f.3 maths問題 (20點!!!!!!!!)

2014-08-04 7:27 am
1.Given that x>5, represent the values of y by inequalities in following questions.
a)y=1/5 x b)y=7x-4
2.A company purchased 100 T-shirts. The original price of each T-shirt is $10. Later on, the company found that 10 of them are damaged. In order to make 50% profit at least, the company decided to sell the rest at a price of $y each. Find the minimum value of y and lowest price of each T-shirt.(Correct the answer to the nearest dollar)
3.If the principal is $20000 and the interest rate is 5% p.a., find the simple interest and the amount after two years.
4.If the principal is $30,000 and the interest rate is 6% p.a. compounded half-yearly, find the compound interest and the amount after three years. (Correct the answers to the nearest dollars.)
5.The value of a computer is $12000. If its depreciation rate is 10% each year, find its value after four years.
6.In a secondary school, 80 students joined the girl guides last year. This year the number of participants has increased by 12.5%. It is expected that there will be 10% less in next year. Find the expected numbers of participants.
7.The rateable value of a flat is $800,000. Find the rates payable quarterly.
8.The property tax payable by Mr. Chan this year is $7920. If the property tax rate is 15%, find the monthly rent.
9.The length of each side of a square is 20 cm. If it is increased by 10%, find the percentage change in its perimeter.
10.If the length of a rectangle is reduced by 20% and its width is increased by 15%, find the percentage change in its area.
11.The total monthly income of Derek's family is $45000.If he is entitled to $350000 allowance, find his salary tax.
12.The salary tax of Mosses this year is $7200.If he is entitled to $130000 allowance, find his total annual income.
13.Roy is going to make an investment. If he wants to have a minimum return of double his principal in five years, what should be the corresponding interest rate? Find out one possible interest rate and verify it.

回答 (5)

2014-08-07 9:39 pm
✔ 最佳答案
HI 頭幾條有人幫你答左 同埋太簡單SO唔特別解釋
第二條呢度

"首先你要知道最後賣哂d T-shirt最少要有幾多錢收到"
"Money = 100 x $10 x (1+50%) = 1500" 邏輯上正確 但唔好唔記得有10件已經賣左 所以呢度應該-番10件賣左的錢(1500-100)=$1400
然後就要知道而家有幾多件可以賣
Number of T-shirt = 100-10 = 90
--> Price per T-shirt = 1500/90 = 16.6666666.."
同佢一樣邏輯只不過我用一條色列出泥
2.(100x10x1.5)-(10x10)=90y
1400=90y
y=16
第三條SIMPLE INTEREST都是一樣
3.20000x(5%x2+1)
=$22000
到第4條COMPOUND INTEREST

"Amount = Principal x (1+interest rate)^(Number of period past)
要注意number of period past唔係 3 years
由於係半年收一次息, 而係3年入面可以收到6次息 (1年2次)
所以個次方係6
"--> Amount = 30000 x (1+6%)^6"錯的地方在這 題目說的interest rate 是6% 但系呢個6%是在說一年6% 結息的時間是HALF YEAR 如果1 year have 6%interest half year又有6%interest 銀行不就虧本 所以6%應該/2
= 42555.5734
= 42556 (Correct to the nearest dollar)
Interest = Amount - Principal
= 42555.5734 - 30000
= 12556 (Correct to the nearest dollar)"

正確答案
4.30000x(1+6%/2)^6
=$35822

interest:
35822-30000
=$5822
第五六條樓上的都解釋清楚了沒問題
5.12000x(1-10%)^4
=$7873.2

6.80x(1+12.5%)x(1-10%)
=80x1.125x0.9
=$81

第七條資料不足...
第8條Y就是一年中property 的rent
8. Yx0.8x15%=7920
Y=66000
Monthly=66000/12
=$5500

Percantage change formular=(New value-Old value/Old value) x100%

9.Percentage change: 題目問square perimeter 就是多了0.1的長度(20)x0.1+20 可寫成20x(1+0.1) 再x4 (New Value)-原本的20x4(Old Value)除 20x4(Old Value) x100%

