Band 5

HMS, HIC EQ-Bank 039 MC

Which statement most accurately reflects how youth engagement with global events has evolved over generations?

Contemporary youth are less politically engaged than previous generations.
Global events historically affected youth through direct participation (like military service), while today's impact is primarily through media consumption.
Today's youth are the first generation to be significantly influenced by international events.
Social media has eliminated geographical boundaries but decreased young people's awareness of global issues.

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$B$

Show Worked Solution

The correct answer is B. Previous generations were affected by direct participation in global events (like military service in world wars), while today’s youth experience global events primarily through media and technology.

Other options:

Answer A is incorrect as evidence suggests contemporary youth remain politically engaged but through different channels.
Answer C ignores the historical impact of global events on previous generations.
Answer D contradicts evidence showing social media has increased awareness of global issues.

$\Rightarrow B$

HMS, HIC EQ-Bank 038 MC

The developmental stage of adolescence in current and previous generations is best characterised by:

Identical physical changes but completely different social expectations.
Consistent physical maturation processes with varying sociocultural contexts affecting identity development.
Faster physical development in contemporary youth but slower emotional maturation.
Reduced importance of peer relationships with increased family influence.

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$B$

Show Worked Solution

The correct answer is B. While physical maturation processes (puberty, brain development) remain biologically consistent across generations, the sociocultural contexts in which young people develop their identities have changed significantly.

Other options:

Answer A is incorrect because social expectations have evolved but aren’t “completely different.”
Answer C lacks evidence for faster physical development.
Answer D contradicts evidence showing peer relationships remain highly influential for young people.

$\Rightarrow B$

HMS, HIC EQ-Bank 048

Discuss how family influence can both positively and negatively affect the mental health of young people. (5 marks)

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*Keyword – Discuss: Identify issues and provide points for and/or against. Note the PEEL method is used below and notably applied separately to both the “for” and “against” case.

[P] Family influence can positively affect young people’s mental health through supportive relationships.
[E] Close family bonds provide a protective factor that enhances resilience during stressful periods.
[E] For example, families that openly communicate about mental health issues normalise help-seeking which makes young people more likely to access support when needed.
[L] In this way, young people who feel connected to their families report better mental health outcomes and reduced rates of depression and anxiety.
[P] However, family influence can also negatively impact young people’s mental health in various ways.
[E] Dysfunctional family dynamics involving abuse or neglect can become significant risk factors for developing mental health conditions.
[E] For instance, children who grow up in homes with domestic violence may experience trauma that is not addressed and affects their long-term psychological wellbeing.
[L] Through these unfortunate circumstances, young people can both develop mental health issues and an inability to seek appropriate help.

Show Worked Solution

*Keyword – Discuss: Identify issues and provide points for and/or against. Note the PEEL method is used below and notably applied separately to both the “for” and “against” case.

[P] Family influence can positively affect young people’s mental health through supportive relationships.
[E] Close family bonds provide a protective factor that enhances resilience during stressful periods.
[E] For example, families that openly communicate about mental health issues normalise help-seeking which makes young people more likely to access support when needed.
[L] In this way, young people who feel connected to their families report better mental health outcomes and reduced rates of depression and anxiety.
[P] However, family influence can also negatively impact young people’s mental health in various ways.
[E] Dysfunctional family dynamics involving abuse or neglect can become significant risk factors for developing mental health conditions.
[E] For instance, children who grow up in homes with domestic violence may experience trauma that is not addressed and affects their long-term psychological wellbeing.
[L] Through these unfortunate circumstances, young people can both develop mental health issues and an inability to seek appropriate help.

HMS, BM EQ-Bank 865

Analyse the interrelationship between the structure and function of the different types of blood vessels in the cardiovascular system. (8 marks)

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Sample Answer

Arteries carry blood away from the heart under high pressure and have thick walls with three layers containing elastic tissue and smooth muscle to withstand this pressure.
The elastic properties of arteries allow them to expand when receiving blood from the heart and recoil afterward, helping maintain blood pressure and creating continuous blood flow.
Arterioles regulate blood flow to tissues through constriction and dilation of their smooth muscle layer in response to local metabolic needs.
Capillaries have walls consisting of only a single layer of endothelial cells that allow for efficient diffusion of oxygen, nutrients, and waste products between blood and tissues.
The extensive branching of capillaries creates a large surface area for exchange, while their narrow diameter slows blood flow, providing adequate time for diffusion.
Different tissues have varying capillary density based on their metabolic demands, with active tissues like muscles having more capillaries than less active tissues.
Veins return blood to the heart under low pressure and have thinner walls and larger lumens than arteries, allowing them to serve as blood reservoirs.
Veins contain one-way valves that prevent backflow of blood, especially in the lower extremities where blood must move against gravity.

Show Worked Solution

Sample Answer

Arteries carry blood away from the heart under high pressure and have thick walls with three layers containing elastic tissue and smooth muscle to withstand this pressure.
The elastic properties of arteries allow them to expand when receiving blood from the heart and recoil afterward, helping maintain blood pressure and creating continuous blood flow.
Arterioles regulate blood flow to tissues through constriction and dilation of their smooth muscle layer in response to local metabolic needs.
Capillaries have walls consisting of only a single layer of endothelial cells that allow for efficient diffusion of oxygen, nutrients, and waste products between blood and tissues.
The extensive branching of capillaries creates a large surface area for exchange, while their narrow diameter slows blood flow, providing adequate time for diffusion.
Different tissues have varying capillary density based on their metabolic demands, with active tissues like muscles having more capillaries than less active tissues.
Veins return blood to the heart under low pressure and have thinner walls and larger lumens than arteries, allowing them to serve as blood reservoirs.
Veins contain one-way valves that prevent backflow of blood, especially in the lower extremities where blood must move against gravity.

