Sunday, 29 September 2013
Sunday, 22 September 2013
Chap 11 MENSURATION
Chap 11
SOME IMPORTANT FACTS
1. PERIMETER : The sum of lengths of all
sides of a plane figure is called the perimeter of the figure.
2. Area : The measurement of the region
enclosed by plane figure is called the area of the plane figure.
3. Area of Rectangle : Length X Breadth
Length
= Area / Breadth
; Breadth = Area / length
4. Area of four walls : = [
2 ( length + Breadth ) x height )
5. Area of Square = (side )2 =
(diagonal )2 /2
6. Side of Square = √Area
7. Area of Parallelogram =
Base x Height
Base =
Area / Height ; Height =
Area / Base
8. Area of Quadrilateral = Diogonal
x ( Sum of perpendicular from opposite
vertices on it )
9. Area of Rhombus = product
of Diagonals/2
10. Area of Triangle = (
Base x Height ) / 2
11. Area of Trapezium = (
Sum of parallel sides ) X ( distance between them )
2
12.
The
Circumference /Perimeter of a circle
= 2 πr
13. Area of a circle of radius r = πr2
14. Cuboid
; ii) Volume
of a Cuboid = Length x Breadth x
Height =
( lbh ) Cu. Units
i) Total Surface Area of a Cuboid = 2 (
lb + bh + lh ) sq. units
iii) Lateral Surface Area of a Cuboid = [ 2 ( l + b ) x h ] Sq. units
15. Cube
; i) Volume
of a Cube = (Edge )3
= a3 Cu. Units
i) Total Surface Area of a Cube = 6 a2
sq. units
iii) Lateral Surface Area of a Cube = 4a2
Sq. units
16.
Cylinder
; suppose a cylinder of Height ‘h’ and
radius ‘ r’
a.
Volume = πr2h Cu. Units
b.
Lateral
Surface Area = 2 πrh sq. Units
c.
Total surface Area = (2 πrh + 2πr2 ) sq. Units
17.
i)
1 cm3 = 1
ml
ii) 1 liter = 1000 cm3
i)
1
m3 = 1000000 cm3 =
1000 liters
Chap 11 COMPARING QUANTITIES
Chap 11
SOME IMPORTANT FACTS
RATIO
1. The
ratio of a number ‘a’ to another number ‘b’ ( b ≠ 0 ) is a fraction a / b and is written
as a : b .
2. In the
ratio a : b , the first term a is called
antecedent and second term b is called consequent.
3. The ratio
is said to be in simplest form if its two terms have no common factors other
than 1.
4. The ratio
of two numbers is usually expressed in its simplest form .
5. A ratio
with its second term 100 is also called a percent.
PERCENTAGE
6. To convert
a ratio into a per cent , we write it as a fraction and multiply it by 100 and
put per cent sign (%)
7. Increase % = ( increase x 100 / original value ) %
Decrease % = ( Decrease x 100 /
original value ) %
PROFIT AND LOSS
8. The money
paid by the shopkeeper to buy the goods from a manufacturer is called the Cost
Price ( CP) of the shopkeeper.
9. The price
at which a shopkeeper sells the goods called the selling price (SP) of the
shopkeeper.
10.
Effective Price = Cost Price + Overhead Charges
11.
If SP< CP, then there is a loss ; Loss =
CP – SP
12.
If
SP > CP, then there is profit ; Profit = SP - CP
13.
Profit or Loss
is calculated on the Cost price of good.
14.
Gain %
= ( Gain X 100) / CP and Loss %
= ( Loss x 100 ) / CP
15.
SP = (
100 + Profit %)CP / 100 ; SP = ( 100 - Loss% )CP /100
16.
CP
= (100 x SP) / (100 + Profit %),
CP = ( 100x SP ) / (100 – Loss %)
17.
Discount : Sometimes
shopkeeper offer certain percent of rebate on the marked price for cash
payments . This rebate is known as discount.
Discount = Marked price x Rate of Discount
SP = Marked Price - Discount
18.
SALES TAX :
The Government levies it at a specified rate on the sale price of the
items and it differs from item to item and from state to state .
Sales Tax =
Selling Price X Rate of sales Tax
SIMPLE INTEREST
19. The money
borrowed from a lender is called the principal.
20. The additional
money paid by the borrower to the lender at the end of the specified period is
called the INTEREST.
21. The total
money which the borrower pays back to the lender at the end of the specified
period is called the AMOUNT.
22. Interest is
said to be Simple if it is calculated on the original Principal throughout the
loan period.
