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HMS, BM EQ-Bank 681

Describe how peer influence can affect a young person's participation in sport.   (3 marks)

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Sample Answer

  • Young people often participate in sports their friends engage in to maintain social connections and avoid feeling excluded from peer groups.
  • Peers can provide encouragement and support during training and competition, enhancing motivation to continue participation.
  • Negative peer interactions or bullying in sporting contexts can discourage participation and cause young people to withdraw from sports they might otherwise enjoy.
Show Worked Solution

Sample Answer 

  • Young people often participate in sports their friends engage in to maintain social connections and avoid feeling excluded from peer groups.
  • Peers can provide encouragement and support during training and competition, enhancing motivation to continue participation.
  • Negative peer interactions or bullying in sporting contexts can discourage participation and cause young people to withdraw from sports they might otherwise enjoy.

Filed Under: Psych–Movement–Performance Interplay (EO-X) Tagged With: Band 2, Band 3, smc-5536-15-Personal Identity

HMS, BM EQ-Bank 678 MC

Sophia has experienced setbacks in her gymnastics career but continues to view challenges as opportunities to improve rather than reasons to give up.

This mindset most directly reflects which personal characteristic that influences sport participation and performance?

  1. Knowledge of various sports
  2. Family support systems
  3. Physical aptitude
  4. Resilience
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\(D\)

Show Worked Solution
  • D is correct: Resilience is defined by the ability to bounce back from setbacks and view challenges as opportunities.

Other Options:

  • A is incorrect: Knowledge of various sports is not directly related to overcoming setbacks.
  • B is incorrect: While family support may contribute to resilience, the scenario focuses on Sophia’s own mindset and approach.
  • C is incorrect: Physical aptitude refers to natural physical abilities rather than psychological characteristics.

Filed Under: Psych–Movement–Performance Interplay (EO-X) Tagged With: Band 2, smc-5536-15-Personal Identity

HMS, BM EQ-Bank 664

The research plan for front-on tackling in rugby league includes the question: "Does age affect how the front-on tackle should be learnt?"

Suggest two further research questions that could extend understanding of age-appropriate skill development in rugby.   (2 marks)

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Sample Answer – Any TWO of the following or similar

  • How should coaching feedback types be modified for different age groups learning front-on tackling technique to maximise safety and skill development?
  • What modifications to practice environments are most effective for different age groups to develop proper tackling technique while minimising injury risk?
  • At what age should full-contact tackling practice begin, and how should progression differ between younger and older beginners?
  • How do cognitive development stages across different ages affect the optimal sequence for teaching complex tackling technique components?
Show Worked Solution

Sample Answer – Any TWO of the following or similar

  • How should coaching feedback types be modified for different age groups learning front-on tackling technique to maximise safety and skill development?
  • What modifications to practice environments are most effective for different age groups to develop proper tackling technique while minimising injury risk?
  • At what age should full-contact tackling practice begin, and how should progression differ between younger and older beginners?
  • How do cognitive development stages across different ages affect the optimal sequence for teaching complex tackling technique components?

Filed Under: Skill learning and performance - Research Tagged With: Band 2, smc-5535-20-Further Research

HMS, BM EQ-Bank 657

  1. What is a "control group" in a research study about skill development.   (1 mark)

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  2. Explain why a control group might be important when researching the effectiveness of a new coaching approach for soccer dribbling skills.   (2 marks)

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Sample Answer

  1. A control group receives standard training rather than the experimental method, providing a comparison baseline.
  2. A control group helps researchers determine if improvements are actually due to the new coaching approach rather than just from regular practice or other factors.
  3. Without a control group, researchers couldn’t tell if skill improvements happened because the new approach works better or simply because any practice leads to improvement over time.

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Sample Answer

  1. A control group receives standard training rather than the experimental method, providing a comparison baseline.
  2. A control group helps researchers determine if improvements are actually due to the new coaching approach rather than just from regular practice or other factors.
  3. Without a control group, researchers couldn’t tell if skill improvements happened because the new approach works better or simply because any practice leads to improvement over time.
  4.  

Filed Under: Skill learning and performance - Research Tagged With: Band 2, Band 3, smc-5535-15-Research Process

HMS, BM EQ-Bank 652

Outline two ways a researcher might collect data when studying how beginners learn the front crawl swimming technique.   (2 marks)

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Sample Answer

  • Researchers could use direct observation with a checklist of technique elements (arm position, breathing timing, kick pattern) to measure improvement over multiple lessons.
  • Video recording of swimming sessions could be collected to allow detailed analysis of technique changes over time, with comparisons between early and later attempts.
Show Worked Solution

Sample Answer 

  • Researchers could use direct observation with a checklist of technique elements (arm position, breathing timing, kick pattern) to measure improvement over multiple lessons.
  • Video recording of swimming sessions could be collected to allow detailed analysis of technique changes over time, with comparisons between early and later attempts.

Filed Under: Uncategorized Tagged With: Band 2, smc-5535-15-Research Process

HMS, BM EQ-Bank 649 MC

What is the MAIN purpose of researching movement skill acquisition in sports?

  1. To identify talented athletes for elite development
  2. To develop better ways of teaching and learning skills
  3. To compare different sports and their techniques
  4. To create more complex sporting competitions
Show Answers Only

\(B\)

Show Worked Solution
  • B is correct: Research aims to improve teaching and learning methods

Other Options:

  • A is incorrect: Talent identification uses research but isn’t main purpose
  • C is incorrect: Technique comparison isn’t central purpose
  • D is incorrect: Competition development not related to skill acquisition

Filed Under: Skill learning and performance - Research Tagged With: Band 2, smc-5535-15-Research Process

HMS, BM EQ-Bank 644

Describe TWO ways researchers could study which types of feedback work best for beginners learning to tackle in rugby league.   (2 marks)

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Sample Answer – Any TWO of the following

  • Researchers could compare two beginner groups learning tackling with different feedback types. One receives knowledge of performance feedback, another receives knowledge of results feedback, then measure technique improvement.
  • Researchers could observe coaching sessions, recording feedback types given and tracking players’ technique development afterwards to identify which feedback produces better outcomes.
  • Researchers could use video analysis to compare tackling technique development between groups receiving immediate feedback versus delayed feedback after practice sessions.
  • Researchers could conduct surveys and interviews with players about their preferred feedback types, then correlate preferences with actual technique improvement measurements.
Show Worked Solution

Sample Answer 

  • Researchers could compare two beginner groups learning tackling with different feedback types. One receives knowledge of performance feedback, another receives knowledge of results feedback, then measure technique improvement.
  • Researchers could observe coaching sessions, recording feedback types given and tracking players’ technique development afterwards to identify which feedback produces better outcomes.
  • Researchers could use video analysis to compare tackling technique development between groups receiving immediate feedback versus delayed feedback after practice sessions.
  • Researchers could conduct surveys and interviews with players about their preferred feedback types, then correlate preferences with actual technique improvement measurements.

Filed Under: Skill learning and performance - Research Tagged With: Band 2, smc-5535-15-Research Process

HMS, BM EQ-Bank 586 MC

In soccer, "marking-up in defence" is an example of a:

  1. Strategic plan
  2. Technical skill
  3. Tactical skill
  4. Performance analysis
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\(C\)

Show Worked Solution
  • C is correct: Tactical skill involves positioning decisions to gain advantage

Other Options:

  • A is incorrect: Strategic plan is broader overall approach
  • B is incorrect: Technical skills are physical movement execution
  • D is incorrect: Performance analysis reviews play after it occurs

Filed Under: Performance elements Tagged With: Band 2, smc-5925-50-Identify element

HMS, BM EQ-Bank 570 MC

A novice gymnast is learning a complex balance beam routine. Her coach breaks down the routine into smaller segments, having her practise the mount first, then the middle section, and finally the dismount, before attempting the entire routine.

This is an example of which practice method?

  1. Massed practice
  2. Part practice
  3. Random practice
  4. Blocked practice
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\(B\)

Show Worked Solution
  • B is correct: Part practice involves breaking complex skills into smaller components

Other Options:

  • A is incorrect: Massed practice is continuous with minimal breaks
  • C is incorrect: Random practice mixes different skills unpredictably
  • D is incorrect: Blocked practice repeats one skill before moving to another

Filed Under: Practice methods Tagged With: Band 2, smc-5924-20-Whole/part, smc-5924-50-Identify method

HMS, BM EQ-Bank 547

Describe the role of feedback in the cognitive stage of learning a new swimming stroke.   (3 marks)

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Sample Answer

  • In the cognitive stage, immediate corrective feedback helps swimmers understand what adjustments are needed since they often cannot recognise their own errors in technique or body positioning.
  • Visual feedback through demonstrations or video replays creates clear mental images of proper technique, allowing swimmers to compare their performance against the model.
  • Positive reinforcement of successful attempts builds confidence and motivation to persist through initial difficulties, encouraging swimmers to continue practising despite experiencing discomfort or awkwardness.
Show Worked Solution

Sample Answer 

  • In the cognitive stage, immediate corrective feedback helps swimmers understand what adjustments are needed since they often cannot recognise their own errors in technique or body positioning.
  • Visual feedback through demonstrations or video replays creates clear mental images of proper technique, allowing swimmers to compare their performance against the model.
  • Positive reinforcement of successful attempts builds confidence and motivation to persist through initial difficulties, encouraging swimmers to continue practising despite experiencing discomfort or awkwardness.

Filed Under: Stages of learning Tagged With: Band 2, Band 3, smc-5921-10-Cognitive

HMS, BM EQ-Bank 541 MC

The table below shows characteristics of different skill acquisition stages.

Focus Error Recognition   Movement Efficiency  
How to do the skill     Can identify errors  Moderately Efficient

Which stage of skill acquisition is being described?

  1. Cognitive stage
  2. Associative stage
  3. Autonomous stage
  4. Preparatory stage
Show Answers Only

\(B\)

Show Worked Solution
  • B is correct: Focusing on “how to do the skill,” being able to identify errors, and moderately efficient movements are key characteristics of the associative stage.

