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BIOLOGY M7 Snapshot: Causes of Infectious Disease

HISTORICAL CONTRIBUTION

  • M7 Infectious Diseases has contributed an average of 24.5% 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 (8.0%), 2-Immunity and Responses to Pathogens (6.2%) and 3-Prevention, Treatment and Control (10.3%).
  • 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 in the period 2019-23. Identifying and distinguishing pathogens given limited detail has proven very challenging (see 2020 HSC 32b and 2019 HSC 33d).
  • Indirect Transmission, Direct Transmission and Vectors has also been tested four times in the extended response section (see 2025 HSC 22b, 2020 HSC 32a and 2019 HSC 31) as well multiple choice in 2024-25.
  • The works of Louis Pasteur and Robert Koch have been tested in 3 of the last 5 exams (most recently 2024) and need to be well understood. Important revision should involve 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 7 years (most recently in 2023). We note that the syllabus states that students must be able to "design" a practical investigation in this topic area (yet to be tested).
  • Effects on agricultural production from infectious diseases on plants was examined for the first time in 2024 HSC 26. Recommended revision should also address infectious diseases of animals in the same context.

BIOLOGY M6 Snapshot: Genetic Technologies

HISTORICAL CONTRIBUTION

  • M6 Genetic Change has contributed an average of 23.1% 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-Mutation (10.9%), 2-Biotechnology (6.1%) and 3-Genetic Technologies (6.1%).
  • 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 exam to date (including two in 2025 and 2021-23) as well as contributing an average of two multiple-choice questions per exam.
  • Transgenic Organisms is the most common question theme that was recently tested in 2025 and each year between 2019-23. 2021 HSC 33a is a "must review" question of this topic area.
  • Whole Organism Cloning was most recently tested in the 2025 HSC 16 MC and 2024 HSC 25, causing problems on both occasions. The database includes numerous other multiple-choice questions that have proven challenging (see 2019 HSC 20 MC and 2018 HSC 18 MC). 
  • 2014 HSC 29 looks at the process of whole organism cloning and represents an important revision question involving cross-topic themes.
  • Gene Cloning has appeared in the longer answer section in 2020 HSC 30 and in three exams via multiple-choice, most recently in 2023. 
  • Be aware that this topic area has significant syllabus overlap with M6 Biotechnology, particularly regarding biodiversity impacts and societal benefits of genetic technologies. We note the key distinction is that Genetic Technologies focuses on specific processes and applications, while Biotechnology emphasises broader ethical and societal evaluation.

BIOLOGY M6 Snapshot: Biotechnology

HISTORICAL CONTRIBUTION

  • M6 Genetic Change has contributed an average of 23.1% 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-Mutation (10.9%), 2-Biotechnology (6.1%) and 3-Genetic Technologies (6.1%).
  • This analysis looks at the sub-topic, Biotechnology.

HSC ANALYSIS - What to expect and common pitfalls

  • Biotechnology has been examined via longer answer questions in 6 of 7 new syllabus exams, as well as the multiple choice section in four of those years.
  • Evaluating Genetic Technology is the key content of this topic area. It is crucial to understand and clearly state how any given technology works and its benefits and potential dangers to biodiversity.
  • Answers should include, where possible, a discussion on societal, agricultural, medical and industrial effects.
  • A sound knowledge of keywords and the associated best answer structure is critical. Within new syllabus exams, high mark allocations in this topic have already used the keywords: evaluate, discuss, to what extent, analyse and explain.
  • 2024 HSC 34 (7 marks) and 2019 HSC 24 (5 marks) both required students to choose two biotechnologies for specific given details. Be prepared for this style of question!
  • Evaluating the benefits and dangers of biotechnology through an explicit ethical framework was tested in 2014 HSC 32e.
  • Note 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 23.1% 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-Mutation (10.9%), 2-Biotechnology (6.1%) and 3-Genetic Technologies (6.1%).
  • This analysis looks at the largest and most important sub-topic, Mutation.

HSC ANALYSIS - What to expect and common pitfalls

  • Mutation is the 18-foot saltwater croc swimming in the Module 6 estuary, one of only 3 topics that contributes over 10% to new syllabus exams. This topic has attracted an average of two longer answer questions (or part thereof) per exam as well as averaging over two multiple choice questions each year.
  • Somatic vs. Germ-Line is a key revision area focusing on the comparison of these two types of mutations, examined in 6 out 7 new syllabus exams in the longer answer section (absent only in 2023).
  • Point & Chromosomal Mutations have been examined every year at least once, with questions evenly split between longer answer and multiple choice. A challenging revision area (see 2025 HSC 12 MC, 2023 HSC 35 and 2019 HSC 25).
  • Mechanisms of Change & Variation was most recently tested in the longer answer section via 2025 HSC 34b (worth 4 marks) and 2023 HSC 32 (worth 7 marks), as well as two MC questions in 2024. Students must have a good understanding of genetic drift and gene flow, as well as structuring "analyse" (keyword) questions to score highly in this area.
  • Non-Coding DNA is regularly examined via multiple-choice (most recently 2025). Challenging questions in this area include 2024 HSC 9 MC and 2022 HSC 16 MC.
  • 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 26.6% 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 (6.4%), 2-Cell Replication (3.3%), 3-DNA and Polypeptide Synthesis (5.6%), Genetic Variation/Inheritance Patterns (11.3%).
  • This analysis looks at the sub-topic, Genetic Variation/Inheritance.

HSC ANALYSIS - What to expect and common pitfalls

  • Genetic Variation/Inheritance is the 600-pound Silverback of the whole Biology course - in the new syllabus period 2019-25, it is the largest contributing topic area across all modules!
  • During this time, it has attracted a whopping average of 2.5 longer answer questions (or part thereof) and 2.5 multiple choice questions per 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 5 out of 7 new syllabus exams (most recently in 2024), including four times in the longer answer section. Drawing and analysing punnet squares is a critical skill for any revision set.
  • Meiosis has been examined within this topic in high-mark questions three times since 2019, most recently in 2024, causing problems on each occasion (see 2024 HSC 33 and 2020 HSC 28). 
  • Allele Frequency Data questions have been a sneaky contributor to new syllabus exams, tested three times in new syllabus exams (most recently 2025 HSC 34a - see M6 Mutation). Substantial mark allocations in 2022 and 2019 along with low mean marks require revision attention.
  • Inheritance Patterns has been examined three times in the longer answer since 2019, most recently in both 2024-25 (see 2021 HSC 27 recommended revision).

BIOLOGY M5 Snapshot: DNA and Polypeptides

HISTORICAL CONTRIBUTION

  • M5 Heredity has contributed an average of 26.6% 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 (6.4%), 2-Cell Replication (3.3%), 3-DNA and Polypeptide Synthesis (5.6%), Genetic Variation/Inheritance Patterns (11.3%).
  • 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 6 of the 7 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 in a clear majority of questions (most recently examined in 2025 HSC 31b). A key content area for revision in this topic.
  • Many questions require students to number steps in a process or draw a flow chart. These skills are critical and are well covered in the database (see 2022 HSC 31b and 2019 HSC 33a).
  • 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.
  • Base pair calculations were examined in 2025 HSC 19 MC and caused problems (31% mean mark).

