mathematics stage 2c 2d calc free 2014

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Student Number: In gures

In words

Western Australian Certicate of Education

Examination, 2014

Question/Answer Booklet

Copyright School Curriculum and Standards Authority 2014

Place one of your candidate identication labels in this box.

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

*MAT2CD-S1*MAT2CD-S1

MATHEMATICS

2C/2DSection One:Calculator-free

Time allowed for this sectionReading time before commencing work: ve minutes

Working time for section: fty minutes

Materials required/recommended for this sectionTo be provided by the supervisor

This Question/Answer Booklet

Formula Sheet

To be provided by the candidate

Standard items: pens (blue/black preferred), pencils (including coloured), sharpener,correction uid/tape, eraser, ruler, highlighters

Special items: nil

Important note to candidatesNo other items may be taken into the examination room. It is yourresponsibility to ensure

that you do not have any unauthorised notes or other items of a non-personal nature in the

examination room. If you have any unauthorised material with you, hand it to the supervisor

beforereading any further.

Number of additionalanswer booklets used

(if applicable):

Ref: 14-078


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Instructions to candidates

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

Year 12 Information Handbook 2014. Sitting this examination implies that you agree toabide by these rules.

2. Write your answers in this Question/Answer Booklet.

3. You must be careful to conne your response to the specic question asked and to follow

any instructions that are specied to a particular question.

4. Spare pages are included at the end of this booklet. They can be used for planning your

responses and/or as additional space if required to continue an answer. Planning: If you use the spare pages for planning, indicate this clearly at the top of

the page. Continuing an answer: If you need to use the space to continue an answer, indicate inthe original answer space where the answer is continued, i.e. give the page number.Fill in the number of the question that you are continuing to answer at the top of thepage.

5. Show all your working clearly.Your working should be in sufcient 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 justication is

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

answer you do not wish to have marked.

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

7. The Formula Sheet is notto be handed in with your Question/Answer Booklet.

Structure of this paper

Section

Number of

questions

available

Number of

questions to

be answered

Working

time

(minutes)

Marks

available

Percentage

of exam

Section One:

Calculator-free 7 7 50 50 3313

Section Two:

Calculator-assumed13 13 100 100 6623

Total 100


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CALCULATOR-FREE 3 MATHEMATICS 2C/2D

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Section One: Calculator-free (50 Marks)

This section has seven (7)questions. Answer allquestions. Write your answers in the spaces

provided.

Spare pages are included at the end of this booklet. They can be used for planning your

responses and/or as additional space if required to continue an answer. Planning: If you use the spare pages for planning, indicate this clearly at the top of the page. Continuing an answer: If you need to use the space to continue an answer, indicate in the

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

number of the question that you are continuing to answer at the top of the page.

Working time: 50 minutes.

Question 1 (5 marks)

(a) In the following Venn diagram, shade the region A B . (1 mark)

(b) Write 4.08103as a numeral without using scientic notation. (1 mark)

(c) Determine the value of sin CAB. (1 mark)

A

CB

25

24

7

(d) The mean weight of a group of miniature horses is 62.8 kg. Another miniature horse

weighing 45 kg is brought into the stable. Will the mean weight increase, decrease or

remain the same? (1 mark)

(e) Factorise 4m2 1. (1 mark)


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(a) Solve the quadratic equationx2+ 8x+ 15 = 0. (3 marks)

(b) The integers below are arranged in ascending order and have a mean of 5.

2, 3, 3,x, 5,y, 9

Determine all the possible values forx

andy

. (4 marks)


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(c) Simplify 118 11

5. Express your answer with a positive power of 11. (2 marks)

(d) Givenf (x) =x3andg (x) =x

2xevaluatef (2) +g(2). (3 marks)


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A group of people were interviewed on their travel experiences. Set A refers to those who have

travelled to the United States of America and set E refers to those who have travelled to Europe.

The results of the interview are displayed in the Venn diagram below.

(a) Use the Venn diagram to complete the table below. (3 marks)

Have travelled to

Europe

Have not travelled to

EuropeTotal

Have travelled to

the United States

of America

Have not travelled

to the United

States of America

Total

(b) How many people in the group have travelled to both the United States of America and

Europe? (1 mark)


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(c) Determine the probability that a person chosen at random from those interviewed

(i) has travelled to Europe. (1 mark)

(ii) has travelled to the United States of America but has not travelled to Europe.

(1 mark)

(iii) has travelled to Europe, given that they have travelled to the United States of

America. (1 mark)


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The frequency table and histogram below show the heights, in centimetres, of 25 members of a

sports squad.

Height (hcm) Frequency

140 < h 150 3

150 < h 160 7

160 < h 170 10

170 < h 180 4

180 < h 190 1

Total 25

On the day the heights were recorded, ve squad members were absent. Their heights were

130 cm, 148 cm, 149 cm, 156 cm and 162 cm.

(a) Complete the amended frequency table below. (3 marks)

Height (cm) Frequency

140 < h 150150 < h 160

160 < h 170

170 < h 180

180 < h 190

Total


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(b) Using the original histogram below, make any amendments required by including the

heights of the additional ve squad members. (2 marks)

(c) Compare the spread of the amended data set with that of the original data set. (2 marks)

(d) Which of the additional heights would have the most signicant effect on the mean?

Explain. (2 marks)


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The diagram below shows the graphs of four functions, A, B, C and D.


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(a) Complete the table to match each graph with its function. (4 marks)

Function Graph

y = 0.2 3x

y = 4.578 + 1.8x 0.2x

3

y = 0.2 + 5.23.x 1.16

.x

2

y = 0.5 1.5x

(b) Use the diagram to estimate all solutions to the simultaneous equationsy = 0.2 3xand

y = 0.2 + 5.23.x 1.16

.x

2. (2 marks)

(c) Use the diagram to estimate all solutions to the equation 4.578 + 1.8x 0.2x3= 2.5.

Express your answer(s) correct to one decimal place. (2 marks)


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The quadratic function with equationy= (x+ 3)(x 1)is represented by one of the parabolas inthe graph below. The other two parabolas also represent quadratic functions.

(a) Which of the three parabolas representsy= (x+ 3)(x 1)? Justify your choice. (2 marks)


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(b) Graph the quadratic functiony= 2(x+ 2)2 4on the diagram below. (3 marks)


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The diagram below shows the position of three pointsA(3, 3),B(7, 0) and C(0,1).

(a) Determine the gradient ofAB. (1 mark)

(b) Given that the gradient ofACis4

3, determine the size of BAC. (1 mark)


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(c) Determine the equation of the lineAC. (2 marks)

End of questions


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Additional working space

Question number:


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Question number:


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Question number:


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303 Sevenoaks Street

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done only within the terms of the Copyright Act 1968or with permission of the copyright owners.

Any content in this document that has been derived from the Australian Curriculum may be used under the terms of the Creative

Commons Attribution-NonCommercial 3.0 Australia licence.

mathematics stage 2c 2d calc free 2014

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