mathematics stage 2c 2d calc assumed exam 2014

7/24/2019 Mathematics Stage 2C 2D Calc Assumed Exam 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-S2*MAT2CD-S2

MATHEMATICS

2C/2DSection Two:

Calculator-assumed

Time allowed for this sectionReading time before commencing work: ten minutesWorking time for section: one hundred minutes

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

This Question/Answer BookletFormula Sheet (retained from Section One)

To be provided by the candidate

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

Special items: drawing instruments, templates, notes on two unfolded sheets of A4 paper,and up to three calculators approved for use in the WACE examinations

Important note to candidatesNo other items may be taken into the examination room. It is yourresponsibility to ensurethat you do not have any unauthorised notes or other items of a non-personal nature in theexamination room. If you have any unauthorised material with you, hand it to the supervisorbeforereading any further.

Number of additionalanswer booklets used(if applicable):

Ref: 14-077


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CALCULATOR-ASSUMEDMATHEMATICS 2C/2D 2

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TOFFInstructions 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 followany 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 yourresponses 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 thepage.

5. Show all your working clearly.Your working should be in sufcient detail to allow youranswers to be checked readily and for marks to be awarded for reasoning. Incorrectanswers given without supporting reasoning cannot be allocated any marks. For anyquestion or part question worth more than two marks, valid working or justication isrequired 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

SectionNumber ofquestionsavailable

Number ofquestions tobe answered

Workingtime

(minutes)

Marksavailable

Percentageof exam

Section One:

Calculator-free 7 7 50 50 3313

Section Two:Calculator-assumed

13 13 100 100 6623

Total 100


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Section Two: Calculator-assumed (100 Marks)

This section has 13 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 yourresponses 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 thenumber of the question that you are continuing to answer at the top of the page.

Suggested working time: 100 minutes.

Question 8 (7 marks)

In a population of 100 people, 30 people have green eyes, ve have both green eyes and brownhair and 50 have neither green eyes nor brown hair.

(a) Represent this information in the Venn diagram below, where Grepresents the set of

people with green eyes and Brepresents the set of people with brown hair. (3 marks)

(b) Determine the number of people having only brown hair. (2 marks)

(c) Determine the probability that a person chosen at random from those with green eyes willalso have brown hair. (2 marks)


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Outside the Perth metropolitan area, the Water Corporation divides the State into Country northand Country south. Annual water usage charges for Country north are given in the table below,with towns being allocated to one of the ve classes shown.

Country north water use and price classes(cost per kilolitre)

Usage (kL)

per yearClass 1 Class 2 Class 3 Class 4 Class 5

First 350 kL $1.055 $1.381 $1.381 $1.381 $1.381

Next 150 kL $1.404 $1.841 $1.841 $1.841 $1.841

Next 250 kL $1.486 $2.043 $2.722 $3.202 $3.766

Over 750 kL $1.734 $2.607 $3.470 $4.800 $6.474

(a) Calculate the annual water usage charge for a property in a Class 1town that uses535 kL of water. (3 marks)


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(b) In 2013, a family living in a Class 2town used 570 kL of water and had an annual wateruse charge of $902.51. Having now moved to a Class 5town and not wishing to pay anymore for water, by how much must they reduce their annual water use? Give your answerto the nearest kilolitre. (4 marks)


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Concern has been raised in a country town that its recreational facilities are inadequate. Thelocal government authority has employed a research company to collect and analyse a sampleof residents opinions. The current population of the town is approximately two thousand.

(a) Describe twodifferent ways in which the sample of residents to be surveyed could bechosen. (2 marks)

(b) Describe two factors that could skew or bias the results of the collected data. (2 marks)

(c) Describe what the analysis of the collected data might show about the recreational

facilities. (1 mark)


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Sandra was investigating odd numbers and made the conjecture that the product of any threeconsecutive odd numbers is divisible by ve.

(a) Test Sandras conjecture with threedifferent sets of three consecutive odd numbers.

(3 marks)

(b) What conclusion can you draw about Sandras conjecture on the basis of your resultsfrom part (a)? Justify your answer. (2 marks)


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A high speed communication network linking 12 centres A, B, C, D, , J, K, L is to beconstructed. The possible connections are given in the following network. The number on eacharc represents the cost, in thousands of dollars, of establishing a direct link between the nodesthat the arc joins.

To minimise the cost, the network design consultant decides to use a minimal spanning treesolution.

(a) Determine the minimum cost and indicate clearly the minimal spanning tree solution onthe network above. (5 marks)


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(b) The network design consultant discovers that the cost for the link FE is incorrect andshould have been $37 000. How does this information change the solution in part (a)?Justify your answer. (3 marks)


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The diagram below shows a transport network connecting a companys warehouse W to its maindistribution centre M. The products are moved from W to M through a number of intermediatecentres A, B, , H. The number on each arc represents the maximum number of units of aproduct that can be moved per day along the network link.

(a) What is the maximum amount of the product, in units per day, that can be moved fromthe warehouse W to the distribution centre M? Show systematic working. (5 marks)


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(b) What effect, if any, would there be on the maximum daily ow of the product from W to Mif the capacity of the link FE was increased by 20 units per day? Justify your answer.

(3 marks)


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A sample of 1000 people was asked to respond to the question, Should the building of high-rises on the beachfront be banned? with either a Yes or a No.

