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BIOLOGY M7 Snapshot: Causes of Infectious Disease

HISTORICAL CONTRIBUTION

  • M7 Infectious Diseases has contributed an average of 24.1% per HSC Biology exam since the new syllabus was introduced in 2019.
  • This topic has been split into three sub-categories for analysis purposes which are: 1-Causes of Infectious Diseases (8.2%), 2-Immunity (4.3%) and 3-Prevention, Treatment and Control (11.6%).
  • This analysis looks at the sub-topic, Causes of Infectious Diseases.

HSC ANALYSIS - What to expect and common pitfalls

  • Classifying Pathogens is an extremely important topic area that has attracted high-mark longer answer questions in every new syllabus exam to date. Identifying and distinguishing pathogens using a limited description of their features has proven very challenging for a majority of students. Any revision should include 2020 HSC 32b and 2019 HSC 33d.
  • Indirect Transmission, Direct Transmission and Vectors has also been tested three times in the extended response section (most recently in 2022). 2019 HSC 31 required an example of a pathogen adaptation to facilitate entry into a host and produced a mean mark of 36%. 
  • The works of Louis Pasteur and Robert Koch have been tested in 3 exams since 2018 and need to be very well understood. In particular, students must be practised at efficiently referencing their findings into broad questions looking at causes and transmission of infectious diseases.
  • Microbial Tests have been examined in the multiple choice section in 4 of the last 5 years (absent in 2022). We note that the syllabus states that students must be able to "design" a practical investigation in this topic area (yet to be tested).

BIOLOGY M6 Snapshot: Genetic Technologies

HISTORICAL CONTRIBUTION

  • M6 Genetic Change has contributed an average of 22.8% per HSC Biology exam since the new syllabus was introduced in 2019.
  • This topic has been split into three sub-categories for analysis purposes which are: 1-Mutation (11.7%), 2-Biotechnology (4.8%) and 3-Genetic Technologies (6.3%).
  • This analysis looks at the sub-topic, Genetic Technologies.

HSC ANALYSIS - What to expect and common pitfalls

  • Genetic Technologies has attracted longer answer questions in every new syllabus Biology exam to date (including two in 2021-23) as well as at least one multiple-choice per exam making it a focus area for any revision.
  • Transgenic Organisms is the most common question theme that has been tested every year between 2019-23. 2021 HSC 33a is a "must review" question of this topic area.
  • Whole Organism Cloning and Gene Cloning are frequently tested within multiple choice and have caused problems. 2019 HSC 20 and 2018 HSC 18 produced mean marks of 23% and 37% respectively and deserve revision attention.
  • 2014 HSC 29 looks at the process of whole organism cloning and represents an important revision question that departs from the more common multiple-choice style of testing.
  • We note that this topic area has a significant overlap with M6 Biotechnology, including the impact of genetic techniques in agriculture and on genetic diversity, as well as the benefits of genetic technologies in various settings and applications.

BIOLOGY M6 Snapshot: Biotechnology

HISTORICAL CONTRIBUTION

  • M6 Genetic Change has contributed an average of 22.8% per HSC Biology exam since the new syllabus was introduced in 2019.
  • This topic has been split into three sub-categories for analysis purposes which are: 1-Mutation (11.7%), 2-Biotechnology (4.8%) and 3-Genetic Technologies (6.3%).
  • This analysis looks at the smallest sub-topic, Biotechnology.

HSC ANALYSIS - What to expect and common pitfalls

  • Biotechnology was examined in longer answer questions in 2023 and 2021, as well as three multiple choice questions since 2019.
  • Evaluating Genetic Technology is the key aspect of this topic. It is crucial to understand and clearly state how any given technology works and then evaluate its benefits and potential dangers to biodiversity.
  • Any evaluation should include, where possible, a discussion on societal, agricultural, medical and industrial effects.
  • 2021 HSC 33c and 2019 HSC 24 are key revision examples that require well set out answers describing a technology's effects on the biodiversity of species (genetic) and ecosystem levels. It is worth noting that in the 2019 example, students could choose two examples of technologies - be prepared!
  • Evaluating the benefits and dangers of biotechnology through an explicit ethical framework was tested in 2014 Q32e and deserves revision attention.
  • This topic has a significant content overlap with M6 Genetic Technologies and numerous questions appear in both areas.

BIOLOGY M6 Snapshot: Mutation

HISTORICAL CONTRIBUTION

  • M6 Genetic Change has contributed an average of 22.8% per HSC Biology exam since the new syllabus was introduced in 2019.
  • This topic has been split into three sub-categories for analysis purposes which are: 1-Mutation (11.7%), 2-Biotechnology (4.8%) and 3-Genetic Technologies (6.3%).
  • This analysis looks at the largest and most important sub-topic, Mutation.

HSC ANALYSIS - What to expect and common pitfalls

  • Mutation is easily the largest and most important sub-topic within M6 Genetic Change, attracting longer answer questions in each new syllabus exams to date (two in 2023, 2022 and 2020) as well as at least two multiple choice questions each year except 2023.
  • Somatic vs. Germ-Line is a key revision area focusing on the comparison of these two types of mutations, with most questions requiring a good understanding of the development of the mutation in off-spring. Examined every year with the notable exception of 2023.
  • Point & Chromosomal Mutations questions also often require comparisons including the process of how they occur and their effects. Longer answer questions have appeared regularly and caused problems making this area an important topic for revision.
  • Mechanisms of Change & Variation attracted a significant 7-mark question in 2023 after being absent the previous 2 years. Students must have a good understanding of aspects such as genetic drift and gene flow to score highly in this area.
  • Non-Coding DNA has been examined via challenging multiple-choice twice in new syllabus exams and deserves attention.
  • Mutagens has contributed modestly to past exams. Database questions look at both chemical and biological variations as well as EMR.

BIOLOGY M5 Snapshot: Genetic Variation

HISTORICAL CONTRIBUTION

  • M5 Heredity has contributed an average of 26.3% per HSC Biology exam since the new syllabus was introduced in 2019.
  • This topic has been split into four sub-categories for analysis purposes which are: 1-Reproduction (6.5%), 2-Cell Replication (3.0%), 3-DNA and Polypeptide Synthesis (5.2%), Genetic Variation/Inheritance Patterns (11.6%).
  • This analysis looks at the largest sub-topic, Genetic Variation/Inheritance.

HSC ANALYSIS - What to expect and common pitfalls

  • Genetic Variation/Inheritance is easily the biggest topic area in Module 5, attracting a whopping average of 2.5 longer answer questions and 2.5 multiple choice questions per new syllabus exam.
  • Pedigrees is a common question type, examined each year with the exception of 2021, including a substantial 6-mark question in 2020 that was poorly answered and deserves attention.
  • Punnet squares have been tested in 4 out of 5 new syllabus exams, including three times in the longer answer section. Drawing and analysing punnet squares is a critical skill for all students and numerous database questions cover this area.
  • Meiosis was examined within this topic in high-mark questions in both 2019 and 2020 (notably absent in 2022-23), causing problems on each occasion. 
  • Allele Frequency Data questions have been a sneaky contributor to new syllabus exams, tested three times in new syllabus exams (most recently in 2022). Substantial mark allocations in 2022 and 2019 along with low mean marks demand a revision focus here.
  • Inheritance Patterns has been examined twice in 3-mark questions (most recently in 2023). 2021 HSC 27 produced a 51% mean mark and is an important revision question.

BIOLOGY M5 Snapshot: DNA and Polypeptides

HISTORICAL CONTRIBUTION

  • M5 Heredity has contributed an average of 26.3% per HSC Biology exam since the new syllabus was introduced in 2019.
  • This topic has been split into four sub-categories for analysis purposes which are: 1-Reproduction (6.5%), 2-Cell Replication (3.0%), 3-DNA and Polypeptide Synthesis (5.2%), Genetic Variation/Inheritance Patterns (11.6%).
  • This analysis looks at the sub-topic, DNA and Polypeptide Synthesis.

HSC ANALYSIS - What to expect and common pitfalls

  • DNA and Polypeptide Synthesis has attracted at least one longer answer question in each new syllabus exam (two in 2023, 2022) and a multiple choice question in 4 out of 5 years.
  • It has many overlapping categories, with a main focus on the production of mRNA (transcription) which goes on to produce proteins/polypeptides (translation).
  • RNA, Translation and Transcription sub-categories dominate mark allocations in this topic area and have produced sub-50% mean marks on all but one occasion in new syllabus exams. The need for a revision focus here cannot be overstated.
  • Many questions require students to number steps in a process or draw a flow chart. These skills are critical and numerous difficult examples appear in the database. 2022 HSC 31b and 2019 HSC 33a are recommended revision.
  • Eukaryotes and Prokaryotes were specifically tested in 2020 and 2022, the latter in a 3-mark longer answer question that produced a 24% mean mark and warrants attention.

BIOLOGY M5 Snapshot: Cell Replication

HISTORICAL CONTRIBUTION

  • M5 Heredity has contributed an average of 26.3% per HSC Biology exam since the new syllabus was introduced in 2019.
  • This topic has been split into four sub-categories for analysis purposes which are: 1-Reproduction (6.5%), 2-Cell Replication (3.0%), 3-DNA and Polypeptide Synthesis (5.2%), Genetic Variation/Inheritance Patterns (11.6%).
  • This analysis looks at the sub-topic, Cell Replication.

HSC ANALYSIS - What to expect and common pitfalls

  • Cell Replication is a relatively small module with questions relating to DNA structure and the process of mitosis and meiosis.
  • Questions relating to DNA structure are the most common, examined most years in the multiple choice section, although 2023 HSC 21 saw a 3-mark longer answer question. Examiners typically test DNA base pairing rules or nucleotide composition (2016 HSC 10 caused problems and deserves attention).
  • While meiosis is less examined within this topic, it remains important gateway knowledge for later topics in M5 Genetic Variation and M6 Mutation.
  • When examined, meiosis has historically proved challenging with 2016 HSC 13-14 and  2018 HSC 29 producing sub-50% mean marks. Revision recommended here.

