Review for Term 1 ExaminationForm 1 MathematicsChapter 0 – Chapter 4

Reminder• Term 1 Examination Syllabus (p.1-185)

▫ Chapter 0: Basic Mathematics▫ Chapter 1: Directed Numbers▫ Chapter 2: Using Algebra to Solve Problems

(I)▫ Chapter 3: Percentages (I)▫ Chapter 4: Using Algebra to Solve Problems

(II)• Date of Term 1 Examination

▫ 12-12-12 (Wed)▫ 8:30 am – 9:30 am (1 hour)▫ Room 104

MathematicsMathematics

Ronald HuiRonald Hui

Tak Sun Secondary SchoolTak Sun Secondary School

Ronald HUIRonald HUI

NumbersNumbers

Numbers (Chapter 0.1, page 2)Numbers (Chapter 0.1, page 2) Natural Number (Natural Number ( 自然數自然數 ))

1, 2, 3, 4, 5, …1, 2, 3, 4, 5, … Whole Number (Whole Number ( 完整數完整數 ))

0,0, 1,1, 2,2, 3,3, 4,4, 5,5, …… Even Number (Even Number ( 偶數，雙數偶數，雙數 ))

0, 2, 4, 6, 8, …0, 2, 4, 6, 8, … Odd Number (Odd Number ( 奇數，單數奇數，單數 ))

1, 3, 5, 7, 9, …1, 3, 5, 7, 9, …

Ronald HUIRonald HUI

CalculationCalculation

Arithmetic OperationsArithmetic Operations ““+” – Addition+” – Addition

Add… to…, Plus, SumAdd… to…, Plus, Sum “–” – “–” – SubtractionSubtraction

Subtract… from…, Minus, DifferenceSubtract… from…, Minus, Difference ““x” – Multiplicationx” – Multiplication

Multiply… by…, Times, ProductMultiply… by…, Times, Product ““” – ” – DivisionDivision

… … is divided by…, Over, Quotientis divided by…, Over, Quotient

Ronald HUIRonald HUI

Calculation orderCalculation order

Please follow the order:Please follow the order: Brackets ( ), [ ], { }Brackets ( ), [ ], { }

(( 小中大括號小中大括號 )) Multiplication / division first,Multiplication / division first,

then addition / subtractionthen addition / subtraction(( 先乘除後加減先乘除後加減 ))

From left to rightFrom left to right(( 由左至右由左至右 ))

Ronald HUIRonald HUI

NumbersNumbers

Prime numbers (Prime numbers ( 質數質數 )) 2,2, 3,3, 5,5, 7,7, 11,11, 13,13, 17,17, 19,19, 23,23, ……

Multiples (Multiples ( 倍數倍數 )) Multiples of 2:Multiples of 2: 2, 4, 6, 8, …2, 4, 6, 8, … Multiples of 3:Multiples of 3: 3, 6, 9, 12, …3, 6, 9, 12, …

Factors (Factors ( 因子因子 )) 2 is a factor of 2, 4, 6, 8, …2 is a factor of 2, 4, 6, 8, … 3 is a factor of 3, 6, 9, 12, …3 is a factor of 3, 6, 9, 12, …

Ronald HUIRonald HUI

Index NotationIndex Notation

Factors of 18: 1, 2, 3, 6, 9, 18Factors of 18: 1, 2, 3, 6, 9, 18 Prime factors of 18: 2, 3Prime factors of 18: 2, 3

18 = 2 x 918 = 2 x 9

= 2 x 3 x 3= 2 x 3 x 3 18 = 2 x 318 = 2 x 322 Index Notation Index Notation

3322 = 3 x 3 = 3 x 3 (( 指數記數法指數記數法 )) 3 is base3 is base 底底 2 is index2 is index 指數指數

Ronald HUIRonald HUI

H.C.F.H.C.F.

Case 1Case 1 1818 == 22 x 3 x 3x 3 x 3 = 2 x 3= 2 x 322

24 = 2 x 2 x 2 x 324 = 2 x 2 x 2 x 3= 2= 233 x 3 x 3 HCF:HCF: 6 6 = 2 x 3= 2 x 3

Case 2Case 2 700 = 2700 = 222 x 5 x 522 x 7 x 7 720720 == 2244 x 3 x 322 x 5 x 5 HCF is 20 = 2HCF is 20 = 222 x 5 x 5

Ronald HUIRonald HUI

L.C.M.L.C.M.

