Mathematics Stage 2A 2B Calc Free 2013

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Western Australian Certificate of EducationExamination, 2013

Question/Answer Booklet

Copyright School Curriculum and Standards Authority 2013

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: 13-080

CALCULATOR-FREEMATHEMATICS 2A/2B 2

See next page See next page

Instructions to candidates

1. The rules for the conduct of Western Australian external examinations are detailed in the Year 12 Information Handbook 2013. 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 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 33

13

Section Two:Calculator-assumed 13 13 100 100 66

23

Total 100

CALCULATOR-FREE 3 MATHEMATICS 2A/2B


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(s) that you are continuing to answer at the top of the page.

Working time: 50 minutes.

Question 1 (12 marks)

(a) Evaluate:

(i) 38 of $160 (1 mark)

(ii) 12 0.2 (1 mark)

(iii) 90% of 35 kg. (2 marks)

(b) Factorise 15 5a. (1 mark)



Question 1 (continued)

(c) Simplify 8 2a + 5b 3 + 6a. (2 marks)

(d) Expand and simplify (3x 2)(2x + 5). (2 marks)

(e) Given Tn+1 = 2Tn 3 and T1 = 4, determine T3. (2 marks)

(f) Write 0.000 000 541 in scientific notation. (1 mark)




(a) Xavier buys shares worth $1200. He sells them for $1500.

(i) What is his profit? (1 mark)

(ii) Express the profit as a percentage of the cost of the shares. (2 marks)

(b) Monique buys 12

kg of bananas at her local shop for $3.60. Her grandfather buys 34

kg of

bananas from a different shop for $5.50.

Use calculations to show who has the better buy. (3 marks)




Students from around Australia took part in the annual CensusAtSchool Australia survey in 2012. They were asked to rate the importance of various issues, giving a value of importance from 0 to 1000. A rating of 0 indicates not very important, and 1000 indicates very important. The table below shows a summary of their responses, where the median result was calculated and recorded.

Table 1: Level of importance of social and environmental issues by State/Territory (median)

Issue ACT NSW NT QLD SA Tas Vic WA

Reducing pollution 755.0 722.0 568.0 632.5 634.0 563.0 687.0 716.0

Recycling our rubbish 769.0 701.0 604.0 598.0 622.0 545.0 671.0 657.0

Conserving water 783.0 722.0 568.0 657.0 687.0 554.0 722.0 769.0

Reducing energy usage (electricity, gas, oil, for heating, lighting, car travel) 657.0 651.0 557.0 580.0 568.0 527.0 616.0 622.0

Conserving old growth forests 635.0 551.0 503.5 539.0 521.0 515.0 539.0 551.0

Protecting coastal/marine environments 755.0 699.0 642.0 683.0 616.0 598.0 669.0 699.0

Having healthy eating habits 843.0 811.0 769.0 764.0 722.0 685.0 785.0 767.0

Reducing bullying in schools 916.0 965.0 793.0 844.0 846.0 823.0 917.0 833.0

Owning a computer 651.0 604.0 554.0 640.0 622.0 598.0 557.0 545.0

Access to the Internet 761.0 767.0 726.5 775.0 722.0 764.0 704.0 685.0

Based on the information in the table above, answer the following questions.

(a) Write true or false below each statement.

(i) Reducing pollution was rated more important to students in South Australia (SA) than those in Tasmania (Tas). (1 mark)

(ii) Conserving water was rated the most important social issue for Western Australian (WA) students. (1 mark)

(b) For which State/Territory was Conserving old growth forests not rated the least important social issue? (1 mark)

(c) In which State/Territory was Conserving water rated higher than in Western Australia? (1 mark)

(d) Which issue was rated as the most important by the students surveyed? (1 mark)

(e) Why would the median have been used in displaying these data instead of the mean? (1 mark)




Three of the relationships below represent exponential functions.

Circle the letters that represent the three exponential functions.

A

x 1 0 1 2y 8 3 2 7

B

2x + 3y = 12

C

y = 24 1.5x

D

5

4

3

2

1

3 2 1 1 2 3

y

x

1

2

E

3 2 1 1 2 3 4 5

4

3

2

1

1

2

3

4

x

yF

x 0 1 2 3y 2 4 8 16




(a) State the y-intercept of line A. (1 mark)

(b) Determine the gradient of line A. (1 mark)

(c) Line B passes through the points (2, 5) and (8, 0). What is the equation of line B? (2 marks)



(d) Sketch the line: y = 3x 1 on the graph opposite. Label it line C. (2 marks)

(e) Does the point (15, 34) lie on line C? Justify your answer. (2 marks)

(f) Show use of the graph in part (d) to solve 3x 1 = 7 and state your solution. (2 marks)


See next page See next pageEnd of questions


(a) Solve algebraically:

(i) x2 1 = 48 (2 marks)

(ii) 2x 1 5. (2 marks)

(b) Solve algebraically the simultaneous equations 2x + y = 11 and y = 3x 9. (3 marks)


See next page See next pageEnd of questions


In a game of soccer the match could result in a win (W), a loss (L), or a draw (D). A win is worth three points, a draw one point and a loss no points. Each team aims to achieve as many points as possible by the end of the soccer season.

(a) For the Ashton soccer team, the probability of winning a match is 13

and the probability of

losing is 16 . What is the probability of a draw? (1 mark)

(b) The Cardup soccer team has played its first three games. A list of all sets of possible results for each of these three games is shown below.

WWW WWL WWD WDW WWD WDL WLW WLD WLLDWW DWL DWD DDW DDD DDL DLW DLD DLLLWW LWD LWL LDW LDD LDL LLW LLD LLL

(i) Determine the probability that the Cardup soccer team won all three games. (1 mark)

(ii) Determine the probability that the Cardup soccer team lost only one of the three games. (1 mark)

(iii) Determine the probability that the Cardup soccer team is on eight points after three games. (1 mark)

(iv) Determine the probability that the Cardup soccer team is on three points after three games. (2 marks)



Additional working space

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Published by the School Curriculum and Standards Authority of Western Australia27 Walters Drive

OSBORNE PARK WA 6017

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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.

ACKNOWLEDGEMENTS

Section One Question 3 Australian Bureau of Statistics. (2012). Level of importance of social

and environmental issues [Table]. Retrieved January 27, 2013, from www.abs.gov.au/websitedbs/CaSHome.nsf/Home/2012+CensusAtSchool+Summary+Data. Used under the Creative Commons Attribution 2.5 Australia licence.

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Mathematics Stage 2A 2B Calc Free 2013