BIOLOGY M5 Snapshot: Reproduction

HISTORICAL CONTRIBUTION

  • M5 Heredity has contributed an average of 26.3% per HSC Biology exam since the new syllabus was introduced in 2019.
  • This topic has been split into four sub-categories for analysis purposes which are: 1-Reproduction (6.5%), 2-Cell Replication (3.0%), 3-DNA and Polypeptide Synthesis (5.2%), Genetic Variation/Inheritance Patterns (11.6%).
  • This analysis looks at the sub-topic, Reproduction.

HSC ANALYSIS - What to expect and common pitfalls

  • Reproduction is a broad content-heavy topic area, examined in longer answer questions in 4 out of 5 new syllabus exams (absent only in 2022).
  • Human/Mammal Reproduction is easily the most commonly examined sub-category in this topic. Questions have appeared covering the chronological progression of menstrual cycle → fertilisation → implantation → birth, with hormones regularly tested as an overarching theme.
  • Internal and external fertilisation was specifically examined in 2023, 2020 and 2019. 2020 HSC 25 was a high-mark longer answer question that caused problems and deserves specific revision attention.
  • Fungi reproduction has been examined twice with healthy mark allocations and produced low mean marks on each occasion. 2023 HSC 33 required a comparison between human and fungi reproduction, while 2019 HSC 27 looked at yeast.
  • We note that plant, bacteria and protist reproduction are specifically mentioned in the syllabus but are yet to attract any meaningful mark allocations in new syllabus exams to date.

PHYSICS M8 Snapshot: Deep Inside the Atom

HISTORICAL CONTRIBUTION

  • M8 From the Universe to the Atom has contributed an average of 22.3% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into four sub-categories for analysis purposes which are: 1-Origins of Elements (3.9%), 2-Structure of the Atom (3.0%), 3-Quantum Mechanical Nature of the Atom (4.8%), Properties of the Nucleus (8.6%) and 5-Deep Inside the Atom (2.0%).
  • This analysis looks at the smallest sub-topic, Deep Inside the Atom (2.0%).

HSC ANALYSIS - What to expect and common pitfalls

  • Deep Inside the Atom has contributed modestly to new syllabus exams with dedicated longer answer questions appearing in the 2019 and 2020 papers and three multiple-choice questions in the past 5 years (most recently in 2022).
  • The most significant question type requires a deep understanding of the Standard Model and related experiments. Attention should be paid to 2023 HSC 33 and 2020 HSC 30a. The former was was an extremely broad cross topic question while the latter required students to explain linear accelerator experiments in this context and caused problems (mean mark of 46%). 
  • Quarks have been examined specifically in multiple-choice questions in 2022 HSC 5 MC and 2019 HSC 12 MC, the latter of which produced a 51% mean mark and deserves attention.

PHYSICS M8 Snapshot: Properties of the Nucleus

HISTORICAL CONTRIBUTION

  • M8 From the Universe to the Atom has contributed an average of 22.3% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into four sub-categories for analysis purposes which are: 1-Origins of Elements (3.9%), 2-Structure of the Atom (3.0%), 3-Quantum Mechanical Nature of the Atom (4.8%), Properties of the Nucleus (8.6%) and 5-Deep Inside the Atom (2.0%).
  • This analysis looks at the largest sub-topic, Properties of the Nucleus (8.6%).

HSC ANALYSIS - What to expect and common pitfalls

  • Properties of the Nucleus is the most frequently and diversely tested topic within Module 8. Questions range from low-band multiple choice to high difficulty extended responses.
  • Radioactive Decay and Conservation of Mass-Energy are frequently examined content areas, each being tested 4 out of the last 5 years (most recently in 2023). Radioactive Decay requires more challenging calculations and should be a revision focus.
  • Nuclear Fission was last examined in 2020 HSC 16 MC and 2019 HSC 36, the latter in a significant 7-mark allocation that produced a 30% mean mark and is a “must review” question (worth noting the 2019 multiple-choice question also produced a 25% mean mark!).
  • 2019 HSC Q36 also demonstrates how students may be required to apply core physics concepts (eg. Law of Conservation of Momentum, Mass/Energy equivalence) to a range of different scenarios. 
  • Students must understand the definitions and differences between the terms binding energy and mass defect. A deep understanding of these terms can greatly simplify difficult questions.

PHYSICS M8 Snapshot: Quantum Mechanical Nature of the Atom

HISTORICAL CONTRIBUTION

  • M8 From the Universe to the Atom has contributed an average of 22.3% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into four sub-categories for analysis purposes which are: 1-Origins of Elements (3.9%), 2-Structure of the Atom (3.0%), 3-Quantum Mechanical Nature of the Atom (4.8%), Properties of the Nucleus (8.6%) and 5-Deep Inside the Atom (2.0%).
  • This analysis looks at the sub-topic, Quantum Mechanical Nature of the Atom (3.5%).

HSC ANALYSIS - What to expect and common pitfalls

  • Quantum Mechanical Nature of the Atom is a modest contributor to new syllabus exams but has nonetheless appeared in the longer answer section every year (sometimes just as “part” of a broader question), and multiple-choice questions every year except 2022.
  • Bohr's model of the atom is the most commonly tested concept, tested every year between 2020-22.
  • De Broglie's and Schrödinger's contributions are less examined but remain important as they generate a cohesive understanding of the development of the atomic model.
  • Developing concise summaries of various scientists' contributions to the model of the atom is critical revision. Attention should be given to 2021 HSC Q29 (state mean mark 40%) which is a classic example that requires an efficient summary and synthesis of this type of information.

PHYSICS M8 Snapshot: Structure of the Atom

HISTORICAL CONTRIBUTION

  • M8 From the Universe to the Atom has contributed an average of 22.3% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into four sub-categories for analysis purposes which are: 1-Origins of Elements (3.9%), 2-Structure of the Atom (3.0%), 3-Quantum Mechanical Nature of the Atom (4.8%), Properties of the Nucleus (8.6%) and 5-Deep Inside the Atom (2.0%).
  • This analysis looks at the sub-topic, Structure of the Atom (3.0%).

HSC ANALYSIS - What to expect and common pitfalls

  • Structure of the Atom has been examined in longer answer questions every year of the new syllabus and a singular multiple choice question in 2019.
  • Cathode Rays, Thomson's Charge to Mass Experiment and Millikan's Oil Drop Experiment are some of the most commonly tested content areas, appearing in the 2023, 2021 and 2019 exams.
  • Critical revision: high-mark, broad scope questions such as 2023 HSC 33 allow students to use their knowledge of this subject area to add evidence to their responses without being directed to describe specific experiments. Prepare for this question style.
  • In discussing models of the atom within Module 8, it is worth noting that Rutherford's model is also commonly tested alongside its relationship with Bohr's Model which has a significant overlap with M8 Quantum Mechanical Nature of the Atom.
  • We also recommend revision attention being given to 2019 HSC Q32 and 2022 HSC Q31. These questions had low state mean marks and required students to provide longer responses that assessed multiple concepts.

PHYSICS M8 Snapshot: Origins of Elements

HISTORICAL CONTRIBUTION

  • M8 From the Universe to the Atom has contributed an average of 22.3% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into four sub-categories for analysis purposes which are: 1-Origins of Elements (3.9%), 2-Structure of the Atom (3.0%), 3-Quantum Mechanical Nature of the Atom (4.8%), Properties of the Nucleus (8.6%) and 5-Deep Inside the Atom (2.0%).
  • This analysis looks at the sub-topic, Origins of Elements (3.9%).

HSC ANALYSIS - What to expect and common pitfalls

  • H-R diagrams and spectra are the most commonly tested concepts within this topic, attracting longer answer questions in 3 of the last 4 exams, as well as a multiple choice most years.
  • H-R diagrams have attracted longer response questions in both 2023 and 2022 with noteworthy allocations of 5 and 4 marks respectively and difficulty level in the band 3–4 range.
  • Specific attention should be given to spectra questions due to their frequency and connection to other topics such as M7:Light-Quantum model and M8:Quantum Mechanical Nature of the Atom.
  • While the Big Bang has not yet been examined in new syllabus exam, it is coming and any topic revision should cover this area.
  • Hubble and the Expansion of the universe has caused serious problems on the two occasions it has been examined via multiple choice (2023 HSC 20 MC produced a mean mark of just 11%) and needs to be covered.
  • Special focus should be paid towards 2021 HSC 32 where students struggled to synthesise their knowledge of scientific theory with their understanding of practical experiments.

PHYSICS M7 Snapshot: Light and Special Relativity

HISTORICAL CONTRIBUTION

  • M7 The Nature of Light looks has contributed an average of 26.1% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into four sub-categories for analysis purposes which are: 1-Electromagnetic Spectrum (3.6%), 2-Light: Wave Model (5.8%), 3-Light: Quantum Model (9.8%) and 4-Light and Special Relativity (7.0%).
  • This analysis looks at the sub-topic, Light and Special Relativity (7.0%).

HSC ANALYSIS - What to expect and common pitfalls

  • Light and Special Relativity has attracted a longer response question every year of the new syllabus exams, including two in 2020. Multiple-choice questions have been asked every year except for 2019.
  • Time Dilation is easily the most examined sub-category in this area with significant 3-6 mark allocations in four new syllabus exams to date (most recently in 2023).
  • Length Contraction has been examined through multiple choice questions three times in new syllabus exams to date. 2023 HSC 19 MC and 2022 HSC 20 MC proved challenging and deserve attention.
  • Momentum Dilation has appeared in longer answer questions in both 2021 and 2020. Effective revision must include explaining this concept in a concise way, which was required in both examples. 
  • Einstein's Postulates looks at questions dealing with inertial frames of reference and the constancy of the speed of light. This area was examined in 2021 and 2020 of the new syllabus exams.
  • We recommend carefully reviewing the thought experiments and experimental evidence regarding time dilation as these areas commonly cause problems. Important revision examples include 2019 HSC 27 and 2022 HSC 30.

PHYSICS M7 Snapshot: Light: Quantum Model

HISTORICAL CONTRIBUTION

  • M7 The Nature of Light looks has contributed an average of 27.0% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into four sub-categories for analysis purposes which are: 1-Electromagnetic Spectrum (5.1%), 2-Light: Wave Model (5.9%), 3-Light: Quantum Model (9.2%) and 4-Light and Special Relativity (6.8%).
  • This analysis looks at the largest sub-topic, Light: Quantum Model (9.2%).