23. If P =
Principal, R = Rate of Interest per annum and T = Time, then the simple
interest is given by SI = P x R x T
100
COMPOUND INTEREST
24. If the
interest is added ( compounded ) with the Principal after a specified period of
time to form a new Principal and the interest for the subsequent period is
calculated on this new Principal, then the interest thus obtain is
called the Compound Interest .
25. If P = Principal, R = Rate of Interest per
annum and T = Time, then
a) Amount
after n years ( Compounded annually ) =
P(1 + R/100)n
b) Amount
after n years ( compounded Half yearly) =
P(1 + R/200)n
c) Amount
after n years ( compounded quarterly ) =
P(1 + R/400)n
d) If
the interest is compounded annually but time being a fraction, says 3⅔
years , then
Amount = P(1 + R/100)n x (1 + 2R/300)
e) If
the rates be R1 % for first year R2 % for
second year, R3 % for third year, than Amount after 3 years
P(1 + R1 /100)x
(1 + R2/100) x (1
+ R3/100)
26. let P be
the population at the beginning of a certain year.
a) If the
constant rate of growth is R% p.a., then Population
after n years = P x (1 + R/100)n
b) If the rate
of growth is R1
% for first year R2 % for second year, R3
% for third year, than population after third years
P(1 + R1 /100)x
(1 + R2/100) x (1
+ R3/100)
c) If the
Population decrease at R%
p.a then
Population
after n years = P x (1 - R/100)n
27. If V is the
value of a machine at a certain time and R% p.a is the rate of depreciation , then
Value of machine after n years = V x (1 - R/100)n
Chap 11 COMPARING QUANTITIES
Chap 11
SOME IMPORTANT FACTS
RATIO
1. The
ratio of a number ‘a’ to another number ‘b’ ( b ≠ 0 ) is a fraction a / b and is written
as a : b .
2. In the
ratio a : b , the first term a is called
antecedent and second term b is called consequent.
3. The ratio
is said to be in simplest form if its two terms have no common factors other
than 1.
4. The ratio
of two numbers is usually expressed in its simplest form .
5. A ratio
with its second term 100 is also called a percent.
PERCENTAGE
6. To convert
a ratio into a per cent , we write it as a fraction and multiply it by 100 and
put per cent sign (%)
7. Increase % = ( increase x 100 / original value ) %
Decrease % = ( Decrease x 100 /
original value ) %
PROFIT AND LOSS
8. The money
paid by the shopkeeper to buy the goods from a manufacturer is called the Cost
Price ( CP) of the shopkeeper.
9. The price
at which a shopkeeper sells the goods called the selling price (SP) of the
shopkeeper.
10.
Effective Price = Cost Price + Overhead Charges
11.
If SP< CP, then there is a loss ; Loss =
CP – SP
12.
If
SP > CP, then there is profit ; Profit = SP - CP
13.
Profit or Loss
is calculated on the Cost price of good.
14.
Gain %
= ( Gain X 100) / CP and Loss %
= ( Loss x 100 ) / CP
15.
SP = (
100 + Profit %)CP / 100 ; SP = ( 100 - Loss% )CP /100
16.
CP
= (100 x SP) / (100 + Profit %),
CP = ( 100x SP ) / (100 – Loss %)
17.
Discount : Sometimes
shopkeeper offer certain percent of rebate on the marked price for cash
payments . This rebate is known as discount.
Discount = Marked price x Rate of Discount
SP = Marked Price - Discount
18.
SALES TAX :
The Government levies it at a specified rate on the sale price of the
items and it differs from item to item and from state to state .
Sales Tax =
Selling Price X Rate of sales Tax
SIMPLE INTEREST
19. The money
borrowed from a lender is called the principal.
20. The additional
money paid by the borrower to the lender at the end of the specified period is
called the INTEREST.
21. The total
money which the borrower pays back to the lender at the end of the specified
period is called the AMOUNT.
22. Interest is
said to be Simple if it is calculated on the original Principal throughout the
loan period.
23. If P =
Principal, R = Rate of Interest per annum and T = Time, then the simple
interest is given by SI = P x R x T
100
COMPOUND INTEREST
24. If the
interest is added ( compounded ) with the Principal after a specified period of
time to form a new Principal and the interest for the subsequent period is
calculated on this new Principal, then the interest thus obtain is
called the Compound Interest .
