
Linear Interpolation
Hi all,
For an interview I'm going next week I have to do a maths test, now I haven't done maths since school so I'm a little out of touch! I was quite good at maths in my time but have forgotten a lot of the principles. I was wondering if I could get some help with the following questions  I'd really appreciate it...
1. You can get a loan for $1000 over the next 35 days at an interest rate of 4.25%. You can also get a loan of $1000 over the next 56 days for 4.79%. Use linear interpolation to calculate the total amount in $s in interest you might expect to pay on a loan of $1000 over the next 47 days.
2. Provide reasoning that the equation
$\displaystyle
10 = exp(2x) + 2^x
$
has at least one solution in the range 0<x<5
Use the Newton Raphson technique to find an approximate solution to the equation.
3. This is a random question but its bothering me a lot!!
A group of students scored an averafe of 65% in an exam. The standard deviation of these results was 1%. A second group of students scored an average of 60% with a standard deviation of 2%. What is the mean and standard deviation of the two groups of students as a whole if 20 students were in each group?
I'd really appreciate any help  the maths part of my brain is a little rusty at the moment!

This section is based on known information, the DAYS
56  35 = 21
47  35 = 12
12 / 21 = 0.571428571
This section models the previous secion, but has a piece missing, the one interest rate.
4.79  4.25 = 0.54
X.xxx  4.25 = yyyy
yyyy / 0.54 = 0.571428571
Can you solve for yyyy?
Of course, you must also realize that yyyy is only the interest RATE. The question asks for $$$$.