alternative education equivalency (aee)...
TRANSCRIPT
Alternative Education Equivalency (AEE) Tests
Year 10
Candidate Preparation Kit
Alternative Education Equivalency Scheme (AEES) Year 10 Candidate Preparation Kit
© 2017 VETASSESS, Level 5, 478 Albert Street, East Melbourne Victoria 3002.
All rights reserved. No part of this book may be reproduced without written permission from
VETASSESS.
20170901
Year 10 Candidate Preparation Kit
Alternative Education Equivalency Scheme (AEES) Tests
INFORMATION ABOUT THE AEES TESTS
1. Overview of the Alternative Education Equivalency Scheme (AEES) tests
2. Test Details
3. Non-Established Venue Testing
4. Candidate Test Attempts
5. Candidate Reminders
6. Results
7. Types of Questions in the AEES Tests
8. How to Prepare for the AEES Tests
9. Reference Materials
10. Sample Questions
11. Attending the Test Session
12. Stationery and Personal Belongings
13. Test Rules
14. Breaching the Test Rules
15. Consequences of Breaching the Test Rules
16. Accessing your Personal Records and Appeals
APPENDICES
A. How to Prepare for the AEES Tests
B. Reference Materials
C. Sample Questions
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D. Answers to Sample Questions
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1. Overview of the Alternative Education Equivalency Scheme (AEES) tests
The Alternative Education Equivalency Scheme (AEES) is an alternative pathway for some
Australian Defence Force candidates who:
• are eligible in all other areas
• do not possess evidence of the required education standard, or
• do not have the required education standard for a specific Defence Force Recruiting
employment category, and
• are able to demonstrate two (2) years of relevant work / life experience and skills post
completion of school
There are two independent levels of the AEES tests:
• Year 10: English, General Mathematics, Advanced Mathematics & Science
• Year 12: English, General Mathematics, Advanced Mathematics & Science
2. Test Details
The tests are independent of each other and you may be required to complete one or more
tests at the required year level.
Below is a table with the description of the Year 10 tests.
Tests Time Allowed Items
English
a) Multiple-choice: reading, comprehension
and language 30 minutes 50
b) Written Expression Task 30 minutes 1 task
General Mathematics
Multiple-choice 30 minutes 30
Advanced Mathematics
Multiple-choice 30 minutes 30
Science
Multiple-choice 30 minutes 35
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Department of Defence, Canberra. ACT 2600. Australia.
3. Non-Established Venue Testing
Candidates who live further than 100 km away from an established test venue may sit the tests
at a non-established venue. Please refer to VETASSESS for more information.
Candidates are responsible for sourcing a non-established venue and an appropriate supervisor
and must pay for any costs associated with the venue and the supervisor.
4. Candidate Test Attempts
You have 92 days to complete a Test Attempt.
You will be given two Test Attempts per subject.
If you do not sit the test/s within the 92 day Test Attempt period, you forfeit the Test
Attempt and this counts as one of your Test Attempts.
You will be given a further 92 day period to complete a second Test Attempt.
If you need to defer your testing within the 92 day Test Attempt period, we will
attempt to re-book your test within the 92 day period.
Please refer to the confirmation letter or candidate voucher sent from VETASSESS for:
• Test Attempt number
• Test Attempt start date
• Test Attempt expiry date
5. Candidate Reminders
Please take note of your ‘Test Attempt expiry date/s.’ (refer confirmation letter / candidate voucher).
You are required to confirm you are attending the test session booked for you. On receipt of a
text message or email from VETASSESS, please reply to confirm or cancel your testing.
Please be aware if you cancel your testing by email or text message, we cannot guarantee
there will be another test date available during the 92 day Test Attempt period. If your testing
cannot be rebooked within this 92 day Test Attempt period, you will forfeit the Test Attempt.
This will count as one of your Test Attempts.
6. Results
Your result for the multiple-choice tests is the number of correct answers given. For the English
assessment, your result is a combination of the multiple-choice test and the writing task scores.
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VETASSESS will report your results to Defence Force Recruiting. You will need to contact
Defence Force Recruiting on 13 19 02 to be advised of your results. Please note, we are unable
to advise you directly of your results or provide you with a results statement.
Advice on your performance against individual topics in the test/s is not available as the results
processing does not include this analysis.
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Department of Defence, Canberra. ACT 2600. Australia.
7. Types of Questions in the AEES Tests
Below is an overview of the content of each test.
ENGLISH
The questions in these test components are based on nationally derived standards and assess
functional knowledge and the application and use of the skills.
The strands covered within these two components are:
• Reading & Comprehension
• Writing
• Language structure and use
• Written Expression Task
GENERAL MATHEMATICS
The questions in this test are based on nationally derived standards and assess functional
knowledge and the application and use of the skills.
The strands covered in this test are:
• Space
• Number
• Measurement
• Chance & Data
• Algebra
• Reasoning & Strategies
ADVANCED MATHEMATICS
This test is required for technical trades. The questions in the test are based on the draft
‘Australian Curriculum’ for Year 10A Mathematics. The ‘Curriculum Descriptions’ can be viewed
at:
www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10
The test assesses functional knowledge and the application of the mathematical skills. The
topic areas covered in the test are:
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• Working with numbers:
multiplication, division, addition, subtraction
fractions, decimals, percentages
rates: km/hr, $/kg, $/m, distance/speed/time; time calculations
location & direction
• Ratio & Proportion
• Money & Financial Mathematics
money transactions
simple interest
compound interest
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Department of Defence, Canberra. ACT 2600. Australia.