Case 1Case 1 44 == 22 x 2x 2 = 2 = 222

6 = 2 x 36 = 2 x 3 = 2 x 3 = 2 x 3 LCM:12 = 2 x 2 x 3 = 2LCM:12 = 2 x 2 x 3 = 222 x 3 x 3

Case 2Case 2 28 = 228 = 222 x 7 x 7 3030 == 2 x 3 x 52 x 3 x 5 LCM: 420 = 2LCM: 420 = 222 x 3 x 5 x 7 x 3 x 5 x 7

Ronald HUIRonald HUI

H.C.F. and L.C.M.H.C.F. and L.C.M.

If the numbers did not have If the numbers did not have common prime factors, their common prime factors, their HCF is 1 and their LCM is the HCF is 1 and their LCM is the product of themproduct of them

20 = 220 = 222 x 5 x 5 6363 == 3322 x 7 x 7 Their HCF is 1Their HCF is 1 Their LCM is 20 x 63 = 1260Their LCM is 20 x 63 = 1260

Ronald HUIRonald HUI

Types of fractionsTypes of fractions

Types of FractionsTypes of Fractions Proper fraction (Proper fraction ( 真分數真分數 )) Improper fractionImproper fraction (( 假分數假分數 ))

Mixed numberMixed number (( 帶分數帶分數 )) The following fractions are equalThe following fractions are equal

7

4

4

7

4

31

50

20

15

6

10

4

5

2

Ronald HUIRonald HUI

Addition, SubtractionAddition, Subtraction

Use improper fractionsUse improper fractions Change to same denominatorsChange to same denominators Do operations on numeratorsDo operations on numerators

LCM LCM ofof

3, 2, 43, 2, 4is 12is 1212

1712

21

12

30

12

84

7

2

5

3

2

4

7

2

12

3

2

Ronald HUIRonald HUI

Multiplication, DivisionMultiplication, Division

Use improper fractionsUse improper fractions Use reciprocal for division Use reciprocal for division Multiply numerators and Multiply numerators and

denominators separatelydenominators separately

SimplestSimplestForm!Form!

21

20

42

407

4

2

5

3

2

4

7

2

12

3

2

Ronald HUIRonald HUI

Tools and unitsTools and units

Select suitable unitsSelect suitable units Length: km / m / cm / mmLength: km / m / cm / mm Time: hr / min / secTime: hr / min / sec Weight: kg / g / lbWeight: kg / g / lb Temperature: Temperature: C / C / FF Volume: L / mlVolume: L / ml

Directed NumbersForm 1 Mathematics

Chapter 1

Revision on Directed NumbersWhat does the negative mean? Money in bank:

+$1,100 – $950 Students in class (36 students in class)

Mon: – 2; Tue: – 1; Wed: 0; Thu: – 3; Fri:0 World time:

Sydney: +2; Rome: – 6; London: – 8; New York: – 13 Stairs in the building (up is “+”):

Go up 3 steps: +3; Go down 4 steps: – 4

Directed numbers on a number line

How do we write & say this?

-2-6 4 70

+–

7 0 -2 -6

-2 0 4 7

> > >

< < <

This called “Descending Order”

This called “Ascending Order”

Rules to Remember (p.50)

( + ) ( + ) = ( + ) ( – ) ( – ) = ( + )

( + ) ( – ) = ( – ) ( – ) ( + ) = ( – )

正正得正 負負得正正負得負 負正得負

Addition

( + ) ( + ) = ( + )

( – ) ( – ) = ( + )

( + ) ( – ) = ( – )

( – ) ( + ) = ( – )

+3 + (+9)= 3 + 9= 12

–7 + (+12)= –7 + 12= 5

Addition

( + ) ( + ) = ( + )

( – ) ( – ) = ( + )

( + ) ( – ) = ( – )

( – ) ( + ) = ( – )

+3 + (– 9)= 3 – 9= – 6

– 6 + (– 7)= – 6 – 7= – 13

Subtraction

( + ) ( + ) = ( + )

( – ) ( – ) = ( + )

( + ) ( – ) = ( – )

( – ) ( + ) = ( – )

7 – (+12)= 7 – 12= – 5

– 3 – (+3)= – 3 – 3= – 6

Subtraction

( + ) ( + ) = ( + )

