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HMS, BM EQ-Bank 334

Outline the relationship between stroke volume and training intensity during exercise.   (3 marks)

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Sample Answer

  • Stroke volume increases progressively as exercise intensity rises from rest. This continues up to approximately 40-60% of maximum intensity.
  • Beyond this point, stroke volume plateaus at its maximum level. Further intensity increases do not produce additional stroke volume gains.
  • At very high intensities, stroke volume may decrease slightly. This occurs because rapid heart rate reduces ventricular filling time.
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Sample Answer 

  • Stroke volume increases progressively as exercise intensity rises from rest. This continues up to approximately 40-60% of maximum intensity.
  • Beyond this point, stroke volume plateaus at its maximum level. Further intensity increases do not produce additional stroke volume gains.
  • At very high intensities, stroke volume may decrease slightly. This occurs because rapid heart rate reduces ventricular filling time.

HMS, BM EQ-Bank 332 MC

During a training session, an athlete experiences an increase in stroke volume. Which of the following best explains this physiological response?

  1. The number of times the heart beats per minute has increased
  2. The volume of blood pumped per beat of the heart has increased
  3. The amount of oxygen the lungs can absorb has increased
  4. The amount of blood circulating through the body has increased
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\(B\)

Show Worked Solution
  • B is correct: Stroke volume is blood pumped per heartbeat

Other Options:

  • A is incorrect: This describes heart rate, not stroke volume
  • C is incorrect: This describes oxygen uptake, not stroke volume
  • D is incorrect: This describes blood volume, not stroke volume

HMS, BM EQ-Bank 329

Explain the relationship between ventilation rate and lactate levels during and after high-intensity exercise.   (5 marks)

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Sample Answer

  • During high-intensity exercise, ventilation rate increases significantly. This occurs because working muscles require more oxygen and produce excess carbon dioxide.
  • As intensity exceeds the aerobic threshold, lactate accumulates in the bloodstream. This happens due to insufficient oxygen for complete aerobic metabolism.
  • The rising lactate levels cause blood pH to decrease, creating an acidic environment. As a result, hydrogen ions accumulate alongside lactate in the blood.
  • This triggers the respiratory control centre to increase ventilation rate further. Therefore, rapid breathing helps buffer the acidity by expelling more carbon dioxide.
  • The relationship creates a compensatory mechanism where higher lactate leads to increased ventilation. This process helps maintain blood pH within tolerable limits during intense exercise.
  • After exercise ceases, ventilation remains elevated because lactate clearance continues. Consequently, breathing rate gradually returns to normal as lactate levels decrease during recovery.
Show Worked Solution

Sample Answer

  • During high-intensity exercise, ventilation rate increases significantly. This occurs because working muscles require more oxygen and produce excess carbon dioxide.
  • As intensity exceeds the aerobic threshold, lactate accumulates in the bloodstream. This happens due to insufficient oxygen for complete aerobic metabolism.
  • The rising lactate levels cause blood pH to decrease, creating an acidic environment. As a result, hydrogen ions accumulate alongside lactate in the blood.
  • This triggers the respiratory control centre to increase ventilation rate further. Therefore, rapid breathing helps buffer the acidity by expelling more carbon dioxide.
  • The relationship creates a compensatory mechanism where higher lactate leads to increased ventilation. This process helps maintain blood pH within tolerable limits during intense exercise.
  • After exercise ceases, ventilation remains elevated because lactate clearance continues. Consequently, breathing rate gradually returns to normal as lactate levels decrease during recovery.

HMS, BM EQ-Bank 328

Compare the ventilation rate response during a 100 metre sprint with that of a 5 kilometre run.   (4 marks)

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Sample Answer

Similarities:

  • Both cause immediate ventilation rate increases above resting levels
  • Both maintain elevated rates during recovery to repay oxygen debt
  • Both responses meet increased oxygen demands of working muscles

Differences:

  • 100 m sprint produces sharp increases to 40-50 breaths per minute
  • 5 km run shows gradual increases stabilising at 30-40 breaths per minute
  • Sprint ventilation remains elevated longer post-exercise for oxygen debt repayment
  • 5 km run maintains consistent ventilation with gradual recovery
  • Sprint uses anaerobic systems; 5 km run uses aerobic systems
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Sample Answer

Similarities:

  • Both cause immediate ventilation rate increases above resting levels
  • Both maintain elevated rates during recovery to repay oxygen debt
  • Both responses meet increased oxygen demands of working muscles

Differences:

  • 100 m sprint produces sharp increases to 40-50 breaths per minute
  • 5 km run shows gradual increases stabilising at 30-40 breaths per minute
  • Sprint ventilation remains elevated longer post-exercise for oxygen debt repayment
  • 5 km run maintains consistent ventilation with gradual recovery
  • Sprint uses anaerobic systems; 5 km run uses aerobic systems

HMS, BM EQ-Bank 325 MC

During a high-intensity interval training session, a netball player experiences several physiological responses. Which of the following best describes what happens to the player's ventilation rate during the active phases?

  1. Increases to provide more oxygen to working muscles
  2. Decreases to conserve energy for explosive movements
  3. Remains constant regardless of exercise intensity
  4. Cycles between high and low rates regardless of activity level
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\(A\)

Show Worked Solution
  • A is correct: Ventilation increases to supply oxygen and remove CO2

Other Options:

  • B is incorrect: Ventilation increases not decreases during exercise
  • C is incorrect: Ventilation varies with exercise intensity
  • D is incorrect: Ventilation rate responds to physiological demands, not cycling independently

HMS, BM EQ-Bank 322

Explain how exercise intensity affects immediate heart rate response during physical activity.   (5 marks)

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Sample Answer

  • Heart rate increases in direct proportion to exercise intensity to meet the increased demand for oxygen in working muscles.
  • Low-intensity exercise (40-50% of maximum)
    • Heart rate increases moderately from resting levels as the body can easily meet oxygen demands aerobically.
  • Moderate intensities (60-70% of maximum)
    • Heart rate increases more significantly as the cardiovascular system works harder to deliver oxygen to working muscles.
  • High-intensity exercise (80-90% of maximum)
    • Heart rate approaches maximal levels as the body attempts to maintain adequate oxygen delivery despite increasing oxygen deficit.
  • The sympathetic nervous system releases adrenaline during intense exercise, further stimulating heart rate increase.
  • These immediate heart rate responses enable the body to adjust cardiac output according to the metabolic demands of the exercise being performed.
  • For example, a runner performing interval training would experience rapid heart rate increases during sprint portions (potentially reaching 170-190 bpm) and partial recovery during jogging intervals (decreasing to perhaps 120-140 bpm).
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Sample Answer

  • Heart rate increases in direct proportion to exercise intensity to meet the increased demand for oxygen in working muscles.
  • Low-intensity exercise (40-50% of maximum)
    • Heart rate increases moderately from resting levels as the body can easily meet oxygen demands aerobically.
  • Moderate intensities (60-70% of maximum)
    • Heart rate increases more significantly as the cardiovascular system works harder to deliver oxygen to working muscles.
  • High-intensity exercise (80-90% of maximum)
    • Heart rate approaches maximal levels as the body attempts to maintain adequate oxygen delivery despite increasing oxygen deficit.
  • The sympathetic nervous system releases adrenaline during intense exercise, further stimulating heart rate increase.
  • These immediate heart rate responses enable the body to adjust cardiac output according to the metabolic demands of the exercise being performed.
  • For example, a runner performing interval training would experience rapid heart rate increases during sprint portions (potentially reaching 170-190 bpm) and partial recovery during jogging intervals (decreasing to perhaps 120-140 bpm).

HMS, BM EQ-Bank 321

Compare the heart rate responses to aerobic and anaerobic training.   (4 marks)

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Sample Answer

Similarities:

  • Both cause immediate heart rate increases from resting levels
  • Both responses are proportional to exercise intensity
  • Both show recovery patterns after exercise stops

Differences:

  • Aerobic training produces steady, moderate increases (60-80% MHR) sustained for extended periods
  • Anaerobic training causes rapid increases to near-maximum (80-95% MHR) maintained only briefly
  • Aerobic training allows heart rate to stabilise at steady state
  • Anaerobic training results in continual elevation until fatigue forces cessation
  • Recovery is faster after aerobic training than anaerobic training
Show Worked Solution

Sample Answer

Similarities:

  • Both cause immediate heart rate increases from resting levels
  • Both responses are proportional to exercise intensity
  • Both show recovery patterns after exercise stops

Differences:

  • Aerobic training produces steady, moderate increases (60-80% MHR) sustained for extended periods
  • Anaerobic training causes rapid increases to near-maximum (80-95% MHR) maintained only briefly
  • Aerobic training allows heart rate to stabilise at steady state
  • Anaerobic training results in continual elevation until fatigue forces cessation
  • Recovery is faster after aerobic training than anaerobic training

HMS, BM EQ-Bank 313

Describe the immediate physiological responses of the respiratory system during an incremental training session from rest to maximum effort.   (5 marks)

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Sample Answer 

  • At rest before training begins, ventilation rate is relatively low as the body’s oxygen demand is minimal.
  • At the onset of low-intensity exercise, both breathing frequency and depth increase to deliver more oxygen to working muscles.
  • As training intensity increases to moderate levels, ventilation continues to rise proportionally with exercise intensity to maintain oxygen supply and remove carbon dioxide.
  • At higher intensities, ventilation increases more rapidly as the body attempts to remove additional carbon dioxide produced when lactic acid is buffered in the blood.
  • At maximum training intensity, ventilation reaches its highest rate as the respiratory system works at its capacity to meet the oxygen demands of high-intensity exercise.
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Sample Answer

  • At rest before training begins, ventilation rate is relatively low as the body’s oxygen demand is minimal.
  • At the onset of low-intensity exercise, both breathing frequency and depth increase to deliver more oxygen to working muscles.
  • As training intensity increases to moderate levels, ventilation continues to rise proportionally with exercise intensity to maintain oxygen supply and remove carbon dioxide.
  • At higher intensities, ventilation increases more rapidly as the body attempts to remove additional carbon dioxide produced when lactic acid is buffered in the blood.
  • At maximum training intensity, ventilation reaches its highest rate as the respiratory system works at its capacity to meet the oxygen demands of high-intensity exercise.

