Topics
Real Numbers
- Concept of Divisibility
- Euclid's Division Lemma
- Euclid’s Division Algorithm
- Application of Euclid Lemma > Finding the HCF of Two Positive Integers
- Application of Euclid Lemma > Finding the HCF of Three Numbers
- Application of Euclid Lemma > On Expressing the HCF of Two Numbers a and b in the Form xa + yb
- Fundamental Theorem of Arithmetic
- Applications of the Fundamental Theorem of Arithmetic
- Rational Numbers
- Irrational Numbers
- Nature of the Decimal Expansions of Rational Numbers
Number Systems
Algebra
Polynomials
- Concept of Polyomial
- Graph of Polynomials
- Geometrical Meaning of the Zeroes of a Polynomial
- Relation Between Zeroes (Roots) and Coefficients of a Polynomial
- Relationship Between the Zeros and Coefficients of a Quadratic Polynomial
- Relationship between Zeros And Coefficients of a Cubic Polynomial
- Division Algorithm for Polynomials
Coordinate Geometry
Pair of Linear Equations in Two Variables
- Linear Equations in Two Variables
- Simultaneous Linear Equations in Two Variables
- Solution of a Given System of Two Simultaneous Equations
- Graphical Representation of Linear Equations
- Methods of Solving Linear Equations in Two Variables > Graphical Method
- Substitution Method
- Elimination Method
- Cross - Multiplication Method
- Conditions for Solvability (or Consistency)
- Application of Simultaneous Equations
- Problems Based on Articles and Their Costs
- Applications to Problems Based on Numbers
- Application to Problems Based on Fractions
- Applications to Problems on Ages
- Application to Problems Based on Time, Distance, and Speed
Quadratic Equations
- Concept of Quadratic Equations
- Formulation of a Quadratic Equation
- Method of Solving a Quadratic Equation>Factorisation Method
- Method of Solving a Quadratic Equation>Quadratic Formula (Shreedharacharya's Rule)
- Nature of Roots of a Quadratic Equation
- Word Problems on Quadratic Equations
- Problems on Numbers
- General Problem on Money Matters
- Problems on Ages
- Problems on Geometry
- Problems on Speed and Time
- Problems on Time and Work
- Problems on Areas or Mensuration
Geometry
Trignometry
Arithmetic Progressions
Coordinate Geometry
- Foundation of Coordinate Geometry
- Distance Formula
- Collinearity of Three Points
- Section Formula in Coordinate Geometry
- Application of Section Formula
- Coordinate Formula for Area of a Triangle
Mensuration
Triangles
- Concept of Similarity
- Similar Polygons
- Similarity of Triangles (Corresponding Sides & Angles)
- Basic Proportionality Theorem
- Angle Bisector Theorem
- Criteria for Similarity of Triangles
- Equiangular Triangles Theorems
- Ratios of Areas of Two Triangles
- Pythagoras Theorem
Statistics and Probability
Circles
- Tangent to a Circle
- Number of Tangents from a Point on a Circle
Introduction to Trigonometry
Some Applications of Trigonometry
- Angles of Elevation and Depression
- Problems based on Elevation and Depression
Areas Related to Circles
Surface Areas and Volumes
Statistics
Probability
Cross Multiplication Method
Cross Multiplication Method- To understand this method properly, we shall take the help of an example
`4x+2y-7=0` ......eq1
`5x+3y-8=0` ......eq2
While practising this method, if we want to find the value of a particular variable, we will take that variable as a numerator, and the denominator will be the subtraction between the cross multiplication of coefficients of the remaining two variables. In this case, it will be like
`x/"(2×-8)-(-7×3)"`
`y/"(4×-8)-(-7×5)"`
`1/"(4×3)-(2×5)"`
All of them are equal to each other, so to find the value of x,
`x/"(2×-8)-(-7×3)" = 1/"(4×3)-(2×5)"`
`x/"-16+21"=1/"12-10"`
`x/5= 1/2`
`x=5/2`
To find the value of y,
`y/"(4×-8)-(-7×5)"= 1/"(4×3)-(2×5)"`
`y/"-32+35" = 1/"12-10"`
`y/3 = 1/2`
`y= 3/2`
Video Tutorials
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Pair of Linear Equation in two variable part 14 (Algebraic Cross Multiplication)
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