#### Topics

##### Sets

- Concept of Sets
- Methods of Writing Sets
- Types of Sets
- Equal Sets
- Venn Diagrams
- Subset
- Universal Set
- Complement of a Set
- Operations on Sets
- Intersection of Sets
- Disjoint Sets
- Union of Sets
- Number of Elements in a Set
- Word Problems Based on Sets

##### Real Numbers

- Rational Numbers
- Properties of Rational Numbers
- Commutative Property of Rational Numbers
- Associative Property of Rational Numbers
- Identity of Addition and Multiplication of Rational Numbers
- Negative Or Additive Inverse of Rational Numbers
- Decimal Representation of Rational Numbers
- Irrational and Real Numbers
- Decimal Representation to Identify Irrational Numbers
- Square Root of Decimal Numbers
- Properties of Order Relation on Real Numbers
- Square Root of a Negative Number
- Root of Positive Rational Number
- Surds
- Simplification of Surds
- Types of Surds
- Comparison of Surds
- Operations on Surds
- Rationalisation of Surds
- Binomial Quadratic Surd
- Simplifying an Expression by Rationalization of the Denominator
- Absolute Value of Real Numbers

##### Polynomials

- Polynomials
- Types of Polynomials
- Degree of Polynomial
- Form of the Polynomial
- Operations on Polynomials
- Synthetic Division
- Value of a Polynomial
- Remainder Theorem
- Factor Theorem
- Factorisation of Polynomials

##### Ratio and Proportion

- Concept of Ratio
- Concept of Direct Proportion
- Concept of Inverse Proportion
- Properties of Ratio
- Comparison of Ratios
- Operations on Equal Ratios
- Application of Properties of Equal Ratios
- Theorem on Equal Ratios
- Concept of Proportion
- k Method for Equal Ratios

##### Linear Equations in Two Variables

- Linear Equation in Two Variables
- Algebraic Methods of Solving a Pair of Linear Equations
- Elimination Method
- Substitution Method
- General Form of Linear Equation in Two Variables
- Application of Linear Equation in Two Variables

##### Financial Planning

- Introduction of Financial Planning
- Saving and Investment
- Levying of Taxes Or Taxation
- Income Tax
- Computation of Income Tax

##### Statistics

- Concept of Bar Graph
- Concept of Double Bar Graph
- Subdivided Bar Graph
- Percentage Bar Graph
- Concepts of Statistics
- Collecting Data
- Organisation of Data
- Frequency Distribution Table
- Cumulative Frequency Table
- Measures of Central Tendency
- Arithmetic Mean - Raw Data
- Concept of Median
- Concept of Mode

## Notes

we discussed how to solve a pair of linear equations graphically. The graphical method is not convenient in cases when the point representing the solution of the linear equations has non-integral coordinates like `( sqrt3, 2sqrt7 )` ,`(–1.75, 3.3)`,`(4/13,1/19)`, etc. There is every possibility of making mistakes while reading such coordinates. Is there any alternative method of finding the solution? There are several algebraic methods

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