HMS, BM EQ-Bank 312

Explain the immediate changes to lactate levels that occur during high-intensity sprint training.   (4 marks)

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Sample Answer 

  • At the onset of high-intensity sprint training, lactate levels begin to rise rapidly as the body uses the lactic acid energy system for immediate energy production.
  • During sprinting, the body produces lactate faster than it can remove it, causing lactate to build up in the blood and muscles.
  • As lactate accumulates during repeated sprints, it leads to increased acidity in the muscles, affecting performance and contributing to fatigue.
  • Between sprint intervals, lactate levels may slightly decrease during recovery periods but generally continue to rise throughout the training session.
  • Immediately after the training session, lactate levels remain high before gradually returning to normal during the recovery period.
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Sample Answer

  • At the onset of high-intensity sprint training, lactate levels begin to rise rapidly as the body uses the lactic acid energy system for immediate energy production.
  • During sprinting, the body produces lactate faster than it can remove it, causing lactate to build up in the blood and muscles.
  • As lactate accumulates during repeated sprints, it leads to increased acidity in the muscles, affecting performance and contributing to fatigue.
  • Between sprint intervals, lactate levels may slightly decrease during recovery periods but generally continue to rise throughout the training session.
  • Immediately after the training session, lactate levels remain high before gradually returning to normal during the recovery period.

HMS, BM EQ-Bank 307 MC

During an intense training session, an athlete's ventilation rate increases. What is the primary reason for this immediate physiological response?

  1. To increase oxygen delivery to working muscles and remove carbon dioxide
  2. To increase oxygen delivery to the lungs
  3. To decrease carbon dioxide levels in the blood
  4. To reduce heart rate during exercise
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\(A\)

Show Worked Solution

Consider Option A:  To increase oxygen delivery to working muscles and remove carbon dioxide

  • Ventilation rate increases to deliver more oxygen to working muscles and remove carbon dioxide produced during exercise.

Other Options:

  • B is incorrect: Ventilation increases oxygen delivery to working muscles, not just the lungs
  • C is incorrect: Ventilation increases to remove carbon dioxide and deliver oxygen, not just decrease carbon dioxide.
  • D is incorrect: Increased ventilation doesn’t reduce heart rate during exercise.

\(\Rightarrow A\)

HMS, BM EQ-Bank 304

Compare the 'Time' component of the FITT principle for glycolytic and aerobic training methods. In your answer, explain how the 'Time' factors affect physiological responses.   (5 marks)

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Sample Answer

Similarities:

  • Both training methods require specific time durations to target their respective energy systems effectively.
  • Both need sufficient time to create training stimulus and promote fitness improvements.
  • Both require planned recovery periods, though at different intervals.

Differences:

  • Glycolytic training uses short work intervals of 30-90 seconds targeting the lactic acid system.
  • Aerobic training involves continuous activity lasting 20-60+ minutes at moderate intensity.
  • Glycolytic sessions total 15-30 minutes of high-intensity work due to accumulated fatigue.
  • Aerobic sessions extend much longer without excessive fatigue because of steady-state exercise.
  • Glycolytic training requires work-to-rest ratios of 1:2-3 to allow partial lactate clearance.
  • Aerobic training needs no rest intervals as steady-state exercise allows ongoing oxygen delivery.

Physiological responses from time differences:

  • Shorter glycolytic intervals create metabolic stress, which improves lactate buffering capacity.
  • This leads to enhanced glycolytic enzyme activity and better lactate removal.
  • Longer aerobic duration stimulates cardiovascular responses resulting in improved oxygen delivery.
  • Extended moderate intensity causes enhanced fat utilisation efficiency.
  • These distinct responses reflect each energy system’s role in different performance demands.
Show Worked Solution

Sample Answer

Similarities:

  • Both training methods require specific time durations to target their respective energy systems effectively.
  • Both need sufficient time to create training stimulus and promote fitness improvements.
  • Both require planned recovery periods, though at different intervals.

Differences:

  • Glycolytic training uses short work intervals of 30-90 seconds targeting the lactic acid system.
  • Aerobic training involves continuous activity lasting 20-60+ minutes at moderate intensity.
  • Glycolytic sessions total 15-30 minutes of high-intensity work due to accumulated fatigue.
  • Aerobic sessions extend much longer without excessive fatigue because of steady-state exercise.
  • Glycolytic training requires work-to-rest ratios of 1:2-3 to allow partial lactate clearance.
  • Aerobic training needs no rest intervals as steady-state exercise allows ongoing oxygen delivery.

Physiological responses from time differences:

  • Shorter glycolytic intervals create metabolic stress, which improves lactate buffering capacity.
  • This leads to enhanced glycolytic enzyme activity and better lactate removal.
  • Longer aerobic duration stimulates cardiovascular responses resulting in improved oxygen delivery.
  • Extended moderate intensity causes enhanced fat utilisation efficiency.
  • These distinct responses reflect each energy system’s role in different performance demands.

HMS, BM EQ-Bank 295

Analyse how the FITT principle would be applied differently for aerobic training in swimming compared to running. Provide examples to support your answer.   (8 marks)

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Sample Answer

Overview Statement:

  • Swimming and running require different FITT applications due to their distinct environmental and biomechanical demands.
  • Key relationships exist between impact stress and frequency, body position and intensity measurement, plus equipment constraints affecting type variety.

Component Relationship 1:

  • Impact stress levels directly influence frequency capabilities between these activities.
  • Swimming enables 5-6 weekly sessions because water buoyancy reduces joint stress, while running limits training to 3-4 sessions due to high impact forces.
  • Water supports body weight, preventing overuse injuries that commonly affect runners.
  • This relationship means swimmers can accumulate greater weekly training volume without injury risk.

Component Relationship 2:

  • Environmental factors connect to intensity measurement accuracy and session duration.
  • Horizontal body position in water causes heart rates to run 10-15 beats lower than land-based activities.
  • This forces swimmers to rely on perceived exertion or pace times rather than heart rate monitoring.
  • Additionally, water resistance increases energy expenditure, resulting in shorter session durations (45-60 minutes) compared to running (60-90 minutes) for equivalent training stimulus.

Implications and Synthesis:

  • These component relationships demonstrate how environmental constraints shape FITT application.
  • Swimming’s supportive environment allows higher frequency but restricts type variety to stroke variations.
  • Running’s impact stress limits frequency but provides diverse terrain options.
  • The significance is that effective aerobic programs must adapt FITT components to match each activity’s unique biomechanical and environmental demands.

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Sample Answer

Overview Statement:

  • Swimming and running require different FITT applications due to their distinct environmental and biomechanical demands.
  • Key relationships exist between impact stress and frequency, body position and intensity measurement, plus equipment constraints affecting type variety.

Component Relationship 1:

  • Impact stress levels directly influence frequency capabilities between these activities.
  • Swimming enables 5-6 weekly sessions because water buoyancy reduces joint stress, while running limits training to 3-4 sessions due to high impact forces.
  • Water supports body weight, preventing overuse injuries that commonly affect runners.
  • This relationship means swimmers can accumulate greater weekly training volume without injury risk.

Component Relationship 2:

  • Environmental factors connect to intensity measurement accuracy and session duration.
  • Horizontal body position in water causes heart rates to run 10-15 beats lower than land-based activities.
  • This forces swimmers to rely on perceived exertion or pace times rather than heart rate monitoring.
  • Additionally, water resistance increases energy expenditure, resulting in shorter session durations (45-60 minutes) compared to running (60-90 minutes) for equivalent training stimulus.

Implications and Synthesis:

  • These component relationships demonstrate how environmental constraints shape FITT application.
  • Swimming’s supportive environment allows higher frequency but restricts type variety to stroke variations.
  • Running’s impact stress limits frequency but provides diverse terrain options.
  • The significance is that effective aerobic programs must adapt FITT components to match each activity’s unique biomechanical and environmental demands.

HMS, BM EQ-Bank 294

Describe how you would modify each component of the FITT principle throughout an 8-week aerobic training program for a recreational soccer player. Use examples to support your answer.   (6 marks)

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Sample Answer

Frequency

  • Weeks 1-2: Start with 3 sessions weekly to establish routine without overtraining.
  • Weeks 3-6: Increase to 4 sessions as as fitness base develops.
  • Weeks 7-8: Maintain 4-5 sessions, ensuring recovery before matches.

Intensity

  • Weeks 1-2: 60-70% MHR builds aerobic base safely.
  • Weeks 3-4: Progress to 70-75% MHR as conditioning improves.
  • Weeks 5-6: Include intervals at 75-80% MHR developing lactate threshold.
  • Weeks 7-8: Incorporate match-intensity periods at 80-85% MHR.

Time

  • Weeks 1-2: 30-minute sessions prevent excessive fatigue.
  • Weeks 3-4: Extend to 40 minutes building endurance capacity.
  • Weeks 5-6: 45-50 minutes with varied intensities.
  • Weeks 7-8: 60 minutes matching game duration requirements.

Type

  • Weeks 1-2: Continuous jogging establishing base fitness.
  • Weeks 3-4: Add fartlek training introducing speed variations.
  • Weeks 5-6: Include ball work maintaining 70%+ MHR through dribbling circuits.
  • Weeks 7-8: Small-sided games (4v4) combining fitness with tactical practice.

Progressive overload:

  • Systematic increases occur across all training variables.
  • Each phase builds upon previous weeks’ foundation.
  • Soccer-specific elements increase throughout the program duration.
Show Worked Solution

Sample Answer

Frequency

  • Weeks 1-2: Start with 3 sessions weekly to establish routine without overtraining.
  • Weeks 3-6: Increase to 4 sessions as as fitness base develops.
  • Weeks 7-8: Maintain 4-5 sessions, ensuring recovery before matches.

Intensity

  • Weeks 1-2: 60-70% MHR builds aerobic base safely.
  • Weeks 3-4: Progress to 70-75% MHR as conditioning improves.
  • Weeks 5-6: Include intervals at 75-80% MHR developing lactate threshold.
  • Weeks 7-8: Incorporate match-intensity periods at 80-85% MHR.

Time

  • Weeks 1-2: 30-minute sessions prevent excessive fatigue.
  • Weeks 3-4: Extend to 40 minutes building endurance capacity.
  • Weeks 5-6: 45-50 minutes with varied intensities.
  • Weeks 7-8: 60 minutes matching game duration requirements.

