all mate ma tics formulea

8/7/2019 All Mate Ma Tics Formulea

1/6

FORMULAE

Algebraic Formulae

[If you dont see all formulae, refresh you browser]

For Factorization Formulae given below are mainly used for factorization purpose

For Value Formulae given below are mainly used for finding value

Formulae for Pair of Linear Equation in Two Variables

For Cross multiplication

The same formula has another version as given below

Now, note the difference, the former formula has -1 whereas the latter has +1. So when touse the particular form? Well, it depends on the given equation. If the constant value is

given after equal to (=) sign, there will be -1, i.e. If a 1x + b 1y = c 1

a2x + b 2y = c 2

Here, c 1 and c 2 are constants and they are given after (=) sign, so use formula with -1

If the equation is given in the form of

a1x + b 1y + c 1 =0

a2x + b 2y + c 2 =0

then we will use +1

Conditions for solvability of linear equations

if

a1x + b 1y + c 1 =0

a2x + b 2y + c 2 =0

is the system of a pair of linear equations then

For more details, refer to chapter wise tutorial

QUADRATIC EQUATION


ARITHMETIC PROGRESSION


2/6

General Term of an AP is given by t n = a + (n 1) x d where

tn = n th term of the series

a = First term

n = Number of terms

d = Common Difference

Sum of n terms of an AP is given by


TRIGONOMETRY

Generally, we read about 6 trigonometric ratios namely

Sine (sin) Cosine (cos) Tangent (tan) Cosecant (cosec) and Secant (sec)

But apart from the above given ratios, there are two more ratios which are

[But examples and problems on these two ratios are not in the syllabus so we wontdiscuss about them in detail]

1. Ratio Formula

[Note this relation in ratio formula -- sin-cosec, cos-sec and tan-cot]

2. Reciprocal Formula

[Note this relation in reciprocal formula -- sin-cosec, cos-sec and tan-cot]3. Product of Reciprocal Formula

sinq x cosecq = 1

cosq x secq = 1

tanq x cotq = 1

4. Standard Formula [Trigonometric Identities]

5. Complementary Angle Formula

sin (90 - q) = cos q

cos (90 - q) = sin q

tan (90 - q) = cot q

cot (90 - q) = tan q


3/6

cosec (90 - q) = sec q

sec (90 - q) = cosec q

Value Formula (Special Table)

0o

30o

45o

60o

90o

sin q 0 1

cos q 1 0

tan q 0 1 N.D.

cot q N.D. 1 0

sec q 1 2 N.D.

cosec q N.D. 2 1

N.D. Not Defined!

For more details and how to derive values of sin, cos, etc. refer to Chapter Wise Tutorial

COORDINATE GEOMETRY

Distance between two points P and Q is give by

This is known as Distance Formula

Here, x2, x1, y2 and y1 are points

Distance of the point P from the origin O

Points to remember which is helpful in proving vertices and figures

To prove the vertices of a rectangle

i. Find the length of four sides using Distance Formula

ii. Find the length of diagonals using Distance Formula

iii. Check if opposite sides are equal and the diagonals are also equal than the given points are the vertices of a rectangle

Square

i. If four sides are equal and

ii. Diagonals are also equal

Isosceles Triangle

i. If any two sides are equal


4/6

Equilateral Triangle

i. If all the three sides are equal

Rhombus

i. All the four sides are equalii. Diagonals are not equal

Parallelogram

i. Opposite sides are equal

ii. Diagonals are not equal

Collinearity Three points A, B and C are said to be collinear if they lie on the samestraight line.

Section Formula

1.The coordinates of the point P(x, y) which divides the line segment joining A(x 1, y 1)and B(x 2,y2) internally in the ratio m:n are given by:

2. Midpoint Formula:

The coordinates of the midpoint M of a line segment AB with end points A(x 1,y1) andB(x 2,y2)are

3. Centroid of a triangle:

The point of intersection of the medians of a triangle is called its centroid.

Area of Triangle:

Condition for collinearity:

If the area of triangle is zero, than the points are collinears.

MENSURATION

Area of plane figure:

In the triangle you see, the base is denoted by b'Perimeter and area of quadrilaterals:

1. Rectangle:

a) Perimeter= 2(l x b)

b) Area = l x b


5/6

3. Square:

a) Area = a 2

b) Perimeter = 4a

4. Quadrilateral:

5. Parallelogram:

Area = base x height

6. Rhombus:

Area = x (product of the diagonals)

7. Trapezium:

Area = (sum of the parallel sides) x distance between them.

8. Circle:

SECTORS AND SEGMENTS

Sector

Segment

VOLUME AND SURFACE AREA OF SOLIDS

Cuboid: (Rectangular Parallelopiped)

i. Lateral Surface Area = [2 (l + b) x h] sq. units

ii. Total Surface Area = 2 (lb + bh + hl) sq. units

iii. Volume = l x b x h cubic units

Cube:

i. Lateral Surface Area = 4a 2

ii. Total Surface Area = 6a 2 sq. units

iii. Volume = a 3

Right circular Cylinder:

i. Curved Surface Area = 2prh sq. unit

ii. Total Surface Area = 2prh (r + h)

iii. pr 2h


6/6

Hollow Cylinder:

i. Curved surface area = 2ph(R-r) sq. units

ii. Total surface area = 2ph (R+r) 2p (R 2-r 2) sq. units

iii. Volume = ph(R 2

-r 2

), where R= external radius and r= internal radius.Right circular Cone:

i. Curved surface area= prl

ii. Total surface area= p r(r+l)

iii. Volume = p r 2h

Sphere:

i. Surface area = 4 pr 2

ii. Volume = pr 3

Hemisphere:

i. Total surface area= 3pr 2

ii. Curved surface area= 2pr 2

iii. Volume = pr 3

Hollow sphere:

Volume= p(R 3-r 3)

Frustum of a cone:

i. Lateral surface area = pl(R+r), where l 2=h2+(R-r) 2

ii. Total surface area=(area of the base + area of the top + lateral surface area)

=pR 2+pr 2+pl(R+r)

iii. Volume = ph(R 2+r 2+Rr)

Here, in all the formulae, R-outer radius, r- inner radius, h- height of the frustum and l-sland height.

Hollow hemisphere:

i. Total surface area= p(3R 2+r 2)

ii. Volume= p (R 3-r 3)

all mate ma tics formulea

Documents