• Real Numbers
rational & irrational numbers
surds & indices
logarithms
• Patterns & Algebra
factorising
polynomials
factor theorem
remainder theorem
• Linear & Non-linear Relationships
linear equations
parabolas
hyperbolas
circles
exponential functions
exponential equations
monic & non-monic quadratic expressions
quadratic equations
• Using Units of Measurement
length, weight, mass, capacity, time, temperature
calculate & estimate measurements
area & volume
pyramids, cones, spheres & related composite solids
• Geometric Reasoning
properties of circles
• Pythagoras & Trigonometry
apply sine, cosine & area rules for any triangle
trigonometric functions
trigonometric equations
use periodicity and symmetry
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solve three-dimensional problems in right-angled triangles
• Chance
Probability
• Data Representation & Interpretation
mean & standard deviation of data
compare data sets
bivariate numerical data sets
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Department of Defence, Canberra. ACT 2600. Australia.
SCIENCE
The questions in this test are based on nationally derived standards and assess functional
knowledge and the application and use of the skills.
The strands covered in this test are:
• Physics
Balance
Pressure
Frequency
Speed
Force
Reflection
Circuits
Efficiency
Pulleys
Energy & Springs
Thinking Scientifically
• Chemistry
Solubility/reactivity
Indicators
Solids
Equilibrium
Elements
• Biology
Classify
Populations
Photosynthesis
• Environmental Science
Salinity/Soil HP
Species
• Earth and Space
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Humidity
Planets
8. How to Prepare for the AEES Tests
To assist you in your preparation for the AEES tests, useful revision tips and helpful information
is provided; see Appendix A.
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A l l r igh ts reserved . No par t of th is book may be reproduced w ithout wr i t ten perm iss ion f rom VETASSESS .
16
Department of Defence, Canberra. ACT 2600. Australia.
9. Reference Materials
Ask your local library for reference books. We also recommend using a tutor from within your
local community.
There are many relevant text books available across Australia that would provide reference
material for each test. A list of text books is provided; see Appendix B.
The text books listed can be reviewed online and ordered through the corresponding publisher
website. There are also many other relevant text books available from these publishers that
would provide suitable reference material.
Publisher Websites:
• Jacaranda: www.jaconline.com.au
• Oxford University Press: www.oup.com.au
• Pearson Australia: www.pearson.com.au
• Haese Mathematics: www.haesemathematics.com.au
• Nelson Cengage Australia: www.cengage.com.au/secondary
• Macmillan Education Australia: www.macmillan.com.au
10. Sample Questions
Year 10 Sample Questions for each topic area have been provided to show the types of items
in the test but they do not necessarily indicate the full range of questions or item difficulty, see
Appendix C. For answers to the sample questions, see Appendix D.
11. Attending the Test Session
On the day of the AEES tests, you must present at the test venue at the time specified in the
confirmation letter received from VETASSESS.
When you arrive at the test venue on the day, you must register before the test session.
You must bring the following:
Candidate Voucher (sent from VETASSESS)
one form of photographic identification (includes: drivers licence, learner’s permit, boat
licence, passport (current), student identification card, employment identification card,
proof of age card or other identification with a photograph that shows your full name)
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If you do NOT have photographic identification, call VETASSESS on 03 9655 4849.
Please note: you will NOT be admitted to the test room without the above items.
© 2017 VETASSESS - Leve l 5 , 478 A lber t St ree t , Eas t Me lbourne V ic to r ia 3002 .
A l l r igh ts reserved . No par t of th is book may be reproduced w ithout wr i t ten perm iss ion f rom VETASSESS .
18
Department of Defence, Canberra. ACT 2600. Australia.
12. Stationery and Personal Belongings
STATIONERY
You will need to bring:
stationery: pens, 2B pencils, soft eraser, sharpener
calculator: silent, battery-operated, non-programmable scientific calculator (for use in
the Mathematics and Science tests only)
ruler (for use in the Year 12 Advanced Mathematics test only)
bottled water (recommended)
Please note:
mobile phones with calculator functionality and CAS/graphics calculators are not
permitted
you will not be permitted to borrow a calculator from another candidate after entering
the test room
it is your responsibility to ensure the calculator is in good working order
we recommend you take extra batteries to the test session
spare calculators and spare batteries will not be available at the test session
PERSONAL BELONGINGS
no dictionary of any kind is permitted in the test room
mobile phones, music players and other electronic devices must be switched off
personal items brought into the test room must be stored in the designated area or
under the desk
MATERIALS PROVIDED ON THE DAY
Once the test session commences, you will be issued with the following test materials:
test booklets
answer sheet
working space sheets (note paper)
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13. Test Rules
You will only be admitted to the test room if you have completed the Candidate Registration
procedure on arrival at the test venue. You will not be permitted to enter the test room after
the test session has commenced.
You are required to observe the rules and instructions normally applied to the proper conduct
of tests:
• You must not attempt to gain an unfair advantage from supervisors, other candidates
or any other personnel involved with the AEES tests at any time during the assessment
process
• You are not permitted to communicate with any other candidate in the test room
• You are not permitted to copy work from any other candidate
• You are not permitted to use any unauthorised electronic devices
• You must not remove any test materials whatsoever from the test room
• You are not permitted to leave the test room after the commencement of the test
session, except:
temporarily due to illness
for a toilet break
• You are required to remain in the test room until you have completed all the tests you
are booked to complete
• You are permitted to leave the test room permanently, but not until the completion of
the particular test component, so as not to disturb others
• If you leave the test room permanently during the test, you will be considered to have
abandoned the test and your answer sheet will not be marked
• You may not re-start or re-attempt a test you have abandoned on the same day
• You may re-enter the test room for other tests but only in the administration period
between tests
14. Breaching the Test Rules
VETASSESS views any breach of rules or instructions extremely seriously.
