2009 Exam 2 MM12 Exam s2

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YEAR 11 EXAM 2009

SUBJECT: MATHEMATICAL METHODS UNIT 2Exam 2 Technology

DATE: Monday 23rdNovember

READING TIME: 8:55am

9:05amWRITING TIME: 9:05am 10:35am

STRUCTURE OF BOOKLET

Section Number of

quest ions

Number of

quest ion s to be

answered

TOTAL

MARKS

1 Multiple Choice2 Extended Response Questions

155

155

1543

58

STUDENT NAME: ___________________________________________

TEACHER: M. Blanco / C. Lebnan / E. Patoulidis

DIRECTIONS TO STUDENTS

Students are permitted to bring into the examination room: pens, pencils, highlighters, erasers, sharpeners,rulers, a protractor, set-squares, aids for curve sketching, 5 A4 pages of bounded notes, one approvedCAS calculator and, if desired, one scientific calculator.

Students are NOT permitted to bring into the examination room: blank sheets of paper and/or white outliquid/tape.

Instructions Section 1Answer all questions in pencil on the answer sheet provided for multiple-choice questions.Choose the response that is correct for the question.A correct answer scores 1, an incorrect answer scores 0.Marks will not be deducted for incorrect answers.No marks will be given if more than one answer is completed for any question.

Instructions Section 2Answer all questions in the spaces provided.An exact answer is required to a question unless otherwise stated.In questions where more than one mark is available, appropriate working must be shown.Unless otherwise indicated, the diagrams in this book are not drawn to scale.

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SECTION 1 Multiple Choice

Question 1The solutions to are 0, -9 and 2. The values of aand bare:A B C D E

Question 2The graph ofis shown in the diagram.

x

y

-3 4

f(x)

The values of for which are:A and B and C and D and and E

Question 3Which of the following statements is false?

A The range of a cubic function is all real numbers.

B The domain of a cubic function is R.

C The range of all quartics is R.

D A quadratic function has a domain of real numbers.

E } where has a range }.

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Question 4

If { then

evaluates to:

A 4B -8C 0D -2E does not exist

Question 5

The graph has stationary points when xis:

A B C

D E 0

Question 6A particle moves in a straight line so that its position, xm, relative to Oat a time tseconds (t> 0), is

given by . The velocity and acceleration would have respective equations:A

and

B and

C and

D and

E and

Question 7

The expression can be simplified to:

A B 1 C D E

Question 8

When simplified

is equal to:

A

B C

D

E

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Question 9The inverse of is:

A B C D E.

Question 10The amplitude and period, of the trigonometric function graphed below are respectively:

x-5-4 -3-2 - 2 3 4 5

y

-2

-1

1

2

3

4

5

6

A 4 and 2

B 4 and 4

C 6 and 2

D 8 and 2

E 8 and 4

Question 11For which of the following equations has exactly one solution:A B C D E

Question 12The angle 255expressed in radians equals:

A

B

C

D

E

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Question 13

The number of 3-digit numbers greater than 500 that can be formed using the digits 2,6,1,5 and 3, ifeach digit can be used more than onceis:

A 125B 50C 15D 12E 60

Question 14A committee of five is to be chosen from a class of 12 girls and 10 boys. What is the probability thatit contains exactly 3 girls?

A.( )( )

( )

B. ( )( )( )

C.( )( )

D.( )( )

E. ( )( )

Question 15Michael is choosing his outfit for his first job interview. He has 3 suits in black, navy pinstripe andcharcoal grey, 4 ties and 8 shirts. Assuming no colours will clash, how many different choices doeshe have?

A 15!B 15

C 56

D 96

E 3!4!8!

END OF SECTION 1

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SECTION 2 Extended Response

Question 1Lisa the lifesaver is training for an endurance competition. Part of the training requires thecompetitors to start on the shoreline and sprint to cones situated on the sand, then she sprints backto the shoreline, dives in the water and swims to some buoys. The drill is completed when she hasswum back to the shoreline.