Other Options:

  • A is incorrect: The cognitive stage focuses on “what to do” with limited error recognition and inefficient movement.
  • C is incorrect: The autonomous stage would show automatic movement execution with high efficiency.
  • D is incorrect: “Preparatory stage” is not a recognised stage in the three-stage process of skill acquisition.

Filed Under: Stages of learning Tagged With: Band 2, smc-5921-45-Identify stage

HMS, BM EQ-Bank 532

Describe how confidence influences skill acquisition in a novice swimmer.   (3 marks)

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Sample Answer

  • A confident novice swimmer is more likely to attempt new skills like submersion or floating without fear, creating more learning opportunities and practice repetitions.
  • Confidence enables the swimmer to focus on technique rather than anxiety, allowing them to process coaching instructions more effectively and make technical corrections.
  • Early success builds a positive self-image, creating a cycle where confidence leads to greater effort and persistence through challenges, accelerating the learning process when difficulties are encountered.
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Sample Answer 

  • A confident novice swimmer is more likely to attempt new skills like submersion or floating without fear, creating more learning opportunities and practice repetitions.
  • Confidence enables the swimmer to focus on technique rather than anxiety, allowing them to process coaching instructions more effectively and make technical corrections.
  • Early success builds a positive self-image, creating a cycle where confidence leads to greater effort and persistence through challenges, accelerating the learning process when difficulties are encountered.

Filed Under: Characteristics of learners Tagged With: Band 2, Band 3, smc-5534-05-Confidence

HMS, BM EQ-Bank 526 MC

Which of the following factors would be classified as a heredity characteristic that influences skill acquisition?

  1. Training experience
  2. Confidence level
  3. Muscle fibre composition
  4. Motivation to learn
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\(C\)

Show Worked Solution
  • C is correct: The relative percentage of fast-twitch to slow-twitch muscle fibres is an inherited characteristic that cannot be changed.

Other Options:

  • A is incorrect: Training experience is acquired, not inherited.
  • B is incorrect: Confidence develops through successful experiences and is not inherited.
  • D is incorrect: Motivation is a personality trait developed through social interactions and experiences, not inherited.

Filed Under: Characteristics of learners Tagged With: Band 2, smc-5534-10-Heredity

HMS, BM EQ-Bank 520

How can skill-related fitness testing be modified to meet the needs of adolescent athletes compared to elite athletes.   (5 marks)

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Sample Answer

  • Skill-related fitness testing is modified for adolescent athletes through age-appropriate protocols which ensures safe and valid assessment. This process involves reducing test intensity and duration because adolescents have developing musculoskeletal systems. For example, agility tests use wider turning angles which prevents excessive joint stress while still measuring directional change ability.
  • Elite athletes require sport-specific modifications which leads to more precise performance data. This occurs by incorporating game-like conditions into tests because elite performance demands highly specific assessments. Therefore, a tennis player’s agility test includes racquet movements which creates more valid results for their sport.
  • Test instructions are modified through simplified language for adolescents which enables better understanding and compliance. Conversely, elite athletes receive detailed technical feedback because they can process complex information. This difference ensures each group maximises test validity.
  • Recovery periods between tests are extended for adolescents which allows complete physiological recovery. This modification occurs because younger athletes have less developed energy systems. Meanwhile, elite athletes follow shorter recovery protocols which replicates competition demands.
Show Worked Solution

Sample Answer

  • Skill-related fitness testing is modified for adolescent athletes through age-appropriate protocols which ensures safe and valid assessment. This process involves reducing test intensity and duration because adolescents have developing musculoskeletal systems. For example, agility tests use wider turning angles which prevents excessive joint stress while still measuring directional change ability.
  • Elite athletes require sport-specific modifications which leads to more precise performance data. This occurs by incorporating game-like conditions into tests because elite performance demands highly specific assessments. Therefore, a tennis player’s agility test includes racquet movements which creates more valid results for their sport.
  • Test instructions are modified through simplified language for adolescents which enables better understanding and compliance. Conversely, elite athletes receive detailed technical feedback because they can process complex information. This difference ensures each group maximises test validity.
  • Recovery periods between tests are extended for adolescents which allows complete physiological recovery. This modification occurs because younger athletes have less developed energy systems. Meanwhile, elite athletes follow shorter recovery protocols which replicates competition demands.

Filed Under: Fitness testing Tagged With: Band 2, Band 3, smc-5637-50-Skill related

HMS, BM EQ-Bank 516

Explain how reaction time affects performance in sprinting events, and describe two specific training methods that could be used to improve this skill-related component.   (5 marks)

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Sample Answer

  • Reaction time affects sprinting performance because it determines how quickly athletes respond to the starter’s gun. This leads to earlier force generation and forward movement. Consequently, faster reaction times result in better race positions from the start. This advantage occurs because even hundredths of seconds saved can determine final placings in sprint events where margins are minimal.

Training method 1: Auditory response drills

  • Athletes respond to varied sound stimuli (whistles, claps, electronic beeps) from different starting positions
  • Progressively decrease time between warning and stimulus to improve anticipation
  • Measure and record reaction times to track improvement
  • Practice 3-4 times weekly for 10-15 minutes per session

Training method 2: Starting block practice with feedback technology

  • Use timing gates or pressure sensors to measure block clearance time
  • Focus on explosive first movement while maintaining legal starting position
  • Provide immediate feedback on reaction time after each attempt
  • Incorporate video analysis to refine anticipatory positioning and technique
Show Worked Solution

Sample Answer

  • Reaction time affects sprinting performance because it determines how quickly athletes respond to the starter’s gun. This leads to earlier force generation and forward movement. Consequently, faster reaction times result in better race positions from the start. This advantage occurs because even hundredths of seconds saved can determine final placings in sprint events where margins are minimal.

Training method 1: Auditory response drills

  • Athletes respond to varied sound stimuli (whistles, claps, electronic beeps) from different starting positions
  • Progressively decrease time between warning and stimulus to improve anticipation
  • Measure and record reaction times to track improvement
  • Practice 3-4 times weekly for 10-15 minutes per session

Training method 2: Starting block practice with feedback technology

  • Use timing gates or pressure sensors to measure block clearance time
  • Focus on explosive first movement while maintaining legal starting position
  • Provide immediate feedback on reaction time after each attempt
  • Incorporate video analysis to refine anticipatory positioning and technique

Filed Under: Fitness testing Tagged With: Band 2, Band 3, smc-5637-50-Skill related

HMS, BM EQ-Bank 508

Describe how body composition affects health and physical performance. In your answer, explain the difference between essential fat and storage fat, and outline the recommended body fat percentages for men and women.   (5 marks)

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Sample Answer

  • Body composition affects health by influencing metabolic function, with excessive fat increasing risk of cardiovascular disease, diabetes, and joint problems.
  • Physical performance is impacted by body composition as excessive fat increases energy demands and reduces power-to-weight ratio in most activities.
  • Essential fat surrounds and protects vital organs like the heart, kidneys, and nerves, and its absence would lead to chronic health problems.
  • Storage fat serves as an energy reserve, providing fuel during extended exercise when blood glucose is depleted and during rest periods.
  • Recommended body fat percentages are 15-20% for men and 20-25% for women according to the syllabus.
  • Women naturally maintain higher body fat percentages than men due to physiological and hormonal differences.
Show Worked Solution

Sample Answer

  • Body composition affects health by influencing metabolic function, with excessive fat increasing risk of cardiovascular disease, diabetes, and joint problems.
  • Physical performance is impacted by body composition as excessive fat increases energy demands and reduces power-to-weight ratio in most activities.
  • Essential fat surrounds and protects vital organs like the heart, kidneys, and nerves, and its absence would lead to chronic health problems.
  • Storage fat serves as an energy reserve, providing fuel during extended exercise when blood glucose is depleted and during rest periods.
  • Recommended body fat percentages are 15-20% for men and 20-25% for women according to the syllabus.
  • Women naturally maintain higher body fat percentages than men due to physiological and hormonal differences.

Filed Under: Fitness testing (EO-X) Tagged With: Band 2, Band 3, smc-5637-60-Health related

HMS, BM EQ-Bank 490 MC

Which of the following fitness tests would be MOST appropriate for assessing the aerobic capacity of a person with a lower limb disability who uses a wheelchair?

  1. Standard beep test
  2. Sit-and-reach test
  3. Wheelchair shuttle-ride test
  4. Hand grip dynamometer test
Show Answers Only

\(C\)

Show Worked Solution
  • C is correct: Wheelchair-specific aerobic capacity test

Other Options:

  • A is incorrect: Requires running
  • B is incorrect: Tests flexibility
  • D is incorrect: Tests grip strength

Filed Under: Fitness testing Tagged With: Band 2, smc-5637-30-Adaptations

HMS, BM EQ-Bank 485

Describe how the sequencing and timing of different fitness tests could affect the outcomes when conducting a comprehensive fitness assessment on athletes.   (4 marks)

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Sample Answer

  • Performing high-intensity tests like the multi-stage fitness test before other assessments can cause excessive fatigue, negatively affecting performance on subsequent tests such as strength or power measurements.
  • Tests requiring fine motor control or balance should be conducted early in the testing sequence when athletes are less fatigued, as skills like coordination (measured by the stick flip test) deteriorate significantly with fatigue.
  • Adequate recovery periods between tests are essential to prevent residual fatigue from confounding results, with recommended minimum rest periods varying based on the energy systems involved in each test.
  • The time of day significantly impacts test outcomes due to diurnal variations in physiological functions, with strength typically peaking in late afternoon while flexibility is often greater in the morning.
Show Worked Solution

Sample Answer 

  • Performing high-intensity tests like the multi-stage fitness test before other assessments can cause excessive fatigue, negatively affecting performance on subsequent tests such as strength or power measurements.
  • Tests requiring fine motor control or balance should be conducted early in the testing sequence when athletes are less fatigued, as skills like coordination (measured by the stick flip test) deteriorate significantly with fatigue.
  • Adequate recovery periods between tests are essential to prevent residual fatigue from confounding results, with recommended minimum rest periods varying based on the energy systems involved in each test.
  • The time of day significantly impacts test outcomes due to diurnal variations in physiological functions, with strength typically peaking in late afternoon while flexibility is often greater in the morning.

