F3 Maths Problems

2014-12-24 11:06 pm

1) Bank A offers an interest rate of 3% p.a. compounded monthly while Bank B offers a simple interest rate of r% p.a. $P is deposited to both banks for 1 year.
(a) Show that the interest esarned form Bank A is $((401/400)^12-1)P.

(b)It is given that the interests eanrned from both bamks are the same.
(1)Find, correct to 3 d.p., the value of r.
(2)Are the interests earned from both banks still the same if $P is deposited fro 2 years?Explain your answer.

2)S3X Class was aked how many times they visited museum last year. The mean of the number of visits is 2.6 and the results are shown in the table below:
Number of visits:1,2,3,4
Number of people:7,10,8,n
(a) Find n
(b) Write down the median number of visits.
(c) Write down the mode(s) number of visits.
(d) If another class S3Y of 40 students was asked the same question and the overall mean number of visits for two classes was 2.48, find the mean number of visits for S3Y.

Need Steps, plz!

回答 (1)

YTC

2014-12-27 11:55 pm

✔ 最佳答案

1a) interest earned from Bank A
=$P[1+(3%/12)]^(12)-P
=$P[(401/400)^(12)-1]

b1)$P[(401/400)^(12)-1]=$P(r%)(1)
[(401/400)^(12)-1]=r/100
r=3.042

2)for 2 years,
Interest earned from Bank A
=$P[1+(3%/12)]^(2x12)-P
=$0.0618P
Interest earned from Bank B
=$P(3.042%)(2)
=$0.0608P
≠$0.0618P
∴No, they are not the same.

2a)[1(7)+2(10)+3(8)+4n]/(7+10+8+n)=2.6
51+4n=65+2.6n
1.4n=14
n=10

b)total students in S3X
=7+10+8+10
=35
∴median
=the 18th term
=3

c)modes=2,4

d)Let the mean number of visits for S3Y=y
[2.6(35)+40y]/(35+40)=2.48
91+40y=186
40y=95
y=2.375
∴the mean number of visits for S3Y=2.375

參考: YTC

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