Lisas path is modelled by

where tis the time in seconds and

is the

distance from the shoreline in metres.

(a) Sketch the graph of this function showing the path of Lisas complete training drill, correct to onedecimal place.

t- 2 2 4 6 8 10 12 14

x

- 24

- 20

- 16

- 12

- 8

- 4

4

8

12

3 marks

(b) How far has Lisa run in the first one second?

1 mark

(c) How far is the cone from the shoreline, correct to one decimal place?

1 mark

(d) At what time(s), correct to 2 decimal places, is Lisa 5 metres from the shore line on the sand?

2 marks

(e) When does Lisa complete the sprinting stage of the drill?

1 mark(f) What distance, does Lisa swim in total, correct to the nearest metre?

1 mark

(g) Howlong does it take for Lisa to complete the total drill?

1 mark

Total 10 marks

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Question 2A plastic brick is made in the shape of a right triangularprism. The triangular end is an equilateral triangle withside length x cm and the length of the brick is ycm.

The volume of the brick is 1000 cm3.

(a) Show that the height (h) of the triangular end is

2 marks

(b) Hence show that .

2 marks

x cm

x cm

x cm

y cm

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(c) Using your answers in part (a)and (b),show that the total surface area, A of the brick isgiven by:

:

2 marks

(d) Find the exact value of x for which the brick has minimum total surface area. Verify thesolution.

4 marks

(e) Find the minimum total surface area correct to the nearest square centimetre.

1 mark

Total 11 marks

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Question 3A swim team of 6 students is to represent the school in the under 16s. They can be chosen from 12girls and 10 boys.

(a) How many different teams are possible without restriction?

1 mark

(b) How many different teams are possible if they must contain equal numbers of boys and girls?

1 mark

(c) How many different teams are possible if the teams contain all boys?

1 mark

(d) What is the exact probability that a team contains at least onegirl?

1 mark

(e) How many different teams are possible if they must have representation from each genderand contain more boys than girls?

2 marks(f) What is the exact probability of choosing a team with the constraints in (e)?

1 mark

Total 7 marks

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t100 200 300 400

s

5

10

15

20

25

Question 4The healing process of certain types of wounds is measured by the decrease in surface area thatthe wound occupies on the skin. A certain skin wound has its surface area modelled by the equation

where S square centimetres is the unhealed area t days after the skin receivedthe wound.

(a) What area did the wound originally cover?

1 mark(b) What area to two decimal places, did the wound cover after 2 days?

1 mark(c) Use logarithms to find how long will it take to the nearest day, before the wound area is

reduced to 10% of its original size?

3 marks

(d) Sketch the graph of the surface area of the wound over the first 400 days. Label asymptotesand the coordinates of any endpoints and axial intercepts to 1 decimal place.

2 marks(e) In theory will the skin wound ever heal? Explain.

1 mark

Total 8 marks

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Question 5The depth, metres, of water at the foot of a rocky outcrop near Port Campbell at hours aftermidnight on any particular day of a year is given by

(a) State the period and amplitude of this function.

2 marks

(b) Write down the maximum and minimum depths of the water.

2 marks

(c) Find the time interval for which metres for Give the extreme points ofthis interval correct to the nearest minute.

2 marks

(d)At what time(s) is the water level a maximum for ?

1 mark

Total 7 marks

End of Section 2

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ANSWER SHEET FOR MULTIPLE CHOICE SECTION OF EXAM2009 MATHEMATICAL METHODS UNIT 2

NAME: __________________________ TEACHER: _____________________

For each question, shade the box corresponding to your answer. You are advised to use pencil.

QUESTION 1 A B C D E





QUESTION 6

A B C D E


QUESTION 8

A B C D E






QUESTION 14

A B C D E


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2009 Exam 2 MM12 Exam s2