BIOLOGY M5 Snapshot: Cell Replication

HISTORICAL CONTRIBUTION

  • M5 Heredity has contributed an average of 26.6% 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 (6.4%), 2-Cell Replication (3.3%), 3-DNA and Polypeptide Synthesis (5.6%), Genetic Variation/Inheritance Patterns (11.3%).
  • 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 in the multiple choice section each year between 2019-22 while 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).
  • Meiosis/mitosis received its highest mark allocation in the 2025 HSC with an impressive 6-mark allocation across two questions. 2025 HSC 33 is a "must review" question (parts 33a and b).
  • Mitosis was examined in 2024 and 2021 via multiple choice at the band 5 level (see 2024 HSC 14 MC and 2021 HSC 17 MC).
  • Old syllabus (pre-2019) exams also provide recommended revision on this topic with 2016 HSC 13-14 and 2018 HSC 29 requiring a deep understanding of this area.
  • We note meiosis/mitosis is also important gateway knowledge for later topics such as M5 Genetic Variation and M6 Mutation.

BIOLOGY M5 Snapshot: Reproduction

HISTORICAL CONTRIBUTION

  • M5 Heredity has contributed an average of 26.6% 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 (6.4%), 2-Cell Replication (3.3%), 3-DNA and Polypeptide Synthesis (5.6%), Genetic Variation/Inheritance Patterns (11.3%).
  • 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 6 out of 7 new syllabus exams (including twice in 2025).
  • 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 has been specifically examined four times since 2019. 2020 HSC 25 was a high-mark longer answer question that caused problems and deserves specific revision attention.
  • Fungi reproduction has been examined three times in the longer answer section, causing problems. Revision attention recommended for 2023 HSC 33, a comparison between human and fungi reproduction, and 2019 HSC 27 which looked at yeast.
  • Plant reproduction was tested for the first time in 2024 in a low band question. We note bacteria and protist reproduction are specifically mentioned in the syllabus but are yet to attract any meaningful mark allocations.

PHYSICS M8 Snapshot: Deep Inside the Atom

HISTORICAL CONTRIBUTION

  • M8 From the Universe to the Atom has contributed an average of 23.1% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into five sub-categories for analysis purposes which are: 1-Origins of Elements (3.8%), 2-Structure of the Atom (3.6%), 3-Quantum Mechanical Nature of the Atom (5.6%), Properties of the Nucleus (7.0%) and 5-Deep Inside the Atom (3.1%).
  • This analysis looks at the smallest sub-topic, Deep Inside the Atom.

HSC ANALYSIS - What to expect and common pitfalls

  • Deep Inside the Atom has contributed modestly to new syllabus exams in the 2019-24 period and peaked in 2025 with a 7-mark allocation across 2 questions.
  • In total, this topic has contributed dedicated longer answer questions in 4 exams (most recently 2025) and 5 multiple-choice questions in the past 7 years.
  • The most significant question type requires a deep understanding of the Standard Model and related experiments (review 2025 HSC 33, 2023 HSC 33 and 2020 HSC 30a). 
  • Broad questions that allow students to incorporate the development of the Standard Model are common and again, we emphasise the need for preparing clear and precise summaries of developments that can be synthesised into such questions (review 2024 HSC 32 and 2019 HSC 32).
  • Quarks were last examined within the longer answer question 2024 HSC 27a and prior to that via multiple-choice questions in 2022 HSC 5 MC and 2019 HSC 12 MC.
  • Linear accelerators were specifically examined in 2025 HSC 20 MC and 2020 HSC 30a. Revision attention here pays dividends as this topic area can also be easily used in more general questions looking at the development of the standard model.

PHYSICS M8 Snapshot: Properties of the Nucleus

HISTORICAL CONTRIBUTION

  • M8 From the Universe to the Atom has contributed an average of 23.1% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into five sub-categories for analysis purposes which are: 1-Origins of Elements (3.8%), 2-Structure of the Atom (3.6%), 3-Quantum Mechanical Nature of the Atom (5.6%), Properties of the Nucleus (7.0%) and 5-Deep Inside the Atom (3.1%).
  • This analysis looks at the largest sub-topic, Properties of the Nucleus.

HSC ANALYSIS - What to expect and common pitfalls

  • Properties of the Nucleus is the most frequently and diversely tested topic within Module 8. Questions can range from low-band multiple choice to high difficulty extended responses.
  •  Conservation of Mass-Energy has been examined three times in both longer answer questions (most recently in 2023) and multiple choice sections (most recently in 2023).
  • Radioactive Decay has appeared in multiple-choice in 5 of the last 6 exams and longer answer questions in 2021 and 2022. It has caused problems in a majority of times that it has been tested and deserves revision attention (see 2025 HSC 16 MC, 2021 HSC 35).
  • Nuclear Fission was last examined in 2020 and has caused major problems each time it has appeared (see 2020 HSC 16 MC and 2019 HSC 36).
  • 2019 HSC 36 is important revision where students are required to apply core physics concepts (eg. Law of Conservation of Momentum, Mass/Energy equivalence) to a range of different scenarios (mean mark 30%). 
  • The Conservation of mass/energy is an important concept where students must understand the definitions and differences between the terms binding energy and mass defect. 

PHYSICS M8 Snapshot: Quantum Mechanical Nature of the Atom

HISTORICAL CONTRIBUTION

  • M8 From the Universe to the Atom has contributed an average of 23.1% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into five sub-categories for analysis purposes which are: 1-Origins of Elements (3.8%), 2-Structure of the Atom (3.6%), 3-Quantum Mechanical Nature of the Atom (5.6%), Properties of the Nucleus (7.0%) and 5-Deep Inside the Atom (3.1%).
  • This analysis looks at the sub-topic, Quantum Mechanical Nature of the Atom.

HSC ANALYSIS - What to expect and common pitfalls

  • Quantum Mechanical Nature of the Atom is a healthy contributor to new syllabus exams that has appeared in the longer answer section every year (sometimes just as “part” of a broader question), as well as the multiple-choice each year except 2022.
  • Bohr's model of the atom is the most commonly tested concept, tested in 5 of the last 6 exams (most recently in 2025 HSC 27 and 2025 HSC 3 MC).
  • Electron transition calculations have been required in longer answer questions in 2024 HSC 24 and 2020 HSC 21 with the latter requiring students to write a clear and precise description of this process.
  • De Broglie's model has attracted specific questions in 2024, 2021 and 2019. Schrödinger's contributions are less specifically examined but remain important as they can meaningfully contribute to more general questions on the development of the atomic model.
  • It cannot be overstated that developing concise summaries of various scientists' contributions to the quantum 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 23.1% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into five sub-categories for analysis purposes which are: 1-Origins of Elements (3.8%), 2-Structure of the Atom (3.6%), 3-Quantum Mechanical Nature of the Atom (5.6%), Properties of the Nucleus (7.0%) and 5-Deep Inside the Atom (3.1%).
  • This analysis looks at the sub-topic, Structure of the Atom.