HSC ANALYSIS - What to expect and common pitfalls

  • The Quantum Model of Light is the largest contributor to M7 The Nature of Light, appearing in two longer answer questions each new syllabus exam (except for 2022) as well as at least two multiple-choice.
  • The Photoelectric Effect is the most commonly tested topic area, attracting a multiple choice question in each exam of the new syllabus, as well as high mark allocations in longer response questions in 2022 and 2019.
  • Experiments which provide evidence for the quantum model of light have been the subject of regular testing, and must be a revision focus (notably absent in the 2023 exam). We note 2021 HSC Q33 which attracted a substantial 9 mark allocation and proved very challenging as key revision.
  • Blackbodies has also been examined frequently, appearing every year of the new syllabus, including two longer answer questions in 2020 with substantial mark allocations. 2020 HSC Q26 caused major problems and deserves specific revision attention.
  • Kinetic energy calcs is a concept which has been examined recently in 2021 HSC 20 MC and 2022 HSC 26b. These examples required cross-topic application of formulas in a photoelectric effect context and proved very challenging.

PHYSICS M7 Snapshot: Light: Wave Model

HISTORICAL CONTRIBUTION

  • M7 The Nature of Light looks has contributed an average of 27.0% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into four sub-categories for analysis purposes which are: 1-Electromagnetic Spectrum (5.1%), 2-Light: Wave Model (5.9%), 3-Light: Quantum Model (9.2%) and 4-Light and Special Relativity (6.8%).
  • This analysis looks at the sub-topic, Light: Wave Model (5.9%).

HSC ANALYSIS - What to expect and common pitfalls

  • Light: Wave Model has been tested via longer answer questions in each of the last 4 HSC exams, including a large multi-part question in 2022, and as a significant contributor to a 9-mark question in 2021. A key revision area.
  • Young's Double Slit Experiment has already been tested 3 times since the new syllabus was introduced (most recently in 2022). Students should be prepared to combine both scientific theory in conjunction with a calculation component.
  • Polarisation has been examined in 4 new syllabus exams (absent only in 2019), including a challenging 4-mark longer answer question in 2023 HSC 29 and difficult multiple choice problems in 2021 and 2020. An important revision area.
  • The experimental evidence for models of light proposed by Newton and Huygens has not yet been examined extensively. There is scope to examine this concept in significantly more detail in our view and revision attention is recommended.
  • 2022 HSC Q27 assesses a range of concepts within this sub-topic. We recommend revision attention be directed towards part a) of this question as the unique way in which it assessed Huygens' model caused problems for students.

PHYSICS M7 Snapshot: Electromagnetic Spectrum

HISTORICAL CONTRIBUTION

  • M7 The Nature of Light looks has contributed an average of 27.0% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into four sub-categories for analysis purposes which are: 1-Electromagnetic Spectrum (5.1%), 2-Light: Wave Model (5.9%), 3-Light: Quantum Model (9.2%) and 4-Light and Special Relativity (6.8%).
  • This analysis looks at the sub-topic, Electromagnetic Spectrum (5.1%).

HSC ANALYSIS - What to expect and common pitfalls

  • Electromagnetic Spectrum has been examined every year of the new syllabus, most commonly as a lower band question in the long response section. We note 2023 attracted just a single multiple choice question.
  • Spectroscopy and Stars are the most commonly tested concepts and are usually tested alongside each other. A huge 8-mark allocation in 2020 HSC 26 is a must review question in this content area.
  • Maxwell's contribution has only been tested once in the new syllabus (2019 HSC 25). Despite being a relatively straightforward question it produced a sub-50% mean mark and deserves attention.
  • Specific revision is recommended for 2020 HSC 18 MC which requires a deeper understanding of scientific theories, rather than memorisation (mean mark 21%).

PHYSICS M6 Snapshot: Applications of the Motor Effect

HISTORICAL CONTRIBUTION

  • M6 Electromagnetism looks has contributed an average of 28.1% per HSC Physics exam since the new syllabus was tested in 2019.
  • This topic has been split into four sub-categories for analysis purposes which are: 1-Charged Particles, Conductors, and Electric/Magnetic Fields (7.0%), 2-The Motor Effect (2.6%), 3-Electromagnetic Induction (11.8%) and 4-Applications of the Motor Effect (6.7%).
  • This analysis looks at the sub-topic, Applications of the Motor Effect (6.7%).

HSC ANALYSIS - What to expect and common pitfalls

  • Torque is the most commonly assessed concept within this subtopic. It has received significant mark allocations in the 2020-23 HSC exams and must be a revision focus.
  • Back Emf is commonly assessed within wide scope explanatory questions where students can choose to use this concept as part of a wider argument or as difficult multiple-choice questions (see 2022 HSC 19 MC and 2021 HSC 12 MC).
  • DC Motor Components was tested for the first time in new syllabus exams in 2023 in a band 4 longer answer question. It is worth noting that this content area was the subject of poorly answered multiple choice questions in 2018 and 2016 HSC exams that deserve attention.
  • AC Induction Motors as well as Generators have only attracted a single multiple choice question each, since 2019. There is scope and a likelihood of longer response questions to appear in future exams, which is reflected in the database.
  • Magnetic breaking has attracted longer answer questions in both 2023 and 2022 and must be revised carefully.

PHYSICS M6 Snapshot: Electromagnetic Induction

HISTORICAL CONTRIBUTION

  • M6 Electromagnetism looks has contributed an average of 28.1% per HSC Physics exam since the new syllabus was tested in 2019.
  • This topic has been split into four sub-categories for analysis purposes which are: 1-Charged Particles, Conductors, and Electric/Magnetic Fields (7.0%), 2-The Motor Effect (2.6%), 3-Electromagnetic Induction (11.8%) and 4-Applications of the Motor Effect (6.7%).
  • This analysis looks at the largest sub-topic, Electromagnetic Induction (11.8%).

HSC ANALYSIS - What to expect and common pitfalls

  • Electromagnetic Induction is the most tested subtopic of Module 6, contributing two longer answer questions in each of the last 3 exams, as well as one multiple choice question per exam, on average. 
  • Lenz and Faraday represent the most commonly examined concepts, being tested extensively in the long answer section of the paper every year since 2020 in questions worth a highly significant 7-9 marks. 
  • Lenz and Faraday questions typically require students to analyse situations where induced currents arise. 2023 HSC 30, 2020 HSC Q33 and 2021 HSC Q31 all caused problems and deserve particular attention.
  • Transformer Calculations have been examined in 4 of the last 5 new syllabus exams, including longer answer questions in 2023 and 2019. While voltage calculations have been well answered, follow up questions looking at efficiency and circuit resistance have proven challenging and represent important revision.
  • Electromagnetic Induction commonly appears in difficult questions towards the end of the multiple choice section. 2019 HSC Q18 and 2021 HSC Q10 represent the upper difficulty level students will encounter and deserve attention.

PHYSICS M6 Snapshot: The Motor Effect

HISTORICAL CONTRIBUTION

  • M6 Electromagnetism looks has contributed an average of 28.1% per HSC Physics exam since the new syllabus was tested in 2019.
  • This topic has been split into four sub-categories for analysis purposes which are: 1-Charged Particles, Conductors, and Electric/Magnetic Fields (7.0%), 2-The Motor Effect (2.6%), 3-Electromagnetic Induction (11.8%) and 4-Applications of the Motor Effect (6.7%).
  • This analysis looks at the smallest sub-topic, The Motor Effect (2.6%).

HSC ANALYSIS - What to expect and common pitfalls

  • The Motor Effect is the shortest and least tested sub-topic of module 6, assessing just 3 main concepts.
  • Force on a Current-Carrying Conductor and Force Between Two Current-Carrying Conductors are the two most commonly tested concepts.
  • Force on a Current-Carrying Conductor has easily attracted the highest mark allocations to date, tested in 4 of 5 new syllabus exams including a 3-mark allocation in 2019 HSC 28 that caused problems.
  • We note that at least one of these two concepts has been assessed in the multiple choice section every year of the new syllabus. 2021 HSC Q17 and 2019 HSC Q17 both produced sub-50% mean marks and deserve revision attention.
  • The third main concept looks at the connection between the ampere and Newton's Third Law which has not yet been appeared in a new syllabus HSC exam. However, it remains recommended revision in our view as it relates to a specific syllabus dot point and has a good possibility of being tested in the coming year(s).

PHYSICS M6 Snapshot: Charged Particles, Conductors …

HISTORICAL CONTRIBUTION

  • M6 Electromagnetism looks has contributed an average of 28.1% per HSC Physics exam since the new syllabus was tested in 2019.
  • This topic has been split into four sub-categories for analysis purposes which are: 1-Charged Particles, Conductors, and Electric/Magnetic Fields (7.0%), 2-The Motor Effect (2.6%), 3-Electromagnetic Induction (11.8%) and 4-Applications of the Motor Effect (6.7%).
  • This analysis looks at the sub-topic, Charged Particles, Conductors, and Electric/Magnetic Fields (7.0%).

HSC ANALYSIS - What to expect and common pitfalls

  • Charged Particles, Conductors, and Electric/Magnetic Fields has attracted two multiple choice questions per year and at least one longer answer question worth between 3-7 marks (note 2023 had the lowest 3-mark allocation).
  • Charged Particles in Electric Fields is easily the most commonly tested sub-topic. We note it is often assessed alongside Charged Particles in Magnetic Fields (most recently in 2023 HSC 24).
  • A deep understanding of the directions of forces on charges travelling in electric and/or magnetic fields is required. Competence in using the right hand palm rule is critical here, as questions typically result in sub-50% mean marks.
  • Kinematic/Work Calculations, where equations covered in M5: Projectile Motion are applied to particles moving in electric fields has proven very challenging and must be a revision focus (see 2020 HSC Q34 which required extensive algebra).

PHYSICS M5 Snapshot: Projectile Motion

HISTORICAL CONTRIBUTION

  • M5 Advanced Mechanics has contributed an average of 22.7% per HSC Physics exam since the new syllabus was tested in 2019.
  • This topic has been split into three sub-categories for analysis purposes which are: 1-Circular Motion (5.9%), 2-Motion in Gravitational Fields (8.9%) and 3-Projectile Motion (7.9%).
  • This analysis looks at the sub-topic, Projectile Motion.

