Year 12 Mathematics B 2009 Term 1 Exam
Knowledge and Proceedures
Put your working and answers on the answer sheets provided
Question 1 (1,1,2 marks)
If f (x) = x+1 and g (x) = 3x -5
(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
(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)
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 ?