(20x(1+0.1)x4-20x4/20x4)x100%
=10%

10.Percentage change:
我設L為Length W為width 方便理解 理論上最後兩個未知 可以化用common factor的原理化簡掉的
(Lx(1-0.2)xWx(1+0.15)-LW/LW)x100%
=(0.8Lx1.15W-LW/LW)x100%
=(LW(0.8x1.15-1)/LW)x100%
=(0.92-1)x100%
=-8%
十一條簡單不解釋 先計NET 再計tax
11.Net= $45000x12-350000
$190000($40000+$40000+$40000+70000)
Salary tax:
40000x2%+40000x7%+40000x12%+70000x17%
=$20300

12條剛剛相反他給了tax的資料要你找 salary 同樣先計Net 再加上Tax allow 就是salary 自己理解一下吧..
12.$7200=40000x2%+40000x7%+Xx12%
$7200=800+2800+0.12X
$3600=0.12X
X=$30000
Net income=30000+40000+40000
=$110000

Salary=$110000+130000
=$240000

13.2P=Px(1+X%)^5
2=(1+X%)^5
1.15=1+X%
X%=0.15
X=0.15%
參考: 讀完F3的學生
2014-08-04 10:49 am
1. 先將x變成主項
(a) y= 1/5 x
x= 5y
由於 x>5, 你就可以代 x=5y落去
5y>5
y>1

(b) Same as (a)

2. 首先你要知道最後賣哂d T-shirt最少要有幾多錢收到
Money = 100 x $10 x (1+50%) = 1500
然後就要知道而家有幾多件可以賣
Number of T-shirt = 100-10 = 90
--> Price per T-shirt = 1500/90 = 16.6666666..
correct to the nearest dollar --> y = 17

3. Simple Interest 計法
Principal x interest rate x number or years = Simple interest
--> 20000 x 5% x 2 = $2000
Amount = Principal + Simple Interest
--> = 20000+2000 = 22000

4. Compounding 就複雜d
Amount = Principal x (1+interest rate)^(Number of period past)
要注意number of period past唔係 3 years
由於係半年收一次息, 而係3年入面可以收到6次息 (1年2次)
所以個次方係6
--> Amount = 30000 x (1+6%)^6
= 42555.5734
= 42556 (Correct to the nearest dollar)
Interest = Amount - Principal
= 42555.5734 - 30000
= 12556 (Correct to the nearest dollar)

5. depreciation 其實同compound interest好相似
但depreciation 係減值
the value after 'n' years = Value now x (1-depreciation rate)^n
--> Value after 4 years = 12000 x (1-10%)^4 = 7873.2

6. simple logic
你可以先搵番 number of participants of THIS year
--> number = 80 x (1+12.5%) = 90
expected number = 90 x (1-10%)
= 81
參考: myself
2014-08-04 9:47 am
基本就是懶小孩不想做暑期作業然後把問題貼上來等答案了.
同學, 問功課不是這樣問的. 你先說說你有甚麼不明白, 哪裡不明白, 不明白到甚麼程度吧.
2014-08-04 9:08 am
1. Given that x>5,

a) y=1/5 x
x>5
1/5 *x>1/5 *5
y>1

b) y=7x-4
x>5
7x>7*5
7x-4>35-4
y>31
2014-08-04 8:48 am
我答最易的9,10
我之前學過,而且英文都算睇得明。
9. original square perimeter 20*4 =80 new side 20*1.1=22 new perimeter=88 %change=(88-80)/80*100%=10%
10. original rectangle area=ab new area of rectangle=a(0.8)b(1.15)=0.92ab %change= (0.92ab-ab)/ab*100%=-8%
如果答案有唔啱,請告訴我。數學not我專長。


收錄日期: 2021-04-20 15:13:57
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20140803000051KK00139

檢視 Wayback Machine 備份