If you suspect there has been a breach of the test rules, you may complete an Incident Report
form at the test session or contact VETASSESS.
If the supervisor suspects a candidate of breaching any rule or instruction during the test
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Department of Defence, Canberra. ACT 2600. Australia.
session, the incident will be reported to VETASSESS in writing with the precise nature of the
alleged breach and the relevant circumstances.
The supervisor may interview a candidate to gather information about the alleged breach when
the test session has been completed.
VETASSESS may require the alleged breach to be investigated further.
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15. Consequences of Breaching the Test Rules
If, after investigation, a candidate has been found to have breached any rule or instruction
related to the test session, VETASSESS may:
• inform Defence Force Recruiting of the nature of the breach and take any other
appropriate action in collaboration with Defence Force Recruiting
• order the cancellation of a candidate’s results in any assessments undertaken
If any penalty is imposed, the candidate will be advised in writing by VETASSESS.
16. Accessing your personal records and Appeals
To make an application to access your personal records with VETASSESS or appeal your results,
contact VETASSESS in writing with the details of your request.
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A l l r igh ts reserved . No par t of th is book may be reproduced w ithout wr i t ten perm iss ion f rom VETASSESS .
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Department of Defence, Canberra. ACT 2600. Australia.
Appendix A How to Prepare for the AEES Tests
Study Space
Your study space will impact on your level of concentration and the quality of your revision.
Following are some tips on how to choose a study space that maximises your study time:
• Choose a private study space to ensure your study time is free of distractions, and
interruptions – hang a “do not disturb” sign on the door if necessary!
• Your table needs to be large enough for your books, computer and any other
resources you will use during your study session.
• Make sure your chair is comfortable and supportive to avoid backache but not too
comfortable that you fall asleep!
• Make sure you have adequate lighting to see clearly.
• Make sure the room temperature is comfortable enough for you to concentrate but
remember: if the room is too warm you may fall asleep!
• Prepare your study space with the supplies you will need – pens, pencils, eraser,
sharpener, paper, calculator etc.
• Turn off your mobile phone.
• Turn the television and stereo off or turn the volume down low (if you must have them
on at all!)
Tips on Revision
How you perform in the assessment will depend on how well prepared you are. Following are
a few revision techniques to help you maximise your study time:
• Identify your weak areas early and get assistance, if necessary, from friends, tutors or
books.
• Pace your studying over time – do not attempt to revise everything in one study
session!
• Be realistic about how much time you need to revise for each subject. For example, if
you are strong in English, but not so strong in Mathematics, spend more time
practising Mathematics equations and problems.
• Try to concentrate on one subject at a time – jumping between Mathematics and
Science, for example, may lead to confusion.
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• Try to ‘internalise’ the important ideas, facts, events, processes and theories.
• Try revising by writing summaries, theories or formulas. Drawing pictures is also an
effective way to recall information.
• Familiarise yourself with the different types of questions and revise the topics given.
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24
Department of Defence, Canberra. ACT 2600. Australia.
Effective Strategies for Undertaking Tests
Following are a few tips on effective test taking strategies:
• Listen carefully to all instructions you are given by the supervisor.
• Read the test instructions on the test paper very carefully.
• Once the test starts, look through the test paper to see how much you have to do.
• Read all the questions fully and carefully.
• Answer the items you find easiest first - if you get stuck on a difficult item early in the
test, you may not get to answer items that you know.
• Plan your time so you have time to review your answers.
• Take the time to do the best work you can.
Tips for Multiple-Choice Tests
• Read all the answer choices before selecting one - it is just as likely for the last answer
choice to be correct as the first.
• Make sure you mark your answer against the corresponding question on the answer
sheet, especially if you skip between questions.
• You must give one answer only per question.
• If you do not answer a question, the question will not be marked.
• Do not change your initial answer unless you are sure another answer choice is correct.
• If you give more than one answer, it is automatically incorrect even if one of the
answers is the correct answer.
• If you make a mistake rub it out with your eraser - do not cross out a mistake.
• No marks will be deducted for incorrect answers.
• If you don’t know the answer at all, try to eliminate any answers you think are wrong
and then make a selection from the remaining options.
• Answer all questions, even if you have to guess.
Tips for English Written Expression Task
• You may be required to describe a situation, construct an argument or express a point
of view.
• Re-read the question and underline the key words so you are clear on what you need
to write.
• Your writing will be judged on how you express yourself, as well as your content and
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use of language.
• Spelling and punctuation will be taken into account as part of the assessment criteria.
• Plan out a response on draft paper first then produce a coherent and considered
response to the topic. (Draft paper is provided in the test session.)
• Make sure your response directly addresses the question asked.
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Department of Defence, Canberra. ACT 2600. Australia.
Test Anxiety
Most candidates will feel some anxiety leading up to a test but too much anxiety can interfere
with your concentration and ability to retain information.
A little anxiety can be helpful in energising you and motivating you to prepare but anxiety in
the test session can affect your performance.
Test anxiety can take many forms. Here are the most common signs:
• You find it difficult to start studying or you become easily distracted while studying.
• You expect a low mark, no matter how much time you spend preparing.
• During the test you have physical symptoms, such as difficulty breathing, upset
stomach, sweaty palms, headache, tension, back stiffness.
• You experience disorganised thinking, have difficulty remembering information or
become easily distracted during the test.
Test Anxiety Remedies
The good news is that you can manage your anxiety to maximise your preparation and
alleviate anxiety during the test session.