HMS, BM EQ-Bank 859

Discuss how an understanding of biomechanics can be applied to increase movement efficiency and performance in wheelchair racing. (8 marks)

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Sample Answer

Wheelchair athletes develop upper body strength to apply maximum force to the wheel rims, creating forward momentum and speed with each push.
The angle at which athletes push on the wheel rim matters – pushing the rim in a direction that maximises forward movement rather than wasting energy pushing downward improves efficiency.
The position of the seat in relation to the wheels affects how effectively the athlete can push. Finding the right position based on the athlete’s body size and arm length helps them generate more power with less effort.
Streamlined body positions reduce air resistance, allowing racers to maintain speed more easily, similar to how cyclists use aerodynamic positions.
Developing a smooth pushing rhythm allows racers to maintain momentum between pushes, rather than slowing down significantly during the recovery phase.
The angle of the wheels (called camber) can be adjusted to improve stability and make it easier for the athlete to reach the rims effectively during pushing.
Lightweight materials like carbon fibre reduce the energy needed to move the wheelchair, allowing more of the athlete’s power to translate into speed.
Specialised gloves improve grip on the rims, allowing the athlete to transfer force more effectively without wasting energy trying to maintain contact with the wheel.

Show Worked Solution

Sample Answer

Wheelchair athletes develop upper body strength to apply maximum force to the wheel rims, creating forward momentum and speed with each push.
The angle at which athletes push on the wheel rim matters – pushing the rim in a direction that maximises forward movement rather than wasting energy pushing downward improves efficiency.
The position of the seat in relation to the wheels affects how effectively the athlete can push. Finding the right position based on the athlete’s body size and arm length helps them generate more power with less effort.
Streamlined body positions reduce air resistance, allowing racers to maintain speed more easily, similar to how cyclists use aerodynamic positions.
Developing a smooth pushing rhythm allows racers to maintain momentum between pushes, rather than slowing down significantly during the recovery phase.
The angle of the wheels (called camber) can be adjusted to improve stability and make it easier for the athlete to reach the rims effectively during pushing.
Lightweight materials like carbon fibre reduce the energy needed to move the wheelchair, allowing more of the athlete’s power to translate into speed.
Specialised gloves improve grip on the rims, allowing the athlete to transfer force more effectively without wasting energy trying to maintain contact with the wheel.

HMS, HIC EQ-Bank 046

Compare and contrast how gender might influence perspectives on health, and explain why these differences exist. (5 marks)

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Different perspectives:

Gender significantly influences health perspectives, with research showing distinct patterns between genders.
Men often conceptualise health primarily through physical capability and absence of illness that would prevent work or physical activities. Symptoms are often addressed only when they interfere with daily functioning.
In contrast, women’s health perspectives, tend to be more multidimensional, encompassing physical, emotional, and relational aspects.
Women are more likely to include mental wellbeing, stress management, and prevention in their health definitions.

Why differences exist:

These different perspectives stem from societal pressures where men are less likely to show vulnerability while women are encouraged to be attuned to both their own and others’ wellbeing.
Additionally, women’s reproductive health necessitates earlier and more regular healthcare engagement.
The implications of these differing perspectives are significant, contributing to disparities in healthcare utilisation. Men are less likely to seek health treatment which contributes to higher mortality and morbidity rates compared to women.

Show Worked Solution

Different perspectives:

Gender significantly influences health perspectives, with research showing distinct patterns between genders.
Men often conceptualise health primarily through physical capability and absence of illness that would prevent work or physical activities. Symptoms are often addressed only when they interfere with daily functioning.
In contrast, women’s health perspectives, tend to be more multidimensional and are more likely to include mental wellbeing, stress management, and prevention in their health definitions.

Why differences exist:

These different perspectives stem from societal pressures where men are less likely to show vulnerability while women are encouraged to be attuned to both their own and others’ wellbeing.
Additionally, women’s reproductive health necessitates earlier and more regular healthcare engagement.
The implications of these differing perspectives are significant, contributing to disparities in healthcare utilisation. Men are less likely to seek health treatment which contributes to higher mortality and morbidity rates compared to women.

HMS, BM EQ-Bank 857

Analyse how biomechanical principles related to efficient force absorption can be applied to reduce injury risk in sport. Provide specific examples in your response. (8 marks)

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Sample Answer

Extending the time and distance over which force is absorbed (such as bending the knees when landing from a jump) reduces peak impact forces on joints, particularly beneficial for preventing ACL injuries in basketball players.
Using larger muscle groups to absorb impact forces, as seen when rugby players engage their quadriceps and pectorals during tackles, distributes force over a greater surface area, reducing pressure on any single point and preventing contusions.
Gradually decelerating objects when catching (rather than stopping them suddenly) extends the stopping time, reducing the force experienced by smaller structures like finger joints and wrist bones, as practiced in cricket or baseball catching techniques.
Creating a wider base of support during contact activities distributes ground reaction forces across a larger area, enhancing stability and preventing falls that could lead to acute injuries, exemplified by defensive stances in basketball or rugby.
Implementing the biomechanical principle of “giving” with impact when receiving force, such as moving the hands backward when catching a fast ball, extends deceleration time and significantly reduces impact forces on wrist joints.
Using protective equipment designed with force-absorbing materials increases the distance over which impact energy is dissipated, as demonstrated by cricket pads or hockey shin guards that transform impact energy into material deformation.
Maintaining proper body alignment during movements ensures forces are directed through appropriate load-bearing structures, as seen in proper squat technique where force is distributed through the legs rather than concentrated on the spine.
Developing sport-specific techniques that optimise the body’s natural shock absorption mechanisms, such as the forefoot strike pattern many elite runners use, can minimise impact forces and reduce the risk of stress fractures and joint injuries.

