mathematics stage 2a 2b calc free 2014

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Western Australian Certificate of EducationExamination, 2014

Question/Answer Booklet

Copyright © School Curriculum and Standards Authority 2014

MATHEMATICS 2A/2BSection One: Calculator-free

Time allowed for this sectionReading time before commencing work: five minutesWorking time for section: fifty minutes

Materials required/recommended for this sectionTo be provided by the supervisorThis Question/Answer BookletFormula Sheet

To be provided by the candidateStandard items: pens (blue/black preferred), pencils (including coloured), sharpener, correction fluid/tape, eraser, ruler, highlighters

Special items: nil

Important note to candidatesNo other items may be taken into the examination room. It is your responsibility 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 before reading any further.

Number of additional answer booklets used(if applicable):

Ref: 14-075

CALCULATOR-FREEMATHEMATICS 2A/2B 2

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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 to abide by these rules.

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

3. You must be careful to confine your response to the specific question asked and to follow any instructions that are specified 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 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.

5. 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.

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

7. The Formula Sheet is not to be handed in with your Question/Answer Booklet.

Structure of this paper

SectionNumber of questions available

Number of questions to be answered

Working time

(minutes)

Marks available

Percentage of exam

Section One: Calculator-free 7 7 50 50 331⁄3

Section Two:Calculator-assumed 13 13 100 100 662⁄3

Total 100

CALCULATOR-FREE 3 MATHEMATICS 2A/2B

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Section One: Calculator-free (50 Marks)

This section has seven (7) questions. Answer all questions. 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 (6 marks)

(a) Evaluate:

(i) 0.6 – 0.23 (1 mark)

(ii) 36 ÷ 32 × 4. (2 marks)

(b) Write 12 350.65 in scientific notation. (1 mark)

(c) Simplify the ratio 12 cm : 2.4 m. (2 marks)


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Isabella downloads data onto her smart phone and has kept a record of her daily data usage over the month of January.

Data usage in megabytes (MB)

Monday Tuesday Wednesday Thursday Friday Saturday SundayJanuary

1–7 10 38 42 40 45 50 50

January 8–14 8 39 43 42 46 51 54

January 15–21 11 29 40 35 46 55 60

January 22–28 12 38 42 50 47 60 65

January 29–31 13 41 47

The graph below shows her daily data usage.

(a) How much data did Isabella use on Thursday, 18th January? (1 mark)


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(b) Describe the overall trend in Isabella’s data usage over the month of January. (1 mark)

(c) Isabella wants to predict the amount of data she will use on the last Monday of February, which is her birthday. She notices that on Mondays she always seems to use less data.

Even if she takes this into account, explain the problem with predicting for the end of the following month. (1 mark)

Kate also downloads data on her phone. During February, she uses a lot of data in the first half of the month and then cuts back on her usage.

(d) Sketch Kate’s total data usage over February on the graph below. Exact points are not required. (2 marks)


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(a) Consider the pattern of shapes below.

(i) Draw the next shape of the pattern in the space above. (1 mark)

(ii) Describe how to obtain each shape from the previous one in the pattern. (3 marks)

(b) Consider the line y = –x and the object drawn on the coordinate plane below.

Draw the image of the object reflected in the line y = –x. (2 marks)


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(a) The following shows two exponential graphs, A and B.

The graphs have equations y = 2x and y = 3x.

Complete the table below by matching the correct graph from above with each equation. (1 mark)

Equation Graphy = 2x

y = 3x

(b) Use the graph(s) to determine the solution to the equation 3x = 15 correct to one decimal place. (1 mark)

(c) On the same set of axes above, sketch the graph of y = 4x. (3 marks)


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(a) The table below, produced by the Australian Bureau of Statistics, shows results compiled from surveys of children’s participation in cultural and leisure activities.

Children participating in selected activities, by sex (2003–2012)

Participation rate (%)Males 2003 2006 2009 2012

Watching TV, videos or DVDs 98.6 97.6 97.0 96.0Reading 67.7 68.8 64.6 65.1Bike riding 70.5 73.4 66.1 69.9Playing a musical instrument 13.2 17.6 18.7 16.0Singing 2.3 2.9 3.1 2.5Drama 2.3 2.8 2.8 3.5Accessing the internet 62.4 65.3 80.0 89.4

Females 2003 2006 2009 2012Watching TV, videos or DVDs 97.9 97.3 97.7 95.6Reading 82.3 80.4 80.2 77.4Bike riding 53.3 61.9 54.4 56.8Playing a musical instrument 20.7 21.6 20.7 19.3Singing 7.0 8.3 9.2 7.9Drama 6.3 6.2 6.6 5.9Accessing the internet 65.6 64.6 78.9 90.0

Use the information in the table to answer the following questions.