Filed Under: Fitness testing (EO-X) Tagged With: Band 2, Band 3, smc-5637-20-Outcomes

HMS, BM EQ-Bank 473

Explain TWO ways that pre-training fitness testing can benefit an athlete beginning a new training program.   (4 marks)

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Sample Answer – Any 2 of the following or similar with appropriate detail

  • Pre-training testing establishes baseline fitness levels which enables objective measurement of progress. This occurs because athletes can compare future results against initial data, allowing accurate tracking of improvements. Consequently, training effectiveness becomes measurable rather than subjective.
  • Fitness testing identifies specific strengths and weaknesses which leads to targeted program design. As a result, athletes focus on improving weak areas while maintaining strengths. This prevents wasted effort on unnecessary training and ensures efficient use of training time.
  • Initial assessment determines sport-specific fitness requirements which helps match athletes to suitable positions. For example, high aerobic capacity results in placement in positions requiring extensive running. Therefore, athletes perform in roles that suit their physical capabilities.
  • Pre-training testing creates measurable goals which enhances motivation throughout the program. Because athletes have clear targets, they maintain focus and effort. This leads to improved adherence and ultimately results in better training outcomes.
Show Worked Solution

Sample Answer – Any 2 of the following or similar with appropriate detail

  • Pre-training testing establishes baseline fitness levels which enables objective measurement of progress. This occurs because athletes can compare future results against initial data, allowing accurate tracking of improvements. Consequently, training effectiveness becomes measurable rather than subjective.
  • Fitness testing identifies specific strengths and weaknesses which leads to targeted program design. As a result, athletes focus on improving weak areas while maintaining strengths. This prevents wasted effort on unnecessary training and ensures efficient use of training time.
  • Initial assessment determines sport-specific fitness requirements which helps match athletes to suitable positions. For example, high aerobic capacity results in placement in positions requiring extensive running. Therefore, athletes perform in roles that suit their physical capabilities.
  • Pre-training testing creates measurable goals which enhances motivation throughout the program. Because athletes have clear targets, they maintain focus and effort. This leads to improved adherence and ultimately results in better training outcomes.

Filed Under: Fitness testing Tagged With: Band 2, Band 3, smc-5637-10-Purpose

HMS, BM EQ-Bank 465

Describe TWO ways fitness testing could be used to improve community health programs.   (4 marks)

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Sample Answer – Any 2 of the following or similar with equivalent depth

Method 1: Targeted Program Development

  • Fitness testing identifies specific health-related fitness deficiencies within communities.
  • Results reveal whether populations lack cardiorespiratory endurance, strength, or flexibility.
  • This data enables targeted interventions addressing actual needs rather than generic approaches.
  • Programs become more effective when tailored to specific community deficiencies.

Method 2: Evidence-Based Evaluation

  • Baseline testing establishes initial fitness levels before program implementation.
  • Follow-up testing provides objective data demonstrating measurable improvements.
  • This evidence helps justify continued funding to stakeholders and policymakers.
  • Quantifiable results strengthen program credibility and support expansion.

Method 3: Identifying Underserved Populations

  • Testing data reveals demographic patterns in fitness levels across community groups.
  • Analysis identifies populations not effectively reached by current programming.
  • This information enables targeted outreach strategies and culturally appropriate programs.
  • Improving participation among underserved populations enhances overall community health outcomes.

Method 4: Health Education Opportunities

  • Testing sessions create teachable moments about fitness components and health relationships.
  • Participants learn how cardiorespiratory endurance affects heart health or flexibility impacts daily function.
  • This increases health literacy as participants understand their results.
  • Enhanced knowledge empowers informed decisions about physical activity participation.
Show Worked Solution

Sample Answer – Any 2 of the following or similar with equivalent depth

Method 1: Targeted Program Development

  • Fitness testing identifies specific health-related fitness deficiencies within communities.
  • Results reveal whether populations lack cardiorespiratory endurance, strength, or flexibility.
  • This data enables targeted interventions addressing actual needs rather than generic approaches.
  • Programs become more effective when tailored to specific community deficiencies.

Method 2: Evidence-Based Evaluation

  • Baseline testing establishes initial fitness levels before program implementation.
  • Follow-up testing provides objective data demonstrating measurable improvements.
  • This evidence helps justify continued funding to stakeholders and policymakers.
  • Quantifiable results strengthen program credibility and support expansion.

Method 3: Identifying Underserved Populations

  • Testing data reveals demographic patterns in fitness levels across community groups.
  • Analysis identifies populations not effectively reached by current programming.
  • This information enables targeted outreach strategies and culturally appropriate programs.
  • Improving participation among underserved populations enhances overall community health outcomes.

Method 4: Health Education Opportunities

  • Testing sessions create teachable moments about fitness components and health relationships.
  • Participants learn how cardiorespiratory endurance affects heart health or flexibility impacts daily function.
  • This increases health literacy as participants understand their results.
  • Enhanced knowledge empowers informed decisions about physical activity participation.

Filed Under: Fitness testing Tagged With: Band 2, Band 3, smc-5637-20-Outcomes

HMS, BM EQ-Bank 462

Outline THREE potential outcomes of fitness testing for individuals with chronic health conditions.   (3 marks)

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Sample Answer 

  • Appropriate testing can establish safe exercise parameters that minimise risk of exacerbating the condition while maximising health benefits, particularly important for conditions like heart disease or diabetes.
  • Testing results provide objective data to track improvements resulting from exercise interventions, which can be motivating and reinforce adherence to prescribed programs.
  • Regular assessment allows healthcare providers to adjust treatment and exercise recommendations based on changing fitness levels, leading to more personalised care.
Show Worked Solution

Sample Answer 

  • Appropriate testing can establish safe exercise parameters that minimise risk of exacerbating the condition while maximising health benefits, particularly important for conditions like heart disease or diabetes.
  • Testing results provide objective data to track improvements resulting from exercise interventions, which can be motivating and reinforce adherence to prescribed programs.
  • Regular assessment allows healthcare providers to adjust treatment and exercise recommendations based on changing fitness levels, leading to more personalised care.

Filed Under: Fitness testing (EO-X) Tagged With: Band 2, Band 3, smc-5637-20-Outcomes

HMS, BM EQ-Bank 457

Outline TWO benefits of conducting regular fitness testing for high school students.   (3 marks)

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Sample Answer – Any 2 of the following or similar

  • Fitness testing provides baseline measurements allowing students to track their progress over time, helping them set realistic goals for improvement and increase motivation.
  • Testing helps physical education teachers identify students who may need additional support or modified activities, ensuring more inclusive and effective programs.
  • Regular assessment helps identify strengths and weaknesses in the school’s physical education program, allowing for evidence-based curriculum adjustments.
Show Worked Solution

Sample Answer – Any 2 of the following or similar

  • Fitness testing provides baseline measurements allowing students to track their progress over time, helping them set realistic goals for improvement and increase motivation.
  • Testing helps physical education teachers identify students who may need additional support or modified activities, ensuring more inclusive and effective programs.
  • Regular assessment helps identify strengths and weaknesses in the school’s physical education program, allowing for evidence-based curriculum adjustments.

Filed Under: Fitness testing (EO-X) Tagged With: Band 2, Band 3, smc-5637-10-Purpose

HMS, BM EQ-Bank 397

Outline TWO ethical considerations when investigating heart rate responses to aerobic training using student participants.   (3 marks)

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Sample Answer – Any 2 of the following

  • Informed consent must be obtained from all participants and parents/guardians if under 18 years of age. This includes clearly explaining the investigation’s purpose, heart rate monitoring procedures, potential physical discomforts, data usage and participant rights throughout the study.
  • Confidentiality of personal health data must be strictly maintained by using participant codes instead of real names. All heart rate records should be secured in password-protected files with restricted access, and only aggregated results presented in findings.
  • Participants must have the absolute right to withdraw from the investigation at any time without penalty, negative consequences, or need for detailed explanation. Researchers must respect withdrawal decisions and immediately cease data collection from those participants.
Show Worked Solution

Sample Answer – Any 2 of the following

  • Informed consent must be obtained from all participants and parents/guardians if under 18 years of age. This includes clearly explaining the investigation’s purpose, heart rate monitoring procedures, potential physical discomforts, data usage and participant rights throughout the study.
  • Confidentiality of personal health data must be strictly maintained by using participant codes instead of real names. All heart rate records should be secured in password-protected files with restricted access, and only aggregated results presented in findings.
  • Participants must have the absolute right to withdraw from the investigation at any time without penalty, negative consequences, or need for detailed explanation. Researchers must respect withdrawal decisions and immediately cease data collection from those participants.

Filed Under: Investigate aerobic training Tagged With: Band 2, smc-5533-30-Ethical considerations

HMS, BM EQ-Bank 396 MC

When collecting respiratory rate data during aerobic training investigation, which of the following represents appropriate ethical practice?

  1. Recording participants without their knowledge
  2. Sharing identified personal data with the whole class
  3. Allowing participants to withdraw at any time
  4. Requiring participants to complete the investigation regardless of discomfort
Show Answers Only

\(C\)

Show Worked Solution
  • C is correct: Respecting participants’ right to withdraw at any time without penalty is a fundamental ethical principle in human research.

Other Options:

  • A is incorrect: Recording without knowledge violates informed consent principles.
  • B is incorrect: Sharing identified data breaches confidentiality.
  • D is incorrect: Requiring completion despite discomfort disrespects participant autonomy and wellbeing.

Filed Under: Investigate aerobic training Tagged With: Band 2, smc-5533-30-Ethical considerations

HMS, BM EQ-Bank 385

Outline TWO methods that could be used to measure heart rate responses during aerobic training.   (3 marks)

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Sample Answer – Any 2 of the following

  • Heart rate monitor with chest strap provides continuous, accurate recordings throughout the aerobic activity without requiring the participant to stop exercising.
  • Manual pulse palpation at the wrist (radial artery) or neck (carotid artery) for 15 seconds multiplied by 4 gives a heart rate reading, though requires momentary pause in activity.
  • Smartphone applications using the phone’s camera and flash to detect pulse through fingertip blood flow changes can provide heart rate measurements between exercise periods.
Show Worked Solution

Sample Answer – Any 2 of the following

  • Heart rate monitor with chest strap provides continuous, accurate recordings throughout the aerobic activity without requiring the participant to stop exercising.
  • Manual pulse palpation at the wrist (radial artery) or neck (carotid artery) for 15 seconds multiplied by 4 gives a heart rate reading, though requires momentary pause in activity.
  • Smartphone applications using the phone’s camera and flash to detect pulse through fingertip blood flow changes can provide heart rate measurements between exercise periods.

