Percentages I Form 1 Mathematics Chapter 3

Percentages (I) Form 1 Mathematics Chapter 3

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)

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%.

Percentage Increase • Last year, Andy was 150 cm tall. His height is increased by 20% this year. What is height now? • Increase or Decrease? • His height now is

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%.

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

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)

Percentage Change • The temperature was 30 C in the afternoon and the temperature dropped to 27 C in the evening. Find the percentage change in the temperature. • The percentage change • So, the percentage decrease in the temperature is 10%.

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%.

Time for Practice • Page 127 of Textbook 1 A ▫ Class Practice • Page 129 of Textbook 1 A ▫ Questions 6 – 14 • Pages 57 - 58 of WB 1 A ▫ Questions 3 - 9

Profit (p. 131) • Selling Price > Cost Price

Loss (p. 134) • Selling Price < Cost Price

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 is

Time for Practice • Pages 134 - 135 of Textbook 1 A ▫ Class Practice • Page 137 of Textbook 1 A ▫ Questions 7 – 19 • Pages 61 - 62 of WB 1 A ▫ Questions 7 - 10

Discount (p. 138) • Western style vs. Chinese style 88折 = 12% off

Discount • Western style vs. Chinese style • 10% discount • 20% discount • 70% discount 9折 8折 3折 • 12% discount • 33% discount • 5% discount 88折 67折 95折

Discount • Marked Price > Selling Price

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.

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.

Time for Practice • Page 141 of Textbook 1 A ▫ Class Practice • Page 142 of Textbook 1 A ▫ Questions 3 – 10 • Pages 65 - 66 of WB 1 A ▫ Questions 7 - 10

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.

Simple Interest • Amount(A) = Principal(P) + Interest(I) • Interest(I) = Principal(P) Interest rate(r%) period of time(T) • Formula:

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 • Simple interest (I) is • So, the amount (A) is T=5 (years)

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.

Time for Practice • Page 149 of Textbook 1 A ▫ Class Practice • Page 150 of Textbook 1 A ▫ Questions 1 – 13 • Pages 69 - 70 of WB 1 A ▫ Questions 4 - 7

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)

Enjoy the world of Mathematics!