HSC ANALYSIS - What to expect and common pitfalls

  • Structure of the Atom has been examined in the longer answer section of each new syllabus exam as well as a singular multiple choice question in 2019.
  • Chadwick (2024, 2020), Bohr-Rutherford (2024, 2022), Millikan and Thomson (2021), and Geiger-Marsden (2022) have all been the specific subject of longer answer questions since 2019. 
  • 2025 HSC 31 was a 5-mark "assess" (keyword) question that looked specifically at cathode ray experiments. Students will again benefit greatly from having prepared and concise summaries of historical experiments and "keyword" requirements.
  • Just as importantly, broad scope high-mark questions where students get to choose their own experiments as evidence, are common (see 2023 HSC 33 and 2019 HSC 32). 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.

PHYSICS M8 Snapshot: Origins of Elements

HISTORICAL CONTRIBUTION

  • M8 From the Universe to the Atom has contributed an average of 23.1% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into five sub-categories for analysis purposes which are: 1-Origins of Elements (3.8%), 2-Structure of the Atom (3.6%), 3-Quantum Mechanical Nature of the Atom (5.6%), Properties of the Nucleus (7.0%) and 5-Deep Inside the Atom (3.1%).
  • This analysis looks at the sub-topic, Origins of Elements.

HSC ANALYSIS - What to expect and common pitfalls

  • H-R diagrams have been examined in 6 of the last 7 exams, split between longer answer and multiple-choice (see 2023 HSC 21, 2022 HSC 21 and 2025 HSC 15 MC).
  • Spectra questions have appeared every year in the period 2020-24. We note the cross-topic overlaps with other content such as M7:Light-Quantum model and M8:Quantum Mechanical Nature of the Atom are common.
  • Hubble and the Expansion of the universe has caused serious problems when it has been examined and deserves attention (see 2024 HSC 22, 2021 HSC 32 and 2023 HSC 20 MC).
  • While the Big Bang has not yet been examined in new syllabus exam, it is coming and any topic revision should cover this area.

PHYSICS M7 Snapshot: Light and Special Relativity

HISTORICAL CONTRIBUTION

  • M7 The Nature of Light looks has contributed an average of 26.3% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into four categories for analysis purposes which are: 1-Electromagnetic Spectrum (5.1%), 2-Light: Wave Model (5.1%), 3-Light: Quantum Model (8.5%) and 4-Light and Special Relativity (7.6%).
  • This analysis looks at the sub-topic, Light and Special Relativity.

HSC ANALYSIS - What to expect and common pitfalls

  • Light and Special Relativity has attracted a longer response question every year of the new syllabus between 2019-25 (including two in 2024 and 2020). Multiple-choice questions have also 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 five new syllabus exams to date (most recently in 2024).
  • Length Contraction has been examined through multiple choice questions four times in new syllabus exams to date (review 2023 HSC 19 MC and 2022 HSC 20 MC).
  • Momentum Dilation has appeared in longer answer questions in 2024, 2021 and 2020. Effective revision must include explaining this concept in a concise way. 
  • Einstein's Postulates looks at questions dealing with inertial frames of reference and the constancy of the speed of light. Multiple questions address this important revision area.
  • Revision should include examples that require students to concisely describe and/or interpret thought experiments that provide evidence for both time and distance dilation (see 2019 HSC 27 and 2022 HSC 30).
  • 2025 HSC 32 was an 8-mark monster that required students to "analyse" (keyword) the theory of special relativity in relation to length, time and motion. Prepared, concise summaries of both theories and experimental evidence in this area are key to high band responses.

PHYSICS M7 Snapshot: Light: Quantum Model

HISTORICAL CONTRIBUTION

  • M7 The Nature of Light looks has contributed an average of 26.3% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into four categories for analysis purposes which are: 1-Electromagnetic Spectrum (5.1%), 2-Light: Wave Model (5.1%), 3-Light: Quantum Model (8.5%) and 4-Light and Special Relativity (7.6%).
  • This analysis looks at the largest sub-topic, Light: Quantum Model.

HSC ANALYSIS - What to expect and common pitfalls

  • The Quantum Model of Light is the 18-foot saltwater crocodile of Module 7, attracting the highest mark allocations of any topic in the module. Since 2019, it has averaged almost two longer answer questions per exam, as well as two multiple-choice (we note 2025 was an outlier with no MC questions).
  • The Photoelectric Effect is the most commonly tested topic area, attracting a multiple choice question every year since 2019, as well as high-mark longer answer questions in 2025, 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 (review 2021 HSC 33 and 2024 HSC 32).
  • Blackbodies has been consistently examined, appearing each year between 2019-24. 2020 HSC 26 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 26.3% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into four categories for analysis purposes which are: 1-Electromagnetic Spectrum (5.1%), 2-Light: Wave Model (5.1%), 3-Light: Quantum Model (8.5%) and 4-Light and Special Relativity (7.6%).
  • This analysis looks at the sub-topic, Light: Wave Model.

HSC ANALYSIS - What to expect and common pitfalls

  • Light: Wave Model has been tested via longer answer questions every year in the period 2020-25, as well as multiple-choice each year over the same period. 
  • Young's Double Slit Experiment has already been tested 4 times since the new syllabus was introduced (most recently in 2025). Students should be prepared to combine both scientific theory in conjunction with a calculation component.
  • Polarisation has been examined in 5 new syllabus exams, most recently in 2025. Both longer answer questions (review 2023 HSC 29) and multiple choice (2025 HSC 12 MC, 2022 HSC 17 MC) on this topic area have proven very challenging and deserve revision attention.
  • The experimental evidence for models of light proposed by Newton and Huygens has been under-examined in our view and represents important revision (see 2022 HSC 27).
  • 2024 HSC 32 is an 8-mark "analyse" (keyword) question that gives students a wide scope for choosing three experiments that "explore the interaction of light and matter". Preparing concise summaries for all major experiments, in conjunction with a sound knowledge of "keyword" requirements, pays big dividends for these types of broad questions.

PHYSICS M7 Snapshot: Electromagnetic Spectrum

HISTORICAL CONTRIBUTION

  • M7 The Nature of Light looks has contributed an average of 26.3% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into four categories for analysis purposes which are: 1-Electromagnetic Spectrum (5.1%), 2-Light: Wave Model (5.1%), 3-Light: Quantum Model (8.5%) and 4-Light and Special Relativity (7.6%).
  • This analysis looks at the sub-topic, Electromagnetic Spectrum.

HSC ANALYSIS - What to expect and common pitfalls

  • Electromagnetic Spectrum has been examined every year of the new syllabus, appearing in the longer response in 5 of 7 years, and via multiple choice also in 5 exams.
  • 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.
  • Measuring the speed of light has now been examined three times and caused problems on two of those occasions (see 2025 HSC 34 and 2020 HSC 18 MC).
  • Maxwell's contribution has been tested twice in new syllabus exams (most recently 2025). 2019 HSC 25 deserves attention in this area - a relatively straightforward question that produced a sub-50% mean mark.