Filed Under: Investigate aerobic training (EO-X) Tagged With: Band 2, smc-5533-20-Data collection

HMS, BM EQ-Bank 384 MC

Which of the following is the most practical method for a student to collect data on perceived exertion during aerobic training?

  1. Blood lactate analyser
  2. Electromyography (EMG)
  3. Rating of Perceived Exertion (RPE) scale
  4. Electrocardiogram (ECG)
Show Answers Only

\(C\)

Show Worked Solution
  • C is correct: RPE scale simple, inexpensive, no specialised equipment needed.

Other Options:

  • A is incorrect: Blood lactate analysers expensive, invasive, require specialised training.
  • B is incorrect: EMG equipment expensive, complex to operate and interpret.
  • D is incorrect: ECG equipment expensive, requires technical expertise.

Filed Under: Investigate aerobic training Tagged With: Band 2, smc-5533-20-Data collection

HMS, BM EQ-Bank 363

Explain what happens to blood lactate levels during aerobic training of increasing intensity.   (5 marks)

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Sample Answer 

  • At rest, blood lactate levels remain low at approximately 1-2 mmol/L. This occurs because the aerobic system meets all energy demands without producing excess lactate.
  • During light to moderate aerobic exercise, lactate production increases slightly as a result of increased energy demands. However, it remains in equilibrium with clearance due to sufficient oxygen availability.
  • When exercise intensity increases to the aerobic threshold, lactate levels begin to rise gradually. The reason for this is that energy demands are approaching the capacity of the aerobic system, though the body can still manage lactate clearance effectively.
  • At the lactate threshold/inflection point, lactate production exceeds the body’s ability to clear it. This happens because insufficient oxygen delivery forces a shift toward anaerobic metabolism.
  • Beyond this point, lactate accumulates rapidly in the bloodstream. Consequently, increased muscle acidity develops, which leads to fatigue and limits performance duration.
Show Worked Solution

Sample Answer 

  • At rest, blood lactate levels remain low at approximately 1-2 mmol/L. This occurs because the aerobic system meets all energy demands without producing excess lactate.
  • During light to moderate aerobic exercise, lactate production increases slightly as a result of increased energy demands. However, it remains in equilibrium with clearance due to sufficient oxygen availability.
  • When exercise intensity increases to the aerobic threshold, lactate levels begin to rise gradually. The reason for this is that energy demands are approaching the capacity of the aerobic system, though the body can still manage lactate clearance effectively.
  • At the lactate threshold/inflection point, lactate production exceeds the body’s ability to clear it. This happens because insufficient oxygen delivery forces a shift toward anaerobic metabolism.
  • Beyond this point, lactate accumulates rapidly in the bloodstream. Consequently, increased muscle acidity develops, which leads to fatigue and limits performance duration.

Filed Under: Responses to training Tagged With: Band 2, Band 3, smc-5532-17-Lactate levels

HMS, BM EQ-Bank 360

Outline the immediate physiological responses to aerobic training.   (3 marks)

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Sample Answer 

  • Heart rate increases to deliver more oxygen to working muscles
  • Ventilation rate increases to take in more oxygen and remove carbon dioxide
  • Cardiac output increases as both heart rate and stroke volume rise to meet increased oxygen demand
Show Worked Solution

Sample Answer 

  • Heart rate increases to deliver more oxygen to working muscles
  • Ventilation rate increases to take in more oxygen and remove carbon dioxide
  • Cardiac output increases as both heart rate and stroke volume rise to meet increased oxygen demand

Filed Under: Responses to training (EO-X) Tagged With: Band 2, smc-5532-08-Heart rate, smc-5532-10-Stroke volume, smc-5532-12-Ventilation rate, smc-5532-15-Cardiac output

HMS, BM EQ-Bank 358 MC

A student's ventilation rate increases during a 5km run. This occurs to:

  1. Increase oxygen intake and carbon dioxide removal
  2. Reduce oxygen delivery to the muscles
  3. Increase carbon dioxide in the bloodstream
  4. Decrease cardiac output
Show Answers Only

\(A\)

Show Worked Solution
  • A is correct: Increases oxygen intake and removes carbon dioxide

Other Options:

  • B is incorrect: Exercise increases oxygen delivery to muscles
  • C is incorrect: Exercise decreases carbon dioxide in bloodstream
  • D is incorrect: Ventilation increases with increased cardiac output

Filed Under: Responses to training Tagged With: Band 2, smc-5532-12-Ventilation rate

HMS, BM EQ-Bank 341

Outline the immediate response of cardiac output during aerobic training.   (3 marks)

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Sample Answer

  • Cardiac output increases immediately during aerobic training
  • This occurs due to an increase in both heart rate and stroke volume
  • The increase supports the delivery of oxygen and nutrients to working muscles
  • Cardiac output rises from approximately 5 L/min at rest to 15 L/min during moderate exercise
Show Worked Solution

Sample Answer

  • Cardiac output increases immediately during aerobic training
  • This occurs due to an increase in both heart rate and stroke volume
  • The increase supports the delivery of oxygen and nutrients to working muscles
  • Cardiac output rises from approximately 5 L/min at rest to 15 L/min during moderate exercise

Filed Under: Responses to training Tagged With: Band 2, smc-5532-15-Cardiac output

HMS, BM EQ-Bank 327

Outline how ventilation rate responds to moderate aerobic exercise.   (3 marks)

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Sample Answer

  • Ventilation rate increases from resting levels during moderate aerobic exercise. Breathing frequency approximately doubles from baseline values.
  • The immediate physiological response supplies additional oxygen to working muscles. Deeper breaths also contribute to increased oxygen intake.
  • Carbon dioxide removal is enhanced during exercise. Increased ventilation clears metabolic waste products from energy production.
  • The response stabilises at a sustainable level during steady-state exercise. Recovery sees gradual return to resting ventilation rates.
Show Worked Solution

Sample Answer

  • Ventilation rate increases from resting levels during moderate aerobic exercise. Breathing frequency approximately doubles from baseline values.
  • The immediate physiological response supplies additional oxygen to working muscles. Deeper breaths also contribute to increased oxygen intake.
  • Carbon dioxide removal is enhanced during exercise. Increased ventilation clears metabolic waste products from energy production.
  • The response stabilises at a sustainable level during steady-state exercise. Recovery sees gradual return to resting ventilation rates.

Filed Under: Responses to training Tagged With: Band 2, smc-5532-12-Ventilation rate

HMS, BM EQ-Bank 320

Outline the immediate heart rate response when an individual begins aerobic exercise.   (3 marks)

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Sample Answer

  • When an individual begins aerobic exercise, there is an immediate increase in heart rate.
  • This occurs due to increased stimulation from the sympathetic nervous system.
  • The heart rate increases in proportion to exercise intensity to deliver more oxygen and nutrients to the working muscles.
Show Worked Solution

Sample Answer

  • When an individual begins aerobic exercise, there is an immediate increase in heart rate.
  • This occurs due to increased stimulation from the sympathetic nervous system.
  • The heart rate increases in proportion to exercise intensity to deliver more oxygen and nutrients to the working muscles.

Filed Under: Responses to training (EO-X) Tagged With: Band 2, smc-5532-08-Heart rate

HMS, BM EQ-Bank 318 MC

During an athletics training session, a coach observes a sprinter's heart rate. Which of the following is the most likely immediate physiological response to high-intensity sprint training?

  1. Decreased heart rate
  2. Increased heart rate
  3. Decreased cardiac output
  4. No change in heart rate
Show Answers Only

\(B\)

Show Worked Solution
  • B is correct: Heart rate increases immediately to supply oxygen to muscles

Other Options:

  • A is incorrect: Heart rate increases not decreases during exercise
  • C is incorrect: Cardiac output increases not decreases during exercise
  • D is incorrect: Heart rate always changes with exercise

Filed Under: Responses to training Tagged With: Band 2, smc-5532-08-Heart rate

HMS, BM EQ-Bank 311

Outline TWO immediate cardiac responses to a training session.   (3 marks)

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Sample Answer – Any 2 of the following

  • Heart rate increases immediately when training begins, causing the heart to beat faster to deliver more oxygen to working muscles.
  • Stroke volume increases during training, meaning more blood is pumped out of the heart with each beat.
  • Cardiac output (amount of blood pumped by the heart per minute) increases during training to supply more blood to muscles that are being used.
Show Worked Solution

Sample Answer – Any 2 of the following

  • Heart rate increases immediately when training begins, causing the heart to beat faster to deliver more oxygen to working muscles.
  • Stroke volume increases during training, meaning more blood is pumped out of the heart with each beat.
  • Cardiac output (amount of blood pumped by the heart per minute) increases during training to supply more blood to muscles that are being used.

Filed Under: Responses to training (EO-X) Tagged With: Band 2, smc-5532-08-Heart rate, smc-5532-10-Stroke volume, smc-5532-15-Cardiac output

v1 Functions, 2ADV F1 2007 HSC 1a

Evaluate  `sqrt (2pi + 7)`  correct to two decimal places.   (2 marks)

Show Answers Only

`3.34\ \ \ text{(to 2 d.p.)}`

Show Worked Solution
`sqrt (2pi + 7)` `= sqrt(2 × 3.14159… + 7)`
  `= sqrt(6.28318… + 7)`
  `= sqrt(13.28318…)`
  `= 3.6446…`
  `= 3.64\ \ \ text{(to 2 d.p.)}`

Filed Under: Algebraic Techniques (Adv-X) Tagged With: Band 2, HSC, smc-983-10-Rounding

HMS, BM EQ-Bank 277

Explain how you would apply each component of the FITT principle when designing an aerobic training program for a recreational tennis player.   (5 marks)

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Sample Answer

  • The FITT principle provides a framework using Frequency, Intensity, Time and Type for designing effective training programs.
  • For a recreational tennis player allowing 3-4 sessions weekly for frequency provides sufficient aerobic stimulus while still having 48-72 hours recovery between sessions. This helps prevent overtraining in recreational athletes.
  • Adopting an intensity of 65-75% MHR which is in the moderate zone, effectively develops aerobic capacity without excessive fatigue for non-competitive athletes.
  • Including one session at 75-80% MHR weekly so players develop their lactate buffering capacity, enhances rally endurance during longer matches.
  • Recreational players will benefit from sessions of 30-40 minutes for time because this duration stimulates cardiovascular improvements while maintaining quality.
  • Progressing session duration by 5-10% every two weeks provides gradual increases that allow fitness development without injury risk.
  • A combination of continuous running with tennis-specific movements is suitable for type and enables aerobic fitness development, while maintaining sport-specific patterns.
  • On-court drills at moderate intensity should be included as this integrates skill maintenance with aerobic development.
  • Moderate intensity training enables higher frequency because recovery demands remain manageable, optimising aerobic development for recreational tennis players.

