mathematics stage 2c 2d calc free 2013

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Western Australian Certicate of Education

Examination, 2013

Question/Answer Booklet

Copyright © School Curriculum and Standards Authority 2013

*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 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 additionalanswer booklets used

(if applicable):

Ref: 13-083



CALCULATOR-FREEMATHEMATICS 2C/2D 2

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D O N O T W R I T E I N

T H I S A R E A A S I T W I L L B E C U

T O F F

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 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 not 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 6 6 50 50 331 ⁄ 3

Section Two:

Calculator-assumed13 13 100 100 662 ⁄ 3

Total 100



CALCULATOR-FREE 3 MATHEMATICS 2C/2D

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OT WRI T E I NT HI S A RE A A S

I T WI L L B E C UT OF F

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

Working time: 50 minutes.

Question 1 (8 marks)

(a) Use set notation to describe the shaded region in the Venn diagram below.

(1 mark)

(b) Given n( A) = 15 and n( ) = 22, determine n(U ). (1 mark)

(c) Determine the gradient of the line with equation – 4 x + 8 y = –16. (1 mark)




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T O F F

Question 1 (continued)

(d) Write 0.020 83 using scientic notation. (1 mark)

(e) The information below shows the frequency of goals scored in each game during the

2011 and 2012 seasons. For which year was the mean number of goals per game

greater? (1 mark)

(f) Factorise 9 x2 – 25. (1 mark)




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(g) Simplify 34 ÷ 3 –2. Express your answer as a power of 3. (1 mark)

(h) Determine the value of cos ACB. (1 mark)




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T O F F


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

(b) Show a minimum spanning tree on the following network. (2 marks)

(c) Are the lines with equations y = 3 –5

4 x and y = 2 +

4

5 x perpendicular? (1 mark)

(d) Evaluate 74 × 7 –6, giving your answer without using index notation. (2 marks)




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(e) Sketch the graph of y = – ( x – 2)( x + 2) on the axes below. (3 marks)

(f) Jean has bought 10 pots, each of which contains ve seedlings, and is provided with

data from previous experiments about the seedlings’ likely survival in the pots. Data in

the table below show the relative frequency of seedlings in each pot that will survive for

at least one week if they are not planted in the garden.

Number of plants per pot surviving for at

least one week when not planted in the

garden

0 1 2 3 4 5

Relative frequency of pots 0.1 0.2 0.24 0.3 0.1 0.06

In how many of the 10 pots can she expect more than three seedlings to survive for at

least one week if she does not plant them in the garden? Justify your answer. (2 marks)

(g) Consider triangle ABC where tan BAC =2

3 and side AB has length 600 m. Determine

the length of side BC . (2 marks)




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T O F F


When learning sounds in words, children are often introduced to small groups of letter sounds

with a mixture of consonants and vowels. For example, the rst group of letters suggested by

various education institutions includes the consonants s, t, p and n and the vowels a and i. One

way of presenting sounds is to use three-letter words of the form c-v-c (consonant-vowel-

consonant) in which letters are not repeated; words such as p i p would not be allowed.

(a) Draw a tree diagram to represent the possible three-letter words from the consonants

s, t, p, and n and the vowels a and i. (3 marks)




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One of these words is selected at random.

(b) What is the probability that the word selected contains an s? (1 mark)

(c) What is the probability that the word selected contains an n or an s? (1 mark)

(d) What is the probability that a word beginning with s does not end in t? (2 marks)




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T O F F


Each of the functions: y =1

2

x

, y = x3, y =1

x, y = –x2 and y = –3 x is represented by either a

table or a graph labelled A, B, C, D or E below.

A x 0 1 2 3 4

y 0 1 8 27 64

B x 0 1 2 3 4

y –1 –3 –9 –27 –81

C x

1

21 2 3 4

y 2 11

2

1

3

1

4

Complete the table below by matching each function with one of the letters A, B, C, D or E from

the tables and graphs above.

Function Table or graph

y =1

2

x

y = x3

y =1

x

y = – x

2

y = – 3 x




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The following diagram shows the graph of the quadratic function f (x) = 0.5 x2 + 2 x – 6.

A second quadratic function is dened by g ( x) = – ( x – 2)2 + 4.

Complete the following table for these two functions.

f ( x ) g ( x )

line of symmetry

x -intercept(s)

y-intercept(s)

turning point




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T O F F


The graph below compares the Physics and Chemistry results of 23 students.

(a) Mal achieved the second highest score in Physics. What was his score in Chemistry?

(1 mark)

(b) Draw a trend line by eye. (1 mark)

(c) (i) Use your trend line to predict the Chemistry result of a student who achieved 66%

in Physics. (1 mark)

(ii) Comment on the reliability of your prediction. (2 marks)




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End of questions

(d) (i) Use your trend line to predict the Physics result of a student who achieved 100%

in Chemistry. (1 mark)

(ii) Comment on the reliability of your prediction. (2 marks)




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T O F F

Additional working space

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mathematics stage 2c 2d calc free 2013

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