PHYSICS M6 Snapshot: Applications of the Motor Effect

HISTORICAL CONTRIBUTION

  • M6 Electromagnetism looks has contributed an average of 27.6% 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 (6.4%), 2-The Motor Effect (3.6%), 3-Electromagnetic Induction (11.4%) and 4-Applications of the Motor Effect (6.2%).
  • This analysis looks at the largest sub-topic, Electromagnetic Induction.
  • This analysis looks at the topic, Applications of the Motor Effect.

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 2020-24 HSC exams (notably absent in 2025) and must be a revision focus.
  • Back Emf is commonly assessed within wide scope explanatory questions. Commonly, students can choose to use this concept as part of a wider argument in longer answer questions (see 2025 HSC 35). Also, it has been tested via difficult multiple-choice questions (review 2025 HSC 11 MC, 2022 HSC 19 MC and 2021 HSC 12 MC).
  • DC Motor Components has been tested in multiple-choice in 2024 and in a band 4 longer answer question in 2023. 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.
  • Magnetic breaking is important revision, having appeared in longer answer questions in both 2023 and 2022 (also review the related M6 EQ-Bank 12403). 
  • 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.

PHYSICS M6 Snapshot: Electromagnetic Induction

HISTORICAL CONTRIBUTION

  • M6 Electromagnetism looks has contributed an average of 27.6% 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 (6.4%), 2-The Motor Effect (3.6%), 3-Electromagnetic Induction (11.4%) and 4-Applications of the Motor Effect (6.2%).
  • This analysis looks at the largest sub-topic, Electromagnetic Induction.

HSC ANALYSIS - What to expect and common pitfalls

  • Electromagnetic Induction is the blue whale of not just Module 6, but the whole Physics course. It's contribution (11.4%) is the highest of any topic area and students can expect between 1-2 longer answer questions per exam as well as an average of two multiple-choice. 
  • Lenz and Faraday represent the most commonly examined concepts, being tested extensively every year since 2020-24 (notably absent in 2025) in questions worth a highly significant 7-9 marks. 
  • Lenz and Faraday questions analyse the critical and difficult area of induced currents. 2024 HSC 33, 2023 HSC 30, 2020 HSC 33 and 2021 HSC 31 all caused problems and deserve particular attention.
  • Transformer Calculations/Efficiency have been examined in 6 of the last 7 new syllabus exams, including longer answer questions in 2023, 2022 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.
  • Energy Distribution received its first significant mark allocation in 2025 HSC 22 which is a "must review" question.
  • Electromagnetic Induction commonly appears in difficult questions towards the end of the multiple choice section. 2024 HSC 18 MC, 2021 HSC 10 MC, and 2019 HSC 18 MC represent the upper difficulty level students will encounter.

PHYSICS M6 Snapshot: The Motor Effect

HISTORICAL CONTRIBUTION

  • M6 Electromagnetism looks has contributed an average of 27.6% 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 (6.4%), 2-The Motor Effect (3.6%), 3-Electromagnetic Induction (11.4%) and 4-Applications of the Motor Effect (6.2%).
  • This analysis looks at the smallest sub-topic, The Motor Effect.

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 has attracted the highest mark allocations to date, tested in 6 of 7 new syllabus exams (most recently in 2025), including longer answer questions on three occasions (review 2021 HSC 27 and 2019 HSC 28).
  • Multiple-choice questions on this content have proven difficult and deserve specific attention (see 2024 HSC 10 MC and 2023 HSC 10 MC).
  • Force between Current-Carrying Conductors most recently appeared in a 6-mark question in 2024. We note it has been examined via multiple-choice every year between 2020-2023. This topic area is consistently examined at the Band 5 difficulty level and is an important revision area.
  • The third concept looks at the connection between the ampere and Newton's Third Law. Although it has not yet appeared in a new syllabus HSC exam, it relates to a specific syllabus dot point and remains recommended revision in our view (review EQ-Bank 12581).

PHYSICS M6 Snapshot: Charged Particles, Conductors …

HISTORICAL CONTRIBUTION

  • M6 Electromagnetism looks has contributed an average of 27.6% 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 (6.4%), 2-The Motor Effect (3.6%), 3-Electromagnetic Induction (11.4%) and 4-Applications of the Motor Effect (6.2%).
  • This analysis looks at the topic, Charged Particles, Conductors, and Electric/Magnetic Fields.

HSC ANALYSIS - What to expect and common pitfalls

  • Charged Particles, Conductors, and Electric/Magnetic Fields has attracted an average two multiple choice questions per exam and at least one longer answer question worth between 3-7 marks.
  • Charged Particles in Electric Fields has been examined every year in either MC (7 times) or longer answer (3 times, most recently in 2024). High-mark and high difficulty questions that can include M5 Projectile Motion calculations are critical revision in this area (see 2024 HSC 28 and 2020 HSC 34).
  • Charged Particles in Magnetic Fields have also appeared three times in the longer answer section of new syllabus exams (most recently in 2023), as well as multiple choice in 2025 (twice), 2024 and 2020. Low mean marks are common and flag this area for revision attention. 
  • Combinations of electric and magnetic fields have been tested via multiple-choice four times in new syllabus exams to date at the band 5-6 level of difficulty.
  • Kinematic/Work calculations, have been tested four times in new syllabus exams (most recently in 2025), including two substantial "must review" longer answer questions (see 2021 HSC 30 and 2020 HSC 34).

PHYSICS M5 Snapshot: Projectile Motion

HISTORICAL CONTRIBUTION

  • M5 Advanced Mechanics has contributed an average of 23.0% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into three sub-categories for analysis purposes which are: 1-Circular Motion (6.0%), 2-Motion in Gravitational Fields (10.1%) and 3-Projectile Motion (6.9%).
  • 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 look at the core equations of projectile motion. Students require a deep understanding of an object's trajectory and how this is affected by launch angle or launch velocity changes (review 2022 HSC Q29 which caused problems).
  • Velocity and Acceleration concepts have been tested in the multiple choice section 4 out of the last 7 years (most recently in 2024). Questions generally focus on how a projectile's velocity and/or acceleration change or remain constant throughout its trajectory.
  • More difficult questions can require an understanding of the vertical and horizontal components of projectile motion to find a projectile's range (2025 HSC 28), launch angle (2020 HSC 24) or time of flight (2021 HSC 34). 2023 HSC 32 is a 7-mark "must review" question that combined both circular and projectile motion topics.
  • Challenging projectile motion calculations have also appeared in cross-topic questions with Module 6. These represent important revision once both topics are covered (see 2024 HSC 28 and 2020 HSC 34).

PHYSICS M5 Snapshot: Motion in Gravitational Fields

HISTORICAL CONTRIBUTION

  • M5 Advanced Mechanics has contributed an average of 23.0% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into three sub-categories for analysis purposes which are: 1-Circular Motion (6.0%), 2-Motion in Gravitational Fields (10.1%) and 3-Projectile Motion (6.9%).
  • This analysis looks at the largest subtopic, Motion in Gravitational Fields.

