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Home
Grade 10
Linear Equations in Two Variables
Conditions for Solvability of a System of Linear Equations
Grade 10 Russia School Math
Conditions for Solvability of a System of Linear Equations
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Master this topic as part of
Linear Equations in Two Variables
Grade 10
1.
Real numbers
1.1.
Euclid's Division Lemma
1.2.
Fundamental Theorem of Arithmetic
1.3.
Prime and Composite Numbers, LCM, HCF, Prime-Factorization
1.4.
Word Problems on HCF and LCM
1.5.
Rational Numbers
1.6.
Irrational Numbers
2.
Polynomials
2.1.
Zeros of a Quadratic Polynomial
2.2.
Zeros of a Cubic Polynomial
2.3.
Division Algorithm for Polynomials
3.
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.
Graphical Method
3.3.2.
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 Unknown Variable When the Equation of Two Lines is Given
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
3.5.1.
Problems on Money Matters
3.5.2.
Problems on Numbers
3.5.3.
Problems on Ages
3.5.4.
Problems on Time and Distance
3.5.5.
Problems on Boats and Stream
3.5.6.
Problems on Time and Work
3.5.7.
Problems on Area
3.5.8.
Problems on Geometry
4.
Triangles
4.1.
Basic Proportionality Theorem (Thales's Theorem) and its Applications
4.2.
Angle-Bisector Theorem and its Applications
4.3.
Similar Triangles
4.3.1.
Theorems and Problems Related to Similar Triangles
4.3.2.
Ratio of the Areas of Two Similar Triangles
4.4.
Pythagoras Theorem
5.
Trigonometry
5.1.
Trigonometric Ratios
5.1.1.
Trigonometric Ratios of an Acute Angle of a Right-Triangle
5.1.2.
Reciprocal Relation Between Trigonometric Ratios
5.1.3.
Quotient Relation of Trigonometric Ratios
5.1.4.
Various Trigonometric Ratios of an Angle
5.1.5.
Trigonometric Ratios of the Acute Angles in a Right-Triangle
5.1.6.
Evaluate Expressions Involving various Trigonometric Ratios of an Angle
5.1.7.
Evaluate Expressions Involving Trigonometric Ratios in a Right-Triangle
5.1.8.
Square Relation of Trigonometric Ratios
5.2.
Trigonometric Ratios of Angles 0°, 30°, 45°, 60°, and 90°
5.3.
Trigonometric Ratios of Complementary Angles
5.4.
Trigonometric Identities
5.4.1.
Trigonometric Identities to solve Expressions Involving Trigonometric Ratios
5.4.2.
Elimination of Trigonometric Ratios Using Identities
5.5.
Heights and Distances
6.
Statistics and Probability
6.1.
Statistics
6.1.1.
Mean of Grouped Data
6.1.1.1.
Mean for an Exclusive Series
6.1.1.1.1.
Direct Method
6.1.1.1.2.
Assumed-Mean Method
6.1.1.1.3.
Step-Deviation Method
6.1.1.2.
Mean for an Inclusive Series
6.1.1.3.
Word Problems on Mean
6.1.2.
Median for Grouped Data
6.1.2.1.
Median for an Exclusive Series
6.1.2.2.
Median for an Inclusive Series
6.1.3.
Mode of Grouped Data
6.1.3.1.
Mode for an Exclusive Series
6.1.3.2.
Mode for an Inclusive Series
6.1.3.3.
Using Empirical Formula
6.1.4.
Miscellaneous Questions on Mean, Mode and Median of Grouped Data
6.2.
Probability
6.2.1.
Card Problems
6.2.2.
Dice Problems
6.2.3.
Coin Problems
6.2.4.
Other Problems
7.
Quadratic Equations
7.1.
Identify Quadratic Equations
7.2.
Verify Solutions of a Quadratic Equation
7.3.
Solve Quadratic Equations by Factorization
7.4.
Solve Quadratic Equations by Completing the Square
7.5.
Solve Quadratic Equations by Using Quadratic Formula
7.6.
