# random stuff to get me in

## random stuff to get me in

﻿TSS
Year 12 Mathematics B 2009 Term 1 Exam

Knowledge and Proceedures

Question 1 (1,1,2 marks)

If f (x) = x+1 and g (x) = 3x -5

Find

(a) f (3)

(b) g [f (3) ]

( c) f [g (x) ]

Question 2 (1,1,2,2,2 marks)

Differentiate giving answers as positive indices.
(i) y = x- x+7
(ii) y =

(iii) y = (3x - 2)

(iv) y =

(v) y =

Question 3 (2,5,3,1 marks)

A function is defined by f (x) = 2x(3 – x )

Use pen and paper methods to find:

(a) x and y intercepts

(b) Coordinates of stationary points and their nature.

(c) Hence sketch the curve over the domain -1 x 4.

(d) What is the minimum value of f (x) for this domain?

Question 4 (1,1 marks)

(i) Find the rate of change of the volume

V = r, of a deflating spherical balloon, with respect to radius, r.

(ii) Find this rate when r = 5cm.

Question 5 (1,2 marks)

Simplify without using calculators

(i)

(ii) 3 log 6 – 3 log 18

Question 6 (2,2,4 marks)

Solve giving answers to three decimal places.

(a) log (3x – 4) = 5

(b) 3x 9 = 729

(c ) e + 3e-10 = 0

Question 7 (2,1,1marks)

The area of an oil spill N m after t days fit an exponential model in the
form N=At.The following measurements were taken after t days of observation.(where A and n are constants)

t
2
4
5
N
50.99
485.13
1002

Model this equation on your graphics calculator as N=At

(i) Give the values of A and n

(ii) Comment on how well your model fits.

(iii) What will be the area of the slick after 14 days ?

(v) What...