# MUFY semester 1 mathematics trial examination 2012

MATHEMATICS PART A MUF0091

TRIAL EXAMINATION1/2012

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

13

ALL

145

Materials Permitted

Directions to Candidates

Candidates are to fill in the following

Examiner Use Only

Question

1

2

3

4

5

6

7

8

9

10

11

12

13

Total

Mark

/8

/6

/13

/13

/6

/12

/13

/15

/14

/15

/16

/9

/5

/145

MONASH UNIVERSITY FOUNDATION YEAR MATHEMATICS PART A

REFERENCE FORMULAS

CALCULUS

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.

MEASUREMENT

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

Question 1 [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.

Question 2[4 + 2 = 6 Marks]

Find the following, to the simplest form:

(a)

(b)

Question 3 [7 + 6 = 13 Marks]

(a) Find and hence evaluate the exact value of

(b) Find and hence evaluate the exact value of

Question 4[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

Question 5 [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.

Question 6[ 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.

(a) Find

(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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