Using the tips and strategies outlined in this section “How to Prepare for the AEES Tests”, you
can boost concentration during your study time and reduce anxiety during the test session to
perform at your best on the day.
Important points to remember:
• Check the date, time and location of the test session and make sure you take all the
supplies required for the test session.
• Maintain a positive attitude so you stay motivated during your preparations.
• See the assessment as an opportunity to demonstrate what you know.
• Eat well leading up to the test session and eat a light nutritious meal before the test
session to assist concentration.
• Try to get a good sleep the night before the test session.
• Stay relaxed and positive during the test session and use slow, deep breathing to calm
yourself when you’re feeling stressed or nervous.
• Use positive affirmations to support yourself during the test session, such as “I am
calm and confident” or “I can do this.”
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© 2017 VETASSESS - Leve l 5 , 478 A lber t St ree t , Eas t Me lbourne V ic to r ia 3002 .
A l l r igh ts reserved . No par t of th is book may be reproduced w ithout wr i t ten perm iss ion f rom VETASSESS .
28
Department of Defence, Canberra. ACT 2600. Australia.
Appendix B Reference Materials
Following is a list of some of the leading publications in Australia for each test.
This list provides suggested reference material only and VETASSESS does not guarantee these
books are available or that the topic areas in the test are covered in these text books.
Year 10 English
Title: English is 10
Authors: Gardiner
Publisher: Jacaranda
Date of Publication: 2012
Title: English Skills Builder 1 AC Edition Student Book + obook/assess (4th edition)
Authors: Mary Manning, Margaret McKenzie, Michael Horne
Publisher: Oxford University Press
Date of Publication: 2013
Title: English Skills Builder 2 AC Edition Student Book + obook/assess (4th edition)
Authors: Mary Manning, Margaret McKenzie, Michael Horne
Publisher: Oxford University Press
Year of Publication: 2013
Title: Oxford English 1 Knowledge and Skills Australian Curriculum Student Book + ob
Authors: Paul Grover
Publisher: Oxford University Press
Year of Publication: 2013
Title: Pearson English 10 Student Book/Activity Book Value Pack
Authors: Michael Pryor
Publisher: Pearson Australia
Year of Publication: 2011
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29
© 2017 VETASSESS - Leve l 5 , 478 A lber t St ree t , Eas t Me lbourne V ic to r ia 3002 .
A l l r igh ts reserved . No par t of th is book may be reproduced w ithout wr i t ten perm iss ion f rom VETASSESS .
30
Department of Defence, Canberra. ACT 2600. Australia.
Year 10 General Mathematics
Title: Pearson Mathematics 10 – 10A Essentials Edition Student Book
Authors: David Coffey
Publisher: Pearson Australia
Year of Publication: 2012
Title: Mathematics for Australia 10
Author: Sandra Haese, Michael Haese, Mark Humphries
Publisher: Haese Mathematics
Year of Publication: 2013
Title: Maths Quest 10 + 10A for the Australian Curriculum 2E & eBookPlus
Author: Boucher
Publisher: Jacaranda
Year of Publication: 2014
Title: New Century Maths 10 for The Australian Curriculum NSW
Author: David Badger, Klaas Bootsma, Sarah Hamper
Publisher: Nelson Cengage Learning
Year of Publication: 2014
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Year 10 Advanced Mathematics
Title: Pearson Mathematics 10 + 10A for the Australian Curriculum 2E & eBookPLUS
Author: Boucher
Publisher: Jacaranda
Year of Publication: 2014
Title: Pearson Mathematics 10 – 10A Essentials Edition Student Book
Authors: Coffey, David et al
Publisher: Pearson Australia
Year of Publication: 2012
Title: Pearson Mathematics 10 – 10A Essentials Edition - Value Pack
Authors: Coffey, David et al
Publisher: Pearson Australia
Year of Publication: 2012
Title: Mathematics for Australia 10A
Author/Series: Michael Haese, Sandra Haese, Mark Humphries
Publisher: Haese Mathematics
Year of Publication: 2013
Title: New Century Maths Advanced 10+10A for The Australian Curriculum NSW Stage 5.2/5.3
Author: David Badger, Klaas Bootsma, Sarah Hamper
Publisher: Nelson Cengage Learning
Year of Publication: 2015
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Department of Defence, Canberra. ACT 2600. Australia.
Year 10 Science
Title: Nelson iScience for the Australian Curriculum Year 10
Author: Annie Termaat, Deb Smith, Neil Champion, Sandra Bishop, Xenia Pappas
Publisher: Nelson Cengage Learning
Year of Publication: 2013
Title: Pearson Science 10 Student Book
Authors: Rickard, Greg et al
Publisher: Pearson Australia
Year of Publication: 2011
Title: Oxford Big Ideas Science 10 AC Student Book + obk/as
Authors: Sally Cash, Geoff Quinton, Craig Tilley, Emma Craven
Publisher: Oxford University Press
Year of Publication: 2012
Title: Science Quest 10 Australian Curriculum Edition
Authors: Lofts
Publisher: Jacaranda
Year of Publication: 2011
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Appendix C Sample Questions
English
The following examples show the types of items in the test, but do not necessarily indicate the
full range of items or test difficulty. For answers to these sample questions, see Appendix D.
ENGLISH COMPREHENSION
Some questions in the multiple-choice test are based on passages or pieces of writing and you
will be required to answer questions recognising the meaning of words, identifying details,
sequencing events in logical order, making inferences, and so on.
Read the following passage and then answer example questions 1 and 2.
When something dies, microbes start to use the dead material as food for their own growth.
The process is called decay. It is the way dead things disappear from our world, so that new
things can grow. By breaking down dead material into simple substances that return to the air
and soil, microbes make it possible for all other forms of life to exist.