Type

  • Weeks 1-2: Continuous jogging establishing base fitness.
  • Weeks 3-4: Add fartlek training introducing speed variations.
  • Weeks 5-6: Include ball work maintaining 70%+ MHR through dribbling circuits.
  • Weeks 7-8: Small-sided games (4v4) combining fitness with tactical practice.

Progressive overload:

  • Systematic increases occur across all training variables.
  • Each phase builds upon previous weeks’ foundation.
  • Soccer-specific elements increase throughout the program duration.

HMS, BM EQ-Bank 293

Describe how you would apply the FITT principle to design an aerobic training program for a beginner jogger.   (3 marks)

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Sample Answer

  • Frequency of training for a beginning jogger be 3 sessions per week, allowing adequate recovery between sessions to prevent overtraining and build fitness gradually.
  • Intensity should remain low to moderate at 50-60% maximum heart rate to develop aerobic base without excessive fatigue or discouragement.
  • Time involves starting with 20 minutes continuous jogging, progressively increasing to 30 minutes as cardiovascular fitness and confidence improve.
  • Type focuses on continuous jogging at steady pace on flat terrain, incorporating walking breaks when needed to maintain target heart rate zone and prevent overexertion.
  • This approach ensures safe, sustainable progression for beginners while establishing proper aerobic training habits and preventing early dropout from excessive demands.

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Sample Answer

  • Frequency of training for a beginning jogger be 3 sessions per week, allowing adequate recovery between sessions to prevent overtraining and build fitness gradually.
  • Intensity should remain low to moderate at 50-60% maximum heart rate to develop aerobic base without excessive fatigue or discouragement.
  • Time involves starting with 20 minutes continuous jogging, progressively increasing to 30 minutes as cardiovascular fitness and confidence improve.
  • Type focuses on continuous jogging at steady pace on flat terrain, incorporating walking breaks when needed to maintain target heart rate zone and prevent overexertion.
  • This approach ensures safe, sustainable progression for beginners while establishing proper aerobic training habits and preventing early dropout from excessive demands.

HMS, BM EQ-Bank 292

Compare how the 'Frequency' and 'Type' components of the FITT principle would be applied in designing anaerobic training programs for a tennis player versus a competitive 100 metre swimmer.   (6 marks)

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Sample Answer

Similarities:

  • Both sports require careful scheduling around skill practice sessions.
  • Both limit anaerobic sessions to 2-3 times weekly to prevent overtraining.
  • Both utilise interval training with work periods under 60 seconds targeting anaerobic systems.
  • Both incorporate resistance training to develop power for sport-specific movements.
  • Both require 48-72 hour recovery periods between high-intensity anaerobic sessions.

Differences:

  • Tennis players can manage 2-3 weekly sessions due to high impact stress from jumping and lunging.
  • 100m swimmers can handle 3 sessions as water-based training reduces joint stress, allowing quicker recovery.
  • Tennis training emphasises multi-directional movements through court sprints, lunging patterns and plyometric jumps.
  • 100m swimming focuses on linear sprint power through 25-50m sprint sets and explosive starts.
  • Tennis sessions include agility ladders and reaction drills for sudden direction changes and net play.
  • 100m swimmers use resistance equipment like parachutes and paddles for stroke-specific power development.
  • Tennis “type” component addresses explosive racquet swing power and rapid court coverage.
  • 100m swimming “type” component develops propulsive force and streamlined body position for maximum speed.

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Sample Answer

Similarities:

  • Both sports require careful scheduling around skill practice sessions.
  • Both limit anaerobic sessions to 2-3 times weekly to prevent overtraining.
  • Both utilise interval training with work periods under 60 seconds targeting anaerobic systems.
  • Both incorporate resistance training to develop power for sport-specific movements.
  • Both require 48-72 hour recovery periods between high-intensity anaerobic sessions.

Differences:

  • Tennis players can manage 2-3 weekly sessions due to high impact stress from jumping and lunging.
  • 100m swimmers can handle 3 sessions as water-based training reduces joint stress, allowing quicker recovery.
  • Tennis training emphasises multi-directional movements through court sprints, lunging patterns and plyometric jumps.
  • 100m swimming focuses on linear sprint power through 25-50m sprint sets and explosive starts.
  • Tennis sessions include agility ladders and reaction drills for sudden direction changes and net play.
  • 100m swimmers use resistance equipment like parachutes and paddles for stroke-specific power development.
  • Tennis “type” component addresses explosive racquet swing power and rapid court coverage.
  • 100m swimming “type” component develops propulsive force and streamlined body position for maximum speed.

HMS, BM EQ-Bank 291

Explain how you would modify the FITT principle when designing an anaerobic training program for a boxer preparing for a championship fight.   (6 marks)

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Sample Answer

Frequency:

  • Would increase gradually from 3 sessions per week during early preparation to 4-5 specialised anaerobic sessions weekly during the specific preparation phase, allowing for adequate recovery while building capacity.

Intensity:

  • Would follow a progressive pattern, starting with moderate bursts (70-80% effort) during general preparation and increasing to high-intensity intervals (85-95%) that simulate the energy demands of three-minute rounds with one-minute recovery.

Time parameters:

  • Would mirror the sport’s demands with work intervals of 10-20 seconds for power punching combinations, 30-60 seconds for sustained output during exchanges, and rest periods that gradually decrease from 1:4 to 1:2 work-to-rest ratio as fight preparation advances.

Type of training:

  • Would include sport-specific movements such as heavy bag work, pad drills, and shadow boxing performed at anaerobic intensities, supplemented with resistance exercises like medicine ball throws and plyometric push-ups for power development.

Progression:

  • During the final two weeks before the fight, intensity would remain high while volume decreases to ensure the boxer remains fresh yet maintains anaerobic power and capacity.

Throughout Training:

  • Boxing-specific metrics like punch output, punch force, and heart rate recovery would be used to monitor adaptations and ensure the FITT variables are optimised.
Show Worked Solution

Sample Answer

Frequency:

  • Would increase gradually from 3 sessions per week during early preparation to 4-5 specialised anaerobic sessions weekly during the specific preparation phase, allowing for adequate recovery while building capacity.

Intensity:

  • Would follow a progressive pattern, starting with moderate bursts (70-80% effort) during general preparation and increasing to high-intensity intervals (85-95%) that simulate the energy demands of three-minute rounds with one-minute recovery.

Time parameters:

  • Would mirror the sport’s demands with work intervals of 10-20 seconds for power punching combinations, 30-60 seconds for sustained output during exchanges, and rest periods that gradually decrease from 1:4 to 1:2 work-to-rest ratio as fight preparation advances.

Type of training:

  • Would include sport-specific movements such as heavy bag work, pad drills, and shadow boxing performed at anaerobic intensities, supplemented with resistance exercises like medicine ball throws and plyometric push-ups for power development.

Progression:

  • During the final two weeks before the fight, intensity would remain high while volume decreases to ensure the boxer remains fresh yet maintains anaerobic power and capacity.

Throughout Training:

  • Boxing-specific metrics like punch output, punch force, and heart rate recovery would be used to monitor adaptations and ensure the FITT variables are optimised.

HMS, BM EQ-Bank 289

Describe two ways that the 'Type' component of the FITT principle can be varied in an anaerobic training program for a rugby player.   (4 marks)

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Any 2 of the following

NOTE: Students should describe any TWO of the training types in detail, ensuring they explain how each type is implemented and its relevance to rugby performance.

Sprint interval training

  • Develops the ATP-PCr system through 10-30 metre maximal sprints with full recovery between efforts.
  • This training replicates explosive bursts needed for line breaks and support play in rugby matches.

Plyometric exercises

  • Develops the ATP-PCr system through 10-30 metre maximal sprints with full recovery between efforts.
  • This training replicates explosive bursts needed for line breaks and support play in rugby matches.

Circuit training

  • Combines 6-8 rugby-specific anaerobic stations such as tackle bags, agility ladders and medicine ball throws.
  • Athletes work at high intensity for 20-30 seconds per station with recovery periods.

Resistance training

  • Uses heavy loads at 80-90% 1RM for 1-5 repetitions with extended rest periods.
  • Compound movements like squats, deadlifts and power cleans build maximal strength for scrummaging and ruck contests.
Show Worked Solution

Any 2 of the following

NOTE: Students should describe any TWO of the training types in detail, ensuring they explain how each type is implemented and its relevance to rugby performance.

Sprint interval training

  • Develops the ATP-PCr system through 10-30 metre maximal sprints with full recovery between efforts.
  • This training replicates explosive bursts needed for line breaks and support play in rugby matches.

Plyometric exercises

  • Develops the ATP-PCr system through 10-30 metre maximal sprints with full recovery between efforts.
  • This training replicates explosive bursts needed for line breaks and support play in rugby matches.

Circuit training

  • Combines 6-8 rugby-specific anaerobic stations such as tackle bags, agility ladders and medicine ball throws.
  • Athletes work at high intensity for 20-30 seconds per station with recovery periods.

Resistance training

  • Uses heavy loads at 80-90% 1RM for 1-5 repetitions with extended rest periods.
  • Compound movements like squats, deadlifts and power cleans build maximal strength for scrummaging and ruck contests.

HMS, BM EQ-Bank 288

Explain how you would modify the 'Frequency' component of the FITT principle for a netball player during pre-season versus in-season anaerobic training.   (4 marks)

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Sample Answer

  • Pre-season allows 3-4 anaerobic sessions weekly because building fitness base is priority without match demands competing for recovery time.
  • This enables 24-48 hour recovery between sessions, which allows fitness development while preventing overtraining in netball players.
  • In-season requires reducing to 1-2 dedicated anaerobic sessions weekly because match play provides game-intensity stimulus that replaces some training needs.
  • Consequently, 48-72 hour recovery becomes necessary due to accumulated fatigue from competitive matches combined with training loads.
  • This modification occurs because pre-season has no competitive stress, whereas in-season requires balancing training with match demands to maintain performance without causing burnout.
  • Therefore, frequency adjustments ensure optimal performance by matching training load to the player’s total stress and recovery capacity.

Show Worked Solution

Sample Answer

  • Pre-season allows 3-4 anaerobic sessions weekly because building fitness base is priority without match demands competing for recovery time.
  • This enables 24-48 hour recovery between sessions, which allows fitness development while preventing overtraining in netball players.
  • In-season requires reducing to 1-2 dedicated anaerobic sessions weekly because match play provides game-intensity stimulus that replaces some training needs.
  • Consequently, 48-72 hour recovery becomes necessary due to accumulated fatigue from competitive matches combined with training loads.
  • This modification occurs because pre-season has no competitive stress, whereas in-season requires balancing training with match demands to maintain performance without causing burnout.
  • Therefore, frequency adjustments ensure optimal performance by matching training load to the player’s total stress and recovery capacity.