HSC ANALYSIS - What to expect and common pitfalls

  • Projectile Motion is commonly assessed in both the multiple-choice section, where it averages two questions per new syllabus exam, and the longer response section, where it has appeared at least once every year (2022 and 2020 included two questions each).
  • Projectile Motion Models looks at the core equations of projectile motion. Students require a deep understanding of the implications resulting from changes such as adjusting launch velocities or launch angles (see 2022 HSC Q29 which caused problems).
  • Velocity and Acceleration concepts have been tested in the multiple choice section 3 out of the last 5 years (most recently in 2022). Questions generally focus on how a projectile's velocity and/or acceleration change or remain constant throughout its trajectory.
  • More difficult questions typically involve a strong understanding of the vertical and horizontal components of projectile motion to find a projectile's range, launch angle or time of flight. 2023 HSC 32 incorporated both circular and projectile motion in a difficult 7-mark question that warrants attention.
  • Questions combining Projectile Motion with cross topics such as the Law of Conservation of Energy and kinetic energy represent important revision.

PHYSICS M5 Snapshot: Motion in Gravitational Fields

HISTORICAL CONTRIBUTION

  • M5 Advanced Mechanics has contributed an average of 22.7% per HSC Physics exam since the new syllabus was tested in 2019.
  • This topic has been split into three sub-categories for analysis purposes which are: 1-Circular Motion (5.9%), 2-Motion in Gravitational Fields (8.9%) and 3-Projectile Motion (7.9%).
  • This analysis looks at the largest subtopic, Motion in Gravitational Fields.

HSC ANALYSIS - What to expect and common pitfalls

  • Motion in Gravitational Fields has been extensively tested every year of the new physics syllabus, attracting an impressive average of 2 longer answer and 2.5 multiple-choice questions per year since 2019.
  • Gravity is the most commonly tested concept within this subtopic and has been tested in both multiple choice and longer answer questions in each of the past three years. Although only examined at a band 3 difficulty level in 2023, it is a key revision area given sub-50% mean marks are regularly produced.
  • Energy Changes involves calculation heavy questions where students need to consider both potential and kinetic energy changes. Examined in the longer answer section of 4 out of 5 new syllabus exams (only absent in 2019), this content area should be a revision focus area.
  • Orbital Velocity has been examined 4 times in new syllabus exams via multiple choice (most recently in 2023) and deserves attention.
  • While less examined, the concept of Newton's Three Laws remains vital due to the difficulty involved. Revise key physics principles here and be prepared to apply them in unfamiliar scenarios!

PHYSICS M5 Snapshot: Circular Motion

HISTORICAL CONTRIBUTION

  • M5 Advanced Mechanics has contributed an average of 22.7% per HSC Physics exam since the new syllabus was tested in 2019.
  • This topic has been split into three sub-categories for analysis purposes which are: 1-Circular Motion (5.9%), 2-Motion in Gravitational Fields (8.9%) and 3-Projectile Motion (7.9%).
  • This analysis looks at the smallest sub-topic, Circular Motion (5.9%).

HSC ANALYSIS - What to expect and common pitfalls

  • Circular Motion is the smallest contributing subtopic within M5 Advanced Mechanics, responsible for ~5.9% of new syllabus exams. It has been examined in the longer answer section of each new syllabus exam with the exception of 2020, as well as contributing an average of one multiple choice question per year.
  • The concept of Centripetal Force and associated calculations is commonly tested, most recently in 2022 and 2019 . 
  • Applications of Circular Motion attracted a significant 7-mark cross topic allocation with projectile motion in 2023 HSC Q32 which proved challenging and deserves revision attention.
  • Common cross-topic questions involve a circular motion component within a gravitational or electric/magnetic field. We recommend revision attention be paid to 2022 HSC Q35 and 2017 HSC Q30 which both caused problems. 

PHYSICS, M7 Snapshot: The Nature of Light

 

HISTORICAL CONTRIBUTION

  • M7 The Nature of Light has contributed an average of 26.6% per HSC Physics exam, since the new syllabus was introduced in 2019.
  • This topic has been split into four sub-topics for analysis purposes which are: 1-Electromagnetic Spectrum (4.0%), 2-The Wave Model of Light (5.8%), 3-The Quantum Model of Light (9.8%), and 4-Light and Special Relativity (7.0%).
  • This analysis looks at the largest sub-topic The Quantum Model of Light.

HSC ANALYSIS - What to expect and common pitfalls

  • The Quantum Model of Light is the one sub-topic that has received a significant mark allocation, each year since 2019, without fail (we note 2019 allocated just the two marks to the The Wave Model of Light).
  • Questions requiring a deep understanding of the wave/particle duality of light were asked in 2020 and 2021. Worth noting the 2021 example received a huge 9 mark allocation and produced a mean mark of just 52%. A key revision question.
  • The photo-electric effect has been examined at least once each year and produced sub-50% mean marks in both 2022 (Q14) and 2021 (Q20).
  • Temperature has been a key theme within this topic and examined every year. We recommend students review this sub-category carefully.

EXT2 N1 Snapshot: Exponential Form

HISTORICAL CONTRIBUTION

  • N1 Introduction to Complex Numbers has contributed 7.5% per new syllabus Ext2 exam since it was introduced in 2020.
  • We have split this topic into three categories for analysis purposes which are: 1-Arithmetic of Complex Numbers (3.3%), 2-Argand Diagrams and Mod/Arg Form (0.5%) and 3-Exponential Form (3.7%).
  • This analysis looks at Exponential Form.

HSC ANALYSIS - What to expect and common pitfalls

  • Exponential Form (3.7%) is an extremely important new comer to Extension 2 complex numbers, having appeared in a dedicated longer answer question within N1 Introduction to Complex Numbers every new syllabus exam, as well as an extra multiple choice question in 2020.
  • Worth noting here that the above contributions do not include exponential form's contribution to N2 Using Complex Numbers which are even greater (and covered in the later topic)!
  • Converting a complex number from Cartesian to exponential form is a core skill that was last examined in 2022 Ext2 11c, which also required the application of De Moivre to the result. An important question to review.
  • While 2021 offered up a simple multiplication question of two complex numbers in exponential form, the 2020 paper challenged students with cross topic questions that combined exponential form with binomial expansion, integration (2020 Ext2 13d) and maximum value calculations (2020 Ext2 9 MC). 
  • Exponential form can also offer an efficient solution strategy without being explicitly stated in the question. 2023 Ext2 3 MC provides a good example of this situation.
  • This database includes numerous examples informed by the new syllabus NESA Topic Guidance and Sample Exam materials.

EXT2 N1 Snapshot: Argand Diagrams

HISTORICAL CONTRIBUTION

  • N1 Introduction to Complex Numbers has contributed 7.5% per new syllabus Ext2 exam since it was introduced in 2020.
  • We have split this topic into three categories for analysis purposes which are: 1-Arithmetic of Complex Numbers (3.3%), 2-Argand Diagrams and Mod/Arg Form (0.5%) and 3-Exponential Form (3.7%).
  • This analysis looks at Argand Diagrams and Mod/Arg Form.

HSC ANALYSIS - What to expect and common pitfalls

  • Argand Diagrams and Mod/Arg Form (0.5%) was regularly examined pre-2020 in 4–5 mark questions although we note this has fallen off a cliff with just two multiple choice questions in new syllabus exams to date.
  • Although dedicated questions with significant mark allocations look unlikely to return at this stage, this topic area represents important foundational knowledge for more difficult later topics within N2 Using Complex Numbers.
  • The most common question type is converting the Cartesian form of a complex number into mod/arg form and then raising it to a power using De Moivre. The database includes numerous examples of this.
  • Revision should cover all basic identities involving modulus and argument. Note 2020 Ext2 N1 4 MC where one third of students answered incorrectly.
  • Revision of 2008 Ext2 N1 2b is recommended where equating real parts of two answers is used to find the exact surd form of a trig ratio.

EXT1 V1 Snapshot: Vectors, Force and Velocity

HISTORICAL CONTRIBUTION

  • Vectors has contributed a highly significant average of 18.6% per new syllabus Ext1 exam since its introduction in 2020.
  • This topic has been split into four categories for analysis purposes: 1-Operations with Vectors (6.8%), 2-Vectors, Force and Velocity (1.1%), 3-Vectors and Geometry (5.0%), and 4-Vectors and Projectile Motion (5.7%).
  • This analysis looks at the smallest topic area, Vectors, Force and Velocity.

HSC ANALYSIS - What to expect and common pitfalls

  • Vectors, Force and Velocity (1.1%) was last examined in 2021 in a challenging longer answer question worth 3 marks. 
  • 2021 Ext1 14a looked at a vector application within motion and caused major problems, producing a mean mark of 31%. This question is key revision in our view, along with other similar examples that have been added to the database.
  • Force and vectors is explicitly mentioned in the new syllabus and appeared in the NESA Ext1 sample examination in a 3-mark question. We have taken note and covered this area in the database.

EXT1 C3 Snapshot: Differential Equations and Slope Fields

HISTORICAL CONTRIBUTION

  • C3 Application of Calculus has contributed a highly significant average 15.3% per new syllabus Ext1 exam since it was introduced in 2020.
  • This topic has been split into two sub-categories for analysis purposes which are: 1-Further Areas and Solids of Revolution (6.4%) and 2-Differential Equations (8.9%).
  • This analysis looks at a sub-topic of Differential Equations - Equations and Slope Fields (4.7%).

HSC ANALYSIS - What to expect and common pitfalls

  • Equations and Slope Fields make up the most significant examinable content within Differential Equations in new syllabus exams to date, appearing in three dedicated questions in 2022 and 2020, and two in 2021.
  • Solving differential equations where the derivative is  `f(y)`  or  `f(x,y)`  is a core competency in this topic area that has been examined each year 2020-22 (notably absent in 2023), including 2 questions worth a total 5 marks in 2020! A key revision focus area.
  • 2022 Ext1 14a produced an outlier mean mark within this area of 43% and deserves specific revision attention.
  • Slope fields is a "highly examinable" topic area that has also been examined in each new syllabus exam. 2021 Q12a asked students to sketch a solution curve and caused major problems with a mean mark of 18%. Please review closely.

