NAME: ________________________ CLASS: ___________________
Time Allowed: 2 hours
Instructions
1. This paper consists of 5 questions.
2. Answer ALL questions.
3. The use of a calculator is expected, where appropriate.
4. You are reminded of the need for clear presentation in your answer.
1. i) Show that 2
4๐2+8๐+3 can be expressed as ๐ด
2๐+1 +๐ต
2๐+3 , where A and B are
constants to be determined.
The sum โ2
4๐2+8๐+3
๐
๐=1 is denoted by Sn.
ii) Find an expression for Sn in terms of n.
iii) Find the smallest value of n for which Sn is within 10-3 of the sum to infinity.
2. a) The function f is defined by f : x โ 1
1โ๐ฅ2 , xโ R, x > 1.
i) Show that f has an inverse.
ii) Find f-1(x) and state the domain of f-1.
b) The function g is defined by g : xโ2+๐ฅ
1โ๐ฅ2 , x โ R, xโ ยฑ1. Find algebraically
the range of g, giving your answer in terms of โ3 as simply as possible.
3. i) Expand โ4 โ ๐ฅ in ascending powers of x up to and including the term in
x2. Also, find the range of values of x for which the expansion is valid.
ii) By choosing a suitable value of x, show that โ13 โ1847
512 .
4. Sheredine puts $20 on 1st January 2011 into a bank account which pays
compound interest at a rate of 1.25% per month on the last day of each month.
