# ICSE Grade 9 - MATHS

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• ##### Rational & Irrational Numbers
Real Numbers
Imaginary Numbers
Rational Numbers- Properties of Rational Numbers, Decimal Representation of Rational Numbers, Terminating, Non terminating Rational Decimals
Irrational Numbers
Surds
Rationalisation of Surds
• ##### Compound Interest (Without Using Formula)
Compound Interest
Compound Interest as a Repeated Simple Interest
Conversion Period
Relationship between Simple Interest and Compound Interest
• ##### Compound Interest (Using Formula)
Formula for Compound Interest
Calculate Principal using Formula
To find the Rate Percentage
To find the Time
Interest compounded half yearly
Other Applications- Growth, Depreciation, Population Problem
• ##### Expansions
Identities
Expansions - ( a+b)3, (x+a)(x+b)
Using Expansions
Special Products
• ##### Factorisation
Methods of Factorisation- Taking out the Common Factors, Grouping
Difference of Two Squares
Sum or Difference of Two Cubes
• ##### Simultaneous (linear) Equations
Methods of Solving Simultaneous Equations - Elimination by Substitution, Elimination by Equating Coefficients, Method of Cross Multiplication
Equations Reducible to Linear Equations
Problems based on Simultaneous Equations
• ##### Indices/ Exponents
Law of Indices
Indices- Positive, Fractional, Negative and Zero
Simplification of Expressions involving Exponents
Use of Laws of Exponents
• ##### Logarithms
Logarithmic Form
Exponential Form- Interchanging
Laws of Logarithms and its Uses
Expansion of Expression with the help of Laws of Logarithm
• ##### Triangles (Congruency in Triangles)
Triangles- Relation between Sides and Angles of Triangles
Properties of Triangles-Median, Altitude, Orthocentre
Types of Triangles
Congruent Triangles
Congruency of Triangle- SSS, SAS, AAS, ASA, RHS
• ##### Isosceles Triangles
Properties of an Isosceles Triangle
Theorem- Angles opposite to equal sides are equal and converse
Theorem -Sum of any two sides of a triangle is greater than the third side
Theorem- If two sides of a triangle are unequal, then the greater angle is opposite the greater side and converse
• ##### Inequalities
Theorem- If two sides of a triangle are unequal, the greater side has greater angle opposite to it
Theorem-The perpendicular distance is the shortest distance to a line drawn from an outside point
• ##### Mid-Point Theorem and Its Converse, Equal Intercept Theorem
Theorem-Line segment joining the mid-point of any two sides of a triangle is parallel to the third side, and equal to half of it
Converse of Mid-Point Theorem
Equal Intercept Theorem
• ##### Pythagoras Theorem
Pythagoras Theorem-In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides
Pythagorean Triplets
Rectilinear Figures or Polygons
Concave Polygon and Convex Polygon
Interior and Exterior Angles of Polygon and their Relations
Regular Polygons
Quadrilaterals- Trapezium, Parallelogram, Rhombus, Rectangle, Square
• ##### Construction of Polygons
Construction -Quadrilaterals, Parallelograms, Trapezium, Rectangles, Square, Regular Hexagon
• ##### Area
Figures Between the same Parallels
Corollary- Parallelograms Between the Same Base and Same Parallels are equal in Areas
Theorem-Median divides the triangles into two triangles of equal areas
• ##### Circle
Types of Circles-Concentric Circles, Equal Circles
Circumscribed Circle
Properties-Arc, Chord, Segment, Sector
• ##### Statistics
Data- Raw and Arrayed Data
Variable- Continuous variable, Discrete variable
Frequency Distribution- Ungrouped and Grouped Frequency Distribution
Types of Frequency Distribution- Inclusive and Exclusive
Class Intervals
Class Limits
Graphical Representation of Data-Histogram, Frequency Polygon
• ##### Mean & Median
Mean of ungrouped data
Median
Properties -Mean, Median
• ##### Area and Perimeter of Plane Figures
Area and Perimeter of Triangles
Heron's Formula
Some Special Types of Triangles- Equilateral, Isosceles, Right- Angled Triangle
Some Special types of Quadrilaterals- Rectangle, Square, Parallelogram, Rhombus, Trapezium
Circumference of a Circle
Area of a Circle
• ##### Solids (Surface Area and Volume of 3-D Solids)
Surface Area and Volume of 3-D solids- Cube, Cuboid and Cylinder
Cross Section
Flow of Water
Problems - Internal and External Dimensions of the Solid
• ##### Trigonometrical Ratios
Trigonometric Ratios- Sine, Cosine, Tangent
Reciprocal Relations
• ##### Trigonometrical Ratios of Standard Angles
Trigonometric Ratios of Standard Angles - 0, 30, 45, 60, 90 degrees
Evaluation of an Expression
Solving a Trigonometric Equation
• ##### Solution of Right Triangles
Problems involving Right-Angled Triangle
Problems on Trigonometric Ratios
• ##### Complementary Angles
Concept of Trigonometric Ratio of Complementary Angles
Complementary Angles of Sine and Cosine
Complementary Angles of Tangent and Cotangent
Complementary Angles of Secant and Cosecant
• ##### Co-ordinate Geometry
Variables-Dependent and Independent
Ordered Pair
Cartesian Plane- X-axis, Y-axis
Co-ordinates of Points