Nature of Roots of a Quadratic Equation
7.7.
Word Problem on Quadratic Equations
7.7.1.
Word Problems on Numbers
7.7.2.
Word Problems on Ages
7.7.3.
Word Problems on Money
7.7.4.
Word Problems on Speed, Time and Distances
7.7.5.
Word Problems on Time and Work
7.7.6.
Word Problems on Areas and Geometry
8.
Arithmetic Progression (AP)
8.1.
Tell if a Progression is an Arithmetic Progression (AP)
8.2.
Find the First Term, Common Difference or the Next Term in an Arithmetic Progression (AP)
8.3.
Find the Unknown Variable(s) in an AP
8.4.
Find the Numbers in AP Under Specified Conditions
8.5.
General Term (
n
th
Term) of an AP
8.5.1.
Find the General Term of an AP
8.5.2.
Find the Number of Terms in an AP
8.5.3.
Find the Middle Term of an Arithmetic Progression
8.5.4.
Find the Position of the Term of an Arithmetic Progression
8.6.
General Term (
n
th
Term) from the End of an AP
8.7.
Arithmetic Mean
8.8.
Sum of
n
Terms of an Arithmetic Progression (AP)
8.8.1.
Find the General Term of an AP When the Sum of
n
Terms is Given
8.8.2.
Find the Common Difference when the Sum of the Series is Given (AP) and the First and the Last Term is Given
8.8.3.
Find the Number of Terms in an AP When the Sum of the Series is Given
8.8.4.
Find the Sum of an AP Under Different Conditions
8.9.
Word Problems on Arithmetic Progressions (AP)
9.
Circles
9.1.
Theorems and Results Related to Tangents of Circles
10.
Coordinate Geometry
10.1.
Distance Between Two Points
10.1.1.
Distance of a Point from the Origin
10.1.2.
Distance Between Two Given Points
10.1.3.
Coordinates of a Point Which is at a Fixed Distance from Another Point
10.1.4.
Point Equidistant from Two Given Points and Related Problems
10.1.5.
Find if the Given Points are Collinear and Solve Related Problems
10.2.
Section Formula and Midpoint Formula
10.3.
Centroid of a Triangle
10.4.
Area of a Triangle
10.5.
Area of a Parallelogram
11.
Mensuration
11.1.
Perimeter and Area of Plane Figures
11.1.1.
Measuring Areas of Triangles
11.1.1.1.
Area of a Triangle Using Base and Altitude
11.1.1.2.
Area of a Triangle Using Heron's Formula
11.1.2.
Measuring Areas of Quadrilaterals
11.1.2.1.
Area Between Two Rectangles
11.1.2.2.
Area of a Quadrilateral
11.1.2.3.
Area of a Parallelogram
11.1.2.4.
Area of a Rhombus
11.1.2.5.
Area of a Trapezium
11.1.2.6.
Area of a Quadrilateral Using Heron's Formula
11.1.2.7.
Application of Results on Area of Polygonal Regions
11.1.3.
Area of circles, sectors and segments
11.1.3.1.
Area and Circumference of a Circle
11.1.3.2.
Area and Circumference of a Semi-Circle
11.1.3.3.
Area and Circumference of a Circular Ring
11.1.3.4.
Area of a Sector, Segment and Length of the Arc
11.1.3.5.
Word Problems on Rotating Wheels
11.1.3.6.
Word Problems on Rotation of the Hands of the Clock
11.1.4.
Areas of Combinations of Plane Figures
11.2.
Volume and Surface Area of Solids
11.2.1.
Volume and Surface Area of Cuboids and Cubes
11.2.2.
Volume and Surface Area of Cylinders
11.2.3.
Volume and Surface Area of Circular Cones
11.2.4.
Volume and Surface Area of Conical Frustum
11.2.5.
Volume and Surface Area of Spheres, Hemispheres and Spherical Shells
11.2.6.
Conversion of Solid from One Shape to Another
11.2.7.
Volume and Surface Area of Combination of Solids
11.2.8.
Mixed Problems on Volume and Surface Area
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