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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