class viii : mathematics cycle - 06( 27 september - 8
TRANSCRIPT
Class VIII : Mathematics
CYCLE - 06( 27th
September - 8th
October, 2021)
CHAPTER 08: COMPARING QUANTITIES
CONTENTS :
8.1 Recalling Ratios and Percentages
8.2 Finding the Increase or Decrease Per cent
8.3 Finding Discounts
8.3.1 Estimation in percentages
8.4 Prices Related to Buying and Selling (Profit and Loss)
8.4.1 Finding cost price/selling price, profit %/loss%
8.5 Sales Tax/Value Added Tax
8.6 Compound Interest
8.7 Deducing a Formula for Compound Interest
8.8 Rate Compounded Annually or Half Yearly (Semi Annually)
8.9 Applications of Compound Interest Formula
BULLET POINTS
Ratio: It is the comparison of two quantities of the same kind by division.
It doesnot have a unit.
Percentage: Percent comes from the words ‘per centum’ which mean per hundred.
Its symbol is %.
Cost price(C.P.):It is the price at which an article is purchased.
Selling Price(S.P.): It is the price at which an article is sold.
Gain: If S.P. > C.P, then there is a gain.
Loss: If C.P. >S.P , then there is a loss.
Profit and Loss are always calculated on the C.P.
Overhead expenses:Sometimes when an article is bought, some additional expenses are
made while buying or before selling it. These expenses are included in the cost price and are
called overhead expenses.
Marked Price (M.P.): The price printed on an article is called its marked price or list
price.
Discount: It is a reduction given on the marked price of the article.
Discount is always calculated on the M.P.
Sales Tax:It is the tax levied by the government on the items we buy.
Sales Tax is calculated on the sale price of an article.
Value Added Tax (VAT) : It is the tax paid by the consumer these days . It is
calculated on the entire value of the product only once.
Simple Interest(S.I.): It is the extra money paid by institutions like banks or post offices
on money deposited with them. Interest is also paid by people when they borrow
money.
Pricipal(P) : The money borrowed or lent is called Principal.
Time Period(T) :The duration for which the money is lent is called Time period.
Rate of Interest (R): The rate at which the interest is calculated is called the rate of
interest.
Amount (A): It is the sum of Principal and the interest.
Compound Interest: It is the interest calculated on the previous years amount.
Some Important Formulae:
Gain = S.P – C.P
Loss = C.P – S.P
Gain % = PC
Gain
.× 100
Loss % =PC
Loss
.× 100
S.P.( when gain% is given) =100
%100 gain × C.P.
S.P.( when loss% is given) =100
%100 loss × C.P.
C.P.( when gain% is given) =%100
100.
gain
PS
C.P .( when loss% is given) =%100
100.
loss
PS
Discount = M.P –S.P
Discount % = PM
Discount
.× 100
Sales Tax = 100
sTaxRateOfSale×S.P.