HMS, BM EQ-Bank 284

Explain how the Time and Intensity components of the FITT principle would be implemented for a sprinter competing in a 100 m event.   (5 marks)

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Sample Answer 

Time:

  • Work intervals must be 5-15 seconds to match the 100m race duration and target the ATP-PCr system.
  • Recovery periods require 2-5 minutes between efforts, which creates work-to-rest ratios of 1:10-20..
  • This extended recovery allows complete phosphate replenishment essential for maintaining sprint quality..

Intensity:

  • Training must occur at 90-100% maximum velocity to recruit fast-twitch muscle fibres.
  • This develops neuromuscular patterns specific to sprinting.
  • Sub-maximal efforts fail to stimulate the improvements required for elite speed development.

Relationship:

  • Short time periods enable maximum intensity maintenance throughout each repetition.
  • Attempting longer durations forces intensity reduction as the glycolytic system activates.
  • This compromises sprint-specific improvements.

Progressive application:

  • Early season uses slightly longer intervals (10-15 seconds) at 90-95% intensity because this builds capacity.
  • Competition phase shifts to race-specific times (9-11 seconds) at 100% intensity.
  • This progression develops speed endurance before pure speed, preventing injury while optimising 100m performance.
Show Worked Solution

Sample Answer 

Time:

  • Work intervals must be 5-15 seconds to match the 100m race duration and target the ATP-PCr system.
  • Recovery periods require 2-5 minutes between efforts, which creates work-to-rest ratios of 1:10-20..
  • This extended recovery allows complete phosphate replenishment essential for maintaining sprint quality..

Intensity:

  • Training must occur at 90-100% maximum velocity to recruit fast-twitch muscle fibres.
  • This develops neuromuscular patterns specific to sprinting.
  • Sub-maximal efforts fail to stimulate the improvements required for elite speed development.

Relationship:

  • Short time periods enable maximum intensity maintenance throughout each repetition.
  • Attempting longer durations forces intensity reduction as the glycolytic system activates.
  • This compromises sprint-specific improvements.

Progressive application:

  • Early season uses slightly longer intervals (10-15 seconds) at 90-95% intensity because this builds capacity.
  • Competition phase shifts to race-specific times (9-11 seconds) at 100% intensity.
  • This progression develops speed endurance before pure speed, preventing injury while optimising 100m performance.

HMS, BM EQ-Bank 283

Describe the FITT principle and its application to anaerobic training.   (4 marks)

Show Answers Only

Sample Answer 

  • The FITT principle provides a framework for designing effective training programs using Frequency (how often), Intensity (how hard), Time (duration), and Type (exercise selection).
  • For anaerobic training, frequency involves 2-4 sessions weekly with 48-72 hours recovery between sessions to allow muscle repair.
  • Intensity requires high effort at 80-95% MHR or maximum effort to effectively target ATP-PCr and glycolytic systems.
  • Time features short work intervals of 10-60 seconds with rest periods 2-3 times longer than work periods.
  • Type includes sprint intervals, plyometrics, resistance training, and sport-specific high-intensity drills that develop power and speed through ATP-PCr and glycolytic pathways.

Show Worked Solution

Sample Answer 

  • The FITT principle provides a framework for designing effective training programs using Frequency (how often), Intensity (how hard), Time (duration), and Type (exercise selection).
  • For anaerobic training, frequency involves 2-4 sessions weekly with 48-72 hours recovery between sessions to allow muscle repair.
  • Intensity requires high effort at 80-95% MHR or maximum effort to effectively target ATP-PCr and glycolytic systems.
  • Time features short work intervals of 10-60 seconds with rest periods 2-3 times longer than work periods.
  • Type includes sprint intervals, plyometrics, resistance training, and sport-specific high-intensity drills that develop power and speed through ATP-PCr and glycolytic pathways.

HMS, BM EQ-Bank 278

Analyse how the "type" component of the FITT principle can be manipulated to improve aerobic capacity in team sport athletes.   (8 marks)

Show Answers Only

Sample Answer

Overview Statement:

  •  The “type” component interacts with other FITT elements to create sport-specific aerobic development that enhances transfer to team sport performance.

Sample Answer – Any 3 – 4 of the following in depth

Small-sided games:

  • Small-sided games (3v3 to 6v6) maintain high heart rates (70-85% MHR) while developing sport-specific movement patterns. This creates high transfer to competition while maintaining athlete motivation compared to traditional aerobic training.

Sport-specific interval training:

  • Intervals replicate movement patterns and work-to-rest ratios of specific sports. Basketball players perform court-length sprints and defensive slides rather than generic running. This enhances transfer of aerobic development to game performance.

Circuit training:

  • Circuits combine aerobic exercises with sport-specific skills to develop aerobic capacity while maintaining technical proficiency. Coaches manipulate work periods and exercise selection to create appropriate stimulus while reinforcing skill development.

Cross-training:

  • Different aerobic activities (cycling, swimming, rowing) provide effective stimulus while reducing strain from repeated sport-specific movements. This is particularly valuable during heavy competition periods or for injured athletes.

Fartlek training:

  • Variable-intensity training with sport-specific movements allows athletes to develop aerobic capacity that mimics the unpredictable nature of team sports. Sessions can be structured or unstructured depending on training phase needs.

Environmental manipulation:

  • Changing environments (sand, hills, water) increases training stimulus while maintaining sport-specific movement patterns. Beach volleyball players performing footwork drills in sand increases intensity while enhancing sport-specific benefits.

High-intensity aerobic intervals:

  • High-intensity intervals (85-95% MHR) develop both aerobic power and lactate buffering capacity. These must be carefully designed to match sport demands and recovery capacities.

Implications:

  • Effective “type” manipulation integrates multiple training methods throughout structured programs, with emphasis shifting from general aerobic development to sport-specific training as competition approaches.

Show Worked Solution

Overview Statement:

  •  The “type” component interacts with other FITT elements to create sport-specific aerobic development that enhances transfer to team sport performance.

Sample Answer – Any 3 – 4 of the following in depth

Small-sided games:

  • Small-sided games (3v3 to 6v6) maintain high heart rates (70-85% MHR) while developing sport-specific movement patterns. This creates high transfer to competition while maintaining athlete motivation compared to traditional aerobic training.

Sport-specific interval training:

  • Intervals replicate movement patterns and work-to-rest ratios of specific sports. Basketball players perform court-length sprints and defensive slides rather than generic running. This enhances transfer of aerobic development to game performance.

Circuit training:

  • Circuits combine aerobic exercises with sport-specific skills to develop aerobic capacity while maintaining technical proficiency. Coaches manipulate work periods and exercise selection to create appropriate stimulus while reinforcing skill development.

Cross-training:

  • Different aerobic activities (cycling, swimming, rowing) provide effective stimulus while reducing strain from repeated sport-specific movements. This is particularly valuable during heavy competition periods or for injured athletes.

Fartlek training:

  • Variable-intensity training with sport-specific movements allows athletes to develop aerobic capacity that mimics the unpredictable nature of team sports. Sessions can be structured or unstructured depending on training phase needs.

Environmental manipulation:

  • Changing environments (sand, hills, water) increases training stimulus while maintaining sport-specific movement patterns. Beach volleyball players performing footwork drills in sand increases intensity while enhancing sport-specific benefits.

High-intensity aerobic intervals:

  • High-intensity intervals (85-95% MHR) develop both aerobic power and lactate buffering capacity. These must be carefully designed to match sport demands and recovery capacities.

Implications:

  • Effective “type” manipulation integrates multiple training methods throughout structured programs, with emphasis shifting from general aerobic development to sport-specific training as competition approaches.

HMS, BM EQ-Bank 282 MC

Which of the following is the most accurate definition of the 'Intensity' component of the FITT principle when applied to anaerobic training?

  1. The number of training sessions performed each week
  2. The duration of each workout or exercise session
  3. The level of exertion or effort during the activity expressed as a percentage of maximum heart rate or RPE
  4. The specific exercise selection within the workout plan
Show Answers Only

\(C\)

Show Worked Solution
  • C is correct: Intensity = level of exertion, measured as % maximum heart rate or RPE scale.

Other Options:

  • A is incorrect: Describes the Frequency component of FITT.
  • B is incorrect: Describes the Time component of FITT.
  • D is incorrect: Describes the Type component of FITT.

HMS, BM EQ-Bank 280 MC

The FITT principle includes which of the following components?

  1. Frequency, Intensity, Time, Type
  2. Flexibility, Intensity, Training, Threshold
  3. Frequency, Intervals, Timing, Technique
  4. Function, Intensity, Time, Type
Show Answers Only

\(A\)

Show Worked Solution
  • A is correct: The FITT principle stands for Frequency, Intensity, Time, and Type.

Other Options:

  • B is incorrect: Flexibility and Threshold are not part of the FITT acronym.
  • C is incorrect: Intervals, Timing, and Technique are not part of the FITT acronym.
  • D is incorrect: Function is not part of the FITT acronym.

Vectors, SPEC2 2024 VCAA 13 MC

If the angle between the vectors  \(2 \underset{\sim}{ i }-\underset{\sim}{ j }+2 \underset{\sim}{ k }\)  and  \(2 \underset{\sim}{ i }+m \underset{\sim}{ j }+6 \underset{\sim}{ k }\)  is  \(\cos ^{-1}\left(\dfrac{13}{21}\right)\), then the value of \(m\), where  \(m \in R^{+}\), is

  1. \(2\)
  2. \(3\)
  3. \(4\)
  4. \(5\)
Show Answers Only

\(B\)

Show Worked Solution

\(\underset{\sim}{a}=\left(\begin{array}{c}2 \\ -1 \\ 2\end{array}\right)  \Rightarrow \abs{\underset{\sim}{a}}=\sqrt{9}=3\)

\(\underset{\sim}{b}=\left(\begin{array}{c}2 \\ m \\ 6\end{array}\right)  \Rightarrow \abs{\underset{\sim}{a}}=\sqrt{2^2+m^2+6^2}=\sqrt{40+m^2}\)

\(\underset{\sim}{a} \cdot \underset{\sim}{b}\) \(=\abs{\underset{\sim}{a}}\abs{\underset{\sim}{b}} \cos \theta\)  
\(16-m\) \(=3 \sqrt{40+m^2} \times \cos \left(\cos ^{-1}\left(\dfrac{13}{21}\right)\right)\)  

 
\(\text{Solve for \(m\) (by CAS):} \ 16-m=3 \sqrt{40+m^2} \times \dfrac{13}{21}\)

\(m=-\dfrac{241}{15}, 3\)

\(\Rightarrow B\)

Complex Numbers, SPEC2 2024 VCAA 6 MC

Let  \(z=3+k i\)  where  \(k \in R\).