HSC ANALYSIS - What to expect and common pitfalls

  • Motion in Gravitational Fields is the 660-pound Silverback of the Module 5 rainforest. It is the second most examined topic in the whole Physics course, attracting an average of 2 longer answer and 2.5 multiple-choice questions per year since 2019.
  • Energy Changes involves calculation heavy questions where students need to consider both potential and kinetic energy conversion. Examined in the longer answer section of 5 out of 7 new syllabus exams (most recently in 2024) with consistent high mark allocations, this content area represents critical revision.
  • Gravitational attraction between 2 objects and gravitational field strength are are commonly tested areas that have appeared in both multiple choice and longer answer questions in the period 2021-24 (review 2024 HSC 31, 2022 HSC 35 and 2021 HSC 14 MC)
  • Orbital Velocity/Period/Radius has been examined twice in longer answer questions (most recently in 2024) and 6 times via multiple choice since 2019. 
  • High mark "Analyse" (keyword) questions were asked in both 2025 and 2022 in questions worth 8 and 5 marks respectively. A very important keyword and question type that warrants revision attention.

PHYSICS M5 Snapshot: Circular Motion

HISTORICAL CONTRIBUTION

  • M5 Advanced Mechanics has contributed an average of 23.0% per HSC Physics exam since the new syllabus was introduced in 2019.
  • This topic has been split into three sub-categories for analysis purposes which are: 1-Circular Motion (6.0%), 2-Motion in Gravitational Fields (10.1%) and 3-Projectile Motion (6.9%).
  • This analysis looks at the sub-topic, Circular Motion.

HSC ANALYSIS - What to expect and common pitfalls

  • Circular Motion is the smallest contributing subtopic within M5 Advanced Mechanics, responsible for ~6.0% 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 consistently examined and should be well covered in any revision (see 2025 HSC 13 MC, 2024 HSC 30). 
  • Applications of Circular Motion attracted significant allocations in both 2023 and 2024 (the cross topic 2023 HSC 32 a must review question).
  • Angular velocity can be revised via 2021 HSC 22.
  • Common cross-topic questions can involve a circular motion component within a gravitational field context (review 2025 HSC 29 and 2022 HSC 35). Note that cross-topic questions with electric fields are covered within Module 6.

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 Snapshot: N1 Exponential Form

HISTORICAL CONTRIBUTION

  • N1 Introduction to Complex Numbers has contributed 7.9% 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 (3.7%), 2-Argand Diagrams and Mod/Arg Form (1.2%) and 3-Exponential Form (3.0%).
  • This analysis looks at Exponential Form.

HSC ANALYSIS - What to expect and common pitfalls

  • Exponential Form (3.0%) is extremely important new content within Ext2 complex numbers, having appeared in 5 longer answer questions (most recently 2025) and 4 multiple choice (most recently 2024) since 2020.
  • Note 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 (see 2022 Ext2 11c).
  • The multiplication of two complex numbers in exponential form has been examined twice in new syllabus exams and should be covered in any revision set (see 2025 Ext2 11b, 2021 Ext2 11a).
  • Exponential form can also offer an efficient solution strategy without being explicitly stated in the question (see 2023 Ext2 3 MC).
  • It is important to note that exponential form has been combined in cross-topic questions with binomial expansion, integration (2020 Ext2 13d) and maximum value calculations (2020 Ext2 9 MC). These are covered in later topics.

EXT2 Snapshot: N1 Argand Diagrams

HISTORICAL CONTRIBUTION

  • N1 Introduction to Complex Numbers has contributed 7.9% 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 (3.7%), 2-Argand Diagrams and Mod/Arg Form (1.2%) and 3-Exponential Form (3.0%).
  • This analysis looks at Argand Diagrams and Mod/Arg Form.

HSC ANALYSIS - What to expect and common pitfalls

  • Argand Diagrams and Mod/Arg Form (1.2%) had hardly been examined in the period 2020-23 but made a welcome comeback in 2024-25 with a multiple choice (2025) and more importantly, a significant 4 mark allocation in 2024.
  • Before 2020, 4–5 mark dedicated questions regularly appeared before allocations fell off a cliff in new syllabus exams. Note this does not take into account its contribution to 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 (see 2024 Ext2 11e).
  • Revision should cover all basic identities involving modulus and argument (2020 Ext2 4 MC is recommended revision).
  • 2008 Ext2 2b is an important revision question that requires students to equate the real parts of two complex numbers before finding the exact surd form of a trig ratio.

EXT1 V1 Snapshot: Vectors, Force and Velocity

HISTORICAL CONTRIBUTION

  • Vectors is the blue whale of the Ext1 Pacific ocean, contributing a massive 18.9% 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 (7.9%), 2-Vectors, Force and Velocity (1.7%), 3-Vectors and Geometry (3.6%), 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 (1.7%) has been examined twice in new syllabus exams, most recently in 2025 via a 4-mark longer answer question.
  • 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 along with other similar examples that have been added to the database.
  • 2025 Ext1 13c also involves motion vectors where students need to apply calculus in combination with angles between vectors and challenging algebra - a "must review" qiuestion.
  • 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 is the 880-pound Silverback of the Extension 1 course, contributing a huge 16.4% per new syllabus Ext1 exam since the new course began 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 (10.0%).
  • This analysis looks at two sub-topics within the larger Differential Equations topic (see graph above) → Slope Fields (1.8%) and Differential Equations (5.5%).

HSC ANALYSIS - What to expect and common pitfalls

  • Equations and Slope Fields have appeared in multiple questions in all but one new syllabus exam, making this a critical focus area for any revision.
  • Solving differential equations where the derivative is `f(y)` or `f(x,y)` is a core competency that has been examined in 4 of the last 5 exams (absent in 2023), including 2 questions in 2025, 2022 and 2020.
  • 2024 Ext1 14a and 2022 Ext1 14a were the most challenging questions looking at this topic area and deserve specific revision attention.
  • Slope fields is a "highly examinable" topic area that has also been examined in each new syllabus exam (note the 2024 example appears later in Applications of DE). 2021 Ext1 12a asked students to sketch a solution curve and caused major problems with a mean mark of 18%.

2ADV C4 Snapshot: Other Integration Applications

HISTORICAL CONTRIBUTION

  • C4 Integration has contributed a substantial 13.5% 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 (2.9%), 2-Areas Under Curves (5.5%), 3-Trapezoidal Rule (2.8%) and 4-Other Integration Examples (2.3%).
  • 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 multiple questions in the 2024, 2023 and 2021 exams, and was omitted in 2025 and 2022. 
  • Database questions look at similar content to C3 Rates of Change, but are allocated in this topic area as they include integration.
  • The most common underlying themes are motion, flow (examined in 2024) and population which are all well represented in the database.
  • Questions often provide the gradient/primitive function of a curve and require students to find the equation of the curve. Most recently examined with a 4-mark allocation in 2023 Adv 28, producing a 51% mean mark.
  • Some EQ-Bank questions in the database take the form of shorter questions that we expect to feature going forward, as shown in NESA's sample exam.

