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
- Construct a Triangle Given the Lengths of Its Three Sides
- Construct a Triangle Given Two Sides and the Angle Included by Them
- 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
- Concept of Negative Numbers
- Concept 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
- Division of Integers
- Multiplication of Two Positive Integers
HCF and LCM
Angles and Pairs of Angles
Operations on Rational Numbers
- Concept of 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 Or 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 Triangle Given Two Sides and the Angle Included by Them:
1) Draw ∆PQR such that l(PQ) = 5.5 cm, m∠P = 50°, l(PR) = 5 cm.
(A rough figure has been drawn showing the given information. ∠P is an acute angle
and that is shown in the rough figure, too. )
Steps:
- According to the rough figure, seg PQ forms the base of length 5.5 cm.
- Ray PG is drawn so that m∠GPQ = 50°.
- Open the compass to 5 cm. Placing the compass point on P, draw an arc to cut ray PG at R. Join points Q and R. ∆PQR is the required triangle.
- The ray PG may be drawn on the other side of the seg PQ. Its rough figure will be as shown below.
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