Mathematics Stage 2A 2B Calc Free 2012

Student Number: In figures

In words

Please place your student identification label in this box

Western Australian Certificate of EducationExamination, 2012

Question/Answer Booklet

Copyright © School Curriculum and Standards Authority 2012

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 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: 12-086

CALCULATOR-FREEMATHEMATICS 2A/2B 2

See next page

Section

Section One:Calculator-free

Section Two:Calculator-assumed

Number of questions available

7

12

Number of questions to be answered

7

12

Working time

(minutes)

50

100

Total

Marks available

50

100

150

Percentage of total exam

331⁄3

662⁄3

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 2A/2B

See next page

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.

Suggested working time: 50 minutes.

Question 1 (12 marks)

(a) Evaluate

(i) 0.2 + 0.17 (1 mark)

(ii) 16 ÷ 0.25 (1 mark)

(iii) 70% of 24 (1 mark)

(iv) 10 − 3 × 4 + 5 (2 marks)


See next page

(b) Simplify the following expressions:

(i) 3 × k × k − 3 × k (1 mark)

(ii) 5k2 − 2k + 2k2 − 5k (1 mark)

(iii) (3 + k)(3 + 2k) (2 marks)

(c) A number sequence is described using the recursive equation:

Tn+1 = Tn + 12, T3 = 43

(i) Determine T4. (1 mark)

(ii) Determine T1. (2 marks)


See next page


(a) Given the expression 403 × 94

18.47

(i) Estimate the value of the above expression by first rounding each of the numbers to the nearest ten. (2 marks)

(ii) A calculator could be used to evaluate the above expression. If this was done, would you find your estimated value to be smaller or larger than the calculated value? Give reasons for your answer. (2 marks)

(b) Each of the numbers 3, 5, 8 and 29 can be written in terms of the other three.

For example 5 = 29 − 8 × 3.

Write each of 3, 8 and 29 in terms of the other three numbers. You may use brackets and any of the number operations. (3 marks)

29 =

8 =

3 =


See next page


Brandon and Karissa have classified the DVDs that they own into five categories each, according to the pie charts below.

(a) What percentage of Karissa’s DVD collection are Barbie DVDs? (1 mark)

(b) What percentage of Brandon’s DVD collection are Pokemon DVDs? (2 marks)

(c) Karissa has eight Dora DVDs. How many Princess DVDs does she have? (2 marks)

(d) Circle the correct response and justify your choice. (2 marks)

A: The person with the most DVDs is Brandon.

B: The person with the most DVDs is Karissa. C: There is not enough information to determine who has the most DVDs.

D: Brandon and Karissa both have the same number of DVDs.

Brandon’s DVD collection Karissa’s DVD collection


See next page


y

xx–6 –4 –2 2 4 6

6

4

2

–2

–4

–6

L M

J

K

E

F

GH

A

B

CD

(a) Describe the transformation(s) of quadrilateral ABCD required to produce quadrilateral EFGH. (2 marks)

(b) Describe the transformation(s) of quadrilateral ABCD required to produce quadrilateral JKLM. (2 marks)

(c) On the above diagram, show the result of each of the following transformations of quadrilateral ABCD (label each answer appropriately):

(i) reflection in the x-axis, (1 mark)

(ii) reflection in the line y = −x. (Hint: First draw the line y = −x). (2 marks)


See next page


The Voster family live in the Perth metropolitan area. In summer their home is cooled by an air cooler which, when running, uses a large amount of electricity. The air cooler is the only appliance that causes a variation in the electricity usage. The Voster’s electricity account received in February 2012 (for the months of December 2011 and January 2012) was for $157.18. Electricity accounts are received every two months.

(a) Complete the graph below to show predicted electricity account amounts for the Voster family for the remainder of 2012. (2 marks)

200180160140120100806040200

February April June August October December

Cos

t ($)

Electricity

Month

(b) If electricity prices increased by 10% in 2013, describe how the 2013 graph would compare with the 2012 graph. (2 marks)


See next page


Agnetha is m years old and Bertie is n years old.

(a) Write algebraic equations for the following:

(i) Agnetha is 15 years older than Bertie. (1 mark)

(ii) Bertie’s age is five years less than half of Agnetha’s age. (1 mark)

(b) It is known that Agnetha’s age can be found by solving the equation

5(m + 3) − 55 = 3m.

Find Agnetha’s age by solving the above equation. (3 marks)

(c) Use your result from Part (b) and one of the equations in Part (a) to find Bertie’s age. (1 mark)


See next page


During one season, Rettown soccer team played 18 games, with the results as shown in Graph 1. (Note: ‘goals for’ represents the score for Rettown, while ‘goals against’ represents the score for the opposition team, e.g. Point T represents a game that Rettown lost 4 goals to 6.)

Graph 1Goals against

Goals for2 4 6

6

4

2

T

(a) Indicate with a cross (‘X’) on the graph a game that was won by Rettown. (1 mark)

(b) How many games did Rettown win? (1 mark)

(c) How many of Rettown’s games ended in a draw? (1 mark)

Graph 2 below shows some of Rettown’s winning margins. (Note: a negative ‘winning margin’ represents a loss.)

Graph 2Number of games

Winning margin–5 –4 –3 –2 –1 1 2 3 4 5

5

4

3

2

1

A

B C

D

E


See next page

Graph 2 is incomplete, with only seven of the required eleven points shown.

● Point A represents the three games that Rettown lost by one goal● Point D represents the one game that Rettown won by five goals● Point E indicates that no games were won by three goals.

(d) What does Point B on Graph 2 represent? (1 mark)

(e) What does Point C on Graph 2 represent? (1 mark)

(f) Complete Graph 2 by plotting the remaining four ‘winning margins’. (2 marks)

End of questions


See next page

Additional working space

Question number:


See next page


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.

Mathematics Stage 2A 2B Calc Free 2012

Documents

Transcript of Mathematics Stage 2A 2B Calc Free 2012