Adapted from “Childcraft – Holidays and Customs Volume 9”
Example 1 What do microbes use as food?
A. Soil
B. Living substances
C. Air
D. Dead material
Example 2 “Decay” is a process in which…
A. air and soil are absorbed.
B. dead material is broken down.
C. microbes are set free.
D. soil mixes with air.
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Study the following letter and answer example questions 3 to 5.
Dear Fiona,
My problem is a serious one. My family is not close. We all fight a lot amongst ourselves
(especially Mum and Dad). We have tried counselling but it only helps for a few days and then
we are back to our normal selves.
Peter (aged 14)
Example 3 The situation in Peter’s family is not…
A. delightful.
B. disruptive.
C. disheartening.
D. disturbing.
Example 4 Which sentence would best serve as a conclusion to Peter’s letter?
A. I’m not kidding, I need new parents!
B. I am pleased with the situation.
C. Do you think Mum and Dad are normal?
D. I really need your help and advice.
Example 5 Which would be the least positive reply to this letter?
A. Dealing with this problem now can help you overcome other obstacles in
your life.
B. Lots and lots of teenagers have had bad family experiences – you need to
work on your immature attitude.
C. Use this bad experience as a springboard to success rather than as an
obstacle in your life.
D. It’s empowering to know that if your family will not change themselves, you
can change yourself.
_______________________________________________________________________________________
Example 6 Which word is spelt correctly?
A. syrinje
B. sirinje
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C. syringe
D. surringe
Example 7 Which word or phrase best starts the following sentence?
…going to the post office.
A. Were…
B. Sam and I are…
C. Sam and me are…
D. Me and Sam are…
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Example 8 Which word or phrase has the same meaning as the underlined phrase?
Restaurants must strictly follow health and hygiene standards.
A. abide by
B. think about
C. agree with
D. clarify
Example 9 Select the word that is closest in meaning to the word allow.
A. succeed
B. reveal
C. enable
D. disclose
Example 10 The underlined part of the following sentence is incorrect. Which of the
following phrases would best complete the sentence?
Jane would like to do that new course if finding the time.
A. having she had the time.
B. when having the time.
C. if she could find the time.
D. being that the time is found.
Example 11 Which part of the following sentence is incorrect?
Lim and me are going to the city to do some shopping.
A. Lim and me
B. the city
C. are going
D. to do
Example 12 Select the word or phrase that best completes the following sentence.
The plumber was qualified and well mannered … she didn’t do a good job.
A. therefore
B. besides
C. also
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D. but
Example 13 What is the relationship between the following two sentences?
Voula purchased new shoes. The heels of her old shoes were worn.
A. The second sentence contradicts the first.
B. The second sentence makes a judgment about Voula.
C. The second sentence states the cause of the first.
D. The first sentence states the cause of the second.
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Example 14 Where should an apostrophe be in the following sentence?
Sarahs cats loved the treats they were given.
A. Sarah’s
B. cat’s
C. treat’s
D. we’re
Example 15 Which of the following group of words should be capitalised?
A. melbourne, shopping, venue
B. brisbane, street, place
C. perth, computer, scissors
D. sydney, europe, elizabeth
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General Mathematics
The following examples show the types of items in the test, but do not necessarily indicate the
full range of items or test difficulty. For the General Mathematics test, you may use a silent,
battery-operated, non-programmable scientific calculator (not CAS/graphics calculator). For
answers to these sample questions, see Appendix D.
Formulae
The following formulae may be used in your calculations:
AREA AND VOLUME
• Area of rectangle = length x width
• Area of triangle = ½ base x height
• Volume of a prism = area of base x height
THEOREM OF PYTHAGORAS
• In any right-angled triangle: c2 = a2 + b2
TEMPERATURE CONVERSION FORMULA
Degrees Celsius to degrees Fahrenheit:
• ºF = (ºC x 1.8) + 32
b
a
c
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TRIGONOMETRY
In any right-angled triangle:
sin θ = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
cos θ = 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
tan θ = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
GROWTH AND DECAY FORMULAE
• Simple growth or decay: A = P (1± ni)
• Compound growth or decay: A = P (1± i)n
Where:
A = amount at the end of n years
P = principal
n = number of years
i = interest rate per year, r % = r
100
Opposite side
Adjacent side
Hypotenuse
θ
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NUMBER
Example 1 0.3 x 0.2 =
A. 0.5
B. 0.05
C. 0.6
D. 0.06
E. 0.09
Example 2 Which of the following fractions represents the largest portion?
A. 1
8
B. 3
9
C. 3
16
D. 11
36
E. 15
64
Example 3 Green and brown paint are to be mixed in the ratio 5:3. If the total amount of
paint is to be 4 litres, how many litres of green paint will be needed?
A. 0.5
B. 1.0
C. 1.5
D. 2.0
E. 2.5
Example 4 63 =
A. 216
B. 128
C. 64
D. 36
E. 18
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SPACE
Example 5 What is the area of the shaded region?
A. 450 mm2
B. 352 mm2
C. 401 mm2
D. 98 mm2
E. 49 mm2
MEASUREMENT
Example 6 How long will it take a person to cover a distance of 240 km by car at a constant
speed of 100 km/h?
A. 2 hr 15 min
B. 2 hr 24 min
C. 2 hr 36 min
D. 2 hr 40 min
E. 2 hr 42 min
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CHANCE AND DATA
Example 7 A series of weights were hung from a coil spring. The data collected is shown in
the graph below.