Show Worked Solution

Sample Answer

Extending the time and distance over which force is absorbed (such as bending the knees when landing from a jump) reduces peak impact forces on joints, particularly beneficial for preventing ACL injuries in basketball players.
Using larger muscle groups to absorb impact forces, as seen when rugby players engage their quadriceps and pectorals during tackles, distributes force over a greater surface area, reducing pressure on any single point and preventing contusions.
Gradually decelerating objects when catching (rather than stopping them suddenly) extends the stopping time, reducing the force experienced by smaller structures like finger joints and wrist bones, as practiced in cricket or baseball catching techniques.
Creating a wider base of support during contact activities distributes ground reaction forces across a larger area, enhancing stability and preventing falls that could lead to acute injuries, exemplified by defensive stances in basketball or rugby.
Implementing the biomechanical principle of “giving” with impact when receiving force, such as moving the hands backward when catching a fast ball, extends deceleration time and significantly reduces impact forces on wrist joints.
Using protective equipment designed with force-absorbing materials increases the distance over which impact energy is dissipated, as demonstrated by cricket pads or hockey shin guards that transform impact energy into material deformation.
Maintaining proper body alignment during movements ensures forces are directed through appropriate load-bearing structures, as seen in proper squat technique where force is distributed through the legs rather than concentrated on the spine.
Developing sport-specific techniques that optimise the body’s natural shock absorption mechanisms, such as the forefoot strike pattern many elite runners use, can minimise impact forces and reduce the risk of stress fractures and joint injuries.

HMS, BM EQ-Bank 854 MC

For a sprinter with a prosthetic lower limb, which biomechanical principle most directly contributes to movement efficiency?

Using upper leg muscles to apply force to the prosthetic limb
Generating rotational force through the prosthetic joint
Decreasing the weight of the prosthetic to reduce momentum
Widening the stance to create a more stable base of support

Show Answers Only

$A$

Show Worked Solution

Consider Option A:

Athletes with prosthetic lower limbs rely on their upper leg muscles (quadriceps and hamstrings) to generate force and apply it to the prosthetic device, which then transfers this force to produce forward movement.

Other Options:

B is incorrect: Prosthetic limbs typically don’t focus on rotational force generation as their primary biomechanical function.
C is incorrect: Decreasing weight alone doesn’t increase movement efficiency; the application of force is more important for generating propulsion.
D is incorrect: While stability is important, a widened stance would actually reduce forward propulsion efficiency for a sprinter.

$\Rightarrow A$

HMS, HIC EQ-Bank 043

Discuss how the evolution of health definitions has affected our understanding of whether a person with a chronic condition can be considered "healthy." (4 marks)

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*Keyword “Discuss”: Identify issues and provide points for and/or against.

The evolution of health definitions has significantly changed our understanding of whether individuals with chronic conditions can be considered healthy.
Prior to World War II, health was narrowly defined as the absence of disease or physical illness, which automatically categorised anyone with a chronic condition as “unhealthy”.
This perspective changed in 1948 when WHO recognised the physical, mental, and social dimensions of health, although it still emphasised “complete” wellbeing.
The WHO’s 1986 clarification marked a crucial shift by redefining health as “a resource for everyday life” rather than an absolute state. This definition acknowledges that health depends on an individual’s personal circumstances and capacities.
This more inclusive definition recognises that a person managing conditions like diabetes or anxiety can still be considered healthy if they maintain good quality of life, meaningful social connections, and the ability to engage in daily activities according to their own capabilities.

Show Worked Solution

*Keyword “Discuss”: Identify issues and provide points for and/or against.

The evolution of health definitions has significantly changed our understanding of whether individuals with chronic conditions can be considered healthy.
Prior to World War II, health was narrowly defined as the absence of disease or physical illness, which automatically categorised anyone with a chronic condition as “unhealthy”.
This perspective changed in 1948 when WHO recognised the physical, mental, and social dimensions of health, although it still emphasised “complete” wellbeing.
The WHO’s 1986 clarification marked a crucial shift by redefining health as “a resource for everyday life” rather than an absolute state. This definition acknowledges that health depends on an individual’s personal circumstances and capacities.
This more inclusive definition recognises that a person managing conditions like diabetes or anxiety can still be considered healthy if they maintain good quality of life, meaningful social connections, and the ability to engage in daily activities according to their own capabilities.

HMS, BM EQ-Bank 851

Analyse how an understanding of biomechanical principles related to force absorption can reduce injury risk during movement activities. Provide specific examples. (8 marks)

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Sample Answer

Force absorption through proper landing technique, such as bending the knees when landing from a jump in basketball, extends the stopping distance and time, reducing the peak force experienced by joints and tissues.
Creating a wider base of support, as seen in rugby players widening their stance before contact, distributes impact forces over a larger area and increases stability, reducing the risk of falling and sustaining contact injuries.
Gradual deceleration when catching objects (“giving” with the hands) in sports like cricket or water polo extends the time of impact, reducing the peak force experienced by the hands and arms.
Using protective equipment such as shin guards in hockey or cricket pads absorbs and distributes impact forces over larger surface areas, protecting vulnerable body parts from direct impacts.
Absorbing tackles or impacts with larger muscle groups (like quadriceps or pectorals) rather than smaller joints or bones reduces pressure by distributing force over a greater surface area.
The heel-to-toe rolling action in walking represents effective force absorption as it transforms the initial impact into forward momentum through a controlled sequence of foot contacts.
Proper footwear with cushioning materials absorbs ground reaction forces during walking or running activities, preventing these forces from directly impacting joints.
Maintaining correct posture during lifting activities ensures forces are directed through appropriate load-bearing structures (like the leg muscles) rather than vulnerable areas (like the lumbar spine).

