AT course eaination uestionnser booet

2020/59025

ATAR course examination, 2020

Question/Answer booklet

MATHEMATICS

SPECIALIST

Place one of your candidate identification labels in this box.

Ensure the label is straight and within the lines of this box.

Section Two:

Calculator-assumed

WA student number:

In figures

In words

Time allowed for this section

Reading time before commencing work:

Working time:

ten minutes

one hundred minutes

Number of additional

answer booklets used

(if applicable):

Materials required/recommended for this section

To be provided by the supervisor

This Question/Answer booklet

Formula sheet (retained from Section One)

To be provided by the candidate

Standard items: pens (blue/black preferred), pencils (including coloured), sharpener,

correction fluid/tape, eraser, ruler, highlighters

Special items:

drawing instruments, templates, notes on two unfolded sheets of A4 paper,

and up to three calculators, which can include scientific, graphic and

Computer Algebra System (CAS) calculators, are permitted in this ATAR

course examination

Important note to candidates

No other items may be taken into the examination room. It is your responsibility to ensure that

you do not have any unauthorised material. If you have any unauthorised material with you, hand

it to the supervisor before reading any further.

Copyright ? School Curriculum and Standards Authority 2020

Ref: 20-053

*MAS-S2*

MAS-S2

MATHEMATICS SPECIALIST

2

CALCULATOR-ASSUMED

Number of

questions

available

Number of

questions to

be answered

Working

time

(minutes)

Marks

available

Percentage

of

examination

Section One:

Calculator-free

8

8

50

49

35

Section Two:

Calculator-assumed

13

13

100

86

65

Total

100

Section

Instructions to candidates

1.

The rules for the conduct of the Western Australian external examinations are detailed in

the Year 12 Information Handbook 2020: Part II Examinations. Sitting this examination

implies that you agree to abide by these rules.

2.

Write your answers in this Question/Answer booklet preferably using a blue/black pen.

Do not use erasable or gel pens.

3.

You must be careful to confine your answers to the specific questions asked and to follow

any instructions that are specific to a particular question.

4.

Show all your working clearly. Your working should be in sufficient detail to allow your

answers to be checked readily and for marks to be awarded for reasoning. Incorrect

answers given without supporting reasoning cannot be allocated any marks. For any

question or part question worth more than two marks, valid working or justification is

required to receive full marks. If you repeat any question, ensure that you cancel the

answer you do not wish to have marked.

5.

It is recommended that you do not use pencil, except in diagrams.

6.

Supplementary pages for planning/continuing your answers to questions are provided at

the end of this Question/Answer booklet. If you use these pages to continue an answer,

indicate at the original answer where the answer is continued, i.e. give the page number.

7.

The Formula sheet is not to be handed in with your Question/Answer booklet.

See next page

DO NOT WRITE IN THIS AREA AS IT WILL BE CUT OFF

Structure of this paper

CALCULATOR-ASSUMED

3

MATHEMATICS SPECIALIST

Section Two: Calculator-assumed

65% (86 Marks)

This section has 13 questions. Answer all questions. Write your answers in the spaces provided.

Supplementary pages for planning/continuing your answers to questions are provided at the end

of this Question/Answer booklet. If you use these pages to continue an answer, indicate at the

original answer where the answer is continued, i.e. give the page number.

Working time: 100 minutes.

Question 9

(4 marks)

y

DO NOT WRITE IN THIS AREA AS IT WILL BE CUT OFF

The shape of a small wine glass is modelled by revolving the curve sin

? = x ¨C 3 about the

y axis, where 0 ¡Ü y ¡Ü 6. All dimensions are in centimetres.

y

6

4

2

¨C5

5

x

Calculate, correct to the nearest 0.01 cm, the depth of wine in the glass if it is to contain 80% of

its maximum volume.

See next page

MATHEMATICS SPECIALIST

4

Question 10

(a)

CALCULATOR-ASSUMED

(7 marks)

The sketch of the locus of a complex number z has been shown below. Write equations

or inequalities in terms of z (without using x = Re(z) or y = Im(z)) for the indicated locus.

(4 marks)

Im

5

4

3

1

¨C1

1

2

3

4

Re

¨C1

¨C2

(b)

Sketch the locus of the equation |z + 2| = |z ¨C i| + ¡Ì 5 in the Argand diagram below.

(3 marks)

Im

4

3

2

1

¨C3

¨C2

¨C1

¨C1

1

2

3

Re

¨C2

¨C3

See next page

DO NOT WRITE IN THIS AREA AS IT WILL BE CUT OFF

2

CALCULATOR-ASSUMED

5

Question 11

MATHEMATICS SPECIALIST

(5 marks)

Let z, w and u be complex numbers where:

w = (1 + i) z

u=

Arg (w) =

?

3

|w| = 2

z

2 ¨C 2i

DO NOT WRITE IN THIS AREA AS IT WILL BE CUT OFF

(a)

Determine Arg (u) exactly.

(3 marks)

(b)

Determine |u| exactly.

(2 marks)

See next page

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