A value of \(k\) that makes  \(z^2+4 i z+3\)  purely imaginary is

  1. \(-2\)
  2. \(-1\)
  3. \(1\)
  4. \(2\)
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Substitute}\ \ z=3+ki\ \ \text{into equation:}\)

\(z^2+4iz+3\) \(=(3+ki)^2+4i(3+ki)+3\)  
  \(=9+6ki-k^2+12i-4k+3\)  
  \(=-k^2-4k+12 +(6k+12)i\)  

 
\(\text{Purely imaginary if}\ \ -k^2-4k+12=0:\)

\(k=-6, 2\)

\(\Rightarrow D\)

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)

Show Answers Only

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.

Statistics, SPEC1 2024 VCAA 6

The production of a brand of weed trimmer involves three stages, Stage 1, Stage 2 and Stage 3, which take \(W_1\) hours, \(W_2\) hours and \(W_3\) hours, respectively. Here \(W_1, W_2\) and \(W_3\) are independent random variables, which may be assumed to be normally distributed. Assume that Stage 2 starts immediately after Stage 1 ends and that Stage 3 starts immediately after Stage 2 ends.

The mean, standard deviation and cost at each stage are shown in the table below.

\begin{array}{|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Stage} & \textbf{Time (h) } & \textbf{Mean(h)} &\textbf{Standard } &  \textbf{Cost (\$/h)} \\
& & & \rule[-1ex]{0pt}{0pt} \textbf{deviation (h)}\\
\hline \rule{0pt}{2.5ex} 1 \rule[-1ex]{0pt}{0pt}& W_1 & 1.0 & 0.3 & 10 \\
\hline \rule{0pt}{2.5ex} 2 \rule[-1ex]{0pt}{0pt}& W_2 & 1.5 & 0.4 & 20 \\
\hline \rule{0pt}{2.5ex} 3 \rule[-1ex]{0pt}{0pt}& W_3 & 2.0 & 0.5 & 15 \\
\hline
\end{array}

  1. Find the mean and the variance of the total time to produce one weed trimmer.   (1 mark)

  2. Find the variance of the total cost to produce one weed trimmer.   (2 marks)
  3. If a single weed trimmer is produced, find the probability that the time spent at Stage 2 will be less than the time spent at Stage 1.
  4. Give your answer correct to two decimal places.
  5. Use  \(\operatorname{Pr}(-1<Z<1)=0.68\),  where \(Z\) is the standard normal variable with mean 0 and standard deviation 1.  (2 marks)

Show Answers Only

a.   \(\text{E}(W_1+W_2+W_3) =4.5\)

\(\text{Var}(W_1+W_2+W_3) = 0.5\)

b.   \(\text{Var}(10W_1+40W_2+15W_3) = 129.25 \)

c.   \(0.16\)

Show Worked Solution

a.   \(\text{Time to make 1 trimmer}\ = W_1+W_2+W3\)

\(\text{Using mean and std dev values from the table:}\)

\(\text{E}(W_1+W_2+W_3) = 1.0+1.5+2.0=4.5\)

\(\text{Var}(W_1+W_2+W_3) = 0.3^2+0.4^2+0.5^2 = 0.5\)
 

b.   \(\text{Cost to make 1 trimmer}\ = 10W_1+20W_2+15W3\)

\(\text{Var}(10W_1+40W_2+15W_3)\)

\(= 10^2\text{Var}(W_1)+20^2\text{Var}(W_2)+15^2\text{Var}(W_1) \)

\(= 100\text{Var}(W_1)+400\text{Var}(W_2)+225\text{Var}(W_1) \)

\(= 100\times 0.09+400 \times 0.16 +225 \times 0.25 \)

\(= 9+64+56.25 \)

\(= 129.25 \)
 

♦ Mean mark (b) 45%.

c.    \(\text{Let}\ \ X=W_1-W_2\)

\(\text{Since}\ \ W_1-W_2\ \ \text{is a linear combination of normally distributed variables}\)

\(W_1-W2\ \ \text{is also normally distributed}\)

\(\text{E}(W_1-W2)=1.0-1.5=-0.5\)

\(\text{Var}(W_1-W2)=0.3^2+0.4^2=0.25\)

\(\text{Pr}(X>0)\) \(=\text{Pr}\left( Z> \dfrac{0+0.5}{0.5}\right) \)  
  \(=\text{Pr}(Z>1)\)  
  \(=0.16\)  
♦ Mean mark (c) 50%.

HMS, BM EQ-Bank 274 MC

A cross-country runner wants to improve their aerobic capacity. Which frequency component of the FITT principle is most appropriate for their training program?

  1. Training once per week with high intensity
  2. Training twice per week with moderate intensity
  3. Training 4-5 times per week with moderate-high intensity
  4. Training daily with maximum intensity
Show Answers Only

\(C\)

Show Worked Solution
  • C is correct: Optimal frequency for aerobic development with adequate recovery.

Other Options:

  • A is incorrect: Once weekly insufficient for aerobic capacity.
  • B is incorrect: Twice weekly below minimum for aerobic development.
  • D is incorrect: Daily training → no recovery, max intensity → anaerobic focus.

HMS, BM EQ-Bank 272 MC

For a basketball guard focusing on improving their aerobic endurance, which of the following best represents the appropriate application of the FITT principle?

  1. Frequency: 1-2 times per week; Intensity: 95% max heart rate; Time: 5-10 minutes; Type: Sprint training
  2. Frequency: 3-4 times per week; Intensity: 70-85% max heart rate; Time: 30-45 minutes; Type: Continuous training
  3. Frequency: daily training; Intensity: 50-60% max heart rate; Time: 60+ minutes; Type: Long slow distance
  4. Frequency: 2-3 times per week; Intensity: maximal effort; Time: 15-20 minutes; Type: Resistance training
Show Answers Only

\(B\)

Show Worked Solution
  • B is correct: For aerobic endurance development in basketball, moderate-to-high intensity continuous training at 70-85% MHR for 30-45 minutes, 3-4 times per week provides the optimal stimulus.

Other Options:

  • A is incorrect: This represents anaerobic training with insufficient frequency for aerobic development.
  • C is incorrect: Daily training would not allow sufficient recovery, and the intensity is too low for optimal aerobic development.
  • D is incorrect: Resistance training primarily develops strength rather than aerobic endurance.

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)

Show Answers Only

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.

HMS, BM EQ-Bank 270

Explain how you would apply the FITT principle when designing an aerobic training program for an adolescent soccer player focusing on pre-season conditioning.   (5 marks)

Show Answers Only

Sample Answer

  • Begin with 3 sessions weekly in early pre-season, then increasing to 4 sessions as fitness improves because this allows recovery while building aerobic base essential for soccer’s continuous running demands.
  • Start intensity at 65-70% MHR for first 2-3 weeks to establish base fitness, then progress to 70-80% MHR as conditioning improves because gradual increases prevent overload in developing athletes.
  • Monitor intensity through heart rate zones because this ensures consistent training stimulus while accommodating adolescent growth variations that can affect training responses.
  • Begin with 20-30 minute sessions, progressively increasing to 35-45 minutes because longer durations develop the aerobic capacity needed for 90-minute match demands.
  • Vary between continuous running, fartlek training and soccer-specific drills with the ball because this maintains engagement while building aerobic foundation required for match fitness.
  • Include small-sided games (3v3, 4v4) as these maintain skill development while providing aerobic stimulus specific to soccer movement patterns.
  • Progressive overload occurs by increasing duration first, then frequency, finally intensity because this gradual progression prevents overtraining in adolescent athletes whose bodies are still developing.
Show Worked Solution

Sample Answer

  • Begin with 3 sessions weekly in early pre-season, then increasing to 4 sessions as fitness improves because this allows recovery while building aerobic base essential for soccer’s continuous running demands.
  • Start intensity at 65-70% MHR for first 2-3 weeks to establish base fitness, then progress to 70-80% MHR as conditioning improves because gradual increases prevent overload in developing athletes.
  • Monitor intensity through heart rate zones because this ensures consistent training stimulus while accommodating adolescent growth variations that can affect training responses.
  • Begin with 20-30 minute sessions, progressively increasing to 35-45 minutes because longer durations develop the aerobic capacity needed for 90-minute match demands.
  • Vary between continuous running, fartlek training and soccer-specific drills with the ball because this maintains engagement while building aerobic foundation required for match fitness.
  • Include small-sided games (3v3, 4v4) as these maintain skill development while providing aerobic stimulus specific to soccer movement patterns.
  • Progressive overload occurs by increasing duration first, then frequency, finally intensity because this gradual progression prevents overtraining in adolescent athletes whose bodies are still developing.

HMS, BM EQ-Bank 269

Explain how you would design an anaerobic training program based on the FITT principle for a 400 m track athlete.   (5 marks)

Show Answers Only

Sample Answer

Frequency:

  • 3 anaerobic-specific sessions per week with at least 48 hours between high-intensity sessions to allow for adequate recovery of the neuromuscular system and replenishment of muscle glycogen.
  • Two additional sessions focusing on technique and lower-intensity work.

Intensity:

  • High to very high intensity (85-95% of maximum effort) to develop the anaerobic glycolytic system that predominates in 400 m events.
  • Heart rate typically reaches 90-100% of maximum during work intervals with incomplete recovery between repetitions.

Time:

  • Work intervals of 30-60 seconds (simulating race pace and duration), with total high-intensity work time of 10-15 minutes per session.
  • Rest intervals begin at 1:3 work-to-rest ratio (e.g., 45-second run, 135-second recovery) and progress to 1:2 as fitness improves.