( – ) ( – ) = ( + )

( + ) ( – ) = ( – )

( – ) ( + ) = ( – )

7 – (– 7)= 7 + 7= 14

– 3 – (–3)= – 3 + 3= 0

Addition and Subtraction

( + ) ( + ) = ( + )

( – ) ( – ) = ( + )

( + ) ( – ) = ( – )

( – ) ( + ) = ( – )

(+ A) + (+ B) = A + B

(+ A) + (– B) = A – B

(– A) + (+ B) = – A + B

(– A) + (– B) = – A – B

(+ A) – (+ B) = A – B

(+ A) – (– B) = A + B

(– A) – (+ B) = – A – B

(– A) – (– B) = – A + B

Multiplication

( + ) ( + ) = ( + )

( – ) ( – ) = ( + )

( + ) ( – ) = ( – )

( – ) ( + ) = ( – )

(+ 7) (+ 7)= 7 7= 49

(– 8) 3= – 8 3= – 24

Same as (– 8) + (– 8) + (– 8) = (– 24)

Multiplication

( + ) ( + ) = ( + )

( – ) ( – ) = ( + )

( + ) ( – ) = ( – )

( – ) ( + ) = ( – )

4 (– 2)= – (4 2)= – 8

(– 8) (– 7)= + (8 7)= 56

Note: (– 8) (– 7) = (– 8) (– 7)

Division

( + ) ( + ) = ( + )

( – ) ( – ) = ( + )

( + ) ( – ) = ( – )

( – ) ( + ) = ( – )

(+ 7) (+ 7)= 7 7= 1

(– 9) 3= – 9 3= – 3

Note: (– 9) = (– 3) + (– 3) + (– 3)

Division

( + ) ( + ) = ( + )

( – ) ( – ) = ( + )

( + ) ( – ) = ( – )

( – ) ( + ) = ( – )

4 (– 2)= – (4 2)= – 2

(– 12) (– 6)= + (12 6)= 2

26

12

6

12612:Note

Multiplication and Division

( + ) ( + ) = ( + )

( – ) ( – ) = ( + )

( + ) ( – ) = ( – )

( – ) ( + ) = ( – )

(+ A) (+ B) = A B

(+ A) (– B) = – (A B)

(– A) (+ B) = – (A B)

(– A) (– B) = A B(+ A) (+ B) = A B

(+ A) (– B) = – (A B)

(– A) (+ B) = – (A B)

(– A) (– B) = A B

Form 1 MathematicsChapter 2 and Chapter 4

Ronald HUI

Pay attention to the followings: Consider A as a variable ( 變數 ) 1 A = A A + A + A = 3A A A A = A3

3A 4A = 12A2

Ronald HUI

When we work on the followings, we should put together the like terms and then simplify!

For examples:1. A +2B +3A +4B = A +3A +2B +4B

= 4A + 6B2. A -2B –3A +4B = A -3A -2B +4B

= (A-3A) + (-2B+4B)= (-2A) + (2B)= -2A +2B

Ronald HUI

Addition of equality ( 等量相加 )X – 7 = 2

X -7 +7 = 2 +7 X = 9

X – 7 = 2 X = 2 +7 X = 9

If a = bThen a + c = b + c

Ronald HUI

Subtraction of equality ( 等量相減 )X + 7 = 12

X +7 - 7 = 12 -7 X = 5

X + 7 = 12 X = 12 -7 X = 5

If a = bThen a - c = b - c

Ronald HUI

Multiplication of equality ( 等量相乘 )X 5 = 4

X 5 5 = 4 5 X = 20

X 5 = 4 X = 4 5 X = 20

If a = bThen ac = bc

Ronald HUI

Division of equality ( 等量相除 ) 5X = 20

5X 5 = 20 5 X = 4

5X = 20 X = 20 5 X = 4

If a = bThen a c = b c(but c 0)

Ronald HUI

Distributive Law ( 分配律 ) 5 (X+2) = 205 (X) + 5 (2) = 20

5X+10 = 20 5X = 10

X = 2

a(b + c) = ab + ac(a + b)c = ac + bc

Ronald HUI

Distributive Law ( 分配律 ) -5 (X-2) = 20(-5) (X) – (-5) (2) = 20

-5X+10 = 20 -5X = 10

X = -2

-a(b + c) = -ab - ac-a(b - c) = -ab + ac

Ronald HUI

Cross Method ( 交义相乘 )

