Trigonometric Ratios of the Other Acute Angle in a Right-Triangle
8.1.6.
If One Trigonometric Ratio is known (or evident) for an Angle, Evaluate Expressions Involving Other Trigonometric Ratios of that Angle
8.1.7.
If One Trigonometric Ratio is known (or evident) for an Angle, Evaluate Expressions Involving Other Trigonometric Ratios of the Other Acute Angle in a Right-Triangle
8.1.8.
Square Relation of Trigonometric Ratios
8.2.
Trigonometric Ratios of Angles 0, 30, 45, 60, and 90 degrees
8.3.
Trigonometric Ratios of Complementary Angles
8.4.
Trigonometric Identities
8.4.1.
Using Trigonometric Identities to Find the Value of the Expressions Involving Trigonometric Ratios
8.4.2.
Elimination of Trigonometric Ratios Using Identities
9.
Some Applications of Trigonometry
9.1.
Heights and Distances
10.
Circles
10.1.
Theorems and Results Related to Tangents of Circles
11.
Constructions
11.1.
Division of a Line Segment
11.2.
Construction of Triangles
11.3.
Construction of Tangents to a Circle
12.
Areas Related to Circle
12.1.
Area and Circumference of a Circle
12.2.
Area and Circumference of a Semi-Circle
12.3.
Area and Circumference of a Circular Ring
12.4.
Area of a Sector, Segment and Length of the Arc
12.5.
Word Problems on Area Related to Circle
13.
Surface Areas and Volumes
13.1.
Volume and Surface Area of Solids
13.1.1.
Volume and Surface Area of Cuboids and Cubes
13.1.2.
Volume and Surface Area of Cylinders
13.1.3.
Volume and Surface Area of Circular Cones
13.1.4.
Volume and Surface Area of Conical Frustum
13.1.5.
Volume and Surface Area of Spheres, Hemispheres and Spherical Shells
13.1.6.
Conversion of Solid from One Shape to Another
13.1.7.
Volume and Surface Area of Combination of Solids
13.1.8.
Mixed Problems on Volume and Surface Area
14.
Statistics
14.1.
Mean of Grouped Data
14.1.1.
Mean for an Exclusive Series
14.1.1.1.
Direct Method
14.1.1.2.
Assumed-Mean Method
14.1.1.3.
Step-Deviation Method
14.1.2.
Mean for an Inclusive Series
14.1.3.
Word Problems on Mean
14.2.
Median for Grouped Data
14.2.1.
Median for an Exclusive Series
14.2.2.
Median for an Inclusive Series
14.3.
Mode of Grouped Data
14.3.1.
Mode for an Exclusive Series
14.3.2.
Mode for an Inclusive Series
14.3.3.
Using Empirical Formula
14.4.
Miscellaneous Questions on Mean, Mode and Median of Grouped Data
15.
Probability
15.1.
Card Problems
15.2.
Dice Problems
15.3.
Coin Problems
15.4.
Other Problems
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