EXT1 S1 Snapshot: Normal Approximations

HISTORICAL CONTRIBUTION

  • S1 The Binomial has contributed an average of 8.3% 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 (1.9%), 2-Statistics and Binomial Distributions (2.1%) and 3-Normal Approximations of Sample Proportions (4.3%).
  • This analysis looks at Normal Approximations of Sample Proportions.

HSC ANALYSIS - What to expect and common pitfalls

  • Normal Approximations of Sample Proportions (4.3%) has appeared in the longer answer section of every new syllabus Ext1 exam in the period 2020-24, but was notably absent in 2025.
  • This topic combines significant mark allocations with high difficulty and represents a critical revision area.
  • Proficiency in understanding and using a probability table of z-scores is clearly becoming a key skill (required in 2024 Ext1 12c, 2023 Ext1 11f and 2022 Ext1 14d). Note that all worksheets in this subtopic automatically include this reference table.
  • Supplementing the 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 is the blue whale of the Ext1 Pacific ocean, contributing a massive 18.9% 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 (7.9%), 2-Vectors, Force and Velocity (1.7%), 3-Vectors and Geometry (3.6%), 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 (3.6%) has appeared in 5 out of 6 new syllabus exams. Mark allocations peaked between 2021–23 which saw longer answer questions worth between 3–7 marks.
  • This topic area can be examined across a broad difficulty spectrum. While the 2020 exam threw up a low difficulty MC question, the 2023 and 2021 exams included high-mark beasts that defined the very best papers.
  • 2025 Ext1 8 MC addressed collinearity and is a "must review" question in any revision set.
  • The database covers numerous geometric proofs, including: rhombus diagonals bisecting, mid-points of quadrilaterals forming a parallelogram, intersections of lines in given ratios, 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 has hardly been examined in a dedicated question in new syllabus exams to date. It is worth mentioning however that it regularly appeared prior to 2020 and represents a great opportunity for high scoring.
  • Log integration is more challenging than the simplistic log differentiation and is examined 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 although its most recent appearance is surprisingly in 2020 Adv 17.
  • 2019 HSC 13c(ii) produced a sub-50% mean mark and is important revision.
  • The new syllabus explicitly mentions the differentiation of  `log_a x`  and is covered in the database within EQ-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 has appeared in the 2022 and 2020 new syllabus Advanced exams, including two questions in 2020 totalling an impressive 5-mark allocation.
  • Differentiating and then integrating caused problems in the 2020 exam and deserves attention (see 2020 Adv 18 and 2016 Adv 12d).
  • The differentiation of `a^f(x)` which receives its own dot point in the new syllabus is important revision. Numerous questions provide coverage of this area (see 2022 Adv 29).
  • 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 8.3% 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 (1.9%), 2-Statistics and Binomial Distributions (2.1%) and 3-Normal Approximations of Sample Proportions (4.3%).
  • 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. 
  • It's mark allocation peaked in 2025 with two questions appearing on the topic worth a substantial total of 5 marks (see 2025 Ext1 4 MC and 2025 Ext1 13d).
  • Prior to 2025, the topic was last examined in 2020 in a low difficulty 3-mark question. We note that both longer answer questions required cross-topic knowledge of normal distribution.
  • Be aware that Topic Guidance exemplar questions have also 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.

EXT1 S1 Snapshot: Binomial Probability

HISTORICAL CONTRIBUTION

  • S1 The Binomial has contributed an average of 8.3% 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 (1.9%), 2-Statistics and Binomial Distributions (2.1%) and 3-Normal Approximations of Sample Proportions (4.3%).
  • This analysis looks at Binomial Probability.

HSC ANALYSIS - What to expect and common pitfalls

  • Binomial Probability (1.9%) has been examined in 4 of the 6 new syllabus exams (most recently in 2024) in questions worth 1–3 marks.
  • Games of Chance questions are a common question type that deserve particular attention (review 2022 Ext1 12e → 35% mean mark).
  • Pre–2020, this topic area accounted for a much higher average of 3+ marks per paper. Questions from this period represent great revision in our view, especially given higher mark allocations are always possible.
  • The results of past HSC questions have been volatile with sub-50% mean marks occurring in approximately half of all questions.
  • Revision should feature harder examples that have required students to express probabilities in algebraic terms and prove identities (review 2024 Ext1 9 MC, 2006 Ext1 6b, and 2011 Ext1 6c).

EXT1 V1 Snapshot: Vectors and Projectile Motion

HISTORICAL CONTRIBUTION

  • Vectors is the blue whale of the Ext1 Pacific ocean, contributing a massive 18.9% 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 (7.9%), 2-Vectors, Force and Velocity (1.7%), 3-Vectors and Geometry (3.6%), 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 significant allocations in the period between 2021–25, with an eye-watering 8-mark question appearing in the 2023 exam.
  • Projectile motion in the new Ext1 course looks at the parametric vector equations of motion (functions of t). High mark allocations and low mean marks → critical revision area.
  • New syllabus exams have veered from prior exams by not providing any scaffolding (read question parts). 2025 Ext1 14b, 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.
  • Sample NESA exam questions required the conversion of parametric equations into a Cartesian equation (y as a function of x). Review Ext1 V1 EQ-Bank 28 to cover this.

EXT1 V1 Snapshot: Operations With Vectors

HISTORICAL CONTRIBUTION

  • Vectors is the blue whale of the Ext1 Pacific ocean, contributing a massive 18.9% 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 (7.9%), 2-Vectors, Force and Velocity (1.7%), 3-Vectors and Geometry (3.6%), 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 (7.9%) has attracted at least three separate questions in 5 out of 6 new syllabus Ext1 exams (the outlier was 2023).
  • Basic vector calculations (addition, subtraction and multiplication), angles between vectors, unit vectors and projections have featured in new syllabus Ext1 exams to date and are all well represented in the database.
  • Perpendicular vectors have been examined on four separate occasions. 2025 Ext1 14c is a cracking question where students need to interpret a real world context before applying calculation - revision attention required!
  • Vector projections were examined each year in the period 2022-25. This topic area has shown it can be potentially examined at a very high level of difficulty and deserves a revision focus.
  • 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 and well covered in the database.

EXT1 F2 Snapshot: Sum, Product and Multiplicity of Roots

HISTORICAL CONTRIBUTION

  • Polynomials has contributed a solid 5.9%, 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 (1.9%) and 2-Sum, Products and Multiplicity of Roots (4.0%).
  • This analysis looks at Sum, Products and Multiplicity of Roots.