Type:

  • Track-based interval training using distances of 200-500 m at race-specific pace, complemented by hill sprints and tempo intervals to develop lactate tolerance specific to 400m racing demands.

Progression:

  • The program would progress over 8-12 weeks by manipulating the work-to-rest ratio and increasing the total volume, while maintaining the specific intensity required for 400 m performance.
Show Worked Solution

Sample Answer

Frequency:

  • 3 anaerobic-specific sessions per week with at least 48 hours between high-intensity sessions to allow for adequate recovery of the neuromuscular system and replenishment of muscle glycogen.
  • Two additional sessions focusing on technique and lower-intensity work.

Intensity:

  • High to very high intensity (85-95% of maximum effort) to develop the anaerobic glycolytic system that predominates in 400 m events.
  • Heart rate typically reaches 90-100% of maximum during work intervals with incomplete recovery between repetitions.

Time:

  • Work intervals of 30-60 seconds (simulating race pace and duration), with total high-intensity work time of 10-15 minutes per session.
  • Rest intervals begin at 1:3 work-to-rest ratio (e.g., 45-second run, 135-second recovery) and progress to 1:2 as fitness improves.

Type:

  • Track-based interval training using distances of 200-500 m at race-specific pace, complemented by hill sprints and tempo intervals to develop lactate tolerance specific to 400m racing demands.

Progess:

  • The program would progress over 8-12 weeks by manipulating the work-to-rest ratio and increasing the total volume, while maintaining the specific intensity required for 400 m performance.

HMS, BM EQ-Bank 268

Outline how the 'Frequency' component of the FITT principle differs for aerobic and anaerobic training programs.   (3 marks)

Show Answers Only

Sample Answer

  • Aerobic training allows 3-5 sessions weekly with consecutive training days because lower intensity enables faster recovery within 24 hours.
  • Anaerobic training requires 2-4 sessions weekly with non-consecutive days due to high muscle fatigue requiring 48-72 hours recovery between sessions.
  • Greater muscle damage from anaerobic training needs longer rest periods compared to aerobic training’s lower stress levels.
  • Beginners should use 2-3 sessions regardless of training type, while advanced athletes can use upper frequency ranges for both.

Show Worked Solution

Sample Answer

  • Aerobic training allows 3-5 sessions weekly with consecutive training days because lower intensity enables faster recovery within 24 hours.
  • Anaerobic training requires 2-4 sessions weekly with non-consecutive days due to high muscle fatigue requiring 48-72 hours recovery between sessions.
  • Greater muscle damage from anaerobic training needs longer rest periods compared to aerobic training’s lower stress levels.
  • Beginners should use 2-3 sessions regardless of training type, while advanced athletes can use upper frequency ranges for both.

HMS, BM EQ-Bank 267

Outline how the 'Time' component of the FITT principle should be applied when designing an anaerobic training program.   (3 marks)

Show Answers Only

Sample Answer

  • Work intervals of 10-30 seconds target ATP-PCr system development while 30-60 seconds target glycolytic (lactic acid) system training.
  • Total session time should be 15-30 minutes of actual high-intensity work, which is shorter than aerobic training due to greater fatigue.
  • Recovery intervals use work-to-rest ratios of 1:3 to 1:5 to allow energy recovery between efforts.
  • Progression involves increasing duration by 5-10% weekly while maintaining quality over quantity to prevent overtraining.

Show Worked Solution

Sample Answer

  • Work intervals of 10-30 seconds target ATP-PCr system development while 30-60 seconds target glycolytic (lactic acid) system training.
  • Total session time should be 15-30 minutes of actual high-intensity work, which is shorter than aerobic training due to greater fatigue.
  • Recovery intervals use work-to-rest ratios of 1:3 to 1:5 to allow energy recovery between efforts.
  • Progression involves increasing duration by 5-10% weekly while maintaining quality over quantity to prevent overtraining.

HMS, BM EQ-Bank 266

Describe how you would apply the 'Intensity' component of the FITT principle when designing an aerobic training program for a basketball player.   (3 marks)

Show Answers Only

Sample Answer

  • Basketball players require moderate intensity of 65-75% MHR to build aerobic base without excessive fatigue during training.
  • Higher intensity sessions at 75-85% MHR develop the player’s ability to maintain effort during repeated sprints and defensive plays.
  • Variable intensity training using basketball-specific drills allows players to experience game-like heart rates while developing aerobic fitness.
  • Intensity should match the player’s fitness level, starting lower for beginners and progressing higher as conditioning improves.
  • Monitoring intensity through heart rate zones ensures training targets the aerobic system effectively for basketball’s continuous movement demands.
  • Game simulation intensities of 70-85% MHR prepare players for the physical demands of actual competition.

Show Worked Solution

Sample Answer

  • Basketball players require moderate intensity of 65-75% MHR to build aerobic base without excessive fatigue during training.
  • Higher intensity sessions at 75-85% MHR develop the player’s ability to maintain effort during repeated sprints and defensive plays.
  • Variable intensity training using basketball-specific drills allows players to experience game-like heart rates while developing aerobic fitness.
  • Intensity should match the player’s fitness level, starting lower for beginners and progressing higher as conditioning improves.
  • Monitoring intensity through heart rate zones ensures training targets the aerobic system effectively for basketball’s continuous movement demands.
  • Game simulation intensities of 70-85% MHR prepare players for the physical demands of actual competition.

HMS, BM EQ-Bank 263 MC

A soccer midfielder is designing an aerobic training program during the off-season. According to the FITT principle, which intensity range would be most appropriate for the initial phase of training?

  1. 30-40% of maximum heart rate
  2. 50-60% of maximum heart rate
  3. 65-75% of maximum heart rate
  4. 85-95% of maximum heart rate
Show Answers Only

\(C\)

Show Worked Solution
  • C is correct: 65-75% of maximum heart rate represents an appropriate moderate intensity to develop aerobic base fitness in the initial off-season phase.

Other Options:

  • A is incorrect: 30-40% is too low for effective aerobic development and represents warm-up intensity.
  • B is incorrect: 50-60% is low-moderate intensity, generally used for active recovery or very early conditioning.
  • D is incorrect: 85-95% is too high for initial aerobic development and represents anaerobic training intensities.

PHYSICS, M1 EQ-Bank 2 MC

A cyclist rides 500 m to the west and then turns to travel 1200 m to the north. What is the cyclist's final displacement?

  1. 1700 m
  2. 1700 m bearing N 23\(^{\circ}\) W
  3. 1300 m bearing N 67\(^{\circ}\) W
  4. 1300 m bearing N 23\(^{\circ}\) W
Show Answers Only

\(D\)

Show Worked Solution

Using vector addition:

\(R=\sqrt{500^2+1200^2} = 1300\ \text{m}\)

\(\tan \theta\) \(=\dfrac{1200}{500}\)  
\(\theta\) \(=\tan^{-1}\left(\dfrac{1200}{500}\right)=67^{\circ}\)  

 
\(\Rightarrow D\)

Calculus, SPEC1 2024 VCAA 3

Let  \(f: R \backslash\{-1\} \rightarrow R, f(x)=\dfrac{(x-1)^2}{(x+1)^2}\)

The rule \(f(x)\) can be written in the form  \(f(x)=A+\dfrac{B}{x+1}+\dfrac{C}{(x+1)^2}\),  where \(A, B, C \in Z\).

  1. Show that  \(A=1, B=-4\)  and  \(C=4\).   (1 mark)

  2. The graph of \(f\) has one turning point.  
  3. Find the coordinates of this turning point.  (2 marks)

  4. Sketch the graph of  \(y=f(x)\)  on the set of axes below. Label the asymptotes with their equations and the axial intercepts with their coordinates.   (3 marks)
     

Show Answers Only

a.   \(\text{See worked solutions.}\)

b.   \(\text{Turning point at}\ (1,0)\)

c.   
       

Show Worked Solution

a.    \(\dfrac{(x-1)^2}{(x+1)^2}\) \(=\dfrac{x^2-2x+1}{x^2+2x+1}\)
    \(=\dfrac{x^2+2x+1}{x^2+2x+1}-\dfrac{4x}{x^2+2x+1}\)
    \(=1-\dfrac{4(x+1)}{(x+1)^2}+\dfrac{4}{(x+1)^2}\)
    \(=1-\dfrac{4}{(x+1)}+\dfrac{4}{(x+1)^2}\)

 

b.   \(f^{′}(x)=\dfrac{4}{(x+1)^2}-\dfrac{8}{(x+1)^3}\)

\(\text{SP’s when}\ \ f^{′}(x)=0:\)

\(\dfrac{4}{(x+1)^2}\) \(=\dfrac{8}{(x+1)^3}\)  
\(4(x+1)\) \(=8\)  
\(x\) \(=1\)  

 
\(f(1)=0\)

\(\therefore \text{Turning point at}\ (1,0)\)
 

c.    \(\text{Vertical asymptote at}\ \ x=-1\)

\(f(0)=\dfrac{(-1)^2}{(1)^2}=1\ \ \Rightarrow \ \ y\text{-intercept at}\ (0,1)\)

\(\text{As}\ x\rightarrow \infty, \ 1-\dfrac{4}{(x+1)}+\dfrac{4}{(x+1)^2} \rightarrow 1^{-} \)

\(\text{As}\ x\rightarrow -\infty, \ 1-\dfrac{4}{(x+1)}+\dfrac{4}{(x+1)^2} \rightarrow 1^{+} \)

\(\text{Horizontal asymptote at}\ \ y=1 \)

♦♦ Mean mark (c) 31%.
 
        

Proof, EXT2 P1 2024 SPEC1 2

Prove that if \(x\) is an odd integer then  \(2 x^2-3 x-7\)  is even.   (3 marks)

Show Answers Only

\(\text{See worked solutions}\)

Show Worked Solution

\(\text{Let}\ \ x=2k+1,\ \ k \in Z\ \ (x\ \text{is odd)}\)

\(2 x^2-3 x-7\) \(=2(2k+1)^2-3(k+1)-7\)  
  \(=2(4k^2+4k+1)-3(2k+1)-7\)  
  \(=8k^2+8k+2-6k-10\)  
  \(=8k^2+2k-8\)  
  \(=2(4k^2+k-4)\ \ \text{(which is even)}\)  

Proof, SPEC1 2024 VCAA 2

Prove that if \(x\) is an odd integer then  \(2 x^2-3 x-7\)  is even, using a direct proof.   (3 marks)

Show Answers Only

\(\text{See worked solutions}\)

Show Worked Solution

\(\text{Let}\ \ x=2k+1,\ \ k \in Z\ \ (x\ \text{is odd)}\)

\(2 x^2-3 x-7\) \(=2(2k+1)^2-3(k+1)-7\)  
  \(=2(4k^2+4k+1)-3(2k+1)-7\)  
  \(=8k^2+8k+2-6k-10\)  
  \(=8k^2+2k-8\)  
  \(=2(4k^2+k-4)\ \ \text{(which is even)}\)  

PHYSICS, M1 EQ-Bank 1 MC

A hiker starts at Camp A and walks 1.2 km east. She then turns to face north and walks a further 0.9 km to arrive at Camp B.

