MATHEMATICS PART A
Question and Answer Booklet
Reading Time: 15 minutes
Writing Time: 2 hours
Structure of the Examination
Number of Questions
Questions to be answered
Total raw marks in Examination
Directions to Candidates
Candidates are to fill in the following
Examiner Use Only
MONASH UNIVERSITY FOUNDATION YEAR MATHEMATICS PART A
Each horizontal straight line is perpendicular to each vertical straight line
Otherwise, two straight lines are perpendicular to each other if the product of their slopes is –1.
Area of triangle
Area of circle
Area of trapezium
Curved surface area of a cylinder
Volume of rt. circular cylinder, height h
Volume of right circular cone, height h
Volume of sphere
Volume of right pyramid, base area A, height h
[5 + 3 = 8 Marks]
Consider the function
(a) Find the derivative of the function, to the simplest form.
(b) Hence, show that the graph of the function has no stationary points.
[4 + 2 = 6 Marks]
Find the following, to the simplest form:
[7 + 6 = 13 Marks]
(a) Find and hence evaluate the exact value of
(b) Find and hence evaluate the exact value of
[5 + 5 + 3 = 13 Marks]
(a) Given below is the graph of On the same axes, sketch the graph of .
(b) Given below is the graph of On the same axes, sketch the graph of
(c) Given below is the graph of On the same axes, sketch the graph of
[1 + 5 = 6 Marks]
Given above is the graph of
(a) Explain why c = 3.5.
(b) Calculate the exact values of a and b. Show complete working.
[ 2 + 3 + 2 + 5 = 12 Marks]
Consider the function
(a) Factorize the function completely.
(b) Hence, find the axial intercepts of the graph of
(c) Find the coordinates of the stationary points of the graph of using your graphic calculator. Give your answer correct to 1 decimal place.
(d) On the axes below, sketch the graph of Label all the important features. y
x Question 7
[2 + 4 + 3 + 4 = 13 Marks]
The number of bacteria present in a lasagne, t minutes after it was found contaminated, can be modelled by
At time t = 0, the number of bacteria is 300 and when t = 10 minutes, the number increased to 450.
(b) Find the value of k, correct to 2 decimal places.
(c) Find the rate of change in the number of the bacteria after for 1 hour.
(d) How long will it take for the number of bacteria to be 600? Give answer...
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