HSC ANALYSIS - What to expect and common pitfalls

  • Sum, Products and Multiplicity of Roots (4.0%) has surprised to the upside in its contributions to Ext1 new syllabus exams, with longer answer questions appearing in four exams as well as a multiple choice in 2020 and 2024.
  • 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.
  • 2025 Ext1 14e was a beast of a question that produced a 26% mean mark and represents the highest level of difficulty students can expect. Other challenging questions worthy of revision attention include 2023 Ext1 14b, 2022 Ext1 13d and 2021 Ext1 11h.
  • Numerous Ext2 past questions that are now examinable within the new Ext1 course are included in the database. Note that 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 5.9%, 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 (1.9%) and 2-Sum, Products and Multiplicity of Roots (4.0%).
  • This analysis looks at Remainder and Factor Theorems.

HSC ANALYSIS - What to expect and common pitfalls

  • Remainder and Factor Theorems (1.9%) has been examined in 4 out of 6 new syllabus exams (notably absent in 2024-25), 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 7.9% 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 (1.9%), 2-Inequalities (2.4%), 3-Inverse Functions (2.6%) and 4-Parametric Functions (1.0%).
  • This analysis looks at Parametric Functions.

HSC ANALYSIS - What to expect and common pitfalls

  • Parametric Equations (1.0%) 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%. 
  • 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 7.9% 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 (1.9%), 2-Inequalities (2.4%), 3-Inverse Functions (2.6%) and 4-Parametric Functions (1.0%).
  • This analysis looks at Inverse Functions.

HSC ANALYSIS - What to expect and common pitfalls

  • Inverse Functions (2.6%) looks at non-trigonometric inverse functions and has been examined in 4 new syllabus exams to date, most recently in 2025 via a cream puff 2-mark gift to students.
  • Be aware that when Inverse Functions are tested, significant mark allocations are common. 2021 Ext1 12d is case in point, contributing 6 marks to the exam – a "must review" question.
  • Multiple choice questions on this topic are spread across a wide difficulty spectrum, including reaching band 5-6 level in 2023 Ext1 9 MC and 2019 Ext1 10 MC.
  • 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 should feature in any revision (see 2018 Ext1 13b and 2010 Ext1 3b).

EXT1 F1 Snapshot: Inequalities

HISTORICAL CONTRIBUTION

  • F1 Further Work With Functions has contributed a healthy 7.9% 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 (1.9%), 2-Inequalities (2.4%), 3-Inverse Functions (2.6%) and 4-Parametric Functions (1.0%).
  • This analysis looks at Inequalities.

HSC ANALYSIS - What to expect and common pitfalls

  • Inequalities (2.6%) has been examined in 4 of 6 new syllabus exams, including a peak of two questions (totalling a 5-mark allocation) in the 2024 exam.
  • Algebraic fraction inequalities are the most common question type from past Ext1 papers, last examined in 2022. A key revision area.
  • Absolute value inequalities were last tested in 2025 via multiple choice. Revision of this topic area should include 2024 Ext1 12e.
  • Quadratic inequalities are gifts from the examiner, appearing in 2024 and 2020. 
  • 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 topic area is expected to present band 3-4 level difficulty questions, often with meaningful mark allocations. Revision here should aim to 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 7.9% 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 (1.9%), 2-Inequalities (2.4%), 3-Inverse Functions (2.6%) and 4-Parametric Functions (1.0%).
  • 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 the most 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 7.9% 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 (1.9%), 2-Inequalities (2.4%), 3-Inverse Functions (2.6%) and 4-Parametric Functions (1.0%).
  • 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 4 out of 6 new syllabus exams, most recently in 2024.
  • 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 was allocated 3 marks and required students to graph  `y=1/(f(x))`  from a given sketch of a quadratic function. An important skill to revise.
  • This topic area is made up of content that was previously found in the old syllabus within Ext2. The database includes past Ext2 questions which provide excellent revision (denoted by EXT1′ in the title).

Combinatorics, EXT1 A1 Snapshot: The Binomial

HISTORICAL CONTRIBUTION

  • Combinatorics has contributed a healthy average of 8.1% 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 (4.0%) and 2-Binomial Expansion (4.0%).
  • This analysis looks at Binomial Expansion.

HSC ANALYSIS - What to expect and common pitfalls

  • Binomial Expansion (4.0%) has been tested in 4 of the last 5 new syllabus exams (absent only in 2024), exclusively in the longer answer section.
  • Binomial proofs represent the most difficult question type, most recently examined in 2025 Ext1 13e. Be aware that 2020 Ext1 14a tested this area with an extremely challenging 8-mark question that upwardly adjusted the possible level of difficulty of binomial proof questions. An important revision question.
  • Combinatorial proofs that receive a specific mention in the syllabus are covered in the database and should be included in any revision.
  • 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 (review 2012 Ext1 11f and 2005 Ext1 2b). Note "greatest coefficient" questions are no longer examinable and have been removed from the database.

EXT1 A1 Snapshot: Permutations and Combinations

HISTORICAL CONTRIBUTION

  • Combinatorics has contributed a healthy average of 8.1% 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 (4.0%) and 2-Binomial Expansion (4.0%).
  • This analysis looks at Permutations and Combinations.

HSC ANALYSIS - What to expect and common pitfalls

  • Permutations and Combinations (4.0%) have appeared in two questions in 5 out of 6 new syllabus exams. This has primarily been via a multiple choice in combination with a longer answer question, although 2025 was an outlier with two separate longer answer questions.
  • 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 has been tested in every new syllabus exam. 2025 Ext1 14a was a cracking example where students needed to recognise that the principle applied (a 33% mean mark says most didn't). 2021 Ext1 10 MC and 2020 Ext1 12c are two other challenging questions that deserve attention here. 
  • Common question types require a deep understanding or ordered and unordered combinations, as well as combinations in a circle (see 2023 Ext1 10 MC which produced a mean mark of just 19%).
  • We recommend students get exposure to questions involving geometry, last examined in 2022 Ext1 7 MC with a mean mark of 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.
  • Sum of a series induction proofs are easily the most common question style, examined in 5 of the last 7 years, most recently in 2025. A subset of this question type involve a deep understanding of factorial notation which should feature in any revision (see 2025 Ext1 12c and 2019 Ext1 14a). 
  • Divisibility is a key question theme that requires students to prove a series is divisible by a given integer. This question type was examined was examined in both 2024 and 2022 and is important revision.
  • 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 7.6% 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 (2.6%) and 2-Identities, Equations and 't' Formulae (5.0%).
  • This analysis look at Identities, Equations and 't' Formulae.

HSC ANALYSIS - What to expect and common pitfalls

  • Identities and Equations (5.0%) was examined in longer answer questions in 5 of 6 new syllabus exams (absent only in 2022).
  • 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 required 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 25 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 7.6% 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 (2.6%) and 2-Identities, Equations and 't' Formulae (5.0%).
  • This analysis looks at Auxiliary Angles.

HSC ANALYSIS - What to expect and common pitfalls

  • Auxiliary Angles (2.6%) have been tested in a dedicated longer answer question in three new syllabus exams to date (most recently in 2025) as well as an extremely challenging multiple choice in 2024. 
  • Allocations are more often in the substantial 3-4 mark range, making this a fertile area for scoring well.
  • 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 attention.