The magnitude of the hiker’s overall displacement \((d)\) can be determined using which of the following expressions?

  1. \(\tan d = \dfrac{0.9\ \text{km}}{1.2\ \text{km}}\)
  2. \(d = 1.2\ \text{km} + 0.9\ \text{km}\)
  3. \(d = (1.2)^2\ \text{km} + (0.9)^2\ \text{km}\)
  4. \(d^2 = (1.2)^2\ \text{km} + (0.9)^2\ \text{km}\)
Show Answers Only

\(D\)

Show Worked Solution
  • By Pythagorean theorem:

\(d^2 = (1.2)^2\ \text{km} + (0.9)^2\ \text{km}\)

\(\Rightarrow D\)

HMS, BM EQ-Bank 255

Compare how continuous aerobic training and High Intensity Interval Training (HIIT) would be applied differently for a triathlete versus a baseball pitcher. Provide specific examples from each sport.   (6 marks)

Show Answers Only

Sample Answer

Similarities:

  • Both athletes use continuous and HIIT training in their programs
  • Both need cardiovascular fitness for overall health
  • Both use training to support sport performance
  • Both adjust training based on competition schedules

Differences:

  • Training volume:
    • Triathlete: 2-4 hour continuous sessions at 70-80% MHR
    • Pitcher: 20-30 minute sessions for recovery only
  • Training emphasis:
    • Triathlete: 80% continuous aerobic, 20% HIIT
    • Pitcher: 20% continuous, 80% anaerobic intervals
  • HIIT application:
    • Triathlete: Race-pace intervals (10 x 400m swim at 85-90% MHR)
    • Pitcher: Pitch-specific bursts (10-second throws, 30-60 second rest)
  • Purpose of continuous training:
    • Triathlete: Builds endurance for 2+ hour events
    • Pitcher: Aids recovery between games
  • Recovery methods:
    • Triathlete: Low-intensity continuous work at 60-70% MHR
    • Pitcher: Complete rest to avoid fatigue
Show Worked Solution

Sample Answer

Similarities:

  • Both athletes use continuous and HIIT training in their programs
  • Both need cardiovascular fitness for overall health
  • Both use training to support sport performance
  • Both adjust training based on competition schedules

Differences:

  • Training volume:
    • Triathlete: 2-4 hour continuous sessions at 70-80% MHR
    • Pitcher: 20-30 minute sessions for recovery only
  • Training emphasis:
    • Triathlete: 80% continuous aerobic, 20% HIIT
    • Pitcher: 20% continuous, 80% anaerobic intervals
  • HIIT application:
    • Triathlete: Race-pace intervals (10 x 400m swim at 85-90% MHR)
    • Pitcher: Pitch-specific bursts (10-second throws, 30-60 second rest)
  • Purpose of continuous training:
    • Triathlete: Builds endurance for 2+ hour events
    • Pitcher: Aids recovery between games
  • Recovery methods:
    • Triathlete: Low-intensity continuous work at 60-70% MHR
    • Pitcher: Complete rest to avoid fatigue

HMS, BM EQ-Bank 253

Explain how continuous aerobic training and High Intensity Interval Training (HIIT) result in different physiological adaptations and performance outcomes for an 800 metre runner.  (5 marks)

Show Answers Only

Sample Answer

Continuous aerobic training for 800 m runner

  • Enhances cardiovascular endurance through adaptations such as increased stroke volume, cardiac output and mitochondrial density, supporting sustained effort throughout the race.
  • Develops aerobic energy system efficiency, allowing greater oxygen utilisation during the race, particularly in the first 400-500m when aerobic contribution is significant.

HIIT

  • Builds the runner’s anaerobic capacity and lactate threshold through higher intensity efforts, crucial for maintaining speed in the final 300m when lactic acid accumulates.
  • Strengthens lactate tolerance and clearance during high-intensity efforts, essential for 800m performance where the lactic acid system is heavily taxed.

Combined effects

  • Provides optimal training specificity for 800 m, which requires both aerobic foundation (approximately 60%) and anaerobic capacity (approximately 40%) for elite performance.
Show Worked Solution

Sample Answer

Continuous aerobic training for 800 m runner

  • Enhances cardiovascular endurance through adaptations such as increased stroke volume, cardiac output and mitochondrial density, supporting sustained effort throughout the race.
  • Develops aerobic energy system efficiency, allowing greater oxygen utilisation during the race, particularly in the first 400-500m when aerobic contribution is significant.

HIIT

  • Builds the runner’s anaerobic capacity and lactate threshold through higher intensity efforts, crucial for maintaining speed in the final 300m when lactic acid accumulates.
  • Strengthens lactate tolerance and clearance during high-intensity efforts, essential for 800m performance where the lactic acid system is heavily taxed.

Combined effects

  • Provides optimal training specificity for 800 m, which requires both aerobic foundation (approximately 60%) and anaerobic capacity (approximately 40%) for elite performance.

HMS, BM EQ-Bank 252

Describe how a soccer player would benefit from incorporating both continuous aerobic training and High Intensity Interval Training (HIIT) in their training program.  (4 marks)

Show Answers Only

Sample Answer

  • Continuous aerobic training improves the soccer player’s aerobic endurance. This enables them to maintain activity throughout a 90-minute match without excessive fatigue.
  • It enhances cardiovascular efficiency through increased stroke volume and cardiac output. More oxygen is delivered to working muscles during play.
  • HIIT improves the player’s ability to perform repeated high-intensity efforts. These efforts include sprinting to make tackles or create scoring opportunities.
  • HIIT develops both aerobic and anaerobic fitness simultaneously. As a result, recovery time between sprints during matches is improved.
  • Using both methods provides complete conditioning for soccer. The combination matches the varied intensity demands of actual games.
Show Worked Solution

Sample Answer

  • Continuous aerobic training improves the soccer player’s aerobic endurance. This enables them to maintain activity throughout a 90-minute match without excessive fatigue.
  • It enhances cardiovascular efficiency through increased stroke volume and cardiac output. More oxygen is delivered to working muscles during play.
  • HIIT improves the player’s ability to perform repeated high-intensity efforts. These efforts include sprinting to make tackles or create scoring opportunities.
  • HIIT develops both aerobic and anaerobic fitness simultaneously. As a result, recovery time between sprints during matches is improved.
  • Using both methods provides complete conditioning for soccer. The combination matches the varied intensity demands of actual games.

PHYSICS, M1 EQ-Bank 5 MC

A stone is tossed vertically upward from the edge of a canyon. It rises 9 meters above the rim before falling down to the canyon floor, which is 27 meters below the rim.

What is the total distance travelled by the stone?

  1. 36 m
  2. 42 m
  3. 45 m
  4. 48 m
Show Answers Only

\(C\)

Show Worked Solution
  • The distance the stone travels from the edge of the canyon up into the air and back down to the edge of the canyon is 9 m + 9 m = 18 m.
  • The distance travelled by the stone from the edge of the canyon to the bottom of the canyon is 27 m.
  • The total distance travelled by the stone is 18 m + 27 m = 45 m.

\(\Rightarrow C\)

EXAMCOPY MattTest Indenting

Consider the function `f`, where `f:\left(-\frac{1}{2}, \frac{1}{2}\right) \rightarrow R, f(x)=\log _e\left(x+\frac{1}{2}\right)-\log _e\left(\frac{1}{2}-x\right).`

Part of the graph of `y=f(x)` is shown below.
 

  1. State the range of `f(x)`.   (1 mark)

  2. Matt 1
    1. lskdjflsdkfj 
    2. sldkjfsldkfj 
    1. Something
    1. abc
    2. def
  5. slkflskdfj
    1. slkdfjlsdkfj
    2. sdlkjfsdlkfj
    1. lskjdflksd
    2. sdkjflsdkfj
  7. See the items below
    1. first
    2. second
    3. third
    4. fourth
    5. fifth
    1. Find `f^{\prime}(0)`.   (2 marks)

    2. State the maximal domain over which `f` is strictly increasing.   (1 mark)
    1. slkdjflskdfj 
    2. slkdfjlsdkfj
  10. lsksdlkfj
    1. sdflkjsd
    2. sdlfkj
    1. sdfsdlkf
  12. slkdfsldkfj
    1. slkdfjsldkfj
  13. Show that `f(x)+f(-x)=0`.   (1 mark)

  14. Find the domain and the rule of `f^{-1}`, the inverse of `f`.   (3 marks)
  15. Let `h` be the function `h:\left(-\frac{1}{2}, \frac{1}{2}\right) \rightarrow R, h(x)=\frac{1}{k}\left(\log _e\left(x+\frac{1}{2}\right)-\log _e\left(\frac{1}{2}-x\right)\right)`, where `k \in R` and `k>0`.
  1. The inverse function of `h` is defined by `h^{-1}: R \rightarrow R, h^{-1}(x)=\frac{e^{k x}-1}{2\left(e^{k x}+1\right)}`.
  2. The area of the regions bound by the functions `h` and `h^{-1}` can be expressed as a function, `A(k)`.
  3. The graph below shows the relevant area shaded.
     