2ADV C4 Snapshot: Other Integration Applications

HISTORICAL CONTRIBUTION

  • C4 Integration has contributed a substantial 14.0% to new syllabus Advanced exams since it was introduced in 2020.
  • This topic has been split into four sub-topics for analysis purposes: 1-Integrals (3.2%), 2-Areas Under Curves (5.8%), 3-Trapezoidal Rule (2.2%) and 4-Other Integration Examples (2.8%).
  • This analysis looks at Other Integration Applications.

HSC ANALYSIS - What to expect and common pitfalls

  • Other Integration Applications has been examined as a feast or famine in new syllabus exams to date. It contributed to three separate questions in the 2023 exam, was omitted in 2022 and received an 8 mark allocation in 2021. 
  • Numerous questions in the database combine with C3 Rates of Change, but are allocated in this topic area as they include integration.
  • The most common underlying themes are motion, flow and population which are all well represented in the database.
  • Another important question type provides the gradient/primitive function of a curve and requires students to find the equation of the curve. Most recently examined with a 4-mark allocation in 2023, producing a 51% mean mark.
  • Some EQ-Bank questions in the database take the form of shorter questions that we expect to feature in the new exam format, consistent with NESA's sample exam.

EXT1 S1 Snapshot: Normal Approximations

HISTORICAL CONTRIBUTION

  • S1 The Binomial has contributed an average of 8.6% per new syllabus exam since it was was introduced in 2020.
  • This topic has been split into three categories for analysis purposes which are: 1-Binomial Probability (2.1%), 2-Statistics and Binomial Distributions (1.5%) and 3-Normal Approximations of Sample Proportions (5.0%).
  • This analysis looks at Normal Approximations of Sample Proportions.

HSC ANALYSIS - What to expect and common pitfalls

  • Normal Approximations of Sample Proportions (5.0%) has appeared in the longer answer section of every new syllabus Ext1 exam to date, including twice in 2022.
  • This topic area represents critical revision as it combines meaningful mark allocations with high difficulty (3 out of 5 new syllabus questions have produced sub-50% mean marks).
  • Students must be able to understand and use a probability table of z-scores. This core skill was required in 2023 Ext1 11f and 2022 Ext1 14d, the latter of which caused major problems and produced a mean mark of just 22% (note that all worksheets in this subtopic automatically include this reference table).
  • Supplementing the limited HSC questions on this new topic, the question database is informed by specific syllabus dot points, NESA Topic Guidance, official NESA "sample" exams and other States who have an exam history of covering similar content.
  • Understand limitations to the normal approximation (see EXT1 S1 EQ-Bank 21).

EXT1 V1 Snapshot: Vectors and Geometry

HISTORICAL CONTRIBUTION

  • Vectors has contributed a highly significant average of 18.6% per new syllabus Ext1 exam since its introduction in 2020.
  • This topic has been split into four categories for analysis purposes: 1-Operations with Vectors (6.8%), 2-Vectors, Force and Velocity (1.1%), 3-Vectors and Geometry (5.0%), and 4-Vectors and Projectile Motion (5.7%).
  • This analysis looks at Vectors and Geometry.

HSC ANALYSIS - What to expect and common pitfalls

  • Vectors and Geometry (5.0%) has appeared in every new syllabus exam to date, with longer answer questions worth 3–7 marks in 2021–23.
  • This topic area can be examined across a very broad difficulty spectrum. While the 2020 exam threw up a low difficulty multiple choice question, the 2023 and 2021 exams included questions that can accurately be described as beasts that defined the best papers.
  • This topic requires a deep understanding of the geometry underlying vector addition and subtraction in two planes.
  • The question database addresses geometric proofs specifically mentioned in the syllabus, including; proving that rhombus diagonals bisect, mid-points of quadrilaterals form a parallelogram and the relationship between the lengths of the sides and diagonals of a parallelogram.
  • Numerous other geometric proofs and results are tested, some of which look at intersections in a given ratio, circular geometry (examined in 2022) and triangular properties.

2ADV E1 Snapshot: Log Calculus

SUMMARY REVISION

  • This subtopic is a database of Log Calculus questions that covers logarithmic differentiation and integration in the one location.
  • It is important to note that this sub-topic is a collection of all questions within C2 Calculus and C4 Calculus that involve logs, providing a convenient location for comprehensively revising both log differentiation and integration.

HSC ANALYSIS - What to expect and common pitfalls

  • Log Calculus (0.5%) has hardly been examined in new syllabus exams. It is worth mentioning however that is has appeared in 5 exams in the last decade, most recently in 2020, and represents a great opportunity for high scoring.
  • Log integration is more challenging than the simplistic log differentiation and is examined much more regularly.
  • Integration of a fraction that results in a logarithm is a 2-3 mark question type has a strong history of being examined, but noticeably just once in the last 6 years (2020 Adv 17).
  • 2019 HSC 13c(ii) surprisingly produced a sub-50% mean mark and should be reviewed.
  • The new syllabus explicitly mentions the differentiation of  `log_a x`  and is covered in the database within SM-Bank questions.

2ADV E1 Snapshot: Exponential Calculus

SUMMARY REVISION

  • This subtopic is a database of Exponential Calculus that covers exponential differentiation and integration questions in the one location.
  • It is important to note that this sub-topic is a collection of all questions within C2 Calculus and C4 Calculus that involve exponentials, providing a convenient location for comprehensively revising both exponential differentiation and integration.

HSC ANALYSIS - What to expect and common pitfalls

  • Exponential Calculus (1.5%) has appeared in the 2022 and 2020 new syllabus Advanced exams, including two questions in 2020 totalling an impressive 5-mark allocation in 2020.
  • Differentiating and then integrating caused problems in the 2020 exam and deserves attention (see 2020 Adv 18 and 2016 Adv 12d).
  • Students are strongly advised to review the differentiation of  `a^f(x)`  which receives its own dot point in the new syllabus - numerous SM-Bank questions provide coverage of this area.
  • We note `a^f(x)` has appeared in significant cross-topic questions in 2021 and 2020 (covered in the later topics), making it particularly important revision.

EXT1 S1 Snapshot: Statistics and Binomial Distributions

HISTORICAL CONTRIBUTION

  • S1 The Binomial has contributed an average of 8.6% per new syllabus exam since it was was introduced in 2020.
  • This topic has been split into three categories for analysis purposes which are: 1-Binomial Probability (2.1%), 2-Statistics and Binomial Distributions (1.5%) and 3-Normal Approximations of Sample Proportions (5.0%).
  • This analysis looks at Statistics and Binomial Distributions.

HSC ANALYSIS - What to expect and common pitfalls

  • Statistics and Binomial Distributions involves new HSC content that looks at the mean and variance of two-outcome (Bernoulli) distributions.
  • Most recently examined in 2020 Ext1 exams in a low difficulty 3-mark question that incorporated normal distribution.
  • The question database is informed by specific syllabus dot points, NESA Topic Guidance and the exam history of other States that cover similar content.
  • We note that Topic Guidance exemplar questions have shown this topic is a natural cross-topic fit with Binomial Probability and recommend a review of  S1 EQ-Bank 13.
  • Further to the above point, students must be able to readily identify binomial distributions from two-outcome scenarios and apply statistical analysis to them. This has proven challenging in other States and numerous examples in the database require a deep understanding of this concept.

EXT1 S1 Snapshot: Binomial Probability

HISTORICAL CONTRIBUTION

  • S1 The Binomial has contributed an average of 8.6% per new syllabus exam since it was was introduced in 2020.
  • This topic has been split into three categories for analysis purposes which are: 1-Binomial Probability (2.1%), 2-Statistics and Binomial Distributions (1.5%) and 3-Normal Approximations of Sample Proportions (5.0%).
  • This analysis looks at Binomial Probability.

HSC ANALYSIS - What to expect and common pitfalls

  • Binomial Probability (2.1%) has been examined each year between 2021–23 (absent 2020) in questions worth 1–3 marks.
  • Games of Chance questions are a common question type that deserve particular attention. 2022 Ext1 12e examined students within this context and proved very challenging for most, producing a 35% mean mark.
  • Historically in the old syllabus (pre–2020), this topic area has accounted for a much higher average of 3+ marks per paper. Questions from this period represent great revision in our view, especially given the possibility that higher mark allocations could return.
  • The results of past HSC questions have been quite volatile and sub-50% mean marks have resulted around half the time.
  • A number of harder examples require students to express probabilities in algebraic terms and prove identities. We recommend reviewing 2006 Ext1 6b, and 2011 Ext1 6c to cover this difficult area.

EXT1 V1 Snapshot: Vectors and Projectile Motion

HISTORICAL CONTRIBUTION

  • Vectors has contributed a highly significant average of 18.6% per new syllabus Ext1 exam since its introduction in 2020.
  • This topic has been split into four categories for analysis purposes: 1-Operations with Vectors (6.8%), 2-Vectors, Force and Velocity (1.1%), 3-Vectors and Geometry (5.0%), and 4-Vectors and Projectile Motion (5.7%).
  • This analysis looks at Vectors and Projectile Motion.

HSC ANALYSIS - What to expect and common pitfalls

  • Vectors and Projectile motion (5.7%) has seen increasing allocations in the 2021–23 period with an eye opening 8-mark question appearing in the 2023 exam.
  • With sub-50% mean marks occurring half the time, it represents a very important topic area for revision.
  • Projectile motion in the new Ext1 course looks at the parametric vector equations of motion (functions of t).
  • New syllabus exams have veered from past exam questions by not providing any scaffolding (read question parts). 2022 Ext1 14c and 2021 Ext1 13b represent "must review" questions for this reason alone. We note 2023 Ext1 13b reverted to the old syllabus style and included four "parts".
  • The vector magnitude and speed of motion relationship is an important "new" concept which is covered in Ext1 V1 SM-Bank 8 and the challenging Ext1 V1 SM-Bank 30.
  • We note that the sample NESA exam questions have also required students to convert these parametric equations into a Cartesian equation (y as a function of x), and Ext1 V1 EQ-Bank 28 should be reviewed to cover this.

EXT1 V1 Snapshot: Operations With Vectors

HISTORICAL CONTRIBUTION

  • Vectors has contributed a highly significant average of 18.6% per new syllabus Ext1 exam since its introduction in 2020.
  • This topic has been split into four categories for analysis purposes: 1-Operations with Vectors (6.8%), 2-Vectors, Force and Velocity (1.1%), 3-Vectors and Geometry (5.0%), and 4-Vectors and Projectile Motion (5.7%).
  • This analysis looks at Operations With Vectors.

