percentages (i) form 1 mathematics chapter 3. reminder standard homework (i) and (ii) ▫today!...
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Percentages (I)Form 1 MathematicsChapter 3
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Reminder• Standard Homework (I) and (II)
▫ Today!• Standard Homework (III) and (IV)
▫ 28 Nov (Wed)• Extra Tutorial
▫ Today’s last CTP▫ MUST: 1, 10, 11, 12, 14, 16, 26, 30, 36▫ Mon & Tue after-school – Consultation on G/F
• Open Book Quiz▫ 28 Nov (Wed)
• Standard Homework (V)▫ 30 Nov (Fri)
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Percentage Increase (p.119)• New value > Original value
• E.g. The Hang Seng Index increases from 11500 to 12150. We also say that the Index is increased by 5.65%.
%100valueOriginal
IncreaseincreasePercentage
valueOriginalvalueNewIncrease
increasePercentagevalueOriginalvalueNew 1
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Percentage Increase•Last year, Andy was 150cm tall. His
height is increased by 20% this year. What is his height now?
•Increase or Decrease?•His height now is
cm
cm
cm
cm
180
2.1150
2.01150
%201150
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Percentage Decrease (p.122)• New value < Original value
• E.g. The price of a flat decrease from $2,200,000 to $1,804,000. We always say that the price of the flat is reduced by 18%.
%100valueOriginal
DecreasedecreasePercentage
valueNewvalueOriginalDecrease
decreasePercentagevalueOriginalvalueNew 1
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Percentage Decrease•The price of a car was $160,000 last
month. What is the price of the car this month if the price is decreased by 15%?
•Increase or Decrease?•The price this month is
000,136$
85.0000,160$
15.01000,160$
%151000,160$
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Percentage Change (p.126)• We can summarize the two formulae into
one and call percentage change.
• If New value > Original value, then + (increase)
• If New value < Original value, then – (decrease)
%100
valueOriginal
valueOriginalvalueNewchangePercentage
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Percentage Change•The temperature was 30C in the afternoon and
the temperature dropped to 27C in the evening. Find the percentage change in the temperature.
•The percentage change
•So, the percentage decrease in the temperature is 10%.
%10
%10030
3
%10030
3027
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Percentage Change•The profit of a company increases from
$450,000 last year to $540,000 this year. What is the percentage change in profit?
•The percentage change
•So, the percentage increase in profit is 20%.
%20
%100450000
90000
%100450000
450000540000
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Time for Practice•Page 127 of Textbook 1A
▫Class Practice•Page 129 of Textbook 1A
▫Questions 6 – 14•Pages 57 - 58 of WB 1A
▫Questions 3 - 9
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Profit (p.131)• Selling Price > Cost Price
%100% PriceCost
ProfitProfit
PriceCostPriceSellingProfit
%ProfitPriceCostProfit
%1 ProfitPriceCostPriceSelling
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Loss (p.134)• Selling Price < Cost Price
%100% PriceCost
LossLoss
PriceSellingPriceCostLoss
%LossPriceCostLoss
%1 LossPriceCostPriceSelling
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Profit and Loss•A shop sold a car at the profit % of 20%. If
the profit was $32000, what was the cost of the car? What was the selling price?
•Profit or Loss?•Let n be the Cost Price. Then,
•So, the Selling Price is000,160$
5000,32$
000,32$5
1
000,32$%20
n
n
n
n
000,192$000,32$000,160$
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Time for Practice•Pages 134 - 135 of Textbook 1A
▫Class Practice•Page 137 of Textbook 1A
▫Questions 7 – 19•Pages 61 - 62 of WB 1A
▫Questions 7 - 10
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Discount (p.138)•Western style vs. Chinese style
88折 = 12% off
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Discount•Western style vs. Chinese style
•10% discount 9 折•20% discount 8 折•70% discount 3 折
•12% discount 88折•33% discount 67折•5% discount 95折
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Discount•Marked Price > Selling Price
%100% PriceMarked
DiscountDiscount
PriceSellingPriceMarkedDiscount
%DiscountPriceMarkedDiscount
%1 DiscountPriceMarkedPriceSelling
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Discount•A pair of scorer shoes is sold at 25%
discount at a marked price of $650. Can Vincent buy the shoes if he has $500?
•Marked price = $650•Selling price of the shoes
•Since Vincent got $500, he can buy the shoes.
5.487$
%75650$
%251650$
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Discount•A golden ring is sold at 30% discount with a
selling price of $441.What is the marked price?
•Selling price = $441.•Let n be Marked price. Then,
•So, the Marked price is $630.
630$7
10441$
441$10
7
441$%301
n
n
n
n
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Time for Practice•Page 141 of Textbook 1A
▫Class Practice•Page 142 of Textbook 1A
▫Questions 3 – 10•Pages 65 - 66 of WB 1A
▫Questions 7 - 10
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Interest (p.144)•When money is deposited in a bank, you will
receive some Interest (I, 利息 ) according to the amount of Principal (P, 本金 ). The sum of P and I is called the Amount (A, 本利和 ).
•The interest is based on a percentage (r%, 利率 ) of the principal. It is normally given in a yearly basis, e.g. 5%p.a. (p.a. = “per annum”).
•There are two methods to find the interests: simple interest or compound interest.
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Simple Interest•Amount(A) = Principal(P) +
Interest(I)
•Interest(I) = Principal(P) Interest rate(r%) period of time(T)
•Formula:100
%
TrPI
TrPI
1001
%1
%
rTPA
TrPA
TrPPA
IPA
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Simple Interest• If $40000 is deposited in a bank for 5 years
at 3%p.a., find the simple interest and the amount.
•P=$40000 r=3 T=5 (years)•Simple interest (I) is
•So, the amount (A) is
6000$
5100
340000$
5%340000$
46000$6000$40000$
TrPI %
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Simple Interest•How long will $20000 amount to $30000 at
5%p.a. simple interest?
•P=$20000 r=5 A=30000• I = $30000-$20000=$10000•Let T be the time. Then,
•The time required is 10 years.10
5
100
2
1100
5
20000$
10000$
10000$%520000$
T
T
T
T
TrPI %
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Time for Practice•Page 149 of Textbook 1A
▫Class Practice•Page 150 of Textbook 1A
▫Questions 1 – 13•Pages 69 - 70 of WB 1A
▫Questions 4 - 7
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Reminder• Standard Homework (I) and (II)
▫ Today!• Extra Tutorial
▫ Today’s last CTP▫ MUST: 1, 10, 11, 12, 14, 16, 26, 30, 36▫ Mon & Tue after-school – Consultation
on G/F• Open Book Quiz
▫ 28 Nov (Wed)• Standard Homework (III), (IV) and (V)
▫ 30 Nov (Fri)
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Enjoy the world of Mathematics!