25. If P = Principal, R = Rate of Interest per
annum and T = Time, then
a) Amount
after n years ( Compounded annually ) =
P(1 + R/100)n
b) Amount
after n years ( compounded Half yearly) =
P(1 + R/200)n
c) Amount
after n years ( compounded quarterly ) =
P(1 + R/400)n
d) If
the interest is compounded annually but time being a fraction, says 3⅔
years , then
Amount = P(1 + R/100)n x (1 + 2R/300)
e) If
the rates be R1 % for first year R2 % for
second year, R3 % for third year, than Amount after 3 years
P(1 + R1 /100)x
(1 + R2/100) x (1
+ R3/100)
26. let P be
the population at the beginning of a certain year.
a) If the
constant rate of growth is R% p.a., then Population
after n years = P x (1 + R/100)n
b) If the rate
of growth is R1
% for first year R2 % for second year, R3
% for third year, than population after third years
P(1 + R1 /100)x
(1 + R2/100) x (1
+ R3/100)
c) If the
Population decrease at R%
p.a then
Population
after n years = P x (1 - R/100)n
27. If V is the
value of a machine at a certain time and R% p.a is the rate of depreciation , then
Value of machine after n years = V x (1 - R/100)n
Chap 11 COMPARING QUANTITIES
Chap 11
SOME IMPORTANT FACTS
RATIO
1. The
ratio of a number ‘a’ to another number ‘b’ ( b ≠ 0 ) is a fraction a / b and is written
as a : b .
2. In the
ratio a : b , the first term a is called
antecedent and second term b is called consequent.
3. The ratio
is said to be in simplest form if its two terms have no common factors other
than 1.
4. The ratio
of two numbers is usually expressed in its simplest form .
5. A ratio
with its second term 100 is also called a percent.
PERCENTAGE
6. To convert
a ratio into a per cent , we write it as a fraction and multiply it by 100 and
put per cent sign (%)
7. Increase % = ( increase x 100 / original value ) %
Decrease % = ( Decrease x 100 /
original value ) %
PROFIT AND LOSS
8. The money
paid by the shopkeeper to buy the goods from a manufacturer is called the Cost
Price ( CP) of the shopkeeper.
9. The price
at which a shopkeeper sells the goods called the selling price (SP) of the
shopkeeper.
10.
Effective Price = Cost Price + Overhead Charges
11.
If SP< CP, then there is a loss ; Loss =
CP – SP
12.
If
SP > CP, then there is profit ; Profit = SP - CP
13.
Profit or Loss
is calculated on the Cost price of good.
14.
Gain %
= ( Gain X 100) / CP and Loss %
= ( Loss x 100 ) / CP
15.
SP = (
100 + Profit %)CP / 100 ; SP = ( 100 - Loss% )CP /100
16.
CP
= (100 x SP) / (100 + Profit %),
CP = ( 100x SP ) / (100 – Loss %)
17.
Discount : Sometimes
shopkeeper offer certain percent of rebate on the marked price for cash
payments . This rebate is known as discount.
Discount = Marked price x Rate of Discount
SP = Marked Price - Discount
18.
SALES TAX :
The Government levies it at a specified rate on the sale price of the
items and it differs from item to item and from state to state .
Sales Tax =
Selling Price X Rate of sales Tax
SIMPLE INTEREST
19. The money
borrowed from a lender is called the principal.
20. The additional
money paid by the borrower to the lender at the end of the specified period is
called the INTEREST.
21. The total
money which the borrower pays back to the lender at the end of the specified
period is called the AMOUNT.
22. Interest is
said to be Simple if it is calculated on the original Principal throughout the
loan period.
23. If P =
Principal, R = Rate of Interest per annum and T = Time, then the simple
interest is given by SI = P x R x T
100
COMPOUND INTEREST
24. If the
interest is added ( compounded ) with the Principal after a specified period of
time to form a new Principal and the interest for the subsequent period is
calculated on this new Principal, then the interest thus obtain is
called the Compound Interest .
25. If P = Principal, R = Rate of Interest per
annum and T = Time, then
a) Amount
after n years ( Compounded annually ) =
P(1 + R/100)n
b) Amount
after n years ( compounded Half yearly) =
P(1 + R/200)n
c) Amount
after n years ( compounded quarterly ) =
P(1 + R/400)n
d) If
the interest is compounded annually but time being a fraction, says 3⅔
years , then
Amount = P(1 + R/100)n x (1 + 2R/300)
e) If
the rates be R1 % for first year R2 % for
second year, R3 % for third year, than Amount after 3 years
P(1 + R1 /100)x
(1 + R2/100) x (1
+ R3/100)
26. let P be
the population at the beginning of a certain year.
a) If the
constant rate of growth is R% p.a., then Population
after n years = P x (1 + R/100)n
b) If the rate
of growth is R1
% for first year R2 % for second year, R3
% for third year, than population after third years
P(1 + R1 /100)x
(1 + R2/100) x (1
+ R3/100)
c) If the
Population decrease at R%
p.a then
Population
after n years = P x (1 - R/100)n
27. If V is the
value of a machine at a certain time and R% p.a is the rate of depreciation , then
Value of machine after n years = V x (1 - R/100)n