Show Worked Solution

Sample Answer

  • The FITT principle provides a framework using Frequency, Intensity, Time and Type for designing effective training programs.
  • For a recreational tennis player allowing 3-4 sessions weekly for frequency provides sufficient aerobic stimulus while still having 48-72 hours recovery between sessions. This helps prevent overtraining in recreational athletes.
  • Adopting an intensity of 65-75% MHR which is in the moderate zone, effectively develops aerobic capacity without excessive fatigue for non-competitive athletes.
  • Including one session at 75-80% MHR weekly so players develop their lactate buffering capacity, enhances rally endurance during longer matches.
  • Recreational players will benefit from sessions of 30-40 minutes for time because this duration stimulates cardiovascular improvements while maintaining quality.
  • Progressing session duration by 5-10% every two weeks provides gradual increases that allow fitness development without injury risk.
  • A combination of continuous running with tennis-specific movements is suitable for type and enables aerobic fitness development, while maintaining sport-specific patterns.
  • On-court drills at moderate intensity should be included as this integrates skill maintenance with aerobic development.
  • Moderate intensity training enables higher frequency because recovery demands remain manageable, optimising aerobic development for recreational tennis players.

Filed Under: Training program design - FITT Tagged With: Band 2, Band 3, smc-5531-15-Aerobic

HMS, BM EQ-Bank 271

Explain how the FITT principle can be applied when designing an aerobic training program for a middle-distance runner.   (5 marks)

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Sample Answer

Frequency:

  • 4-5 sessions per week allowing for sufficient recovery between sessions to prevent overtraining while providing adequate stimulus for adaptation.

Intensity:

  • 70-85% of maximum heart rate to develop aerobic capacity and improve lactate threshold which is critical for middle-distance events.

Time:

  • 30-60 minutes per session to develop endurance without excessive fatigue that could lead to injury.

Type:

  • Combination of continuous running, tempo runs and fartlek training to develop aerobic capacity while simulating race conditions.

Progession:

  • The FITT principle ensures a structured approach to training that addresses specific requirements of middle-distance running while allowing for progressive overload.
Show Worked Solution

Sample Answe

Frequency:

  • 4-5 sessions per week allowing for sufficient recovery between sessions to prevent overtraining while providing adequate stimulus for adaptation.

Intensity:

  • 70-85% of maximum heart rate to develop aerobic capacity and improve lactate threshold which is critical for middle-distance events.

Time:

  • 30-60 minutes per session to develop endurance without excessive fatigue that could lead to injury.

Type:

  • Combination of continuous running, tempo runs and fartlek training to develop aerobic capacity while simulating race conditions.

Progession:

  • The FITT principle ensures a structured approach to training that addresses specific requirements of middle-distance running while allowing for progressive overload.

Filed Under: Training program design - FITT (EO-X) Tagged With: Band 2, Band 3, smc-5531-15-Aerobic

HMS, BM EQ-Bank 262 MC

A swimmer aims to improve their anaerobic capacity for 100 metre sprint events. Which training program based on the FITT principle is most appropriate?

  1. Frequency: daily; Intensity: 60% MHR; Time: 45 minutes; Type: continuous swimming
  2. Frequency: 3-4 times per week; Intensity: 85-95% MHR; Time: 20-30 minutes; Type: interval training
  3. Frequency: twice weekly; Intensity: 70% MHR; Time: 60 minutes; Type: fartlek training
  4. Frequency: 5 times per week; Intensity: 65-75% MHR; Time: 90 minutes; Type: long slow distance
Show Answers Only

\(B\)

Show Worked Solution
  • B is correct: High-intensity intervals, 85-95% MHR, with adequate recovery for anaerobic capacity.

Other Options:

  • A is incorrect: Moderate intensity, continuous → aerobic training.
  • C is incorrect: Low frequency, low intensity for anaerobic development.
  • D is incorrect: Endurance training parameters, not sprint-focused.

Filed Under: Training program design - FITT Tagged With: Band 2, smc-5531-10-Anaerobic

HMS, BM EQ-Bank 258 MC

A volleyball player completes an aerobic continuous training session by riding a stationary bike at a constant pace for 50 minutes at 65% of maximum heart rate.

What is the primary energy system being targeted by this type of training?

  1. ATP-PC system
  2. Lactic acid system
  3. Aerobic energy system
  4. All energy systems equally
Show Answers Only

\(C\)

Show Worked Solution
  • C is correct: Extended duration at moderate intensity targets aerobic system.

Other Options:

  • A is incorrect: ATP-PC system only operates for 10-15 seconds.
  • B is incorrect: Lactic acid system operates for 30 seconds to 2 minutes.
  • D is incorrect: This training specifically targets aerobic energy system.

Filed Under: Aerobic vs Anaerobic training Tagged With: Band 2, smc-5530-10-Aerobic

HMS, BM EQ-Bank 251

Outline the key differences between continuous aerobic training and High Intensity Interval Training (HIIT).   (3 marks)

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Sample Answer

Continuous aerobic training

  • Sustained moderate-intensity exercise (60-75% MHR)
  • Extended periods without rest (20+ minutes)
  • Typically 30-60 minutes total duration
  • Predominantly aerobic energy system

HIIT:

  • Alternates high-intensity periods (85-95% MHR) with recovery
  • Varied work-to-rest ratios
  • Shorter total duration (15-30 minutes)
  • More intense overall
  • Engages both aerobic and anaerobic systems
Show Worked Solution

Sample Answer

Continuous aerobic training

  • Sustained moderate-intensity exercise (60-75% MHR)
  • Extended periods without rest (20+ minutes)
  • Typically 30-60 minutes total duration
  • Predominantly aerobic energy system

HIIT:

  • Alternates high-intensity periods (85-95% MHR) with recovery
  • Varied work-to-rest ratios
  • Shorter total duration (15-30 minutes)
  • More intense overall
  • Engages both aerobic and anaerobic systems

Filed Under: Aerobic vs Anaerobic training (EO-X) Tagged With: Band 2, smc-5530-20-Anaerobic v aerobic

HMS, BM EQ-Bank 247

Explain how heart rate monitoring can be used to ensure appropriate intensity in both aerobic and anaerobic training sessions.  (3 marks)

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Sample Answer

  • Heart rate monitoring ensures aerobic training stays within 70-85% MHR zones. This works because sustained moderate intensity improves cardiovascular fitness without excessive fatigue. Runners maintain 140-160 bpm throughout sessions. As a result, athletes develop endurance efficiently.
  • For anaerobic training, monitoring shows peak rates (85-95% MHR) and recovery. The reason is reaching target zones ensures sufficient intensity for improvement. HIIT sessions need 170+ bpm during work periods. Therefore, athletes train at optimal intensity while avoiding overtraining.
Show Worked Solution

Sample Answer

  • Heart rate monitoring ensures aerobic training stays within 70-85% MHR zones. This works because sustained moderate intensity improves cardiovascular fitness without excessive fatigue. Runners maintain 140-160 bpm throughout sessions. As a result, athletes develop endurance efficiently.
  • For anaerobic training, monitoring shows peak rates (85-95% MHR) and recovery. The reason is reaching target zones ensures sufficient intensity for improvement. HIIT sessions need 170+ bpm during work periods. Therefore, athletes train at optimal intensity while avoiding overtraining.

Filed Under: Aerobic vs Anaerobic training Tagged With: Band 2, Band 3, smc-5530-20-Anaerobic v aerobic

HMS, BM EQ-Bank 153 MC

Which energy system produces ATP at the fastest rate?

  1. Glycolytic
  2. Aerobic
  3. ATP-PCr
  4. All systems produce ATP at the same rate
Show Answers Only

\(C\)

Show Worked Solution
  • C is correct: ATP-PCr has fastest production rate but limited stores

Other Options:

  • A is incorrect: Slower than ATP-PCr but faster than aerobic
  • B is incorrect: Slowest but most efficient system
  • D is incorrect: Systems have different production rates

Filed Under: Energy systems Tagged With: Band 2, smc-5528-15-ATP efficiency

HMS, BM EQ-Bank 138

Outline how inefficient jumping technique can affect the skeletal system and require first aid intervention.   (3 marks)

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Sample Answer

  • Incorrect landing mechanics – Poor technique causes excessive joint compression in ankles, knees and hips, potentially leading to acute injuries.
  • Abnormal force distribution – Impact forces travel through misaligned bones creating stress fractures, particularly in weight-bearing bones like tibia and metatarsals.
  • First aid requirements – RICER protocol needed for acute injuries, joint stabilisation to prevent further damage, and medical referral for suspected fractures.
Show Worked Solution

Sample Answer

  • Incorrect landing mechanics – Poor technique causes excessive joint compression in ankles, knees and hips, potentially leading to acute injuries.
  • Abnormal force distribution – Impact forces travel through misaligned bones creating stress fractures, particularly in weight-bearing bones like tibia and metatarsals.
  • First aid requirements – RICER protocol needed for acute injuries, joint stabilisation to prevent further damage, and medical referral for suspected fractures.

