#### Topics

##### Rational and Irrational Numbers

##### Compound Interest [Without Using Formula]

##### Compound Interest [Using Formula]

##### Expansions

##### Factorisation

- Factorisation by Taking Out Common Factors
- Factorisation by Taking Out Common Factors
- Factorisation by Taking Out Common Factors
- Factorisation by Grouping
- Factorisation of a Quadratic Trinomial by Splitting the Middle Term
- Method of Factorisation : Difference of Two Squares
- Method of Factorisation : the Sum Or Difference of Two Cubes

##### Simultaneous (Linear) Equations [Including Problems]

- Methods of Solving Simultaneous Linear Equations by Elimination Method
- Methods of Solving Simultaneous Linear Equations by Elimination Method
- Method of Elimination by Equating Coefficients
- Equations Reducible to Linear Equations
- Simultaneous Linear Equations
- Methods of Solving Simultaneous Linear Equations by Cross Multiplication Method
- Simple Linear Equations in One Variable
- Linear Equation in Two Variables

##### Indices [Exponents]

##### Logarithms

##### Triangles [Congruency in Triangles]

##### Isosceles Triangles

##### Inequalities

- Inequalities in a Triangle
- If two sides of a triangle are unequal, the greater side has the greater angle opposite to it.
- If Two Angles of a Triangle Are Unequal, the Greater Angle Has the Greater Side Opposite to It.
- Of All the Lines, that Can Be Drawn to a Given Straight Line from a Given Point Outside It, the Perpendicular is the Shortest.

##### Mid-point and Its Converse [ Including Intercept Theorem]

##### Pythagoras Theorem [Proof and Simple Applications with Converse]

##### Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]

- Introduction of Rectilinear Figures
- Names of Polygons
- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Types of Quadrilaterals
- Diagonal Properties of Different Kinds of Parallelograms
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Property: The diagonals of a rhombus are perpendicular bisectors of one another.
- Property: The Diagonals of a Rectangle Are of Equal Length.
- Property: The diagonals of a square are perpendicular bisectors of each other.

##### Construction of Polygons (Using Ruler and Compass Only)

##### Area Theorems [Proof and Use]

##### Circle

- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Arc, Segment, Sector
- Chord Properties - a Straight Line Drawn from the Center of a Circle to Bisect a Chord Which is Not a Diameter is at Right Angles to the Chord
- Chord Properties - the Perpendicular to a Chord from the Center Bisects the Chord (Without Proof)
- Theorem: Equal chords of a circle are equidistant from the centre.
- Theorem : The Chords of a Circle Which Are Equidistant from the Centre Are Equal.
- Chord Properties - There is One and Only One Circle that Passes Through Three Given Points Not in a Straight Line
- Arc and Chord Properties - If Two Arcs Subtend Equal Angles at the Center, They Are Equal, and Its Converse

##### Statistics

##### Mean and Median (For Ungrouped Data Only)

##### Area and Perimeter of Plane Figures

##### Solids [Surface Area and Volume of 3-d Solids]

##### Trigonometrical Ratios [Sine, Consine, Tangent of an Angle and Their Reciprocals]

##### Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]

##### Solution of Right Triangles [Simple 2-d Problems Involving One Right-angled Triangle]

##### Complementary Angles

##### Co-ordinate Geometry

##### Graphical Solution (Solution of Simultaneous Linear Equations, Graphically)

##### Distance Formula

##### Profit , Loss and Discount

##### Construction of Triangles

##### Changing the Subject of a Formula

##### Similarity

#### formula

- (a + b)
^{3}= a^{3}+ 3a^{2}b + 3ab^{2}+ b^{3}.

#### notes

**Expansion of (a + b)**^{3}:

^{3}:

(a + b)^{3} = (a + b)(a + b)(a + b) = (a + b)(a + b)^{2}

(a + b)^{3} = (a + b)(a^{2} + 2ab + b^{2})

(a + b)^{3} = a(a^{2} + 2ab + b^{2}) + b(a^{2} + 2ab + b^{2})

(a + b)^{3} = a^{3} + 2a^{2}b + ab^{2} + ba^{2} + 2ab^{2} + b^{3}

(a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}

**∴ (a + b) ^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}.**

#### Example

**Expand:** (x + 3)^{3}.

(x + 3)^{3}

We know that (a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}.

In the given example, a = x and b = 3.

∴ `(x + 3)^3 = (x)^3 + 3 xx x^2 xx 3 + 3 xx x xx (3)^2 + (3)^3`.

∴ `(x + 3)^3 = x^3 + 9x^2 + 27x + 27`.

#### Example

**Expand: **(3x + 4y)^{3}.

(3x + 4y)^{3}

`= (3x)^3 + 3(3x)^2(4y) + 3(3x)(4y)^2 + (4y)^3`.

`= 27x^3 + 3 xx 9x^2 xx 4y + 3 xx 3x xx 16y^2 + 64y^3`.

`= 27x^3 + 108x^2y + 144xy^2 + 64y^3`

#### Example

**Expand:** (41)^{3}

(41)^{3}

= (40 + 1)^{3}

= (40)^{3} + 3 × (40)^{2} × 1 + 3 × 40 × (1)^{2} + (1)^{3}

= 64000 + 4800 + 120 + 1

= 68921

#### Example

**Expand: **`((2m)/n + n/(2m))^3`.

`((2m)/n + n/(2m))^3`

`= ((2m)/n)^3 + 3((2m)/n)^2(n/(2m)) + 3((2m)/n)(n/(2m))^2 + (n/(2m))^3`

`= (8m^3)/(n^3) + 3((4m^2)/(n^2))(n/(2m)) + 3((2m)/n)(n^2/(4m^2)) + ((n^3)/8m^3)`

`= ((8m^3)/(n^3)) + ((6m)/n) + (3n)/(2m) + (n^3)/(8m^3)`

#### Example

**Simplify.**

(p + q)^{3} + (p - q)^{3}

(p + q)^{3} + (p - q)^{3}

= p^{3} + 3p^{2}q + 3pq^{2} + q^{3} + p^{3} - 3p^{2}q + 3pq^{2} - q^{3}

= 2p^{3} + 6pq^{2}