If a c = b dThen ad = bc(but c0 and d0)

15

28

2815

47355

7

4

3

x

x

x

x

Ronald HUI

Use a letter x to represent unknown number設 x 為變數 ( 即想求的答案 )

Follow the question and form an equation根據問題，製造算式

Solve for x算出 x 的值

Write answer in words (with units!)寫出答案 ( 包括單位 )

Ronald HUI

Page 99 Question 3:◦ If the sum of two consecutive natural numbers is

37, find the smaller number.◦ Step 1: Let the smaller number be x.◦ Step 2: Then, the larger number will be x + 1

So, x + (x + 1) = 37◦ Step 3: x + x + 1 = 37

2x = 36 x = 18

◦ Step 4: Therefore, the smaller number is 18.◦ Checking: 18 + 19 = 37!

Ronald HUI

Page 99 Question 5:◦ The number of candies Susan has is represented

by the algebraic expression 6 + 10x, where x stands for the number of boxes of candies she buys, If Susan has 36 candies after the purchases, find the number of boxes of candies she buys.

◦ Step 1: Given x is the number of boxes.◦ Step 2: Then, 6 + 10x = 36◦ Step 3: 10x = 30

x = 3◦ Step 4: Therefore, the number of boxes is 3.

or Susan buys 3 boxes of candies.

Ronald HUI

Page 99 Question 8:◦ There are three $100 notes and some $10 coins

inside a bag. If there are altogether $460, how many $10 coins are there?

◦ Step 1: Let there are x $10 coins.◦ Step 2: Then, 3 ($100) + x ($10) = $460◦ Step 3: 300 + 10x = 460

10x = 160 x = 16

◦ Step 4: There are 16 $10 coins.

Ronald HUI

“>”: Greater than

“<”: Less than

“”: Greater than or equal to (or Not less than)◦ A combination of “>” and “=”

“”: Less than or equal to (or Not greater than)◦ A combination of “<“ and “=”

Ronald HUI

P.166 Question 9: Add 5 to 4 times of a number p and the sum is greater than 33.

Add 5 “+5” 4 times of a number p “4p” The sum “4p+5” Then, the inequality is “4p+5 > 33”

Ronald HUI

P.166 Question 11: When the sum of a number s and 3 is multiplied by 2, the product is smaller than -10.

The sum of s and 3 “s+3” Multiplied by 2 “2” The product “(s+3) 2” or 2(s+3) The inequality is “2(s+3) < -10”

Write 3 numbers by guessing!

Ronald HUI

P.166 Question 13a: Mike has 2 packs of $1.9 stamps, 1 pack of $2.4 stamps and y packs of $1.4 stamps. Each pack contains 10 pieces of stamps. Write an inequality…

2 packs of $1.9 2 $1.9 10 = $38 1 pack of $2.4 1 $2.4 10 = $24 y packs of $1.4 y $1.4 10 = $14y Total value $38+$24+$14y The inequality is $38+$24+$14y <$100

or 14y+62 < 100

Ronald HUI

P.166 Question 13b: Find the value of y if the total value of the stamps that Mike has is $76.

Total value $38+$24+$14y The equation is $38+$24+$14y = $76

or 14y+62 = 76 14y = 14

y = 1 Therefore, y = 1. or “Mike has one pack of $1.4 stamps.”

Ronald HUI

A formula is an equation with◦ At least 1 variables on the right of equal sign.◦ Only 1 variable (Subject) on the left of equal sign.

e.g. A = (U + L) H 2◦ A is the subject of the formula◦ U, L and H are the variables of the formula

Do you know what this formula means?

Ronald HUI

P.169 Question 18: v = u + gt(u = -8, g = 10, t = 3, v = ?)

v = u + gt = (-8) + (10) (3) Method of

substitution = -8 + 30 = 22

Ronald HUI

P.169 Question 20: In the formula S=88+0.5t , if S=120, find the value of t.

S = 88 + 0.5t (120) = 88 + 0.5t

120 - 88 = 0.5t 32 = 0.5t

32 2 = t 64 = t

t = 64

Ronald HUI

P.169 Question 22a: It is given that V=Ah3. If V = 40 and h = 6, find the value of A.