Filed Under: Role of First Aid Tagged With: Band 2, smc-5527-15-Inefficient movement

HMS, BM EQ-Bank 133

Explain how the circulatory and respiratory systems respond to dehydration during movement and outline appropriate first aid interventions.   (5 marks)

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Sample Answer

  • Dehydration affects the circulatory system because fluid loss reduces blood volume. This causes the heart to increase its rate to maintain adequate circulation. As a result, blood becomes thicker and more viscous, making it harder to pump efficiently through vessels.
  • The respiratory system responds to dehydration through increased breathing rates. This occurs due to the body’s attempt to maintain oxygen delivery despite reduced blood efficiency. Consequently, airways become dry and gas exchange becomes less efficient, further compromising oxygen delivery.
  • These system responses create a cycle of increasing stress during movement. This relationship demonstrates why dehydration severely impacts athletic performance. Therefore, recognizing early signs is crucial for intervention.
  • First aid interventions must address both immediate and ongoing needs. This involves ceasing activity immediately and moving to a cool environment. Following this, provide small sips of electrolyte solution rather than plain water.
  • Monitoring remains essential because vital signs indicate recovery progress. This process ensures gradual rehydration prevents shock while heart rate returns to normal. Hence, systematic first aid prevents serious complications.
Show Worked Solution

Sample Answer

  • Dehydration affects the circulatory system because fluid loss reduces blood volume. This causes the heart to increase its rate to maintain adequate circulation. As a result, blood becomes thicker and more viscous, making it harder to pump efficiently through vessels.
  • The respiratory system responds to dehydration through increased breathing rates. This occurs due to the body’s attempt to maintain oxygen delivery despite reduced blood efficiency. Consequently, airways become dry and gas exchange becomes less efficient, further compromising oxygen delivery.
  • These system responses create a cycle of increasing stress during movement. This relationship demonstrates why dehydration severely impacts athletic performance. Therefore, recognizing early signs is crucial for intervention.
  • First aid interventions must address both immediate and ongoing needs. This involves ceasing activity immediately and moving to a cool environment. Following this, provide small sips of electrolyte solution rather than plain water.
  • Monitoring remains essential because vital signs indicate recovery progress. This process ensures gradual rehydration prevents shock while heart rate returns to normal. Hence, systematic first aid prevents serious complications.

Filed Under: Role of First Aid Tagged With: Band 2, Band 3, smc-5527-20-Dehydration

HMS, BM EQ-Bank 129

Describe how the digestive system can create undue stress on the body during physical activity and outline appropriate first aid responses.   (5 marks)

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Sample Answer

Digestive System Stress:

  • Exercise redirects blood flow away from digestive organs to working muscles, reducing digestive efficiency and causing painful abdominal cramping.
  • Eating within 2-3 hours of exercise leaves undigested food in stomach, leading to nausea, vomiting and uncomfortable bloating during activity.
  • Dehydration impairs digestive secretions and intestinal function, resulting in severe cramping and potential diarrhea during prolonged exercise.
  • High-intensity movement creates mechanical stress on abdominal organs, causing side stitches and acid reflux that impair performance.

First Aid Responses:

  • Stop activity immediately when severe cramping occurs to prevent further digestive distress and allow blood flow redistribution.
  • Place person in comfortable left side-lying position, which relieves pressure on stomach and reduces reflux symptoms.
  • Provide small sips of room-temperature water every 5-10 minutes if tolerated, avoiding cold fluids that may worsen cramping.
  • Monitor vital signs and observe for deterioration including persistent vomiting, severe dehydration or signs of heat illness.
  • Seek immediate medical attention if symptoms persist beyond 30 minutes or worsen despite first aid measures.
Show Worked Solution

Sample Answer

Digestive System Stress:

  • Exercise redirects blood flow away from digestive organs to working muscles, reducing digestive efficiency and causing painful abdominal cramping.
  • Eating within 2-3 hours of exercise leaves undigested food in stomach, leading to nausea, vomiting and uncomfortable bloating during activity.
  • Dehydration impairs digestive secretions and intestinal function, resulting in severe cramping and potential diarrhea during prolonged exercise.
  • High-intensity movement creates mechanical stress on abdominal organs, causing side stitches and acid reflux that impair performance.

First Aid Responses:

  • Stop activity immediately when severe cramping occurs to prevent further digestive distress and allow blood flow redistribution.
  • Place person in comfortable left side-lying position, which relieves pressure on stomach and reduces reflux symptoms.
  • Provide small sips of room-temperature water every 5-10 minutes if tolerated, avoiding cold fluids that may worsen cramping.
  • Monitor vital signs and observe for deterioration including persistent vomiting, severe dehydration or signs of heat illness.
  • Seek immediate medical attention if symptoms persist beyond 30 minutes or worsen despite first aid measures.

Filed Under: Role of First Aid Tagged With: Band 2, Band 3, smc-5527-10-Undue stress

HMS, BM EQ-Bank 128 MC

During a cross-country run, an athlete experiences severe abdominal cramping. Which first aid response would be most appropriate?

  1. Continue running at race pace
  2. Increase fluid intake rapidly
  3. Start walking immediately
  4. Stop activity and lie in a comfortable position
Show Answers Only

\(D\)

Show Worked Solution
  • D is correct: Stopping activity and finding a comfortable position allows assessment of digestive system stress and prevents further complications.

Other Options:

  • A is incorrect: Would increase digestive system stress
  • B is incorrect: Rapid fluid intake may worsen symptoms
  • C is incorrect: Immediate walking may exacerbate cramping

Filed Under: Role of First Aid Tagged With: Band 2, smc-5527-10-Undue stress

HMS, BM EQ-Bank 123

Explain how the respiratory and circulatory systems respond to movement and describe appropriate first aid responses when these systems show signs of stress.   (5 marks)

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Sample Answer

  • The respiratory system responds to movement through increased oxygen demand. This occurs because working muscles require more oxygen for energy production. As a result, breathing rate and depth increase to supply adequate oxygen and remove carbon dioxide.
  • The circulatory system responds by increasing heart rate and stroke volume. This leads to greater cardiac output, which enables faster oxygen delivery to muscles. Consequently, blood flow is redirected from non-essential organs to working muscles.
  • This demonstrates how both systems work together during movement. The interaction allows efficient oxygen delivery and waste removal. This relationship results in sustained energy production for continued movement.
  • Signs of respiratory stress include abnormal breathing patterns, wheezing or gasping. This happens when oxygen demand exceeds supply. Therefore, first aid requires immediately stopping activity, sitting the person upright, and encouraging controlled breathing.
  • Circulatory stress presents as irregular pulse, chest pain or dizziness. This triggers the need for immediate intervention. The appropriate response involves lying the person down with elevated legs, monitoring vital signs, and implementing the STOP protocol if symptoms persist.
Show Worked Solution

Sample Answer

  • The respiratory system responds to movement through increased oxygen demand. This occurs because working muscles require more oxygen for energy production. As a result, breathing rate and depth increase to supply adequate oxygen and remove carbon dioxide.
  • The circulatory system responds by increasing heart rate and stroke volume. This leads to greater cardiac output, which enables faster oxygen delivery to muscles. Consequently, blood flow is redirected from non-essential organs to working muscles.
  • This demonstrates how both systems work together during movement. The interaction allows efficient oxygen delivery and waste removal. This relationship results in sustained energy production for continued movement.
  • Signs of respiratory stress include abnormal breathing patterns, wheezing or gasping. This happens when oxygen demand exceeds supply. Therefore, first aid requires immediately stopping activity, sitting the person upright, and encouraging controlled breathing.
  • Circulatory stress presents as irregular pulse, chest pain or dizziness. This triggers the need for immediate intervention. The appropriate response involves lying the person down with elevated legs, monitoring vital signs, and implementing the STOP protocol if symptoms persist.

Filed Under: Role of First Aid Tagged With: Band 2, Band 3, smc-5527-10-Undue stress

HMS, BM EQ-Bank 122

Outline how the muscular and skeletal systems work together during movement and identify when first aid intervention is required.   (3 marks)

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Sample Answer

  • The muscular and skeletal systems work together as lever systems. Muscles attach to bones at origin and insertion points, creating movement through contraction and relaxation.
  • First aid intervention is required when movement causes sudden sharp pain or muscle inability to contract. Visible deformity or loss of joint stability indicates possible strain, sprain or fracture.
  • Warning signs include hearing a “pop” sound at time of injury, immediate swelling, or inability to bear weight on the affected area.
Show Worked Solution

Sample Answer

  • The muscular and skeletal systems work together as lever systems. Muscles attach to bones at origin and insertion points, creating movement through contraction and relaxation.
  • First aid intervention is required when movement causes sudden sharp pain or muscle inability to contract. Visible deformity or loss of joint stability indicates possible strain, sprain or fracture.
  • Warning signs include hearing a “pop” sound at time of injury, immediate swelling, or inability to bear weight on the affected area.

Filed Under: Role of First Aid Tagged With: Band 2, smc-5527-10-Undue stress

HMS, BM EQ-Bank 109

Outline how the skeletal and muscular systems work together during a squat movement.   (3 marks)

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Sample Answer

Descent:

  • Hip, knee and ankle joints flex while quadriceps and gluteal muscles lengthen eccentrically to control downward movement.
  • Skeletal system provides stable framework as muscles work to control lowering speed.

Bottom Position:

  • Skeletal joints maintain alignment while muscles sustain isometric contraction to hold position.
  • Bones bear body weight as muscles stabilise.

Rising:

  • Quadriceps and gluteal muscles contract concentrically to extend joints.
  • Skeleton provides mechanical leverage while muscles generate upward force through bone attachments.
Show Worked Solution

Sample Answer

Descent:

  • Hip, knee and ankle joints flex while quadriceps and gluteal muscles lengthen eccentrically to control downward movement.
  • Skeletal system provides stable framework as muscles work to control lowering speed.

Bottom Position:

  • Skeletal joints maintain alignment while muscles sustain isometric contraction to hold position.
  • Bones bear body weight as muscles stabilise.

Rising:

  • Quadriceps and gluteal muscles contract concentrically to extend joints.
  • Skeleton provides mechanical leverage while muscles generate upward force through bone attachments.