Show Worked Solution

Sample Answer

Force absorption through proper landing technique, such as bending the knees when landing from a jump in basketball, extends the stopping distance and time, reducing the peak force experienced by joints and tissues.
Creating a wider base of support, as seen in rugby players widening their stance before contact, distributes impact forces over a larger area and increases stability, reducing the risk of falling and sustaining contact injuries.
Gradual deceleration when catching objects (“giving” with the hands) in sports like cricket or water polo extends the time of impact, reducing the peak force experienced by the hands and arms.
Using protective equipment such as shin guards in hockey or cricket pads absorbs and distributes impact forces over larger surface areas, protecting vulnerable body parts from direct impacts.
Absorbing tackles or impacts with larger muscle groups (like quadriceps or pectorals) rather than smaller joints or bones reduces pressure by distributing force over a greater surface area.
The heel-to-toe rolling action in walking represents effective force absorption as it transforms the initial impact into forward momentum through a controlled sequence of foot contacts.
Proper footwear with cushioning materials absorbs ground reaction forces during walking or running activities, preventing these forces from directly impacting joints.
Maintaining correct posture during lifting activities ensures forces are directed through appropriate load-bearing structures (like the leg muscles) rather than vulnerable areas (like the lumbar spine).

HMS, BM EQ-Bank 847 MC

When lifting a heavy box from the floor, which application of biomechanical principles would MOST effectively reduce the risk of lower back injury?

Keeping the knees straight and bending at the waist
Holding the box far from the body to distribute weight evenly
Positioning the feet close together for better balance
Keeping the weight close to the body and bending at the knees

Show Answers Only

$D$

Show Worked Solution

Consider Option D:

Keeping the weight close to the body reduces the lever arm and torque on the spine.
Additionally, bending at the knees engages the stronger leg muscles rather than putting strain on the back muscles and spine.

Other Options:

A is incorrect: Keeping knees straight and bending at the waist places significant stress on the lower back and increases risk of injury.
B is incorrect: Holding a box far from the body increases the lever arm, creating greater torque on the spine and increasing injury risk.
C is incorrect: Positioning feet close together decreases stability during lifting, increasing the chance of losing balance and causing injury.

$\Rightarrow D$

HMS, BM EQ-Bank 843

Analyse how biomechanical principles related to balance and stability are applied to enhance safety and movement efficiency in gymnastics floor routines. (6 marks)

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Sample Answer

Gymnasts manipulate their centre of gravity relative to their base of support to maintain balance during various movements.
During a handstand, the gymnast must position their centre of gravity directly above their base of support (hands) by engaging shoulder, arm, and core muscles to maintain alignment.
To prevent falls, gymnasts widen their base of support during skill transitions by positioning hands/feet further apart, lowering their centre of gravity closer to the floor.
When executing a forward roll, gymnasts tuck their chin to chest, contracting neck muscles and flexing the cervical spine to protect the neck and maintain a smooth roll along the spine.
During landings from tumbling passes, gymnasts bend at the knee, hip, and ankle joints to absorb impact forces gradually rather than suddenly.
This controlled absorption of force through muscular eccentric contraction of the quadriceps and gluteal muscles reduces stress on joints and lowers injury risk.
For dynamic movements, gymnasts shift their line of gravity to the edge of their base of support, creating controlled instability that facilitates efficient movement initiation.
In spinning elements like pirouettes, gymnasts contract core muscles to stabilise their torso while maintaining a narrow base of support around a vertical axis.
Efficient weight transfer during complex sequences requires precise control of the centre of gravity through coordinated muscular contractions and joint movements.

Show Worked Solution

Sample Answer

Gymnasts manipulate their centre of gravity relative to their base of support to maintain balance during various movements.
During a handstand, the gymnast must position their centre of gravity directly above their base of support (hands) by engaging shoulder, arm, and core muscles to maintain alignment.
To prevent falls, gymnasts widen their base of support during skill transitions by positioning hands/feet further apart, lowering their centre of gravity closer to the floor.
When executing a forward roll, gymnasts tuck their chin to chest, contracting neck muscles and flexing the cervical spine to protect the neck and maintain a smooth roll along the spine.
During landings from tumbling passes, gymnasts bend at the knee, hip, and ankle joints to absorb impact forces gradually rather than suddenly.
This controlled absorption of force through muscular eccentric contraction of the quadriceps and gluteal muscles reduces stress on joints and lowers injury risk.
For dynamic movements, gymnasts shift their line of gravity to the edge of their base of support, creating controlled instability that facilitates efficient movement initiation.
In spinning elements like pirouettes, gymnasts contract core muscles to stabilise their torso while maintaining a narrow base of support around a vertical axis.
Efficient weight transfer during complex sequences requires precise control of the centre of gravity through coordinated muscular contractions and joint movements.

HMS, BM EQ-Bank 841 MC

The image below shows a tennis player preparing to return a serve.

Which biomechanical principle is this player primarily using to optimise stability?

Lowering the centre of gravity and widening the base of support
Narrowing the base of support to increase agility
Raising the centre of gravity to improve reaction time
Increasing the line of gravity outside the base of support

Show Answers Only

$A$

Show Worked Solution

Consider Option A:

The tennis player has lowered their centre of gravity by bending their knees and has widened their stance (base of support), which increases stability when preparing to receive a fast serve.

Other Options:

B is incorrect: Narrowing the base of support would decrease stability, making it harder to maintain balance when receiving a powerful shot.
C is incorrect: Raising the center of gravity would decrease stability and make the player more likely to be off-balance.
D is incorrect: Moving the line of gravity outside the base of support would create instability and potentially cause the player to fall.