  1. You are not required to find or define `A(k)`.
  1. Determine the range of values of `k` such that `A(k)>0`.   (1 mark)

  2. Explain why the domain of `A(k)` does not include all values of `k`.   (1 mark)

Show Answers Only
a.     `R`
b.i `f^{\prime}(0)=4`
b.ii `\left(-\frac{1}{2}, \frac{1}{2}\right)`
c. `0`
d. `x \in \mathbb{R}`
e.i  ` k > 4`
e.ii No bounded area for `0<k \leq 4`
Show Worked Solution

a.   `R` is the range.

b.i    `f(x)`
 `= \log _e\left(x+\frac{1}{2}\right)-\log _e\left(\frac{1}{2}-x\right)`  
  `f^{\prime}(x)` `= \frac{1}{x+\frac{1}{2}}+\frac{1}{\frac{1}{2}-x}`  
    `= \frac{2}{2 x+1}-\frac{2}{2 x-1}`  
  `f^{\prime}(0)` `= \frac{2}{2 xx 0+1}-\frac{2}{2 xx 0-1}`  
    `= 4`  

 
b.ii  `\left(-\frac{1}{2}, \frac{1}{2}\right)`

c.   `f(x)+f(-x)` `= \log _e\left(x+\frac{1}{2}\right)-\log _e\left(\frac{1}{2}-x\right)+\log _e\left(-x+\frac{1}{2}\right)-\log _e\left(\frac{1}{2}+x\right)`  
  `= 0`  

 
d.   To find the inverse swap `x` and `y` in `y=f(x)`

`x` `= \log _e\left(y+\frac{1}{2}\right)-\log _e\left(\frac{1}{2}-y\right)`  
`x` `= \log _e\left(\frac{y+\frac{1}{2}}{\frac{1}{2}-y}\right)`  
`e^x` `=\frac{y+\frac{1}{2}}{\frac{1}{2}-y}`  
`y+\frac{1}{2}` `= e^x\left(-y+\frac{1}{2}\right)`  
`y+\frac{1}{2}` `= -e^x y+\frac{e^x}{2}`  
`y\left(e^x+1\right)` `= \frac{e^x-1}{2}`  
`:.\ f^(-1)(x)` `= \frac{e^x-1}{2(e^x + 1)}`  

 
  `:.`  Domain: `x \in \mathbb{R}`
  

e.i   The vertical dilation factor of  `f(x)` is  `1/k`

For `A(k)>=0` , `h^{\prime}(0)<1`

`\frac{1}{k}(4)<1`   [Using CAS]

`:.\  k > 4`


♦♦♦♦ Mean mark (e.i) 10%.
MARKER’S COMMENT: Incorrect responses included `k>0` and `4<k<33`.

e.ii  When `h \geq h^{-1}` for  `x>0` (or `h \leq h^{-1}` for  `x<0`) there is no bounded area.

`:.`  There will be no bounded area for `0<k \leq 4`.


♦♦♦♦ Mean mark (e.ii) 10%.

PHYSICS, M1 EQ-Bank 12

A skydiver jumps from a stationary aircraft and yells as soon as she starts falling. Four seconds later, while still falling, she hears the echo of her shout from the ground below.

  1. Calculate how far the skydiver has fallen after 4 seconds.   (1 mark)
  2. What is the total distance the sound of their shout travelled in 4 seconds? (Hint: the speed of sound is 340 m/s)   (1 mark)
  3. Determine the altitude from which the skydiver jumped if this scenario occurred.   (2 marks)
Show Answers Only

a.    \(78.4\ \text{m}\)

b.    \(1360\ \text{m}\)

c.    \(719.2\ \text{m}\)

Show Worked Solution

a.    \(u=0,\ \ t=4,\ \ a=9.8\)

Using the formula  \(s=ut + \dfrac{1}{2}at^2\)

\(s = (0 \times 4) + (\dfrac{1}{2} \times 9.8 \times 4^2) = 78.4\ \text{m}\)
 

b.    \(d=vt = 340 \times 4 = 1360\ \text{m}\)
 

c.    Let initial height of the skydiver be \(h\ \text{m}\).

  • When the skydiver hears the echo of their scream they would be at a height of \((h-78.4)\ \text{m}\).
  • As the sound of the scream travelled both of those distances:
\(h+h-78.4\) \(=1360\)  
\(2h\) \(=1438.4\)  
\(h\) \(=719.2\ \text{m}\)  

PHYSICS, M1 EQ-Bank 2-3 MC

Using the velocity-time graph below
 

 
Part 1

Determine the magnitude of the displacement:

  1. \(32\ \text{m}\)
  2. \(40\ \text{m}\)
  3. \(48\ \text{m}\)
  4. \(64\ \text{m}\)

 
Part 2

Determine the average acceleration between 4 and 8 seconds:

  1. \(-4\ \text{ms}^{-2}\)
  2. \(-2\ \text{ms}^{-2}\)
  3. \(-1\ \text{ms}^{-2}\)
  4. \(2\ \text{ms}^{-2}\)
Show Answers Only

Part 1: \(C\)

Part 2: \(B\)

Show Worked Solution

Part 1

  • The displacement for the motion can be calculated by finding the area under the velocity time graph. 
  • By splitting the graph up into the square and triangle, the area under the curve is:

\(\text{Area}\ =(4 \times 8) + (\dfrac{1}{2} \times 4 \times 8) = 32 +16 = 48\ \text{m}\)

\(\Rightarrow C\)
 

Part 2

  • Average acceleration between t=4 and t=8 is:

\(a= \dfrac{\Delta v}{\Delta t} = \dfrac{0-8}{8-4} = -2\ \text{ms}^{-2}\)

\(\Rightarrow B\)

PHYSICS, M1 EQ-Bank 1 MC

An airplane, initially moving at 15 m/s, accelerates for 12 seconds until it reaches a take-off speed of 75 m/s. What is its average acceleration?

  1. \(3\ \text{ms}^{-2}\)
  2. \(4\ \text{ms}^{-2}\)
  3. \(5\ \text{ms}^{-2}\)
  4. \(6\ \text{ms}^{-2}\)
Show Answers Only

\(C\)

Show Worked Solution

Average acceleration:

\(\dfrac{\Delta v}{\Delta t} = \dfrac{75-15}{12} = 5\ \text{ms}^{-2}\)

\(\Rightarrow C\)

HMS, BM EQ-Bank 250

Explain how different training methods could be modified to maintain fitness during a 6-week injury rehabilitation period for a soccer player with a knee injury.   (6 marks)

Show Answers Only

Sample Answer

  • Initially, non-weight bearing aerobic training replaces running. Upper body cycling is used because it maintains cardiovascular fitness without knee stress. Sessions include 3 x 10 minutes at 65-75% max HR. As a result, aerobic fitness continues developing while the knee heals.
  • Deep water running begins in weeks 3-4. This works because water buoyancy supports body weight during running movements. Interval sessions include 8 x 2 minutes at 80-85% max HR. Consequently, sport-specific fitness is maintained without impact stress.
  • Stationary cycling incorporates modified HIIT as recovery progresses. The reason for this is cycling allows controlled knee movement within safe ranges. Sessions include 6 x 1 minute at 85% max HR with recovery. This leads to maintained anaerobic fitness despite injury limitations.
  • Modified field training returns in the final week. Straight-line running comes before direction changes because this minimises rotational knee stress. Ball work combines with 4-minute efforts at 80-90% max HR. Therefore, the player regains match fitness through careful progression.
Show Worked Solution

Sample Answer

  • Initially, non-weight bearing aerobic training replaces running. Upper body cycling is used because it maintains cardiovascular fitness without knee stress. Sessions include 3 x 10 minutes at 65-75% max HR. As a result, aerobic fitness continues developing while the knee heals.
  • Deep water running begins in weeks 3-4. This works because water buoyancy supports body weight during running movements. Interval sessions include 8 x 2 minutes at 80-85% max HR. Consequently, sport-specific fitness is maintained without impact stress.
  • Stationary cycling incorporates modified HIIT as recovery progresses. The reason for this is cycling allows controlled knee movement within safe ranges. Sessions include 6 x 1 minute at 85% max HR with recovery. This leads to maintained anaerobic fitness despite injury limitations.
  • Modified field training returns in the final week. Straight-line running comes before direction changes because this minimises rotational knee stress. Ball work combines with 4-minute efforts at 80-90% max HR. Therefore, the player regains match fitness through careful progression.

HMS, BM EQ-Bank 248

Describe how aerobic and anaerobic training methods can be combined effectively in a basketball training session.  (6 marks)

Show Answers Only

Sample Answer

Warm-up

  • Begins with continuous aerobic activity for 10 minutes at 60-65% max HR.
  • Uses structured court drills including dribbling, passing and shooting.
  • Gradually increases intensity to prepare cardiovascular and muscular systems.

Main session

  • Alternates between different intensity levels to combine training methods effectively.
  • Example: 4 x 5 minute periods switching between full-court weave drills at aerobic intensity (70-75% max HR) and defensive sliding at anaerobic intensity (85-90% max HR).
  • This pattern mimics game demands of continuous movement with explosive bursts.

Small-sided games (3v3)

  • Integrate both energy systems through 4 x 4 minute competitive games.
  • Include 1-minute active recovery walking between games.
    High intensity naturally occurs through competition and quick transitions.
  • Develops decision-making while training both energy systems simultaneously.

Final round

  • Focuses on anaerobic power through sprint/dribble combinations.
  • Perform 6 x 20 second full-court efforts at maximum intensity.
  • Allow 40 seconds passive recovery between efforts.

Cool-down

  • Returns to aerobic intensity (60% max HR) with free-throw shooting drills.
  • Continue for 5-10 minutes to remove waste products and aid recovery.
Show Worked Solution

Sample Answer

Warm-up

  • Begins with continuous aerobic activity for 10 minutes at 60-65% max HR.
  • Uses structured court drills including dribbling, passing and shooting.
  • Gradually increases intensity to prepare cardiovascular and muscular systems.

Main session

  • Alternates between different intensity levels to combine training methods effectively.
  • Example: 4 x 5 minute periods switching between full-court weave drills at aerobic intensity (70-75% max HR) and defensive sliding at anaerobic intensity (85-90% max HR).
  • This pattern mimics game demands of continuous movement with explosive bursts.

Small-sided games (3v3)

  • Integrate both energy systems through 4 x 4 minute competitive games.
  • Include 1-minute active recovery walking between games.
    High intensity naturally occurs through competition and quick transitions.
  • Develops decision-making while training both energy systems simultaneously.

Final round

  • Focuses on anaerobic power through sprint/dribble combinations.
  • Perform 6 x 20 second full-court efforts at maximum intensity.
  • Allow 40 seconds passive recovery between efforts.

Cool-down

  • Returns to aerobic intensity (60% max HR) with free-throw shooting drills.
  • Continue for 5-10 minutes to remove waste products and aid recovery.

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)

Show Answers Only

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.