V = Ah 3 (40) = A (6) 3

40 3 = 6A 120 = 6A

120 6 = A 20 = A A = 20

Ronald HUI

P.169 Question 22b: It is given that V=Ah3. Find the value of h such that A = 5 and the value of V is half of that given in (a)

In (a), V = 40. So, in (b), V = 20.V = Ah 3

(20) = (5) h 3 20 3 = 5h

60 = 5h 60 5 = h

h = 12

Ronald HUI

Consider a sequence: 2, 4, 6, 8, 10, …

Can you guess what are the next numbers? What is the 10th term? What is the 100th term? What is the nth term?

1, 2, 3, 4, 5, …, 10, …, 100, …, n ( 第幾個 ) 2, 4, 6, 8, 10, …, 20, …, 200, …, 2n ( 答案 )

Ronald HUI

A Sequence is a group of numbers with number pattern.

Each number in the sequence is called a Term.

The first one in the sequence is called the First Term.

In the sequence, 2, 4, 6, 8, 10, … 2 is the first term, 4 is the 2nd term, 6 is … The general term ( 通項 ) is 2n or an=2n

Ronald HUI

Given a general term: an=2n-1 What is the first 5 terms? The first 5 terms are:

◦ a1 = 2(1)-1 = 1

◦ a2 = 2(2)-1 = 3

◦ a3 = 2(3)-1 = 5

◦ a4 = 2(4)-1 = 7

◦ a5 = 2(5)-1 = 9 What is the 17th term? The 17th term is a17 = 2(17)-1 = 33

Ronald HUI

P.176 Questions 8-10: Find the first 3 terms of the sequence:

8. an=n+4

a1=1+4=5; a2=2+4=6; a3=3+4=7

9. an=n/3

a1=1/3; a2=2/3; a3=3/3=1

10. an=20-3n

a1=20-3(1)=17; a2=20-3(2)=14; a3=20-3(3)=11

Ronald HUI

P.176 Question 14: The general term of a sequence is 9(n+6). Find the first term, the 6th term and the 10th term of the sequence.

General term: an = 9(n+6) First term = a1 = 9(1+6) = 9 (7) =

63 6th term = a6 = 9(6+6) = 9 (12) = 108 10th term = a10 = 9(10+6) = 9 (16) =

144

Ronald HUI

P.176 Question 15: The general term an of a sequence is n(n+3). Find the first 5 terms and the 20th term of the sequence.

General term: an = (n)(n+3) 1st term = a1 = (1)(1+3) = 1(4) = 4 2nd term =a2 = (2)(2+3) = 2(5) = 10 3rd term = a3 = (3)(3+3) = 3(6) = 18 4th term = a4 = (4)(4+3) = 4(7) = 28 5th term = a5 = (5)(5+3) = 5(8) = 40 20th term = a20 = (20)(20+3) = 20(23)=460

Ronald HUI

P.176 Question 17b: Consider the sequence6, 12, 18, 24, 30, … Use an algebraic expression to represent the general term an of the sequence

n = 1, 2, 3, 4, 5, ……, n an = 6, 12, 18, 24, 30, ……, ??

an = 6n

Ronald HUI

A function is an input-process-output relationship between numbers.

For each input, there is one (and only one) output.

Sequence an = 2n is a function. Formula A = r2 is a function.

Percentages (I)Form 1 MathematicsChapter 3

What is Percentage? (p.110)• “%” is the symbol of percentage. Per

cent means “per one hundred”.• e.g.

4

1

100

25%25

100

81%81 9.0

100

90%90

35.0%35 4567.0%67.45 0314.0%14.3

%20%5

100%100

5

1

5

1

%5.37%2

137%

2

75%

8

300%100

8

3

8

3

%7474.0 %5.12125.0

Simple Percentage Problems•P.116 Q2(c): 125% of $365.2

•P.117 Q10(c): 132 g is 88% of t g

•Remark: same units!

5.456$2

913$

4

5

10

3652$

100

125

1

2.365$%1252.365$

1502

1003

88

100132

%88132

132%88

t

t

t

t

t

Simple Percentage Problems•P.118 Q14. 1100 boys and 700 girls took an

examination. 15% of boys and 5% of girls failed. Find the total number of students passed.