The spring length for a weight of 300 g is most likely to be closest to:
A. 18 mm
B. 28 mm
C. 30 mm
D. 32 mm
E. 35 mm
ALGEBRA
Example 8 If x and y are positive whole numbers, what is the smallest value of x + y such
that
2x + 5y is divisible by 16?
A. 1
B. 3
C. 5
D. 7
E. 9
Example 9 What is the hundredth number in the following sequence?
3, 7, 11, 15, 19, …
A. 395
B. 399
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C. 403
D. 407
E. 411
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REASONING AND STRATEGIES
Example 10 The mass of a jar filled with jam is 1.125 kg. The same jar half-filled with jam has
a mass of 0.875 kg. Determine the mass of the empty jar, in kilograms.
A. 0.625
B. 0.500
C. 0.375
D. 0.250
E. 0.125
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Advanced Mathematics
The following examples show the types of items in the test, but do not necessarily indicate the
full range of items or test difficulty. For the Advanced Mathematics test, you may use a silent,
battery-operated, non-programmable scientific calculator (not CAS/graphics calculator). For
answers to these sample questions, see Appendix D.
Formulae
The following formulae may be used in your calculations:
MEASUREMENT
• Area of rectangle = length x width
• Area of triangle = ½ base x height = ½ absinC (where C is the included angle)
• Area of a circle = π x radius²
• Circumference of a circle = 2π x radius
• Volume of a sphere = 4
3π x radius³
• Surface area of a sphere = 4π x radius²
• Volume of any regular prism = area of base x height
• Volume of any right pyramid = ⅓ area of base x height
• Volume of cylinder = πr2 × h where r = radius, h = height
• Total surface area of cylinder = 2πr2 + 2πrh where r = radius, h = height
• Volume of a cone = ⅓πr²h
UNITS
• 100 cm = 1 metre
• 1000 m = 1 kilometre
• 1000 cm3 = 1000 ml = 1 Litre
TEMPERATURE CONVERSION FORMULA
• Degrees Celsius to degrees Fahrenheit: °F = (°C x 1.8) + 32
EQUATION OF A CIRCLE CENTRE
• Equation of a circle centre (0,0)
x2 + y2 = radius2
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Pi
• pi = 3.14
AVERAGE DAILY RAINFALL (IN A GIVEN MONTH)
x̅ = total rainfall for the month
number of days in that month
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THEOREM OF PYTHAGORAS
• In any right-angled triangle: c2 = a2 + b2
• In any triangle: c² = a² + b² – 2absinC
TRIGONOMETRY
In any right-angled triangle:
sin θ = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
cos θ = 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
tan θ = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
Sine Rule: where a, b, and c are the lengths of the sides opposite angles at A, B and C,
respectively.
b
B
Opposite side
a
A
Adjacent side
c
C
Hypotenuse
a
θ
b c
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𝑎
𝑠𝑖𝑛𝐴 =
𝑏
𝑠𝑖𝑛𝐵=
𝑐
𝑠𝑖𝑛𝐶
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SIMPLE INTEREST FORMULA
• I = PRT
Where:
P = principal
R = interest rate per year
T = number of years
GROWTH AND DECAY FORMULAE
• Simple growth or decay: A = P (1± ni)
• Compound growth or decay: A = P (1± i)n
Where:
A = amount at the end of n years
P = principal
n = number of years
i = interest rate per year, r % =r
100
LINEAR RELATIONSHIPS
• Distance between 2 points 𝑑 = √(𝑦2 − 𝑦1)2+(𝑥2 − 𝑥1)2
• Coordinates of midpoint (𝑥1 + 𝑥2
2,
𝑦1 + 𝑦2
2)
• Gradient of a line = 𝑟𝑖𝑠𝑒
𝑟𝑢𝑛=
𝑦2− 𝑦1
𝑥2− 𝑥1
FACTOR THEOREM
• The factor theorem states that a polynomial f (x) has a factor (x − k) if and only if f (k) =
0.
REMAINDER THEOREM
• The remainder when P(x) is divided by (x-a) is equal to P(a).
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WORKING WITH NUMBERS
Example 1 A TV cost $9,999 including GST of 10%. How much would the TV have cost
before the GST was added?
A. $9,090
B. $8,999
C. $9,000
D. $9,900
E. $9,009
Example 2 28 x 2-2 =
A. 2-16
B. 26
C. 12
D. 2-4
E. -4
RATIO & PROPORTION
Example 3 Of 1350 military personnel, the proportion of males to females is 7:2. What is
the number of females?
A. 270
B. 1050
C. 160
D. 300
E. 350
MONEY & FINANCIAL MATHEMATICS
Example 4 A sale advertised “Buy 2 shirts and get the 2nd shirt (of equal or lesser value) at
50% off.” Thomas bought 2 shirts originally priced at $90 and $120. How much
did he pay in total?
A. $220
B. $150
C. $105
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D. $210
E. $165
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1
0
Example 5 Andrew borrows $12,000 to buy a second hand car. The fixed simple interest rate
is 11% pa and the loan is to be repaid over 5 years. The total amount Andrew
will pay to the bank is
A. $13,320
B. $18,000
C. $18,600
D. $16,500
E. $12,000
REAL NUMBERS
Example 6 Simplify 3x0 (4y 3 ) 2
A. 48y 6
B. 24xy 6
C. 48y 5
D. 12xy 5
E. 24xy 5
Example 7 The Richter Scale measuring earthquake strength is related to the logarithmic scale.