HSC ANALYSIS - What to expect and common pitfalls

  • Operations With Vectors (6.8%) attracted at least 3 separate questions in every new syllabus Ext1 exam between 2020-2022 and just a solitary multiple choice in 2023.
  • Basic vector calculations (addition, subtraction and multiplication), angles between vectors (note perpendicular vectors have been examined in 2022 and 2020), unit vectors and projections have featured in new syllabus Ext1 exams to date and are all well represented in the database.
  • Vector projections were examined in 2023 and twice in the 2022 exam, causing problems on each occasion. A key area for revision.
  • The 2020 vector projection question shows the advantage of a clear geometrical understanding of this concept (see 2020 Ext1 9 MC).
  • Questions requiring the equivalence of the two scalar dot product formulae to solve problems is a likely concept to be examined (as other States' exam history attests to). This question type is well covered in the database.
  • Many teachers have provided feedback that column vector notation helps students visualise vector calculations better and minimises errors. We agree and the worked solutions reflect this.

EXT1 F2 Snapshot: Sum, Product and Multiplicity of Roots

HISTORICAL CONTRIBUTION

  • Polynomials has contributed a solid 7.2%, on average, to new syllabus Ext1 exams since being introduced in 2020.
  • This topic has been split into two categories for analysis purposes which are: 1-Remainder and Factor Theorems (2.9%) and 2-Sum, Products and Multiplicity of Roots (4.3%).
  • This analysis looks at Sum, Products and Multiplicity of Roots.

HSC ANALYSIS - What to expect and common pitfalls

  • Sum, Products and Multiplicity of Roots (4.3%) continues to surprise to the upside in its contributions to Ext1 new syllabus exams, with longer answer questions (or parts thereof) appearing in each exam as well as a multiple choice in 2020.
  • The removal of Polynomials from the new Ext2 syllabus has resulted in Sum, Products and Multiplicity of Roots being examined to a greater degree of difficulty than in the past.
  • 2023 Ext1 14b, 2022 Ext1 13d and 2021 Ext1 11h provide case in point with mean mark results between 19-56%. All new syllabus questions in this area must be given specific revision attention.
  • Numerous Ext2 past questions that are now examinable within the new Ext1 course are included in the database - a number focus on the multiplicity of roots which we regard as an important revision area.

EXT1 F2 Snapshot: Remainder and Factor Theorems

HISTORICAL CONTRIBUTION

  • Polynomials has contributed a solid 7.2%, on average, to new syllabus Ext1 exams since being introduced in 2020.
  • This topic has been split into two categories for analysis purposes which are: 1-Remainder and Factor Theorems (2.9%) and 2-Sum, Products and Multiplicity of Roots (4.3%).
  • This analysis looks at Remainder and Factor Theorems.

HSC ANALYSIS - What to expect and common pitfalls

  • Remainder and Factor Theorems (2.9%) has been examined in every new syllabus Ext1 exam to date, twice in the longer answer section (2023 and 2020) and twice in the multiple choice (2022 and 2021).
  • 2022 Ext1 3 MC represents the upper difficulty level of this topic area, producing a 51% mean mark. Review carefully.
  • Notwithstanding the above point, this topic area is typically examined around a band 3-4 level of difficulty and represents a great opportunity to score highly. Revise this area carefully to eliminate silly errors and get ahead of the exam clock, in that order.

EXT1 F1 Snapshot: Parametric Equations

HISTORICAL CONTRIBUTION

  • F1 Further Work With Functions has contributed a healthy 8.5% per new syllabus Ext1 exam since it was introduced in 2020.
  • This topic has been split into four categories for analysis purposes which are: 1-Graphical Relationships (2.5%), 2-Inequalities (1.4%), 3-Inverse Functions (3.2%) and 4-Parametric Functions (1.4%).
  • This analysis looks at Parametric Functions.

HSC ANALYSIS - What to expect and common pitfalls

  • Parametric Equations (1.4%) looks at linear, quadratic and circle equations in the context of parametric representation.
  • It has been examined by a low band 2-mark question in 2023 and in the multiple choice section of the 2021 and 2022 exams.
  • 2021 Ext1 8 MC involved the parametric equation of a semi-circle caused problems for most students, producing a mean mark of just 31%. Please review closely.
  • The most common question type requires students to convert equations from parametric form into Cartesian form (see 2023 Ext1 11a) and then possibly sketch the resulting graph, .
  • A less common question type will require the opposite conversion from Cartesian to parametric form. We recommend students pay attention to Ext1 F1 SM-Bank 8 which looks at this conversion for a circle equation.

EXT1 F1 Snapshot: Inverse Functions

HISTORICAL CONTRIBUTION

  • F1 Further Work With Functions has contributed a healthy 8.5% per new syllabus Ext1 exam since it was introduced in 2020.
  • This topic has been split into four categories for analysis purposes which are: 1-Graphical Relationships (2.5%), 2-Inequalities (1.4%), 3-Inverse Functions (3.2%) and 4-Parametric Functions (1.4%).
  • This analysis looks at Inverse Functions.

HSC ANALYSIS - What to expect and common pitfalls

  • Inverse Functions (3.2%) in this topic looks at non-trigonometric inverse functions.
  • This topic has been examined in new syllabus exams three times since 2020 (omitted only in 2022). Worth noting that 2021 Ext1 12d was allocated a significant 6 marks on this topic area and is a "must review" question.
  • When Inverse Functions has been tested, significant mark allocations are common with 2021, 2018, 2012, 2010, 2008, and 2007 receiving no less that 5 marks each!
  • 2023 Ext1 9 MC provided an interesting way to test students in this area, producing a 47% mean mark. Attention required here.
  • We note in past years, allocations between this topic and the larger Inverse Trig Functions topic tend to cannibalise each other.
  • Pitfalls: The graph and associated range and domain of an inverse exponential function has been the most poorly answered question type in this area and harder examples deserve revision attention (see 2018 Ext1 13b and 2010 Ext1 3b).

EXT1 F1 Snapshot: Inequalities

HISTORICAL CONTRIBUTION

  • F1 Further Work With Functions has contributed a healthy 8.5% per new syllabus Ext1 exam since it was introduced in 2020.
  • This topic has been split into four categories for analysis purposes which are: 1-Graphical Relationships (2.5%), 2-Inequalities (1.4%), 3-Inverse Functions (3.2%) and 4-Parametric Functions (1.4%).
  • This analysis looks at Inequalities.

HSC ANALYSIS - What to expect and common pitfalls

  • Inequalities (1.4%) was most recently examined with a dedicated question in the 2022 and 2020 new syllabus Ext1 exams. Going further back, it has been a super consistent contributor, tested 7 times in the last decade.
  • When examined, the mark allocation has typically been 3 marks, with 2020 and 2013 the only outliers with an allocation of just 1 mark.
  • Algebraic fraction inequalities are easily the most common question type from past Ext1 papers, last examined in 2022. A key revision area.
  • Absolute value inequalities were regularly examined in the old Mathematics course and are a gift from examiners if asked. Numerous examples are included in the database.
  • Graphing inequality regions was a sneaky contributor to the old Mathematics course, asked 6 times since 2011 and producing sub-50% mean marks half the time. 
  • The content in this area is expected to present band 3-4 level difficulty questions with meaningful mark allocations. Revision here should aim of eliminate errors and get ahead of the exam clock, in that order!

EXT1 F1 Snapshot: Addition / Multiplication of 2 Graphs

HISTORICAL CONTRIBUTION

  • F1 Further Work With Functions has contributed a healthy 8.5% per new syllabus Ext1 exam since it was introduced in 2020.
  • This topic has been split into four categories for analysis purposes which are: 1-Graphical Relationships (2.5%), 2-Inequalities (1.4%), 3-Inverse Functions (3.2%) and 4-Parametric Functions (1.4%).
  • This analysis looks at Graphical Relationships - Addition/Multiplication of 2 graphs.

HSC ANALYSIS - What to expect and common pitfalls

  • Graphical Relationships - Addition/Multiplication of 2 graphs was most recently examined in the multiple choice section of the 2022 and 2021 new syllabus exams.
  • 2022 Ext1 4 MC looked at the addition of a quadratic and linear graph and caused little trouble. Worth noting the "By Elimination" solution given which is quite often more time efficient for this question type.
  • 2021 Ext1 7 MC looked at this area in the context of trig graphs (which should be the focus of revision in this topic). One out of three students got this incorrect and revision attention is recommended.
  • Consistent with the NESA topic guidance released and as mentioned above, the database looks disproportionately at trigonometric functions in this context.

EXT1 F1 Snapshot: Reflections and Harder Graphs

HISTORICAL CONTRIBUTION

  • F1 Further Work With Functions has contributed a healthy 8.5% per new syllabus Ext1 exam since it was introduced in 2020.
  • This topic has been split into four categories for analysis purposes which are: 1-Graphical Relationships (2.5%), 2-Inequalities (1.4%), 3-Inverse Functions (3.2%) and 4-Parametric Functions (1.4%).
  • This analysis looks at Graphical Relationships - Reflections and Harder Graphs.

HSC ANALYSIS - What to expect and common pitfalls

  • Graphical Relationships - Reflections and Harder Graphs has been examined in 2023, 2022 and 2020, the last of which involved a 3-mark longer answer question that was well answered.
  • Reflections and Harder Graphs looks at the following manipulations of  `y=f(x):`  `y=1/(f(x)),`  `y=sqrt((f(x)),`  `y=|\ f(x)\ |`  and  `y=f(| x |).`
  • 2020 Ext1 11c required students to graph  `y=1/(f(x))`  from a given sketch of a quadratic function which was well answered.
  • This topic area is made up of content that was previously found in the old syllabus within Ext2. The database contains many examples from past Ext2 exams which provide excellent revision (denoted by EXT1′ in the title).
  • The difficulty level of questions on this sub-topic are typically band 3 to 4 and offer well-prepared students a great opportunity to score highly.