$\Rightarrow A$

HMS, HIC EQ-Bank 038

Choose and analyse a specific project that applies social justice principles to address health inequities in rural communities. (6 marks)

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*Solution is structured using the PEEL method; [P] Identify the point, [E] expand on the point with a link to question asked, [Ev] apply evidence/examples, [L] linking sentence back to question.

Project: Hear Our Heart Ear Bus Project

[P] The Hear Our Heart Ear Bus Project applies social justice principles by addressing the health inequity of hearing services in rural communities through a mobile screening clinic for children.
[E] This initiative applies the principle of access by bringing specialised healthcare directly to underserved communities using a mobile bus service. This solves the issue of distance from services that typically prevents rural children from receiving hearing assessments.
[E] The project demonstrates the principle of equity by allocating resources to areas of highest need. This ensures that children in remote locations, where hearing health is well below the national average, receive comparable care to people living in the city.
[E] The project’s collaborative structure involving health specialists, educators, and community members demonstrates the participation principle, creating sustainable outcomes through local empowerment.
[Ev] Research demonstrates the initiative’s effectiveness in addressing educational disadvantage. Improved hearing detection enables earlier intervention, preventing speech delays, literacy challenges, and classroom disengagement.
[L] In this way, the Hear Our Heart Ear Bus Project employs various social justice principles to improve the health outcomes for a clearly disadvantaged group of ATSI children in rural communities.

Show Worked Solution

*Solution is structured using the PEEL method; [P] Identify the point, [E] expand on the point with a link to question asked, [Ev] apply evidence/examples, [L] linking sentence back to question.

Project: Hear Our Heart Ear Bus Project

[P] The Hear Our Heart Ear Bus Project applies social justice principles by addressing the health inequity of hearing services in rural communities through a mobile screening clinic for children.
[E] This initiative applies the principle of access by bringing specialised healthcare directly to underserved communities using a mobile bus service. This solves the issue of distance from services that typically prevents rural children from receiving hearing assessments.
[E] The project demonstrates the principle of equity by allocating resources to areas of highest need. This ensures that children in remote locations, where hearing health is well below the national average, receive comparable care to people living in the city.
[E] The project’s collaborative structure involving health specialists, educators, and community members demonstrates the participation principle, creating sustainable outcomes through local empowerment.
[Ev] Research demonstrates the initiative’s effectiveness in addressing educational disadvantage. Improved hearing detection enables earlier intervention, preventing speech delays, literacy challenges, and classroom disengagement.
[L] In this way, the Hear Our Heart Ear Bus Project employs various social justice principles to improve the health outcomes for a clearly disadvantaged group of ATSI children in rural communities.

v1 Financial Maths, STD2 F1 2024 HSC 8 MC

A bill for servicing a car is made up of:

- $275 for parts, which includes 10% GST
- $120 for labour, excluding GST.

The mechanic needs to add 10% GST onto the labour charge.

How much GST does the customer pay in total?

$27.50
$30.00
$35.50
$37.00

Show Answers Only

$D$

Show Worked Solution

$\text{Let } X = \text{ parts cost ex-GST}$

	$X + X \times 0.1$	$= 275$
	$1.1X$	$= 275$
	$X$	$= 250$

$\text{Total GST} = 0.1(250 + 120) = \$37.00$

$\Rightarrow D$

♦ Mean mark 43%.

HMS, HIC EQ-Bank 037

Explain how the Royal Flying Doctor Service (RFDS) addresses multiple social justice principles to improve health outcomes in rural and remote communities. (5 marks)

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*Solution is structured using the PEEL method; [P] Identify the point, [E] expand on the point with a link to question asked, [Ev] apply evidence focusing on cause/effect link, [L] linking sentence back to question.

Model answer (addressing each “PEAR” principle):

[P] The Royal Flying Doctor Service (RFDS) uses multiple social justice principles to improve healthcare for people living in remote areas of Australia.
[E] The RFDS enables participation by consulting with local communities to tailor services to their specific needs and employing local staff where possible.
[E] It promotes equity by allocating resources to rural and remote areas to reduce the health gap between metropolitan and regional Australia.
[E] The RFDS helps with access by flying doctors and nurses to far-away communities and bringing sick patients to hospitals, as well as providing telehealth services.
[E] The service upholds the right to healthcare for all Australians regardless of where they live, ensuring that geographic location doesn’t determine health outcomes.
[Ev] The impact is clear in the numbers: the RFDS helps over 330,000 patients each year in areas where death rates are 40% higher than in cities, showing how they’re bridging the gap between rural and city health.
[L] By combining planes, technology, and community input, the RFDS shows how using different social justice principles together can overcome Australia’s distance challenges to help people in remote areas stay healthy.

Show Worked Solution

Model answer (addressing each “PEAR” principle):

[P] The Royal Flying Doctor Service (RFDS) uses multiple social justice principles to improve healthcare for people living in remote areas of Australia.
[E] The RFDS enables participation by consulting with local communities to tailor services to their specific needs and employing local staff where possible.
[E] It promotes equity by allocating resources to rural and remote areas to reduce the health gap between metropolitan and regional Australia.
[E] The RFDS helps with access by flying doctors and nurses to far-away communities and bringing sick patients to hospitals, as well as providing telehealth services.
[E] The service upholds the right to healthcare for all Australians regardless of where they live, ensuring that geographic location doesn’t determine health outcomes.
[Ev] The impact is clear in the numbers: the RFDS helps over 330,000 patients each year in areas where death rates are 40% higher than in cities, showing how they’re bridging the gap between rural and city health.
[L] By combining planes, technology, and community input, the RFDS shows how using different social justice principles together can overcome Australia’s distance challenges to help people in remote areas stay healthy.