An earthquake measuring ‘2’ on the Richter scale represents log10100. An
earthquake measuring ‘4’ on the Richter scale would be
A. Twice as strong
B. Four times as strong
C. 10 times as strong
D. 100 times as strong
E. 1000 times as strong
PATTERNS & ALGEBRA
Example 8 The factorised form of 4xy² + 2y is:
A. 2xy (y + 1)
B. 4xy (y + 1)
C. 2y (2xy + 1)
D. 2xy (2y + 1)
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E. 2xy (y + 2)
Example 9 The expression (y + 3)2 can be expanded as:
A. y 2 + 6
B. y 2 + 3y + 6
C. y 2 + 9
D. y 2 + 6y + 6
E. y 2 + 6y + 9
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LINEAR AND NON-LINEAR RELATIONSHIPS
Example 10 The circle shown with radius 1 unit has equation x 2 + y 2 = 1
This circle is dilated by a factor of 3. Its new equation would be:
A. x 2 + y 2 = 3
B. x 2 + y 2 = 9
C. x 2 + y 2 = 6
D. 3x 2 + 3y 2 = 1
E. x 2 + y 2 = √3
Example 11 The parabola with equation y = x 2 is reflected in the x axis. Its new equation is
A. y = 1 – x 2
B. y = x 2 – 1
C. y = -x 2
D. y = x 2 + 1
E. y = -x 2 – 1
Example 12 The shape of the curved seat of a swing is modelled by the equation
h = 2(x - 1)2 + 0.5 where h metres is the height of the swing above the ground
and x is the horizontal distance in metres from the left hand post of the frame.
What is the lowest height of the seat above the ground?
A. 0.5
3
2
1
0
0 1 2 3 -1 -2 -3
-2
-1
-3
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B. 1.0
C. 1.5
D. 2.0
E. 2.5
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USING UNITS OF MEASUREMENT
Example 13 The formula C = 5
9 (F – 32) converts degrees Fahrenheit (F) into degrees
Centigrade (C). If the temperature is 100o Fahrenheit, what would this be in
degrees Centigrade?
A. 68.0º
B. 23.6º
C. 212.0º
D. 43.4º
E. 37.8º
Example 14 A cylinder has a volume of 900 cm3. If the radius of the base is 5 cm what is the
length of the cylinder?
A. 36.00 cm
B. 11.46 cm
C 16.93 cm
D. 57.30 cm
E. 42.25 cm
GEOMETRIC REASONING
Example 15 When the object marked ORIGINAL has both its length and width doubled, the
enlargement is
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A. Figure 1
B. Figure 2
C. Figure 3
D. Figure 4
E. Figure 5
Original Figure 2
Figure 4
Figure 1
Figure 3
Figure 5
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PYTHAGORAS AND TRIGONOMETRY
Example 16 Soldiers at points A and B know that the distance from A to B is 21.6 km and
from B to the Base is 14.2 km. They have also taken bearings which show the
angle at B is 81.5º.
Due to a lake being in the way, they will have to rely on calculations for the
distance from A to the Base. This direct distance from A to the BASE is
A. 22.8 km
B. 26.3 km
C. 24.0 km
D. 31.1 km
E. 25.6 km
Example 17 Given sin 60º = √3
2 the exact value of sin300º is
A. 2
√3
B. − √3
2
C. 12
D. − 2
√3
E. 2
Example 18 A wooden ‘roof truss’ consists of a symmetrical triangle and a vertical support to
the apex as shown below. The angle of slope is 22º and the vertical height of the
truss is 1.5 metres. Ignoring joins, approximately how much wood is required?
A. 26.6 metres
Base
14.2 21.6
B
A
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B. 16.9 metres
C. 8.9 metres
D. 15.4 metres
E. 18.6 metres
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CHANCE
Example 19 There are 2.5 kg, 5 kg, 10 kg and 20 kg weights available at the gym. Amos
randomly chooses 2 weights to fit onto the rowing machine. What is the
probability that the total weight he puts on the machine is 20 kg or more?
Completing the lattice diagram may assist you.
First weight selected
Second
weight
selected
2.5 kg 5 kg 10 kg 20 kg
2.5 kg 2.5 + 2.5
5 kg
10 kg
20 kg
A. 1
2
B. 1
4
C. 5
16
D. 3
8
E. 1
8
DATA REPRESENTATION AND INTERPRETATION
Example 20 The composition of the atmosphere by volume is approximately Nitrogen 78%,
Oxygen 20.6% and other Gases 1.4%. Which of the pie charts shown below best
represents this?
A. B. C.
Oxygen
Other Other
Nitrogen Oxygen Oxygen
Other
Nitrogen Nitrogen
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D. E.
Science
The following examples show the types of items in the test, but do not necessarily indicate the
full range of items or test difficulty. For the Science test, you may use a silent, battery-
operated, non-programmable scientific calculator (not CAS/graphics calculator). For answers
to these sample questions, see Appendix D.
Read the following information about ‘relative velocity’ and answer example questions 1
and 2.
Velocity brings together the two notions of speed and direction. Velocities can be added and
subtracted. When a car is driving along the road, the direction in which the car is travelling
may be considered as positive. A positive velocity is then assigned to cars travelling in the
same direction and a negative velocity is assigned to cars travelling in the opposite direction.
Example 1 A car is driving at 90 km/h in a northerly direction and passes another car driving
at 60 km/h in a northerly direction. What is the first car’s velocity relative to the
second car?
A. 150 km/h
B. 90 km/h
C. 60 km/h
D. 30 km/h
Other Other Oxygen
Nitrogen Nitrogen
Oxygen
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Example 2 A car is driving east at 100 km/h and passes another car driving west at 80 km/h.
What is the first car’s velocity relative to the second car?
A. 180 km/h
B. 100 km/h
C. 80 km/h
D. 20 km/h
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Read the following information about ‘sky diving’ and answer example questions 3 and 4.