Combinatorics, EXT1 A1 Snapshot: The Binomial

HISTORICAL CONTRIBUTION

  • Combinatorics has contributed a healthy average of 9.3% per new syllabus Ext1 exam since it was introduced in 2020.
  • This topic has been split into two sub-categories for analysis purposes which are: 1-Permutations and Combinations (4.3%) and 2-Binomial Expansion (5.0%).
  • This analysis looks at Binomial Expansion.

HSC ANALYSIS - What to expect and common pitfalls

  • Binomial Expansion (5.0%) has been tested in the longer answer section of each new syllabus Ext1 exam to date.
  • This topic area can be examined over a very wide range of difficulties.
  • 2020 Ext1 14a tested this topic area with an extremely challenging 8-mark question that reframed the possible level of difficulty of binomial proofs that may appear. An important revision question.
  • The 2021 exam, in contrast, served up a band 3 softball that was a gift to students. 
  • A common question type, last examined in 2022, requires the calculation of the constant/independent term or a specific coefficient in a given binomial expansion. We note that the NESA topic guidance states that "greatest coefficient" questions are no longer examinable and have been removed from the database.
  • These types of questions are generally well answered, although significant problems were caused in 2012 Ext1 11f and 2005 Ext1 2b and should be carefully reviewed.
  • Combinatorial proofs that receive a specific mention in the syllabus are covered in the database.

EXT1 A1 Snapshot: Permutations and Combinations

HISTORICAL CONTRIBUTION

  • Combinatorics has contributed a healthy average of 9.3% per new syllabus Ext1 exam since it was introduced in 2020.
  • This topic has been split into two sub-categories for analysis purposes which are: 1-Permutations and Combinations (4.3%) and 2-Binomial Expansion (5.0%).
  • This analysis looks at Permutations and Combinations.

HSC ANALYSIS - What to expect and common pitfalls

  • Permutations and Combinations (4.3%) has been examined in both the multiple choice and longer answer sections of every new syllabus Ext1 exam to date.
  • Recent multiple choice questions have ratcheted up the typical band 4 difficulty level of this question type, and multiple choice questions in the period 2019-23 deserve particular attention.
  • The pigeonhole principle represents new Ext1 content whose importance is underlined by its inclusion in every new syllabus exam, including longer answer questions in both 2022 and 2020. We recommend particular attention be given to 2021 Ext1 10 MC and 2020 Ext1 12c that caused problems with mean marks of 31% and 52% respectively. 
  • Common question types require a deep understanding or ordered and unordered combinations, as well as combinations in a circle where 2023 Ext1 10 MC produced a mean mark of just 19%! All question styles are well represented in the database.
  • We recommend students get exposure to questions involving geometry, last examined in 2022 where it was poorly answered (mean mark 37%).  
  • Be aware that this topic area is the source of some of the most difficult questions examiners have thrown at students (some of the beasts include 2015 Ext1 14c, 2014 Ext1 14b and 2010 Ext1 7c).

EXT1 P1 Snapshot: Induction

HISTORICAL CONTRIBUTION

  • P1 Proof - Induction has contributed an average of 4.3% per new syllabus Ext1 exam since it was introduced in 2020.

HSC ANALYSIS - What to expect and common pitfalls

  • P1 Induction has been a great topic area for students to pick up marks. It is examined every year like clockwork with a majority of questions coming in at a band 3/4 level of difficulty.
  • Efficiency in answering questions requires students to employ a clear and ordered structure to their solution.
  • A common induction question type is divisibility, where a series must be proven to be divisible by a given integer. This question type was last examined in 2022 after a 4 year absence and should feature in any revision.
  • Sum of a series induction proofs were last examined in 2023, and in each of the years 2018-21. These questions can take myriad forms and it is recommended specific revision is given to factorial notation examples within this question type. 
  • New syllabus adjustments are important to note here: Inequality Induction has been moved from Ext1 to the Ext2 course, along with induction where the initial n does not start or increase strictly by 1, proving results related to probability and calculus, and other more exotic examples.

EXT1 T3 Snapshot: Proving Identities and ‘t’ formulae

HISTORICAL CONTRIBUTION

  • T3 Trig Equations is easily the biggest sub-topic within Trigonometry and has contributed an impressive average of 7.0% per new syllabus Ext1 exam since its introduction in 2020. 
  • This topic has been split into two sub-categories for analysis purposes which are: 1-Auxiliary Angles (2.5%) and 2-Identities, Equations and 't' Formulae (4.5%).
  • This analysis look at Identities, Equations and 't' Formulae.

HSC ANALYSIS - What to expect and common pitfalls

  • Identities and Equations (4.5%) was last examined in longer answer questions in 2023, 2021 (twice) and 2020. It was allocated a significant 4-marks within a very challenging 7-mark cross topic question in 2020 Ext1 14b, a question that represents the highest level of difficulty that students can expect.
  • A revision focus here is important. The use of compound and double angle identities is not only core knowledge for this topic area, but it will also prove extremely valuable in later applications of calculus.
  • The 't' formulae was last examined in 2023 (we note its usage was not explicitly stated in the question) for the first time in 16 years. Ensure you revise and understand this solution methodology!
  • NESA Topic Guidance explicitly states that students can be asked to provide "all" solutions to some trig equations. Carefully review Ext1 T3 EQ-Bank 3 to see a worked solution that does not require knowledge of the general solution formulae.

EXT1 T3 Snapshot: Auxiliary Angles

HISTORICAL CONTRIBUTION

  • T3 Trig Equations is easily the biggest sub-topic within Trigonometry and has contributed an impressive average of 7.0% per new syllabus Ext1 exam since its introduction in 2020. 
  • This topic has been split into two sub-categories for analysis purposes which are: 1-Auxiliary Angles (2.5%) and 2-Identities, Equations and 't' Formulae (4.5%).
  • This analysis looks at Auxiliary Angles.

HSC ANALYSIS - What to expect and common pitfalls

  • Auxiliary Angles (2.5%) have been tested in a dedicated longer answer question in both the 2022 and 2020 new syllabus exams (omitted in 2023, 2021). This continues a longer trend of this question type being asked in a clear majority of papers (6 times in the last decade).
  • Mark allocations are more often in the substantial 3-4 range, making this a fertile area for scoring well, although we note 2014 and 2017 examined this topic via multiple choice.
  • Efficiency in answering auxiliary angle questions requires students to have a clear and precise answer structure in their mind before they start. We highly recommend revision that develops this structured approach which is illustrated in the worked solutions. 
  • Most questions in this area test around the band 4 difficulty level, although 2010 Ext1 4b proved more challenging and deserves close attention.

EXT1 T2 Snapshot: Further Trig Identities

HISTORICAL CONTRIBUTION

  • Trigonometry has contributed a very healthy 10.3%, on average, to new syllabus Ext1 exams since being introduced in 2020. It looks at trigonometric algebra, graphs and identities and is an important area that is examined both in its own right and used within calculus applications that are covered in later topics.
  • Trigonometry is split into three topic areas by the syllabus which are: T1-Inverse Trig Functions (2.1%), T2-Compound Angles (1.1%) and 3-Trig Equations (7.1%).
  • This analysis looks at Compound Angles.

HSC ANALYSIS - What to expect and common pitfalls

  • Compound Angles (1.1%) is a small content area that was last examined in 2021. Although this question type only attracts a dedicated question sporadically, it establishes gateway knowledge for other more challenging topics like solving trig identities (found within Y12 content T3 Trig Equations).
  • Students should be able to construct right angled triangles to obtain exact trig ratios and then calculate the exact value of double angles. See 2013 Ext1 8 MC which caused significant problems to illustrate this solution method.
  • Similarly, NESA exemplar questions require students to construct compound angles and use exact trig ratios to solve. This question style should also be reviewed using the numerous EQ-Bank and SM-Bank examples in the database.

EXT1 T1 Snapshot: Inverse Trig Functions

HISTORICAL CONTRIBUTION

  • Trigonometry has contributed a very healthy 10.3%, on average, to new syllabus Ext1 exams since being introduced in 2020. It looks at trigonometric algebra, graphs and identities and is an important area that is examined both in its own right and used within calculus applications that are covered in later topics.
  • Trigonometry is split into three topic areas by the syllabus which are: T1-Inverse Trig Functions (2.1%), T2-Compound Angles (1.1%) and 3-Trig Equations (7.1%).
  • This analysis looks at Inverse Trig Functions.

HSC ANALYSIS - What to expect and common pitfalls

  • Inverse Trig Functions (2.1%) has been examined in a dedicated question in 2023 (twice), 2022 (twice) and 2021 after being omitted in the 2020 exam.
  • "Dedicated question" is used above as this topic area also commonly appears in difficult cross-topic calculus questions that are tested towards the end of the Ext1 exam (not included here).
  • Drawing or identifying an inverse trig graph is a common question type and we recommend a careful revision of this sub-category of questions.
  • 2022 Ext1 13c required a deep understanding of domain and range of an inverse function (mean mark 24%) and deserves particular revision attention.
  • Exact values of inverse functions was tested in 2023 Ext1 5 MC and 2022 Ext1 1 MC, proving challenging on both occasions. Please review.
  • Note the syllabus explicitly states that students must understand the notation arcsin etc.., which was required in 2023 and 2022 and features in numerous database questions.
  • Content changes: the general solution to trig equations, which caused problems in the past, is no longer examinable. Note that NESA guidance has responded to enquiries on this issue to make it clear that "all" solutions may still be required. This is addressed in the later topic T3 Trig Equations.

EXT1 C3 Snapshot: Further Areas and Solids of Revolution

HISTORICAL CONTRIBUTION

  • C3 Application of Calculus has contributed a highly significant average 15.3% per new syllabus Ext1 exam since it was introduced in 2020.
  • This topic has been split into two sub-categories for analysis purposes which are: 1-Further Areas and Solids of Revolution (6.4%) and 2-Differential Equations (8.9%).
  • This analysis looks at Further Areas and Solids of Revolution.