HMS, HIC EQ-Bank 036

Assess how the social justice principle of equity has been applied to improve the health outcomes of people with disabilities in Australia. (5 marks)

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The application of equity through the NDIS has been effective in providing individualised support, though implementation challenges have limited its impact for some participants.
Education support and workplace modifications have moderately improved participation rates in education and employment, but significant employment gaps persist (53% of people with disabilities are employed vs 82% without disabilities).
While Medicare and PBS subsidies have successfully increased affordability of basic healthcare, out-of-pocket costs remain relatively high for people with disabilities, indicating partial success in applying equity principles.
Transport concessions and accessibility requirements have shown mixed results, with urban areas seeing greater improvements than regional locations. This demonstrates an inconsistent application of equity.
Overall, while equity initiatives have yielded important improvements for people with disabilities, significant disparities remain, suggesting that more comprehensive and consistent application of equity principles is still needed.

Show Worked Solution

Model answer:

The application of equity through the NDIS has been effective in providing individualised support, though implementation challenges have limited its impact for some participants.
Education support and workplace modifications have moderately improved participation rates in education and employment, but significant employment gaps persist (53% of people with disabilities are employed vs 82% without disabilities).
While Medicare and PBS subsidies have successfully increased affordability of basic healthcare, out-of-pocket costs remain relatively high for people with disabilities, indicating partial success in applying equity principles.
Transport concessions and accessibility requirements have shown mixed results, with urban areas seeing greater improvements than regional locations. This demonstrates an inconsistent application of equity.
Overall, while equity initiatives have yielded important improvements for people with disabilities, significant disparities remain, suggesting that more comprehensive and consistent application of equity principles is still needed.

v1 Financial Maths, STD2 F1 2023 HSC 6 MC

An item was purchased for a price of $660, including 10% GST.

What is the amount of GST included in the price?

$6.00
$6.60
$60.00
$66.00

Show Answers Only

`=> C`

Show Worked Solution

`text{Let}\ C =\ text{Original cost}`

`C + 0.1 × C`	`= 660`
`1.1C`	`= 660`
`C`	`= 660 / 1.1`
	`= $600`

`:.\ \text{GST} = 660-600 = $60`

`=> C`

♦ Mean mark 4

v1 Financial Maths, STD2 F1 2018 HSC 14 MC

To determine the retail price of an item, a shop owner increases the cost price by 25%. In a sale, the retail price is reduced by 25% to give the sale price.

How does the sale price compare to the cost price?

The sale price is less than the cost price.
The sale price is the same as the cost price.
The sale price is more than the cost price.
It is impossible to compare without knowing the cost price.

Show Answers Only

`text(A)`

Show Worked Solution

`text{Assume the item costs $100:}`

`=>\ \text{Retail price} = 100 × 1.25 = $125`

`=>\ \text{Sale price} = 125 × 0.75 = $93.75`

`:.\ \text{Sale price < Cost price}`

`=>\ \text{A}`

Statistics, SPEC2 2024 VCAA 6

A machine fills bottles with olive oil. The volume of olive oil dispensed into each bottle may be assumed to be normally distributed with mean $\mu$ millilitres (mL) and standard deviation $\sigma=$4.2 mL. When the machine is working properly $\mu=1000$.

The volume dispensed is monitored regularly by taking a random sample of nine bottles and finding the mean volume dispensed.

The machine will be paused and adjusted if the mean volume of olive oil in the nine bottles is significantly less than 1000 mL at the 5% level of significance.

When checked, a random sample of nine bottles gave a mean volume of 997.5 mL .

A one-sided statistical test is to be performed.

Write down suitable null and alternative hypotheses $H_0$ and $H_1$ for the test. (1 mark)

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1. Find the $p$ value for this test correct to three decimal places. (1 mark)
  
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2. Using the $p$ value found in part b.i, state with a reason whether the machine should be paused. (1 mark)
  
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Assuming that the mean volume dispensed by the machine each time is in fact 997 mL and not 1000 mL, find the probability of a type $\text{II}$ error for the test using nine bottles at the 5% level of significance. Assume that the population standard deviation is 4.2 mL, and give your answer correct to two decimal places. (2 marks)

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Let $\overline{X}$ denote the sample mean of a random sample of nine bottles. As a quality-control measure, the machine will be paused if $\overline{X}<a$ or if $\overline{X}>b$, where $\operatorname{Pr}(\overline{X}<a)=0.01$ and $\operatorname{Pr}(\overline{X}>b)=0.01$.
Assume $\mu=1000$ mL and $\sigma=4.2$ mL.
Find the values of $a$ and $b$ correct to one decimal place. (1 mark)

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A new machine is purchased, and it is observed that the volume dispensed by the new machine in 50 randomly chosen bottles provided a sample mean of 1005 mL and a sample standard deviation of 4 mL .