When a person jumps from a plane to sky dive, they experience the effects of air resistance
pushing against their body. Air resistance occurs because air molecules collide with the
person’s body. The following measurements were taken during the first 20 seconds of a sky
dive. The parachute was not opened in the first 20 seconds of the dive – the person was falling
freely.
Sky Diving Results: first 20 seconds of jump
Time elapsed (s) Distance fallen (m) Velocity (m/s) Acceleration (m/s²) Air resistance (N)
0 0 0 9.8 0
1 6 12 9.1 205
5 37 34 5.9 320
10 54 52 1.7 685
15 62 59 0.35 755
20 64 61 0 776
The units used in the table are:
s = seconds
m = metres
N = Newton (a measure of force).
Example 3 When five seconds had elapsed, what distance had the sky diver fallen?
A. 5.9 metres
B. 34 metres
C. 37 metres
D. 54 metres
Example 4 Which one of these statements is supported by the data?
Over the initial 15 second period since jumping, as air resistance increases…
A. both acceleration and velocity increase.
B. both acceleration and velocity decrease.
C. there is no change to acceleration or velocity.
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D. acceleration decreases while velocity increases.
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Read the following information about ‘atoms’ and answer example questions 5 to 7.
The atomic model of matter states that the basic building blocks of all materials are atoms.
Atoms are made up of three components: electrons, protons and neutrons. The protons and
neutrons are contained in the centre of the atom and together they form the ‘nucleus’ of the
atom. The electrons circle outside the nucleus in a series of set orbits called ‘shells’. These
shells are filled from the innermost outwards and each shell must be completely filled before
electrons can start filling the next one. The first shell may contain no more than two electrons,
and the second no more than eight. Protons have an electrical charge of +1 and electrons
have an electrical charge of -1. Neutrons have no electrical charge. Therefore an atom in its
neutral state will have an equal number of electrons and protons.
Using this model, scientists have defined a set of approximately 110 different types of atoms
called ‘elements’. In different combinations these elements make up all the materials that we
find in the world, from wood to metal to the air we breathe.
The following table lists some of the properties of the first 10 elements.
Element Symbol Total number of electrons in neutral state
Hydrogen H 1
Helium He 2
Lithium Li 3
Beryllium Be 4
Boron B 5
electron
second electron shell
maximum of 8 electrons
first electron shell
maximum of 2 electrons
neutron
proton neucleus
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Element Symbol Total number of electrons in neutral state
Carbon C 6
Nitrogen N 7
Oxygen O 8
Fluorine F 9
Neon Ne 10
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Example 5 For an atom to be electrically ‘neutral’, i.e. neither positive nor negative in total
charge, it will have…
A. an equal number of protons and neutrons.
B. an equal number of protons and electrons.
C. an equal number of neutrons and electrons.
D. an equal number of protons, neutrons and electrons.
Example 6 How many electrons will a fluorine atom have in its outer shell?
A. 2
B. 7
C. 8
D. 9
Example 7 The atomic number of an atom is the number of protons it has. Using the
information and the table above, what is the atomic number of oxygen?
A. 16
B. 10
C. 8
D. 6
Read the following information about ‘resistance’ and answer example questions 8 to 10.
An important formula in electrical theory is Ohm’s law. This is written as: V = I.R
Where:
V = voltage (in volts)
I = current (in amperes)
R = resistance (in ohms)
NB: This equation can be rewritten as I = 𝑉
𝑅 or R =
𝑉
𝐼
Example 8 Consider the series circuit shown below and answer the following question:
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If the battery voltage is 6 volts and the resistance of the globe is 100 ohms, what
is the current flowing in this circuit?
A. 6.0 amperes
B. 600 amperes
C. 0.06 amperes
D. 16.67 amperes
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Example 9 Consider the series circuit shown below and answer the following question:
A voltage drop is the voltage across a component in a circuit. In a series circuit,
the sum of the voltage drops across all the components in the circuit will equal
the supply (e.g. battery) voltage.
In the above circuit assume that the globes are the only resistances. If the battery
voltage is 9v and Voltmeter 1 shows 6v, what will Voltmeter 2 show?
A. 3 volts
B. 6 volts
C. 9 volts
D. 12 volts
Example 10 In a parallel circuit, the total current is the sum of the currents through the
individual loops. Consider the parallel circuit shown below and answer the
following question.
If the current flowing at the point shown is 1 ampere, what is the current flowing
through Globe 1?
A. 2 ampere
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B. 1 ampere
C. 0.5 ampere
D. 0.25 ampere
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Appendix D Year 10 Answers to Sample Questions
Subject Question Answer Question Answer
English Question 1 D Question 9 C
Question 2 B Question 10 C
Question 3 A Question 11 A
Question 4 D Question 12 D
Question 5 B Question 13 C
Question 6 C Question 14 A
Question 7 B Question 15 D
Question 8 A
General
Mathematics
Question 1 D Question 6 B
Question 2 B Question 7 C
Question 3 E Question 8 C
Question 4 A Question 9 B
Question 5 C Question 10 A
Advanced
Mathematics
Question 1 A Question 11 C
Question 2 B Question 12 A
Question 3 D Question 13 E
Question 4 E Question 14 B
Question 5 C Question 15 D
Question 6 A Question 16 C
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Subject Question Answer Question Answer
Question 7 D Question 17 B
Question 8 C Question 18 B
Question 9 E Question 19 A
Question 10 B Question 20 E
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Subject Question Answer Question Answer
Science Question 1 D Question 6 B
Question 2 A Question 7 C
Question 3 C Question 8 C
Question 4 D Question 9 A
Question 5 B Question 10 C
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