#### Topics

##### Commercial Mathematics

##### Compound Interest

##### Shares and Dividends

##### Banking

##### Gst (Goods and Services Tax)

- Sales Tax, Value Added Tax, and Good and Services Tax
- Computation of Tax
- Concept of Discount
- List Price
- Concepts of Cost Price, Selling Price, Total Cost Price, and Profit and Loss, Discount, Overhead Expenses and GST
- Basic/Cost Price Including Inverse Cases.
- Selling Price
- Dealer
- Goods and Service Tax (Gst)
- Gst Tax Calculation
- Gst Tax Calculation
- Input Tax Credit (Itc)

##### Algebra

##### Co-ordinate Geometry Distance and Section Formula

##### Quadratic Equations

##### Factorization

##### Ratio and Proportion

##### Linear Inequations

##### Arithmetic Progression

##### Geometric Progression

##### Matrices

##### Reflection

##### Co-ordinate Geometry Equation of a Line

- Slope of a Line
- Concept of Slope
- Equation of a Line
- Various Forms of Straight Lines
- General Equation of a Line
- Slope – Intercept Form
- Two - Point Form
- Geometric Understanding of ‘m’ as Slope Or Gradient Or tanθ Where θ Is the Angle the Line Makes with the Positive Direction of the x Axis
- Geometric Understanding of c as the y-intercept Or the Ordinate of the Point Where the Line Intercepts the y Axis Or the Point on the Line Where x=0
- Conditions for Two Lines to Be Parallel Or Perpendicular
- Simple Applications of All Co-ordinate Geometry.

##### Geometry

##### Loci

##### Circles

- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Areas of Sector and Segment of a Circle
- Tangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments
- Tangent Properties - If a Chord and a Tangent Intersect Externally, Then the Product of the Lengths of Segments of the Chord is Equal to the Square of the Length of the Tangent from the Point of Contact to the Point of Intersection
- Tangent to a Circle
- Number of Tangents from a Point on a Circle
- 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.
- Converse: 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 - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle
- Theorem: Angles in the Same Segment of a Circle Are Equal.
- Arc and Chord Properties - Angle in a Semi-circle is a Right Angle
- Arc and Chord Properties - If Two Arcs Subtend Equal Angles at the Center, They Are Equal, and Its Converse
- Arc and Chord Properties - If Two Chords Are Equal, They Cut off Equal Arcs, and Its Converse (Without Proof)
- Arc and Chord Properties - If Two Chords Intersect Internally Or Externally Then the Product of the Lengths of the Segments Are Equal
- Cyclic Properties
- Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers

##### Constructions

##### Symmetry

##### Similarity

##### Mensuration

##### Trigonometry

##### Statistics

- Median of Grouped Data
- Graphical Representation of Data as Histograms
- Ogives (Cumulative Frequency Graphs)
- Concepts of Statistics
- Graphical Representation of Data as Histograms
- Graphical Representation of Ogives
- Finding the Mode from the Histogram
- Finding the Mode from the Upper Quartile
- Finding the Mode from the Lower Quartile
- Finding the Median, upper quartile, lower quartile from the Ogive
- Calculation of Lower, Upper, Inter, Semi-Inter Quartile Range
- Concept of Median
- Mean of Grouped Data
- Mean of Ungrouped Data
- Median of Ungrouped Data
- Mode of Ungrouped Data
- Mode of Grouped Data
- Mean of Continuous Distribution

##### Probability

#### formula

- Volume of a Cylinder = πr
^{2}h.

#### notes

**Volume of a** **Cylinder:**

The volume of a cylinder can be obtained as: base area × height

= area of circular base × height = πr^{2}h

So, the Volume of a Cylinder = πr^{2}h, where r is the base radius and h is the height of the cylinder.

#### Example

A rectangular paper of width 14 cm is rolled along its width and a cylinder of radius 20 cm is formed. Find the volume of the cylinder. (Take `22/7` for π)

A cylinder is formed by rolling a rectangle about its width. Hence the width

of the paper becomes height and the radius of the cylinder is 20 cm.

Height of the cylinder = h = 14 cm

Radius = r = 20 cm

Volume of the cylinder = V = πr

^{2}h= `22/7` × 20 × 20 × 14

= 17600 cm

^{3}Hence, the volume of the cylinder is 17600 cm

^{3}.#### Example

A rectangular piece of paper 11 cm × 4 cm is folded without overlapping to make a cylinder of height 4 cm. Find the volume of the cylinder.

Length of the paper becomes the perimeter of the base of the cylinder and

width becomes height.

Let radius of the cylinder = r and height = h

Perimeter of the base of the cylinder = 2πr = 11

or `2 xx 22/7 xx r = 11`

Therefore,

r = `7/4` cm

Volume of the cylinder = V = πr

^{2}h= `22/7 xx 7/4 xx 7/4 xx 4` cm

^{3}= 38.5 cm

^{3}Hence the volume of the cylinder is 38.5 cm

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