The results were recorded on the basis of where the respondents lived, as shown in the table

below. Beach residents were classied as those living within 10 km of the ocean.

Response Yes No

Beach resident 60% 15%

Non-beach resident 20% 5%

The second table shows the gender distribution of those in the sample who responded with aYes.

Beach resident Non-beach resident

Male 45% 10%Female 30% 15%

(a) How many people in the sample responded with a No? (2 marks)

(b) Determine the probability that a person selected at random from the sample of 1000people was a non-beach resident who responded with a No. (1 mark)

(c) (i) How many people in the sample were females who responded with a Yes?(2 marks)

(ii) How many of the females from part (c) (i) were non-beach residents? (1 mark)


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(d) Given that a person chosen at random responded with a Yes and was a female,determine the probability that she was a non-beach resident. (2 marks)

(e) Determine the probability that a person chosen at random who voted with a Yes was amale. (1 mark)


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The following table displays the percentage distributions of persons aged 2564 years, by levelof educational achievement, across 12 countries in 2010.

Level of educational achievement of persons aged 2564 years in 2010

Country

Below upper

secondary

education (%)

Upper secondary

and non-tertiary

education (%)

Tertiary

education (%)

Tertiary andadvanced

research

programs (%)

Australia 29 34 10 27

Canada 13 38 24 25

France A 41 12 18

Germany 14 59 9 17

Greece 36 41 7 17

Italy 46 40 14Japan 56 19 25

Korea(Republic of)

20 41 12 27

New Zealand 21 39 17 23

Sweden 14 52 9 25

United

Kingdom11 52 10 27

United

States of

America

11 48 10 31

(a) Determine the value forAin the table. (2 marks)

(b) Give a reason to explain why there are empty cells in the table for Italy and Japan. (1 mark)

(c) What was the median level of educational achievement in Australia for people aged2564 years in 2010? (1 mark)


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(d) Which country appears to have had the highest proportion of its population aged2564 years who had not achieved education at the tertiary level? Justify your answer.

(2 marks)

(e) Consider the claim that In 2010, Australia had more people whose level of educationalachievement was below upper secondary than Germany. State whether you agree withthis claim and give tworeasons to justify your conclusion. (3 marks)

(f) Some students studying this data added up all the numbers in the tertiary education (%)column and averaged them to get 11.75%. They concluded that Throughout the world,11.75% of people aged 2564 years have completed a tertiary education. Give tworeasons for rejecting this conclusion. (2 marks)


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In preparation for developing a spreadsheet to investigate the inuence of the other variables on

a,Kerry decided to rearrange the formulas= ut +at2

2.

(a) Show how the formula can be rearranged to give a formula for calculating a. (2 marks)

(b) Using your formula from part (a), nd the value of awhens= 66, u= 5and t= 6.(2 marks)


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A ladder has 21 rungs and from the bottom to the top each rung is shorter than the one before itby a constant amount. The bottom rung is 400 mm long and the top rung is 320 mm.

(a) How much shorter is each rung than the rung below it? (3 marks)

(b) Give a recursive rule for calculating the length (Tn)of the nthrung from the rung below it.

(2 marks)

(c) Give a non-recursive formula for calculating the length of any rung. (1 mark)


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(a) On April 16 Mitch borrowed $15 500 from his parents to purchase a car. He agreed toan interest rate of 7.2% per annum on the amount owing and to make repayments everysix months. How much interest was added to the loan on October 16 when his rstrepayment was due? (2 marks)

(b) On April 16, Magda borrowed $15 500 to purchase a car. She makes repayments of $400each month. The interest on the loan is charged at 7.2% per annum reducible monthly.

(i) Complete the following table to determine how much Magda still owes aftermaking her sixth repayment. (4 marks)

Date Amount Interest Repayment Amount remaining

April 16 $15 500.00

May 16 $15 500.00 $93.00 $400.00 $15 193.00

June 16 $15 193.00 $91.16 $400.00 $14 884.16

July 16 $14 884.16 $89.30 $400.00 $14 573.46

August 16 $14 573.46 $87.44 $400.00 $14 260.90

September 16 $14 260.90 $85.57 $400.00 $13 946.47

October 16 $400.00


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(ii) Write a recursive rule for the amount, Tn,Magda owes after nmonths. (3 marks)


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The diagram below (not drawn to scale) shows a section of a construction consisting of three

steel beamsAB,BCandAC.

(a) Use trigonometry to determine the size of the angleABCto the nearest degree. (5 marks)


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(b) Use the sine rule to determine the size of the angleBCA. (3 marks)

(c) The sectionABCneeds to be covered with insulation material. The cost of insulation is$22 per square metre. Determine the total cost of insulation. (3 marks)


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The functionsy = 3xandy = x

3are represented in the graph below.

(a) Comment, with reasons, on the conjecture 3x>x

3for all whole numbersx> 1. (2 marks)


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End of questions

(b) Graph the functiony = 1.5x3+ 18x

2+ 67.5x+ 85on the axes on page 22. Label all

important features clearly. (5 marks)

(c) Comment, with reasons, on the conjecture 3x


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Additional working space

Question number:


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Question number:


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mathematics stage 2c 2d calc assumed exam 2014

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