Find a 95% confidence interval for the population mean volume dispensed by the new machine, giving values correct to one decimal place. You may assume a population standard deviation of 4 mL . (1 mark)

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Forty samples, each consisting of 50 randomly chosen bottles, are taken, and a 95% confidence interval is calculated for each sample.
In how many of these confidence intervals would the population mean volume dispensed by the machine be expected to lie? (1 mark)

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What minimum size sample should be used so that, with 95% confidence, the sample mean is within 1 mL of the population mean volume dispensed by the new machine? Assume a population standard deviation of 4 mL. (1 mark)

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a. $H_0: \mu=1000, \ H_1: \mu<1000$

b.i. $p \text{–value}=0.037$

b.ii. $p<0.05 \Rightarrow \text{Pause the machine}$

c. $0.31$

d. $a=996.7, b=1003.3$

e. $(1003.9,1006.1)$

f. $38$

g. $\text{Mean sample size}=62.$

Show Worked Solution

a. $H_0: \mu=1000$

$H_1: \mu<1000$

b.i. $\text {Sample mean:}\ \mu_{\overline{X}}=1000$

$\dfrac{\sigma_{\overline{X}}}{\sqrt{n}}=\dfrac{4.2}{3}=1.4$

$p \text{–value}=\operatorname{Pr}\left(z<\dfrac{997.5-1000}{1.4}\right)=0.037$

b.ii. $p<0.05 \Rightarrow \text{Pause the machine}$

c. $\text{Let \(\overline{X}$}=\text{sample mean}\)

$\text{Null hypothesis rejected when}\ \overline{X}<c$

$\operatorname{Pr}\left(z<\dfrac{c-1000}{1.4}\right)=0.05$

$\text{Solve for \(c$:}\)

$\dfrac{c-1000}{1.4}=-1.6449 \ \Rightarrow \ c=997.697$

$\text{Probability of a type II error:}$

$\operatorname{Pr}(\overline{X}>997.697 \mid \mu=997)=\operatorname{Pr}\left(z<\dfrac{0.697}{1.4}\right) \approx 0.31$

♦ Mean mark (c) 50%.

d. $\text{Sample mean has mean}=1000, \dfrac{\sigma}{\sqrt{n}}=\dfrac{4.2}{\sqrt{9}}=1.4$

$\text{Solve (by CAS):}$

$\operatorname{Pr}\left(z<\dfrac{a-1000}{1.4}\right)=0.01 \ \Rightarrow \ a=996.7$

$\operatorname{Pr}\left(z>\dfrac{b-1000}{1.4}\right)=0.01 \ \Rightarrow \ b=1003.3$

e. $\text{95% C.I.}\ (\overline{x}=1005):$

$\left(1005-1.96 \times \dfrac{4}{\sqrt{50}}, 1005+1.96 \times \dfrac{4}{\sqrt{50}}\right)=(1003.9,1006.1)$

f. $\text{Expect \(95 \%$ of C.I.’s to contain population mean}\)

$\text{Number of C.I.’s}=0.95 \times 40=38$

g. $\text{CI. extends \(1.96 \times \dfrac{4}{\sqrt{n}}$ each side of the mean.}\)

$\text{Solve for \(n$:}\ 1.96 \times \dfrac{4}{\sqrt{n}}<1\ \Rightarrow \ n \approx 61.5\)

$\therefore \text{Mean sample size}=62.$

♦ Mean mark (f) 51%.
♦ Mean mark (g) 46%.

HMS, BM EQ-Bank 838

Analyse how the agonist/antagonist relationship facilitates efficient movement in sporting activities. (5 marks)

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Sample Answer

The agonist/antagonist relationship creates smooth movement because when one muscle contracts (the agonist), the opposite muscle relaxes (the antagonist). This prevents the muscles from fighting against each other, allowing efficient movement to occur.
This relationship allows for precise control of both the speed and force of movements, as seen in a tennis player adjusting their stroke based on the game situation.
During rapid movements like sprinting, the proper sequencing of agonist contraction and antagonist relaxation maximises power output and movement efficiency.
The relationship protects joints from injury by providing balanced muscle development and preventing excessive movement beyond a joint’s normal range of motion.
In skilled movements requiring fine motor control, such as archery, the precise coordination between agonists and antagonists enables the stability and accuracy needed for consistent performance.

Show Worked Solution

Sample Answer

The agonist/antagonist relationship creates smooth movement because when one muscle contracts (the agonist), the opposite muscle relaxes (the antagonist). This prevents the muscles from fighting against each other, allowing efficient movement to occur.
This relationship allows for precise control of both the speed and force of movements, as seen in a tennis player adjusting their stroke based on the game situation.
During rapid movements like sprinting, the proper sequencing of agonist contraction and antagonist relaxation maximises power output and movement efficiency.
The relationship protects joints from injury by providing balanced muscle development and preventing excessive movement beyond a joint’s normal range of motion.
In skilled movements requiring fine motor control, such as archery, the precise coordination between agonists and antagonists enables the stability and accuracy needed for consistent performance.

HMS, BM EQ-Bank 834

Analyse the role of different types of muscle contractions during a tennis serve. (5 marks)

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Sample Answer

The preparation phase involves isometric contractions in the core muscles to stabilise the trunk while the player positions for the serve.
As the player tosses the ball, concentric contractions occur in the shoulder muscles to raise the arm upward.
During the loading phase, eccentric contractions in the shoulder rotators and triceps control the racquet as it moves into the “trophy position” behind the head.
The forward swing features powerful concentric contractions of the pectoralis major, anterior deltoid, and triceps to accelerate the racquet toward the ball.
The follow-through phase involves eccentric contractions of the shoulder muscles to decelerate the arm after contact, protecting the joint from injury while controlling the completion of the movement.

Show Worked Solution

Sample Answer

The preparation phase involves isometric contractions in the core muscles to stabilise the trunk while the player positions for the serve.
As the player tosses the ball, concentric contractions occur in the shoulder muscles to raise the arm upward.
During the loading phase, eccentric contractions in the shoulder rotators and triceps control the racquet as it moves into the “trophy position” behind the head.
The forward swing features powerful concentric contractions of the pectoralis major, anterior deltoid, and triceps to accelerate the racquet toward the ball.
The follow-through phase involves eccentric contractions of the shoulder muscles to decelerate the arm after contact, protecting the joint from injury while controlling the completion of the movement.

HMS, BM EQ-Bank 828 MC

A marathon runner is more likely to have a higher percentage of which type of muscle fibres in their leg muscles?