HSC ANALYSIS - What to expect and common pitfalls

  • Further Areas and Solids of Revolution (6.4%) is a sneaky large contributor to new syllabus Ext1 exams, having been tested within the longer answer section every year, and attracting two questions in 2023 and 2021.
  • The minor topic of Further Area has been examined in both 2023 and 2021, the latter in a 3-mark question that required students to calculate an enclosed area between a curve and absolute value graph (2021 Q13c).
  • The database is dominated by Solids of Revolution questions that are consistently around band 4 level difficulty. 2023 Ext1 12e is the exception, raising the difficulty to Band 5 and producing a 49% mean mark - a revision focus question.
  • Questions taken from actual Ext1 exams include 2020-23 (each year) and 2013-14 in old syllabus papers. The rest of the database is taken from past Advanced exams which can be identified by EXT1* in their title. 
  • Notwithstanding the expected band difficulty comment above, 2010 EXT1* 10b and 2011 EXT1* 8b represent the highest level of difficulty in the topic area and deserve specific attention.
  • History shows students have more difficulty with `y`-axis rotations, as evidenced by sub-50% mean marks in 2015, 2013, and 2011 (last examined in 2021 but well answered). Ensure this question-type is carefully reviewed.

EXT1 C2 Snapshot: Harder Trig Calculus

HISTORICAL CONTRIBUTION

  • C2 Further Calculus Skills has contributed a substantial average of 13.1% per Ext1 new syllabus exam since its introduction in 2020.
  • This topic has been split into three sub-categories for analysis purposes which are: 1-Integration By Substitution (4.6%), 2-Inverse Function Calculus (7.1%) and 3-Harder Trig Calculus (1.4%).
  • This analysis looks at Harder Trig Calculus.

HSC ANALYSIS - What to expect and common pitfalls

  • Harder Trig Calculus (1.4%) was tested in both new syllabus Ext1 exams between 2020–21 (notably absent in 2022–23).
  • The difficulty level of past questions (from the new and old syllabus) has ranged from a lower band 3–4 level, to very challenging band 6 applied questions involving tangent concepts. 
  • 2020 Ext1 13c saw Inverse Trig Function Calculus overlap with this topic area in a question that caused all sorts of problems and deserves specific attention.
  • A key skill - students must be able to competently and quickly use the identities  `cos 2theta = 1-2sin^2theta=2cos^2 theta-1`. These are regularly examined and prone to silly errors - review carefully!
  • Although not included in this analysis, this topic area provides core integration skills for later calculus topics such as Solids of Revolution.

EXT1 C2 Snapshot: Inverse Trig Calculus

HISTORICAL CONTRIBUTION

  • C2 Further Calculus Skills has contributed a substantial average of 13.1% per Ext1 new syllabus exam since its introduction in 2020.
  • This topic has been split into three sub-categories for analysis purposes which are: 1-Integration By Substitution (4.6%), 2-Inverse Function Calculus (7.1%) and 3-Harder Trig Calculus (1.4%).
  • This analysis looks at Inverse Function Calculus.

HSC ANALYSIS - What to expect and common pitfalls

  • Inverse Function Calculus (7.1%) has surprised to the upside by attracting two separate questions in every new syllabus exam to date (including two longer answer questions in 2023 and 2021).
  • The most common question type involves standard inverse trig differentiation or integration - a classic example of low hanging fruit that well-prepared students should expect to score highly in.
  • The 2020 exam tweaked this common question type and caused significant problems. 2020 Ext1 13c is a must-review question.
  • 2023 Ext1 14a is another "must review" question that required an explanation if an inverse function exists (mean mark 54%) and the use of a composite function for differentiation that a large majority could not answer (mean mark 32%).
  • 2022 Ext1 12c involved a tangent application of this topic area for the first time and deserves revision attention. It is worth noting that this is also the first question that arcsin terminology was used exclusively vs `sin^(-1)` notation.
  • Examiners have ratcheted up the difficulty in this topic area periodically by requiring students to differentiate inverse trig equations that contain two inverse trig functions and sketch the graph. We recommend students carefully review 2018 Ext1 12c, 2015 Ext1 13d and 2010 Ext1 5b.

EXT1 C2 Snapshot: Integration By Substitution

HISTORICAL CONTRIBUTION

  • C2 Further Calculus Skills has contributed a substantial average of 13.1% per Ext1 new syllabus exam since its introduction in 2020.
  • This topic has been split into three sub-categories for analysis purposes which are: 1-Integration By Substitution (4.6%), 2-Inverse Function Calculus (7.1%) and 3-Harder Trig Calculus (1.4%).
  • This analysis looks at Integration By Substitution.

HSC ANALYSIS - What to expect and common pitfalls

  • Integration by Substitution (4.6%) is examined like clockwork, asked in a dedicated longer answer question every year of the last decade.
  • Questions are in the band 3–4 range and present low hanging fruit for high scoring. 
  • Approach this area by concentrating on making no mistakes and developing speed, in that order!
  • Pitfalls: One of the few problem areas flagged by markers has been when definite integral limits look inverted after the substitution (see 2007 Ext1 1e).

EXT1 C1 Snapshot: Motion and Time

HISTORICAL CONTRIBUTION

  • C1 Rates of Change has contributed 4.6% per new syllabus Ext1 exam since it was introduced in 2020.
  • This topic has been split into three sub-categories for analysis purposes which are: 1-Growth and Decay (3.2%), 2-Rates of Change with respect to Time (0%), and 3-Related Rates of Change (1.4%).
  • This analysis looks at Motion and Time.

HSC ANALYSIS - What to expect and common pitfalls

  • Rates of Change with respect to Time has not been examined in new syllabus Ext1 exams to date. This topic area is prominent in the syllabus and its omission between 2020-23 makes it more important to review thoroughly, in our view.
  • Rates of Change with respect to Time is primarily reallocated content from the old Mathematics course. Past HSC questions on motion taken from this course dominate the question database and are identified by EXT1* in the title.
  • Identifying whether motion questions fit into the Adv or Ext1 course has been a challenge, although we note the use of  `dotx, \ ddotx`  notation is specific to the Ext1 course. Our current view is that this area is examinable within both Advanced and Ext1, and the use of notation and the degree of difficulty will differentiate which course a question is most likely to be examined in. 
  • Historically, Rates of Change with respect to Time has seen a combination of high mark allocations and a high degree of difficulty (note all results and band allocations for EXT1* questions are taken from the Mathematics course exam data).
  • Flow questions are fair game within this topic area (see NESA Calculus Topic Guide p.7) and we recommend a review of Calculus, EXT1 C1 EQ-Bank 12 for exposure to this question type.

EXT1 C1 Snapshot: Related ROC

HISTORICAL CONTRIBUTION

  • C1 Rates of Change has contributed 4.6% per new syllabus Ext1 exam since it was introduced in 2020.
  • This topic has been split into three sub-categories for analysis purposes which are: 1-Growth and Decay (3.2%), 2-Motion and Time (0%), and 3-Related Rates of Change (1.4%).
  • This analysis looks at Related Rates of Change.

HSC ANALYSIS - What to expect and common pitfalls

  • Related Rates of Change (1.4%) has been examined in 3 out of 4 new syllabus exams, twice in the longer answer section.
  • Allocated marks in new syllabus exams are below this topic's historical average. Notwithstanding this, effective revision should include high mark "old syllabus" examples which are well represented in the database.
  • 2023 Ext1 13a combined this topic with differential equations in an extremely challenging "must review" question.
  • The toughest examination of this topic was between 2011-2013 where sub-50% mean marks resulted each year. Any revision should include these examples.
  • The most popular underlying subject matter of recent past questions is worth noting: areas/volumes (7 times) and Pythagoras theorem (4 times).
  • Marker's comments have flagged that students can often achieve half-marks by simply stating a correct chain rule and that students who draw diagrams in their solution are more successful. Great advice. Follow it.
  • Pitfalls: The use of non-right angled trig in this context was examined in 2012 and poorly answered. Not tested again since and worthy of a revision focus.
  • If a constant rate of change is established, students have struggled with follow up questions in 2013 Ext1 13a and 2009 Ext1 5b. A red-flagged knowledge gap worthy of attention.

EXT1 C1 Snapshot: Growth and Decay

HISTORICAL CONTRIBUTION

  • C1 Rates of Change has contributed 4.6% per new syllabus Ext1 exam since it was introduced in 2020.
  • This topic has been split into three sub-categories for analysis purposes which are: 1-Growth and Decay (3.2%), 2-Rates of Change with respect to Time (0%), and 3-Related Rates of Change (1.4%).
  • This analysis looks at Growth and Decay.

HSC ANALYSIS - What to expect and common pitfalls

  • Exponential Growth and Decay (3.2%) has appeared in a single multiple-choice question in 2023 and more substantial 4-mark questions in both the 2022 and 2021 new syllabus Ext1 exams (omitted in 2020).
  • This topic area covers both "standard" Growth and Decay found in the old Mathematics course and the more challenging "modified" Growth and Decay found in the old Ext1 course that models systems with natural carrying capacities.
  • "Standard" Growth and Decay is key gateway knowledge for this topic area and should be revised. Note the simultaneous growth and decay of fish populations in 2013 Adv 16b that caused major problems and deserves particular attention.
  • "Modified" Growth and Decay (examined 2021-23) is the most likely question-style and any revision plan should reflect this. 2017 Ext1 14c applies a blow torch to students' ability to work with log laws and represents the highest difficulty level of this topic - a must review question.

2ADV F2 Snapshot: Non-Calculus Graphing

HISTORICAL CONTRIBUTION

  • F2 Graphing Techniques has contributed an average of 5.4% per Advanced exam since the new syllabus was introduced in 2020.
  • We have split the topic into 2 categories for analysis purposes: 1-Transformations (3.0%) and 2-Non-Calculus Graphing (2.4%).
  • This analysis looks at Non-Calculus Graphing.

HSC ANALYSIS - What to expect and common pitfalls

  • Non-Calculus Graphing (2.4%) was last examined in 2024 in a band 6 cross-topic question with M1 Financial Modelling. In 2023, it attracted a significant 4-mark allocation in a more traditional style question.
  • The most common question type is easily the graphing of quotient functions that require students to find intercepts and both vertical and horizontal asymptotes. This was last examined in the 2021 exam and relatively well answered.
  • The database includes old Ext1 HSC examples that have been recategorised into this Advanced topic. These will prove challenging and provide high quality revision. They are identified by the inclusion of ADV' in their title.
  • The algebraic manipulation of some quotient functions before graphing can save significant time. We recommend reviewing F2 EQ-Bank 11 to illustrate this.
  • Students should be looking for the possibility of functions being odd or even. When identified, graphing solutions can be produced much more efficiently (see 2ADV′ F2 2012 HSC 13b).