Mathematics Stage 2C 2D Calc Free 2012

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Western Australian Certificate of EducationExamination, 2012

Question/Answer Booklet

Copyright School Curriculum and Standards Authority 2012

*MAT2CD-S1*MAT2CD-S1

MATHEMATICS 2C/2DSection 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 tape/fluid, 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: 12-089

CALCULATOR-FREEMATHEMATICS 2C/2D 2

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Section

Section One:Calculator-free

Section Two:Calculator-assumed

Number of questions available

6

12

Number of questions to be answered

6

12

Working time

(minutes)

50

100

Total

Marks available

50

100

150

Percentage of total exam

3313

6623

100

Instructions to candidates

1. The rules for the conduct of Western Australian external examinations are detailed in the Year 12 Information Handbook 2012. Sitting this examination implies that you agree to abide by these rules.

2. Write your answers in the spaces provided in this Question/Answer Booklet. 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.

3. 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 an answer to any question, ensure that you cancel the answer you do not wish to have marked.

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

5. The Formula Sheet is not handed in with your Question/Answer Booklet.

Structure of this paper

CALCULATOR-FREE 3 MATHEMATICS 2C/2D

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Section One: Calculator-free (50 Marks)

This section has six (6) 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 (9 marks)

(a) On the Venn diagram below, shade the region given by B. (1 mark)

A B

(b) Determine the gradient of the line 3x + 4y = 2. (1 mark)

(c) Determine the y-intercept of the line 2y = x 4. (1 mark)


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Question 1 (continued)

(d) The graphs below show the test results for two different science classes.

Class A Class B

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6 7 8 9 10 Test scores

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Which science class has the smaller mean? (1 mark)

(e) The graphs below show the test results for two different mathematics classes.

Class A Class B

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y


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Which mathematics class has the larger standard deviation? (1 mark)

(f) For the recursive rule Tn+1 = Tn 4 with T3 = 15, determine T1. (1 mark)


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(g) Simplify 56

5-2. Give the answer as a power of 5. (1 mark)

(h) Determine the number of significant figures in the number 820. (1 mark)

(i) Determine the value of tan BAC in the following triangle. (1 mark)

A

BC

6

8

10


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(a) Solve 2(x 4)(2x + 3) = 0. (2 marks)

(b) Five integers satisfy the following description: they have a median of 7, the mode is 5, the range is 15 and the mean is 9. Write the five integers below in order from smallest to largest. (2 marks)

(c) The two graphs shown are for the functions y = 2x and y = 3x. The point (2, q) belongs to one of these functions. Decide which function the given point belongs to and hence determine the value of q. (2 marks)

y

x

(2, q)

(d) Estimate the solution to the equation 2x = 80. Give the answer to the nearest integer.(2 marks)


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(e) Sketch the function y = x 1 on the given axes. (2 marks)

y

x

(f) Determine the value of 232 172. (2 marks)

(g) Describe in words how the graph of y = x2 can be transformed to the graph of y = (x + 4)2. (2 marks)

(h) A survey of a town gave these probabilities for the number of children living in each house.

Number of children 0 1 2 3 4 5Probability 0.15 0.30 0.35 0.10 0.05 0.05

There are 600 houses in the town. How many of the houses have fewer than three children living in them? (2 marks)

(i) Consider the triangle ABC where sin BCA = 35 displayed below:

A

B C

500 m

Side AC has length 500 m. Determine the length of the side AB. (2 marks)


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Vehicle licence plates in Western Australia can be customised to suit individual requirements.

Jessica has decided on the wording of her customised licence plates, and has restricted her choice to the following options:

colour pink (P), red (R), green (G) or black (B) material metal (M) or acrylic (A) size normal size (N) or slim-line (S).

(a) Draw a tree diagram to show her available options. (3 marks)


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Jessica randomly selects her customised licence plates from the available options.

(b) Determine the probability that she selects green slim-line licence plates. (1 mark)

(c) Determine the probability that she does not select red licence plates. (1 mark)

Jessica has now decided that she definitely does not want pink or acrylic licence plates.

(d) Determine the probability that she selects normal-sized plates that are made from metal. (2 marks)


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Given f (x) = x2 + 2x + 1 and g (x) = 2 x 2.

(a) Determine the value of f (1) g(2). (2 marks)

(b) Solve for x if f (x) = 1. (2 marks)


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Peter was investigating prime numbers and made a conjecture that if one is added to the product of two or more prime numbers, then the result is also a prime number.

(a) Test the conjecture with three different sets of prime numbers. (3 marks)

(b) What conclusion can you make about Peters conjecture based on your results from Part (a)? (1 mark)


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The World Health Organisation (WHO) monitors the percentage of a countrys target population that has been vaccinated against a number of diseases as well as the child (under 5 years) mortality rate for that country. The information for 12 countries is shown in the table below.

CountryPercentage of target

population vaccinated against Hepatitis B

Child (under 5 years) mortality rate/1000 live

birthsA 92 5B 66 199C 59 209D 94 15E 96 21F 90 4G 83 84H 56 68I 66 138J 73 191K 64 112L 83 39

(a) The information for the first six countries (A to F) has been plotted on the scatter plot below. Complete the scattergraph. (2 marks)

500

450

400

350

300

250

200

150

100

50

Chi

ld m

orta

lity

(dea

ths/

1000

birt

hs)

10 20 30 40 50 60 70 80 90 100 Percentage of population vaccinated


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(b) Fit a trend line by eye to your graph. (1 mark)

(c) Use your trend line to estimate the change in the child (under 5 years) mortality rate for a country that increases its immunisation level of Hepatitis B from 10% to 30%. (3 marks)

(d) Comment on the reliability of your estimate in Part (c). Justify your answer. (2 marks)

End of questions


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Additional working space

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Question number:


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Question number:


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Question number:


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Question number:


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Question number:

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

OSBORNE PARK WA 6017

This examination paper 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 it is not changed and that the School Curriculum and Standards Authority is acknowledged as the copyright owner.

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

ACKNOWLEDGEMENTSACKNOWLEDGEMENTS

Section One Question 3 Department of Transport. (2012). Custom series plate [Image]. Retrieved

March 29, 2012, from www.transport.wa.gov.au/licensing/20416.asp. Question 6 Data source: World Health Organization. (n.d.). WHO Vaccine

Preventable Diseases Monitoring System 2011 global summary. Retrieved March 17, 2012, from http://apps.who.int/immunization_monitoring/en/globalsummary/countryprofileselect.cfm.

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