Filed Under: Body systems working together Tagged With: Band 2, smc-5526-10-Muscular/skeletal, smc-5526-20-Respiratory/circulatory

HMS, BM EQ-Bank 103 MC

During a netball game, a player performs a layup shot. Which body systems are working together to execute this movement?

  1. Skeletal and respiratory only
  2. Muscular and circulatory only
  3. Skeletal, muscular and nervous
  4. Respiratory and circulatory only
Show Answers Only

\(C\)

Show Worked Solution
  • C is correct: The skeletal (provides framework), muscular (produces force) and nervous systems (timing and precision) work together to execute coordinated movement.

Other Options:

  • A is incorrect: Misses muscular control needed
  • B is incorrect: Omits skeletal framework required
  • D is incorrect: Misses skeletal and muscular components

Filed Under: Body systems working together Tagged With: Band 2, smc-5526-10-Muscular/skeletal, smc-5526-15-Nervous

HMS, BM EQ-Bank 26 MC

The muscle group indicated in the image below is primarily responsible for:

  1. Hip flexion
  2. Knee extension
  3. Knee flexion
  4. Hip extension
Show Answers Only

\(B\)

Show Worked Solution
  • B is correct. The quadriceps are the primary knee extensors

Other Options:

  • A is Incorrect: Hip flexion is primarily performed by the iliopsoas
  • C is Incorrect: Knee flexion is performed by the hamstrings
  • D is Incorrect: Hip extension is primarily performed by the gluteus maximus and hamstrings

Filed Under: Skeletal and muscular systems Tagged With: Band 2, smc-5521-30-Major muscles

HMS, HAG 2022 HSC 4 MC

A person had knee surgery. They were able to choose their own doctor, hospital and the date for their surgery.

Which of the following enabled the person to make these choices?

  1. Medicare Safety Net
  2. Private health insurance
  3. Health care concession card
  4. Pharmaceutical Benefits Scheme
Show Answers Only

\(B\)

Show Worked Solution

  • B is correct: Private health insurance provides choice of doctor, hospital and surgery timing.

Other Options:

  • A is incorrect: Safety Net provides financial assistance but limited choice.
  • C is incorrect: Concession cards reduce costs but don’t increase choice.
  • D is incorrect: PBS covers medications, not surgical procedures.

Filed Under: Person centred health - Govt/Non-Govt orgs Tagged With: Band 2, smc-5481-05-System components

HMS, HIC 2022 HSC 2 MC

To reduce the number of young people smoking, the sale of tobacco products to people under 18 years of age was made illegal.

Which action area of the Ottawa Charter is this strategy an example of?

  1. Developing personal skills
  2. Reorienting health services
  3. Building healthy public policy
  4. Strengthening community action
Show Answers Only

\( C\)

Show Worked Solution
  • C is correct: Legislation prohibiting tobacco sales creates healthy public policy through government regulation

Other Options:

  • A is incorrect: Focuses on individual education and skills development.
  • B is incorrect: Involves changing how health services operate.
  • D is incorrect: Community-led initiatives rather than government legislation.

Filed Under: Models of health promotion Tagged With: Band 2, smc-5515-10-Ottawa Charter

Functions, MET1 2024 VCAA 5

The function  \(h:[0, \infty) \rightarrow R, \ h(t)=\dfrac{3000}{t+1}\)  models the population of a town after \(t\) years.

  1. Use the model \(h(t)\) to predict the population of the town after four years.   (1 mark)

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  2. A new function, \(h_1\), models a population where  \(h_1(0)=h(0)\) but \(h_1\) decreases at half the rate of \(h\) at any point in time.
  3. State a sequence of two transformations that maps \(h\) to this new model \(h_1\).   (2 marks)

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  4. In the town, 100 people were randomly selected and surveyed, with 60 people indicating that they were unhappy with the roads.
    1. Determine an approximate 95% confidence interval for the proportion of people in the town who are unhappy with the roads.
    2. Use  \(z=2\)  for this confidence interval.   (2 marks)

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    3. A new sample of \(n\) people results in the same sample proportion.
    4. Find the smallest value of \(n\) to achieve a standard deviation of  \(\dfrac{\sqrt{2}}{50}\)  for the sample proportion.   (1 mark)

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a.    \(600\)

b.   \(\text{Transformations:}\)

\(\text{1- Vertical dilation by a factor of }\frac{1}{2}\ \text{from the }t\ \text{axis}\)

\(\text{2- Translation of 1500 units upwards}\)

ci.   \(\left(\dfrac{3}{5}-\dfrac{\sqrt{6}}{25},\ \dfrac{3}{5}+\dfrac{\sqrt{6}}{25}\right)\)

cii.  \(300\)

Show Worked Solution

a.  \(h(4)=\dfrac{3000}{4+1}=600\)

b.     \(h(t)\) \(=3000(t+1)^{-1}\)
  \(h^{\prime}(t)\) \(=-\dfrac{3000}{(t+1)^2}\)
  \(h_1^{\prime}(t)\) \(=\dfrac{1}{2}h^{\prime}(t)=-\dfrac{1500}{(t+1)^2}\)
  \(h_1(t)\) \(=\dfrac{1500}{t+1}+C\)

♦♦♦ Mean mark (a) 17%.

\(\text{Given}\ \ h(0)=h_1(0):\)

\(\dfrac{1500}{0+1} +C= 3000\ \ \Rightarrow\ \ C=1500\)

\(h_1(t)=\dfrac{1500}{t+1}+1500\)
 

\(\text{Transformations:}\)

\(\text{1- Vertical dilation by a factor of }\frac{1}{2}\ \text{from the }t\ \text{axis}\)

\(\text{2- Translation of 1500 units upwards}\)
 

ci.    \(\hat{p}=\dfrac{60}{100}=\dfrac{3}{5},\quad 1-\hat{p}=\dfrac{2}{5},\quad z=2\)

\(\text{Approx CI}\) \(=\left(\dfrac{3}{5}-2\sqrt{\dfrac{\dfrac{3}{5}\times\dfrac{2}{5}}{100}},\ \dfrac{3}{5}+2\sqrt{\dfrac{\dfrac{3}{5}\times\dfrac{2}{5}}{100}}\right)\)
  \(=\left(\dfrac{3}{5}-\dfrac{2\sqrt{6}}{50},\quad \dfrac{3}{5}+\dfrac{2\sqrt{6}}{50}\right)\)
  \(=\left(\dfrac{3}{5}-\dfrac{\sqrt{6}}{25},\quad \dfrac{3}{5}+\dfrac{\sqrt{6}}{25}\right)\)

  

cii.   \(\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\) \(=\dfrac{\sqrt{2}}{50}\)
  \(\sqrt{\dfrac{\dfrac{3}{5}\times\dfrac{2}{5}}{n}}\) \(=\dfrac{\sqrt{2}}{50}\)
  \(\dfrac{6}{25n}\) \(=\dfrac{2}{2500}\)
  \(\dfrac{25n}{6}\) \(=1250\)
  \(n\) \(=\dfrac{6}{25}\times 1250\)
    \(=300\)
♦♦ Mean mark (c.ii.) 33%.

Filed Under: Normal Distribution, Transformations Tagged With: Band 2, Band 4, Band 5, Band 6, smc-719-20-95% confidence intervals, smc-719-40-Find sample size, smc-753-40-Combinations, smc-753-85-Other functions

BIOLOGY, M8 2024 HSC 31

A study monitored the changes in the body temperature of a kookaburra (an Australian bird) and a human over a 24-hour period. The results of the study are shown in the graph.
 

  1. At what time was the kookaburra's body temperature the lowest?   (1 mark)

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  1. Some endothermic organisms can display torpor (a significant decrease in physiological activity).

    With reference to the graph, explain whether the human or the kookaburra was displaying torpor and if so, state the time this occurred.   (3 marks)

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  1. Outline an adaptation that may lead to an increase in the kookaburra's body temperature during the inactive period.   (2 marks)

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a.   4 am

b.   Signs of torpor:

  • The human maintained a steady body temperature throughout the observed period, showing no signs of torpor or reduced physiological activity
  • In contrast, the kookaburra exhibited classic torpor behaviour.
  • Its body temperature dropped significantly between 5 pm and 4 am, demonstrating the characteristic reduction in physiological functions during this period.

c.   Kookaburra adaptation:

  • Kookaburras have an effective insulation mechanism where they puff out their feathers, creating space between them.
  • This fluffing action traps a layer of warm air between the feathers and the bird’s body, forming an insulating barrier
  • The trapped air pocket acts like natural insulation, minimising heat loss and helping the kookaburra maintain its body temperature efficiently.

Show Worked Solution

a.   4 am

b.   Signs of torpor:

  • The human maintained a steady body temperature throughout the observed period, showing no signs of torpor or reduced physiological activity
  • In contrast, the kookaburra exhibited classic torpor behaviour.
  • Its body temperature dropped significantly between 5 pm and 4 am, demonstrating the characteristic reduction in physiological functions during this period.
Mean mark (b) 56%.

c.   Kookaburra adaptation:

  • Kookaburras have an effective insulation mechanism where they puff out their feathers, creating space between them.
  • This fluffing action traps a layer of warm air between the feathers and the bird’s body, forming an insulating barrier
  • The trapped air pocket acts like natural insulation, minimising heat loss and helping the kookaburra maintain its body temperature efficiently.
♦ Mean mark (c) 47%.

Filed Under: Homeostasis Tagged With: Band 2, Band 4, Band 5, smc-3659-15-Temperature, smc-3659-20-Adaptations/Endotherms

Data Analysis, GEN2 2024 VCAA 1

Table 1 lists the Olympic year, \(\textit{year}\), and the gold medal-winning height for the men's high jump, \(\textit{Mgold}\), in metres, for each Olympic Games held from 1928 to 2020. No Olympic Games were held in 1940 or 1944, and the 2020 Olympic Games were held in 2021.