Total Amount of the bill = S.P. +Sales tax
S.I = 100
TRP
Amount =P 1 +100
R
𝑛
where n is the number of years
C.I = A-P
SUBJECT MATHEMATICS
CLASS VIII
CHAPTER 08 Ch 8 : COMPARING QUANTITIES
E-book/video link
Notes
. https://www.learncbse.in/ncert-solutions-for-class-8-maths
https://ncert.nic.in/exemplar-problems.php?ln=
https://youtu.be/uVWcIB6oxBs
https://youtu.be/wt776bay3iY
https://youtu.be/aCBcFPsWvGA
https://youtu.be/BpwUcWi_iHs
https://youtu.be/vSMtm_yEkGQ
If you have any doubts, clear them with your subject teacher
PERIOD 1
Page no 117 to 119
Explain the concept of ratio and percentage
CW : Ex-8.1 , 1(a , b ) , 2 ( a ) , Q3 , Q4
HW : Ex – 8.1, 1 ( c ) , 2 (b) ,
PERIOD 2
Page no 120 to 121
Explain the concept of increase ,decrease % and Discounts
CW : Ex-8.1 , Q5 , Try these – page 121 , 1(a) ,Q2 , Q3
HW : Ex – 8.1, Q6 , Try these – page 121 , 1( b, c )
PERIOD 3
Explain the concept of profit and loss
CW : Try these – page 123 , 1(b) ,Q1 below
HW : Try these – page 123 , 1( a , c )
PERIOD 4
Explain the concept of ST , VAT and GST
CW : Try these – page 124 ,125 Q1 (b, c ) ,Q2 (a)
HW : Try these – page 124 , 125 Q1( a ) , Q2 (b)
PERIOD 5
Page no 125
CW : Ex-8.2 , Q1 , 2 , 4
HW : Ex – 8.2 , Q3
PERIOD 6
Page no 125
CW : Ex-8.2 , Q5 , 7 , 8
HW : Ex – 8.2 , Q6
PERIOD 7
Explain the concept of S.I and C.I. ,annually , semi-anually, quarterly
CW : Try these – page 130 , Q1 ,Q2
HW : Try these – page 131 , Q1 , Q2
PERIOD 8
Page no 125
CW : Ex-8.3 , Q1 ( a , b , c )
HW : Ex – 8.3 , Q1 ( d, e )
PERIOD 9
Project 1:
ART INTEGRATED PROJECT :VERIFICATION OF PYTHAGORAS THEOREM IN
DIFFERENT WAYS
Need to mention the following heads :
Background,Objective, Description, conclusion, Application.
PERIOD 10
Project 1 ( Continued … )
ART INTEGRATED PROJECT :VERIFICATION OF PYTHAGORAS THEOREM IN
DIFFERENT WAYS
For reference, project 1 is given below with different example
PROJECT 01
Project on proof of Pythagoras Theorem in different ways.
Pythagoras Theorem is an important topic in Maths, which explains the relation between the sides of
a right-angled triangle. It is also sometimes called the Pythagorean Theorem. The theorem is named after a
greek Mathematician called Pythagoras
Pythagoras theorem is basically used to find the length of an unknown side and angle of a triangle. By this
theorem, we can derive base, perpendicular and hypotenuse formula.
Pythagoras Theorem Statement
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to
the sum of squares of the other two sides“. The sides of this triangle have been named as Perpendicular,
Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
PROOF:1
.
²
PROOF 2:
3.
Right angle triangle and Pythagoras theorem has large number of applications in
our daily life .It is used for designing like designing building , bridges , dams ,
ships etc, and also use to design on cloths , titles , wall paintings etc. Its pattern
gives very beautiful design.
PRACTICE PAPER
1. Ravi got an increase of 10% in his salary. If his salary after increase was Rs. 72,710, find his salary before increase.
2. A flask was sold at Rs. 72 incurring a loss of 10%. What was its cost price?
3. A ceiling fan was bought for Rs. 1,375 including 10% VAT. What was the selling price of the fan?
4. Find the compound interest on Rs. 60,000 for one year at the rate of 6% p.a. compounded half yearly.
5. Fatima’s income was Rs. 10,000. She spent 12% of her income on rent and 64% on
other things. How much money did she save every month?
6. Amar purchased an old bike for Rs. 73,500. He spent Rs. 10,300 on repairs and paid
Rs. 2,600 for its insurances. Then he sold it to Suraj at a loss of 2.5%. At what price did
Suraj buy the bike from Amar?
7. A shopkeeper allows successive discounts of 10% and 5%. Find the net selling price of
a DVD whose marked price is Rs. 4,500.
8. Rakhi lent Rs. 5,000 to Jyoti at the rate of 83
1% compound interest. Find the interest
and the amount payable to Jyoti to Rakhi after 2 years.
9. A trader marks his goods 20% above the cost price. He sells them at a discount of 20%.
If the cost price is Rs. 1,100, what is his gain or loss percent?
10. Find the compound interest on Rs. 15, 625 for 9 months at 16% per annum, the interest
is compounded quarterly.