F.3 Maths .. Fast !!!Thank you

2013-04-24 12:30 am

Percentage :
1. If the yearly depreciation rate of a machine is 40% , its value after 2 years will decrease by ? % ?

2. Darwin would like to make an investment. A bank offers a plan with an interest rate of 6 % p.a. compounded half - yearly. If he would like to earn $4000 interest after 2 years , how much should he invest ?

3. Felix borrows $36 000 from a bank at the beginning if this month at an interest rate of 21 % p.a. compounded monthly . If he repays $12400 at the end of each month, can he settle the loan after 3 repayments ? If not , how much does he still owe the bank ?

Probability:
1. In an examination , there are 20 multiple choice questions, To prevent students from choosing an answer randomly , X marks will be deducted for each wrong answer, and 5 marks will be given for each right answer.Assume that each question has 5 choice .
(a) If all question in the exam are answered at random , what is the expected value of the marks of each question ?( express youe answer in terms of X )
(b) If all question in the exam are answered at randim , what is the expected value of the examination marks ? ( express your answer in terms of X )
(c) If the teacher expectx the students who have answered all question at random to get zero marks, find the value of X .

可5可以將所有steps 列出同解釋點解會咁計??Thank you so much !!!!!!!!!

回答 (1)

Kitty Fung

2013-04-24 1:04 am

✔ 最佳答案

Percentage
1. Let P be the original value of the machine.
The percentage decrease
[P-P(1-40%)^2]/Px100%
=P(1-0.36)/Px100%
=0.64x100%
=64%

2. Let $P be the amount that he should invest.
P(1+6%/2)^(2x2)-P=4000
P(1.03^4-1)=4000
P=4000/(1.03^4-1)
P=31900, cor. to 3 sig. fig.
Therefore, he should invest $31900.

3. After the first payment, the amount he owes the bank
=$[36000(1+21%/12)-12400]
=$24230
After the second payment, the amount he owes the bank
=$[24230(1+21%/12)-12400]
=$12254.025
After the third payment, the amount he owes the bank
=$[12254.025(1+21%/12)-12400]
=$68.5, cor. to 3 sig. fig.
Therefore, he cannot settle the loans in 3 payments and he still owes the bank $68.5.

Probability
1. (a) P(get a correct answer)=1/5
P(get a wrong answer)=4/5
The expected value of the marks=1/5x5-4/5X=1-4/5X
(b)The expected value of the examination marks=20(1-4/5X)=20-16X
(c) From the condition given, 20-16X=0
Therefore, X=1.25

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