(i) Write true or false next to each statement. (2 marks)

● A greater percentage of females participate in Singing and Drama than males.

● There is an increasing trend in Reading participation rates over time among females.

(ii) For which activity did males consistently have a higher participation rate than females? (1 mark)

(iii) Which activity had the greatest increase in participation rates from 2003 to 2012? (1 mark)


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(b) A number of people were surveyed about their favourite sport. The results are shown in the pie chart below.

Favourite sport

Use the information in the pie chart to answer the following questions.

(i) What percentage of people chose basketball as their favourite sport? (1 mark)

(ii) Which two sports combined were preferred by half of the people surveyed? (1 mark)

(iii) If 300 people were surveyed, determine the number of people who chose tennis as their favourite sport. (2 marks)


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(a) Simplify:

3p × 5 + 10p. (1 mark)

(b) Expand and simplify:

(2y + 7)(1 + 3y). (2 marks)

(c) Solve algebraically:

(i) x4

= –2 (1 mark)

(ii) 3x + 2 ≥ 23 (2 marks)

(iii) 2m3 – 16 = 0. (2 marks)


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(d) Solve algebraically the simultaneous equations 3x – y = 5 and 2x + y = 10. (3 marks)


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A shop introduced a rewards program to encourage customers to come back again. Customers were given the opportunity to win a prize each time they made a purchase by spinning a wheel as shown below.

(a) Jemima purchased an item in the store for $24 and spun the wheel. Which of the four prizes would save her the most money? Show your workings. (2 marks)

(b) Lloyd purchased an item for $120. Which of the four prizes would save him the most money?

(1 mark)

(c) What is the probability that a customer spun ‘Bad luck – try again’? Express your answer as a simplified fraction. (1 mark)


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(d) Simon purchased items at the store each day for five days. Every time he spun ‘Bad luck – try again’.

(i) Comment on the validity of the following statement.

‘For his next spin Simon will definitely spin a ‘Bad luck – try again’.’ (1 mark)

(ii) For the next 12 spins, how many times would you expect Simon to spin ‘Bad luck – try again’? (1 mark)

(e) Jaye decided to analyse the spins for a number of customers at this store. He obtained the following results.

Prize Frequency

$5 off your purchase 19

Save 8c for each dollar spent 18

5% off your purchase 22

Save 18 of your purchase 15

Bad luck – try again

Which of the following would Jaye most reasonably expect for the frequency of ‘Bad luck – try again’? Circle the expected frequency from the list below. (1 mark)

20, 40, 60, 80

(f) The spins could also be randomly generated by a computer. Describe clearly one other method you could use to simulate the spins of the wheel in this situation. (2 marks)

End of questions


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Additional working space

Question number:

ACKNOWLEDGEMENTS

Section One

Question 5 (a) Data source: Australian Bureau of Statistics. (2012, December 21). Children’s participation in sport and leisure time activities 2003–2012. Retrieved January 24, 2014 from www.ausstats.abs.gov.au/Ausstats/subscriber.nsf/0/ABA491F2AC01415FCA257ADA000E3EAA/$File/4901055001_2003%20-%202012.pdf

This document—apart from any third party copyright material contained in it—may be freely copied, or communicated on an intranet, for non-commercial purposes in educational institutions, provided that the School Curriculum and Standards Authority is acknowledged as the copyright owner, and that the Authority’s moral rights are not infringed.

Copying or communication for any other purpose can be done only within the terms of the Copyright Act 1968 or with prior written permission of the School Curriculum and Standards Authority. Copying or communication of any third party copyright material can be done only within the terms of the Copyright Act 1968 or 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.

Published by the School Curriculum and Standards Authority of Western Australia303 Sevenoaks Street

CANNINGTON WA 6107

ACKNOWLEDGEMENTS

Section One

Question 5 (a) Data source: Australian Bureau of Statistics. (2012, December 21). Children’s participation in sport and leisure time activities 2003–2012. Retrieved January 24, 2014 from www.ausstats.abs.gov.au/Ausstats/subscriber.nsf/0/ABA491F2AC01415FCA257ADA000E3EAA/$File/4901055001_2003%20-%202012.pdf

This document—apart from any third party copyright material contained in it—may be freely copied, or communicated on an intranet, for non-commercial purposes in educational institutions, provided that the School Curriculum and Standards Authority is acknowledged as the copyright owner, and that the Authority’s moral rights are not infringed.

Copying or communication for any other purpose can be done only within the terms of the Copyright Act 1968 or with prior written permission of the School Curriculum and Standards Authority. Copying or communication of any third party copyright material can be done only within the terms of the Copyright Act 1968 or 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.

Published by the School Curriculum and Standards Authority of Western Australia303 Sevenoaks Street

CANNINGTON WA 6107

mathematics stage 2a 2b calc free 2014

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