#### Topics

##### Geometrical Constructions

- Constructing a Bisector of an Angle
- Drawing a Perpendicular to a Line at a Point on the Line
- The Property of the Angle Bisectors of a Triangle
- Perpendicular Bisectors of the Sides of an Acute-angled Triangle
- Perpendicular Bisectors of the Sides of an Obtuse-angled Triangle
- Construction of Triangles
- Constructing a Triangle When the Length of Its Three Sides Are Known (SSS Criterion)
- Constructing a Triangle When the Lengths of Two Sides and the Measure of the Angle Between Them Are Known. (SAS Criterion)
- Construct a Triangle Given Two Angles and the Included Side
- Construct a Right-angled Triangle Given the Hypotenuse and One Side
- Congruence Among Line Segments
- Congruence of Angles
- Congruence of Circles

##### Multiplication and Division of Integers

- Concept for Natural Numbers
- Concept for Whole Numbers
- Negative and Positive Numbers
- Concept of Integers
- Concept for Ordering of Integers
- Addition of Integers
- Addition of Integers on Number line
- Subtraction of Integers
- Multiplication of a Positive and a Negative Integers
- Multiplication of Two Negative Integers
- Multiplication of Two Positive Integers
- Division of Integers

##### HCF and LCM

##### Angles and Pairs of Angles

##### Operations on Rational Numbers

- Rational Numbers
- Addition of Rational Number
- Additive Inverse of Rational Number
- Subtraction of Rational Number
- Multiplication of Rational Numbers
- Division of Rational Numbers
- Rational Numbers Between Two Rational Numbers
- Decimal Representation of Rational Numbers
- BODMAS - Rules for Simplifying an Expression

##### Indices

- Concept of Exponents
- Concept of Square Number
- Concept of Cube Number
- Laws of Exponents
- Multiplying Powers with the Same Base
- Dividing Powers with the Same Base
- Taking Power of a Power
- Multiplying Powers with Different Base and Same Exponents
- Dividing Powers with Different Base and Same Exponents
- Numbers with Exponent Zero, One, Negative Exponents
- Miscellaneous Examples Using the Laws of Exponents
- Expressing Large Numbers in the Standard Form
- Finding the Square Root of a Perfect Square

##### Joint Bar Graph

##### Algebraic Expressions and Operations on Them

- Algebraic Expressions
- Terms, Factors and Coefficients of Expression
- Like and Unlike Terms
- Types of Algebraic Expressions as Monomials, Binomials, Trinomials, and Polynomials
- Addition of Algebraic Expressions
- Subtraction of Algebraic Expressions
- Multiplication of Algebraic Expressions
- Multiplying Monomial by Monomials
- Multiplying a Monomial by a Binomial
- Multiplying a Binomial by a Binomial
- Equations in One Variable

##### Direct Proportion and Inverse Proportion

##### Banks and Simple Interest

##### Circle

##### Perimeter and Area

##### Pythagoras’ Theorem

##### Algebraic Formulae - Expansion of Squares

##### Statistics

## Notes

**Construct a Right-angled Triangle Given the Hypotenuse and One Side:**

1) Draw ∆LMN such that m∠LMN = 90°, hypotenuse = 5 cm, l(MN) = 3 cm.

Let us draw the rough figure using the given information.

As m∠LMN = 90°, we draw a right-angled triangle approximately and mark the right angle. Thus we show the given information in the rough figure.

**Steps:**

- As shown in the rough figure, draw the base seg MN of length 3 cm.
- At point M of seg MN, draw ray MT to make an angle of 90° to seg MN.
- Opening the compass to 5 cm and with the point at N, draw an arc to cut seg MT at L.

∆LMN is the required triangle. - Note that a similar figure can be drawn on the other side of the base.

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