•Number of boys failed = 1100 15% = 165•Number of girls failed = 700 5% = 35•Number of students failed = 165+35 = 200•Number of students = 1100+700 = 1800•Number of students passed = 1800-200 = 1600

Simple Percentage Problems•P.118 Q14. 1100 boys and 700 girls took an

examination. 15% of boys and 5% of girls failed. Find the total number of students passed.

•Number of boys passed= 1100 (1 – 15%) = 1100 (85%) = 935

•Number of girls passed= 700 (1 – 5%) = 700 (95%) = 665

•Number of students passed = 935-665 = 1600

Percentage Increase (p.119)• New value > Original value

• Last year, Andy was 150cm tall. His height is increased by 20% this year. His height now is

%100% valueOriginal

IncreaseIncrease

valueOriginalvalueNewIncrease

%1 increasevalueOriginalvalueNew

cmcmcm 1802.1150%201150

Percentage Decrease (p.122)• New value < Original value

• The price of a car was $160,000 last month. If it is reduced by 15% this month, the new price

%100valueOriginal

DecreasedecreasePercentage

valueNewvalueOriginalDecrease

decreasePercentagevalueOriginalvalueNew 1

000,136$85.0000,160$%151000,160$

Percentage Change (p.126)• We can summarize the two formulae into

one and call percentage change.

• New value > Original value + (increase)• New value < Original value – (decrease)

• The temperature was dropped from 30C to 27C in the evening. The percentage change is

%100%

valueOriginal

valueOriginalvalueNewChange

%10%10030

3%100

30

3027

Percentage Change•P.130 Q19. James had $5000 in his savings

account last year. This year, he has $10000.

•Change %

•James then takes out 40% of his savings. The amount now is = $10000 (1 – 40%) = $6000

•New change %

%100%1005000

5000%100

5000

500010000

%20%1005000

1000%100

5000

50006000

Profit ( 盈利 , p.131)• Selling Price ( 售價 ) > Cost Price (成本

價 )

%100% PriceCost

ProfitProfit

PriceCostPriceSellingProfit

%ProfitPriceCostProfit

%1 ProfitPriceCostPriceSelling

Loss ( 虧蝕 , p.134)• Selling Price ( 售價 ) < Cost Price (成本

價 )

%100% PriceCost

LossLoss

PriceSellingPriceCostLoss

%LossPriceCostLoss

%1 LossPriceCostPriceSelling

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$000,160$

%profitCostProfit

Profit and Loss•P.138 Q22. A merchant bought a chair for

$500 and a desk for $750. He sold the chair at a loss of 30% and the desk at a profit of 24%.

•Selling price of chair•Selling price of desk•Total selling prices = $350 + $930 = $1280•Total cost prices = $500 + $750 = $1250•So, the profit % is

350$%70500$%301500$ 930$%124750$%241750$

%4.2%100024.0%1001250

30%100

1250

12501280

Discount ( 折扣 , p.138)•Western style vs. Chinese style

•10% discount 9 折•20% discount 8 折•70% discount 3 折

•12% discount 88折•25% discount 75折•5% discount 95折

Discount•Marked Price > Selling Price

%100% PriceMarked

DiscountDiscount

PriceSellingPriceMarkedDiscount

%DiscountPriceMarkedDiscount

%1 DiscountPriceMarkedPriceSelling

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$

%1 discountMP

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

%1 discountMP

Discount•P.142 Q10. In shop A, the marked price of a

MD is $1920 and the selling price is $1248. In shop B, the prices are $1760 and $1320 respectively.

•A’s discount %

•B’s discount %

•So, B’s discount is smaller.

%35%1001920

672%100

1920

12481920

%25%1001760

440%100

1760

13201760

Simple Interest ( 單利息 , p.144)•Amount(A) = Principal(P) +

Interest(I)

•Interest(I) = Principal(P) Interest rate(r%)

Time(T)

•Formula: 100

%

TrPI

TrPI

1001

100Tr

PA

TrPPA

IPA

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 %

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 %

Simple Interest•P.151 Q14. Judy borrows $1000000 for 10

years. Bank A’s interest is 5% p.a. and B is 4.5% p.a.

•A’s interest

•B’s interest

•The difference is $50000.•She pays $50000 less in Bank B from in Bank A.

500000$10%51000000$

450000$10%5.41000000$

Good luck!!!

Ronald HUI