Anonymous
Anonymous asked in 科學及數學數學 · 6 years ago

# f.3 maths問題 (20點!!!!!!!!)

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.

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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%

Source(s): 讀完F3的學生
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• 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

Source(s): myself
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• 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.

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• 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

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