F.2 Math急急！！！！

1. Consider the sequence 2,4,6,8,...
The pattern for this sequence is 2n, so the nth term of the original sequence is 1/(2n).
OR T(n) = 1/(2n)
2. 144 < 153 < 169
So, √(144) < √(153) < √(169)
OR 12 < √(153) < 13
Answer: a = 12, b = 13
3. Let $A be the price of an apple,
and $B be the price of an orange
4A+3B = 22 ---(1)
2A+5B = 25 ---(2)
(2)*2-(1): 10B-3B = 50-22
7B = 28
B = 4
sub B = 4 into (2)
2A+5(4) = 25
2A = 5
A = 2.5
So, the price of an apple = $2.5 and the price of an orange = $4.
4. Let hcm be the depth/height of the jar
volume of cylinder jar = π*(r^2)*h = 1000cm^3
π(4.5)^2*h = 1000
h = 1000/[π(4.5)^2]
h = 15.719
h = 16 (correct to 2 sig. fig.)
So the depth of the jar is 16cm.

Q1: Consider the squence 1/2,1/4,1/6,1/8........, the nth term of the sequnce is ?

see the denominator of all the term
1st term is 2 , 2nd term is 4 , 3rd term is 6 .....
so the n th term of the sequence is 1/2n


Q2: If a<√153< b, where a and b are two consecutive integers , find the values of a and b.

√153 = √(9*17) = 3√17
Because √17 bigger than 4 and smaller than 4.2
so 3*4 < √153 <3*4.2
for a and b are two CONSECUTIVE integers
ans: 12 < √153 < 13


Q3: Mrs Lee buys 4 apples and 3 oranges at $22 . Mrs Chan buys 2 apples and 5 oranges at $25. Find the price of an apple and the price of an orange.

Let x be apple and y be orange
4x+3y = 22 --------[1]
2x+5y = 25 --------[2]

[2] - [1],
-2x+2y= 3
y=1.5+x -------[3]

Put [3] into [1]
4x+3(1.5+x) =22
7x =17.5
x =2.5

Put x =2.5 into [3]
y = 4

The price of an apple is $2.5 and the price of an orange is $4


Q4 1L of orange juice is poured into a cylindrical jar of radius 4.5 cm and no orange juice spilt out .Find the depth of the orange juice in the jar correct to 2 significant figures.

The depth of the orange juice in the jar = Volume of jar / the area of the base
=1000 / (4.5*4.5*丌)
=16 cm ( corr. to 2 sig. fig. )

Hope that i can help you!

2009-01-28 18:45:30 補充：
Q2

a =12
b=13

1.because 1/(2+2) = 1/4, 1/(4+2)=1/6......
therefore, nth term = 1/(n+2)

2.because &radic;153=12.369(correct to 3 decimal places)
And a and b must be consecutive integers.
Therefore, &radic;153 (12) must be between 11 and 13.
So a=11, b=13

3.tips
4a+3o=22
2a+5o=25
(I don&#039;t know)

4.(I don&#039;t know ) because F.2 not yet learn

2009-01-28 17:39:08 補充：
hey upstairs!
I haven't learn such things yet! but i am f.2 !!!