HSC Final Study: P1 Induction (~4.3% historical contribution)
Key Areas addressed by this worksheet
Induction (4.3%)
• All new syllabus Ext1 exams have allocated 3-marks to this topic area,
consistent with its historic allocation.
• Sum of a Series has been asked in each of the years 2018-2021 and is well
covered.
• Divisibility is another common question type where a series must be proven to
be divisible by a given integer. This question type was examined in 2022 after
a 4-year absence and is featured in the revision set.
• Skill in dealing with factorial notation has been required in the past and we
Thank you for subscribing to SmarterMaths Teacher Edition (Silver) in 2023. look at a number of questions requiring this.
• We note that inequality induction has been moved to Ext2 and is no longer
Key features of the Extension 1 “2023 HSC Comprehensive Revision Series” examinable in Ext1.
include:
• ~16 hours of cherry picked HSC revision questions by topic
• Targeted at motivated students aiming for a Band 5 or 6 result
• Weighting toward more difficult examples
• Mark allocations of topic areas reflect their HSC exam allocations
• Attempt, carefully review and annotate this revision set in Term 3
• This question set provides the foundation of a concise and high quality
revision resource for the run into the HSC exam.
Our analysis on each topic, the common question types, past areas of difficulty
and recent HSC trends all combine to create this revision set that ensures
students cover a wide cross-section of the key areas. --------------------------------------------------------
IMPORTANT: If students have been exposed to questions in these SmarterMaths HSC Teacher Edition
worksheets during the year, we say great. Many top performing students attest
SmarterMaths is an affordable, simple to use,
to the benefits of doing quality questions 2-3 times before the HSC. This type
fully online program for schools.
of revision set is aimed at creating confidence and speed through the exam,
with cherry picked questions that cover all important elements of revision while ● Sort past HSC and other supplementary "It's the best thing I've ever
avoiding low percentage rabbit hole excursions. questions with the most powerful search
tool out there.
bought (for HSC revision). It is
saving me and the faculty staff
● We analyse and incorporate your school’s
so much time, we love it."
RAP data into the program at no extra cost.
● Produce high quality, differentiated revision
worksheets in a few clicks. ~ Sean Donohue,
Chifley College
Register for a free trial by visiting our website
at www.smartermaths.com.au.
, EXTENSION 1 5. Proof, EXT1 P1 2021 HSC 12c
2023 Comprehensive Revision Series
PROOF Use mathematical induction to prove that
P1 Induction (Y12)
Exam Equivalent Time: 36 minutes (based on HSC target speed of ~1.5 minutes per mark)
for all integers . (3 marks)
Questions
1. Proof, EXT1 P1 2015 HSC 13c 6. Proof, EXT1 P1 2022 HSC 12f
Prove by mathematical induction that for all integers , Use mathematical induction to prove that is divisible by 7 for all integers . (3 marks)
. (3 marks)
7. Proof, EXT1 P1 2011 HSC 6a
2. Proof, EXT1 P1 2020 HSC 12a Use mathematical induction to prove that for ,
Use the principle of mathematical induction to show that for all integers , . (3 marks)
. (3 marks)
8. Proof, EXT1 P1 2010 HSC 7a
3. Proof, EXT1 P1 2019 HSC 14a Prove by induction that
Prove by mathematical induction that, for all integers ,
. (3 marks) is divisible by for all integers . (3 marks)
Copyright © 2004-22 The State of New South Wales (Board of Studies, Teaching and Educational Standards NSW)
4. Proof, EXT1 P1 2007 HSC 4b
Use mathematical induction to prove that is divisible by 12, for all integers . (3 marks)
Key Areas addressed by this worksheet
Induction (4.3%)
• All new syllabus Ext1 exams have allocated 3-marks to this topic area,
consistent with its historic allocation.
• Sum of a Series has been asked in each of the years 2018-2021 and is well
covered.
• Divisibility is another common question type where a series must be proven to
be divisible by a given integer. This question type was examined in 2022 after
a 4-year absence and is featured in the revision set.
• Skill in dealing with factorial notation has been required in the past and we
Thank you for subscribing to SmarterMaths Teacher Edition (Silver) in 2023. look at a number of questions requiring this.
• We note that inequality induction has been moved to Ext2 and is no longer
Key features of the Extension 1 “2023 HSC Comprehensive Revision Series” examinable in Ext1.
include:
• ~16 hours of cherry picked HSC revision questions by topic
• Targeted at motivated students aiming for a Band 5 or 6 result
• Weighting toward more difficult examples
• Mark allocations of topic areas reflect their HSC exam allocations
• Attempt, carefully review and annotate this revision set in Term 3
• This question set provides the foundation of a concise and high quality
revision resource for the run into the HSC exam.
Our analysis on each topic, the common question types, past areas of difficulty
and recent HSC trends all combine to create this revision set that ensures
students cover a wide cross-section of the key areas. --------------------------------------------------------
IMPORTANT: If students have been exposed to questions in these SmarterMaths HSC Teacher Edition
worksheets during the year, we say great. Many top performing students attest
SmarterMaths is an affordable, simple to use,
to the benefits of doing quality questions 2-3 times before the HSC. This type
fully online program for schools.
of revision set is aimed at creating confidence and speed through the exam,
with cherry picked questions that cover all important elements of revision while ● Sort past HSC and other supplementary "It's the best thing I've ever
avoiding low percentage rabbit hole excursions. questions with the most powerful search
tool out there.
bought (for HSC revision). It is
saving me and the faculty staff
● We analyse and incorporate your school’s
so much time, we love it."
RAP data into the program at no extra cost.
● Produce high quality, differentiated revision
worksheets in a few clicks. ~ Sean Donohue,
Chifley College
Register for a free trial by visiting our website
at www.smartermaths.com.au.
, EXTENSION 1 5. Proof, EXT1 P1 2021 HSC 12c
2023 Comprehensive Revision Series
PROOF Use mathematical induction to prove that
P1 Induction (Y12)
Exam Equivalent Time: 36 minutes (based on HSC target speed of ~1.5 minutes per mark)
for all integers . (3 marks)
Questions
1. Proof, EXT1 P1 2015 HSC 13c 6. Proof, EXT1 P1 2022 HSC 12f
Prove by mathematical induction that for all integers , Use mathematical induction to prove that is divisible by 7 for all integers . (3 marks)
. (3 marks)
7. Proof, EXT1 P1 2011 HSC 6a
2. Proof, EXT1 P1 2020 HSC 12a Use mathematical induction to prove that for ,
Use the principle of mathematical induction to show that for all integers , . (3 marks)
. (3 marks)
8. Proof, EXT1 P1 2010 HSC 7a
3. Proof, EXT1 P1 2019 HSC 14a Prove by induction that
Prove by mathematical induction that, for all integers ,
. (3 marks) is divisible by for all integers . (3 marks)
Copyright © 2004-22 The State of New South Wales (Board of Studies, Teaching and Educational Standards NSW)
4. Proof, EXT1 P1 2007 HSC 4b
Use mathematical induction to prove that is divisible by 12, for all integers . (3 marks)