Table 1

\begin{array}{|c|c|}
\hline \quad \textit{year} \quad & \textit{Mgold}\,\text{(m)} \\
\hline 1928 & 1.94 \\
\hline 1932 & 1.97 \\
\hline 1936 & 2.03 \\
\hline 1948 & 1.98 \\
\hline 1952 & 2.04 \\
\hline 1956 & 2.12 \\
\hline 1960 & 2.16 \\
\hline 1964 & 2.18 \\
\hline 1968 & 2.24 \\
\hline 1972 & 2.23 \\
\hline 1976 & 2.25 \\
\hline 1980 & 2.36 \\
\hline 1984 & 2.35 \\
\hline 1988 & 2.38 \\
\hline 1992 & 2.34 \\
\hline 1996 & 2.39 \\
\hline 2000 & 2.35 \\
\hline 2004 & 2.36 \\
\hline 2008 & 2.36 \\
\hline 2012 & 2.33 \\
\hline 2016 & 2.38 \\
\hline 2020 & 2.37 \\
\hline
\end{array}

  1. For the data in Table 1, determine:
  2.  i. the maximum \(\textit{Mgold}\) in metres   (1 mark)

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  3. ii. the percentage of \(\textit{Mgold}\) values greater than 2.25 m.   (1 mark)

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  4. The mean of these \(\textit{Mgold}\) values is 2.23 m, and the standard deviation is 0.15 m.
  5. Calculate the standardised \(z\)-score for the 2000 \(\textit{Mgold}\) of 2.35 m.   (1 mark)

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  6. Construct a boxplot for the \(\textit{Mgold}\) data in Table 1 on the grid below.   (2 marks)

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  1. A least squares line can also be used to model the association between \(\textit{Mgold}\) and \(\textit{year}\).
  2. Using the data from Table 1, determine the equation of the least squares line for this data set.
  3. Use the template below to write your answer.
  4. Round the values of the intercept and slope to three significant figures.   (2 marks)

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  1. The coefficient of determination is 0.857
  2. Interpret the coefficient of determination in terms of \(\textit{Mgold}\) and \(\textit{year}\).   (1 mark)

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a.i.   \(2.39\)

a.ii.  \(50\%\)

b.    \(0.8\)

c.     

d.   
    

e.    \(\text{A coefficient of determination of 85.7% shows the variation in}\)

\(\text{the}\ Mgold\ \text{that is explained by the variation in the }year.\)

Show Worked Solution

a.i.   \(2.39\)

a.ii.  \(\dfrac{11}{22}=50\%\)

b.     \(z\) \(=\dfrac{x-\overline x}{s_x}\)
    \(=\dfrac{2.35-2.23}{0.15}\)
    \(=0.8\)

  
c.   
\(Q_2=\dfrac{2.33+2.25}{2}=2.29\)

\(Q_1=2.12, \ Q_3=2.36\)

\(\text{Min}\ =1.94, \ \text{Max}\ =2.39\)
  

d.   \(\text{Using CAS:}\)


  
 

Mean mark (d) 52%.
Mean mark (e) 52%.

e.    \(\text{A coefficient of determination of 85.7% shows the variation in}\)

\(\text{the}\ Mgold\ \text{that is explained by the variation in the }year.\)

Filed Under: Correlation and Regression, Graphs - Stem/Leaf and Boxplots, Normal Distribution Tagged With: Band 2, Band 3, Band 4, smc-265-20-Find LSRL Equation/Gradient, smc-265-75-Explanatory / Response, smc-265-80-Rounding (Sig Fig), smc-600-10-Single z-score, smc-643-10-Single Box-Plots

Vectors, EXT2 V1 2024 HSC 12a

The vector \(\underset{\sim}{a}\) is \(\left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right)\) and the vector \(\underset{\sim}{b}\) is \(\left(\begin{array}{c}2 \\ 0 \\ -4\end{array}\right)\).

  1. Find \(\dfrac{\underset{\sim}{a} \cdot \underset{\sim}{b}}{\underset{\sim}{b} \cdot \underset{\sim}{b}}\, \underset{\sim}{b}\).   (1 mark)

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  2. Show that  \(\underset{\sim}{a}-\dfrac{\underset{\sim}{a} \cdot \underset{\sim}{b}}{\underset{\sim}{b} \cdot \underset{\sim}{b}}\, \underset{\sim}{b}\)  is perpendicular to \(\underset{\sim}{b}\).  (2 marks)

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1.     \(\left(\begin{array}{c}-1 \\ 0 \\ 2\end{array}\right)\)

ii.    \(\underset{\sim}{a}-\dfrac{\underset{\sim}{a} \cdot \underset{\sim}{b}}{\underset{\sim}{b} \cdot \underset{\sim}{b}}\, \underset{\sim}{b}=\left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right)-\left(\begin{array}{c}-1 \\ 0 \\ 2\end{array}\right)=\left(\begin{array}{l}2 \\ 2 \\ 1\end{array}\right)\)

\( \left(\underset{\sim}{a}-\dfrac{\underset{\sim}{a} \cdot \underset{\sim}{b}}{\underset{\sim}{b} \cdot \underset{\sim}{b}}\underset{\sim}{b}\right)\left(\begin{array}{c}-1 \\ 0 \\ 2\end{array}\right)=\left(\begin{array}{l}2 \\ 2 \\ 1\end{array}\right)\left(\begin{array}{c}-1 \\ 0 \\ 2\end{array}\right) = -2+0+2=0\)

\(\therefore\ \text {Vectors are perpendicular.}\)

Show Worked Solution

i.    \(\underset{\sim}{a}=\left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right), \quad \underset{\sim}{b}=\left(\begin{array}{c}2 \\ 0 \\ -4\end{array}\right)\)
 

\(\dfrac{\underset{\sim}{a} \cdot \underset{\sim}{b}}{\underset{\sim}{b} \cdot \underset{\sim}{b}}\, \underset{\sim}{b}=\dfrac{2+0-12}{4+0+16}\left(\begin{array}{c}2 \\ 0 \\ -4\end{array}\right)=-\dfrac{1}{2}\left(\begin{array}{c}2 \\ 0 \\ -4\end{array}\right)=\left(\begin{array}{c}-1 \\ 0 \\ 2\end{array}\right)\)

 
ii.
    \(\underset{\sim}{a}-\dfrac{\underset{\sim}{a} \cdot \underset{\sim}{b}}{\underset{\sim}{b} \cdot \underset{\sim}{b}}\, \underset{\sim}{b}=\left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right)-\left(\begin{array}{c}-1 \\ 0 \\ 2\end{array}\right)=\left(\begin{array}{l}2 \\ 2 \\ 1\end{array}\right)\)
 

\( \left(\underset{\sim}{a}-\dfrac{\underset{\sim}{a} \cdot \underset{\sim}{b}}{\underset{\sim}{b} \cdot \underset{\sim}{b}}\,\underset{\sim}{b}\right)\left(\begin{array}{c}-1 \\ 0 \\ 2\end{array}\right)=\left(\begin{array}{l}2 \\ 2 \\ 1\end{array}\right)\left(\begin{array}{c}-1 \\ 0 \\ 2\end{array}\right) = -2+0+2=0\)

 
\(\therefore\ \text{Vectors are perpendicular.}\)

Filed Under: Basic Concepts and Arithmetic Tagged With: Band 2, Band 3, smc-1195-30-Perpendicular Vectors, smc-1195-40-Unit Vectors and Projections

Complex Numbers, EXT2 N1 2024 HSC 11e

  1. Write the number  \(\sqrt{3}+i\)  in modulus-argument form.   (2 marks)

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  2. Hence, or otherwise, write  \((\sqrt{3}+i)^7\)  in exact Cartesian form.   (2 marks)

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Show Answers Only

i.     \(2 \text{cis}\left(\dfrac{\pi}{6}\right)=2\left(\cos \left(\dfrac{\pi}{6}\right)+i \sin \left(\dfrac{\pi}{6}\right)\right)\)

ii.    \(-64 \sqrt{3}-64 i\)

Show Worked Solution

i.     \(z=\sqrt{3}+i\)

\(|z|=\sqrt{3+1}=2\)

\(\arg (z)=\tan ^{-1}\left(\dfrac{1}{\sqrt{3}}\right)=\dfrac{\pi}{6}\)

\(z=2 \text{cis}\left(\dfrac{\pi}{6}\right)=2\left(\cos \left(\dfrac{\pi}{6}\right)+i \sin \left(\dfrac{\pi}{6}\right)\right)\)
 

ii.     \((\sqrt{3}+i)^7\) \(=2^7\left(\cos \left(\dfrac{7 \pi}{6}\right)+i \sin \left(\dfrac{7 \pi}{6}\right)\right)\)
    \(=128\left(-\dfrac{\sqrt{3}}{2}-\dfrac{1}{2} i\right)\)
    \(=-64 \sqrt{3}-64 i\)

Filed Under: Argand Diagrams and Mod/Arg form Tagged With: Band 2, Band 3, smc-1049-20-Cartesian to Mod/Arg, smc-1049-50-Powers

Complex Numbers, EXT2 N1 2024 HSC 11b

Let  \(z=2+3 i\)  and  \(w=1-5 i\).

  1. Find  \(z+\bar{w}\).   (1 mark)

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  2. Find  \(z^2\).   (1 mark)

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i.    \(z+\bar{w}=3+8 i\)

ii.   \(z^2=-5+12 i\)

Show Worked Solution

i.     \(z=2+3 i\)

\(w=1-5 i \ \Rightarrow \ \bar{w}=1+5 i\)

\(z+\bar{w}=2+3 i+1+5 i=3+8 i\)
 

ii.    \(z^2\) \(=(2+3 i)^{2}\)
    \(=4+12 i+9 i^2\)
    \(=-5+12 i\)

Filed Under: Arithmetic of Complex Numbers Tagged With: Band 2, smc-1048-10-Basic Arithmetic

Calculus, EXT2 C1 2024 HSC 11a

Find \(\displaystyle \int x e^x\, d x\)   (2 marks)

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Show Answers Only

\(x e^x-e^x+c\)

Show Worked Solution

\(u=x \quad \ \ u^{\prime}=1\)

\(v^{\prime}=e^x \quad v=e^x\)

  \(\displaystyle\int x e^x \,d x\) \(=u v^{\prime}-\displaystyle \int v u^{\prime}\, d x\)
    \(=x e^x- \displaystyle \int e^x \cdot 1\, d x\)
    \(=x e^x-e^x+c\)

Filed Under: Integration By Parts Tagged With: Band 2, smc-1055-20-Exponential

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