EXT1 T2 Snapshot: Further Trig Identities

HISTORICAL CONTRIBUTION

  • Trigonometry has contributed a very healthy 11.7%, on average, to new syllabus Ext1 exams since being introduced in 2020. 
  • Trigonometry is split into three topic areas for analysis purposes which are: T1-Inverse Trig Functions (2.9%), T2-Compound Angles (1.2%) and 3-Trig Equations (7.6%).
  • This analysis looks at Compound Angles.

HSC ANALYSIS - What to expect and common pitfalls

  • Compound Angles (1.2%) is a small content area that was last examined in 2024 (in a cross topic question with T3 Trig Equations) and before that in 2021.
  • Although this topic area only attracts a dedicated question sporadically, it establishes gateway knowledge for other more challenging topics like solving trig identities (found within 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 question type.
  • Similarly, NESA exemplar questions require students to construct compound angles and use exact trig ratios to solve. Numerous questions in the database cover this area.

EXT1 T1 Snapshot: Inverse Trig Functions

HISTORICAL CONTRIBUTION

  • Trigonometry has contributed a very healthy 11.7%, on average, to new syllabus Ext1 exams since being introduced in 2020. 
  • Trigonometry is split into three major topic areas for analysis purposes which are: T1-Inverse Trig Functions (2.9%), T2-Compound Angles (1.2%) and 3-Trig Equations (7.6%).
  • This analysis looks at T1 Inverse Trig Functions.

HSC ANALYSIS - What to expect and common pitfalls

  • Inverse Trig Functions (2.9%) has been examined in dedicated questions in each of the last five Ext1 exams, including allocations of two questions between 2022-24.
  • "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 in this topic's statistics).
  • Drawing or identifying an inverse trig graph is a common question type, examined in both 2024 and 2025.
  • A deep understanding of domain and range of an inverse function is critical and regularly tested (see 2022 Ext1 13c and 2024 Ext1 4 MC).
  • Exact values of inverse functions was tested in 2023 Ext1 5 MC and 2022 Ext1 1 MC, proving challenging on both occasions.
  • 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.

EXT1 C3 Snapshot: Further Areas and Solids of Revolution

HISTORICAL CONTRIBUTION

  • C3 Application of Calculus is the 880-pound Silverback of the Extension 1 course, contributing a huge 16.4% per new syllabus Ext1 exam since the new course began 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 (10.0%).
  • 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, having been tested within the longer answer section of each new syllabus exam, including two questions in four of those years.
  • The smaller topic of Further Area has been examined in 3 separate exams and is an important revision area (see 2021 Ext1 13c and 2024 Ext1 11g).
  • Solids of Revolution questions are typically examined around the band 4 difficulty level. One exception to this is 2023 Ext1 12e where the difficulty level hit band 5 (49% mean mark) - a revision focus question.
  • Note the database is a combination of Ext1 exam questions and others taken from past Advanced exams which can be identified by EXT1* in their title. 
  • History shows students have more difficulty with `y`-axis rotations. Ensure this question-type is well represented in any revision.

EXT1 C2 Snapshot: Harder Trig Calculus

HISTORICAL CONTRIBUTION

  • C2 Further Calculus Skills has contributed a substantial average of 14.4% 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 (4.8%), 2-Inverse Function Calculus (6.7%) and 3-Harder Trig Calculus (2.9%).
  • This analysis looks at Harder Trig Calculus.

HSC ANALYSIS - What to expect and common pitfalls

  • Harder Trig Calculus (2.9%) hit its peak allocation in the 2025 HSC with two separate longer answer questions (worth a total of 5 marks). Prior to this, it was examined in 2024 and each year between 2020–21.
  • 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 Function Calculus

HISTORICAL CONTRIBUTION

  • C2 Further Calculus Skills has contributed a substantial average of 14.4% 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 (4.8%), 2-Inverse Function Calculus (6.7%) and 3-Harder Trig Calculus (2.9%).
  • This analysis looks at Inverse Function Calculus.

HSC ANALYSIS - What to expect and common pitfalls

  • Inverse Function Calculus (6.7%) 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. This question type was tweaked in 2025 Ext1 14d and 2020 Ext1 13c which represent the most challenging problems in this area.
  • 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. 
  • 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 (review 2018 Ext1 12c, 2015 Ext1 13d and 2010 Ext1 5b).
  • This topic can also present beastly difficult multiple choice, as seen in 2025 Ext1 10 MC and 2022 Ext1 9 MC.

EXT1 C2 Snapshot: Integration By Substitution

HISTORICAL CONTRIBUTION

  • C2 Further Calculus Skills has contributed a substantial average of 14.4% 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 (4.8%), 2-Inverse Function Calculus (6.7%) and 3-Harder Trig Calculus (2.9%).
  • This analysis looks at Integration By Substitution.

HSC ANALYSIS - What to expect and common pitfalls

  • Integration by Substitution (4.8%) has been examined every exam in the last decade - nine times via longer answer questions with 2025 the outlier where it was tested via multiple choice.
  • Questions are in the band 3–4 range and present low hanging fruit for high scoring. 2024 Ext1 13d is at the upper difficulty students will encounter in this area and is a must review question.
  • 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 4.2% 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 (2.1%), 2-Rates of Change with respect to Time (0%), and 3-Related Rates of Change (2.1%).
  • This analysis looks at Rates of Change with respect to 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. It does however remain examinable content and should be revised.
  • 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. 
  • 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 4.2% 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 (2.1%), 2-Rates of Change with respect to Time (0%), and 3-Related Rates of Change (2.1%).
  • This analysis looks at Related Rates of Change.

HSC ANALYSIS - What to expect and common pitfalls

  • Related Rates of Change (2.1%) has been examined in 5 out of 6 new syllabus exams, four of those times in the longer answer section.
  • 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.
  • Important underlying themes that represent key revision include areas/volumes (most recently tested in 2025) and Pythagoras theorem (see 2014 Ext1 13b).
  • Marker's comments have flagged that students can often achieve half-marks by simply stating a correct chain rule.
  • Pitfalls: If a constant rate of change is established, students have struggled with follow up questions (see 2013 Ext1 13a and 2009 Ext1 5b).

EXT1 C1 Snapshot: Growth and Decay

HISTORICAL CONTRIBUTION

  • C1 Rates of Change has contributed 4.2% 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 (2.1%), 2-Rates of Change with respect to Time (0%), and 3-Related Rates of Change (2.1%).
  • This analysis looks at Growth and Decay.

HSC ANALYSIS - What to expect and common pitfalls

  • Exponential Growth and Decay (2.1%) most recently appeared in a single multiple-choice question in 2023 and in 4-mark questions each year between 2021-22.
  • 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 5.0% 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 (2.0%).
  • This analysis looks at Non-Calculus Graphing.

HSC ANALYSIS - What to expect and common pitfalls

  • Non-Calculus Graphing (2.0%) 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 graphing quotient functions that requires students to find intercepts and both vertical and horizontal asymptotes. Last examined in 2021 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 (see F2 EQ-Bank 22).
  • 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).