Fast-twitch fibres
Slow-twitch fibres
Intermediate fibres
Explosive fibres

Show Answers Only

$B$

Show Worked Solution

Consider Option B:

Slow-twitch muscle fibres have greater endurance capacity due to their aerobic nature, making them ideal for long-duration, lower-intensity activities like marathon running.

Other Options:

A is incorrect: Fast-twitch fibres are better suited for short, explosive activities rather than endurance events.
C is incorrect: “Intermediate fibres” is not a standard classification of muscle fibres.
D is incorrect: “Explosive fibres” is not a standard classification of muscle fibres.

$\Rightarrow B$

HMS, BM EQ-Bank 827

Explain how major muscles in the upper body work together to perform an overhead throw. (5 marks)

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Sample Answer

The initial wind-up phase engages the latissimus dorsi and posterior deltoids to position the arm behind the body, creating potential energy.
The pectoralis major and anterior deltoid then contract forcefully to bring the arm forward, generating momentum for the throw.
The rotator cuff muscles (supraspinatus, infraspinatus, teres minor, and subscapularis) stabilise the shoulder joint throughout the movement, preventing injury during the high-velocity action.
The triceps brachii extends the elbow explosively during the release phase, adding significant power to the throw.
Core muscles including the rectus abdominis and obliques contract to transfer force from the lower body to the upper body, enhancing the power and control of the throw.

Show Worked Solution

Sample Answer

The initial wind-up phase engages the latissimus dorsi and posterior deltoids to position the arm behind the body, creating potential energy.
The pectoralis major and anterior deltoid then contract forcefully to bring the arm forward, generating momentum for the throw.
The rotator cuff muscles (supraspinatus, infraspinatus, teres minor, and subscapularis) stabilise the shoulder joint throughout the movement, preventing injury during the high-velocity action.
The triceps brachii extends the elbow explosively during the release phase, adding significant power to the throw.
Core muscles including the rectus abdominis and obliques contract to transfer force from the lower body to the upper body, enhancing the power and control of the throw

HMS, BM EQ-Bank 823

Analyse how flexion and extension at different joints are coordinated during the action of throwing a ball. (5 marks)

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Sample Answer

Initial preparation involves shoulder extension as the arm moves backward, while the elbow undergoes flexion to position the ball behind the body.
The throwing sequence begins with rotation of the trunk, followed by shoulder flexion as the arm moves forward from its extended position.
The elbow transitions from flexion to rapid extension, propelling the forearm and hand forward with increasing velocity.
The wrist moves from extension to flexion at the point of release, adding final acceleration to the ball.
This coordinated sequence of flexion and extension across multiple joints creates a kinetic chain, transferring energy efficiently from the larger muscles of the trunk to the smaller muscles of the arm and hand, maximising throwing velocity.

Show Worked Solution

Sample Answer

Initial preparation involves shoulder extension as the arm moves backward, while the elbow undergoes flexion to position the ball behind the body.
The throwing sequence begins with rotation of the trunk, followed by shoulder flexion as the arm moves forward from its extended position.
The elbow transitions from flexion to rapid extension, propelling the forearm and hand forward with increasing velocity.
The wrist moves from extension to flexion at the point of release, adding final acceleration to the ball.
This coordinated sequence of flexion and extension across multiple joints creates a kinetic chain, transferring energy efficiently from the larger muscles of the trunk to the smaller muscles of the arm and hand, maximising throwing velocity.

HMS, BM EQ-Bank 820

Explain how the structure of the pelvic girdle and hip joint contributes to its function in weight-bearing and movement. (5 marks)

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Sample Answer

The pelvic girdle consists of several fused bones that form a strong, stable base that effectively supports the weight of the upper body.
The hip joint is a deep ball-and-socket joint where the head of the femur inserts into the acetabulum of the pelvis, providing stability while allowing movement in multiple directions.
Supporting ligaments in the pelvic region are short and strong compared to those in the shoulder, limiting mobility but enhancing stability for weight-bearing functions.
The depth of the acetabulum socket and strong ligamentous support allow the hip joint to bear significant loads while maintaining stability during activities like walking and running.
The design balances the need for stability in supporting body weight with sufficient mobility for locomotion, making it ideal for its dual role in weight bearing and movement.

Show Worked Solution

Sample Answer

The pelvic girdle consists of several fused bones that form a strong, stable base that effectively supports the weight of the upper body.
The hip joint is a deep ball-and-socket joint where the head of the femur inserts into the acetabulum of the pelvis, providing stability while allowing movement in multiple directions.
Supporting ligaments in the pelvic region are short and strong compared to those in the shoulder, limiting mobility but enhancing stability for weight-bearing functions.
The depth of the acetabulum socket and strong ligamentous support allow the hip joint to bear significant loads while maintaining stability during activities like walking and running.
The design balances the need for stability in supporting body weight with sufficient mobility for locomotion, making it ideal for its dual role in weight bearing and movement.

HMS, BM EQ-Bank 817 MC

Which of the following correctly identifies the bones that form the elbow joint?

Humerus, radius and ulna
Radius, ulna and carpals
Scapula, humerus and radius
Humerus, radius and carpals

Show Answers Only

$A$

Show Worked Solution

Consider Option A:

The elbow joint is formed by the humerus in the upper arm connecting with both the radius and ulna in the forearm.

Other Options:

B and D are incorrect: Carpals are wrist bones and do not form part of the elbow joint.
C is incorrect: Scapula is part of the shoulder joint, not the elbow joint.

$\Rightarrow A$

HMS, BM EQ-Bank 814

Explain the structure and function of tendons in relation to joint movement. (5 marks)

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Sample Answer

Tendons are tough, inelastic cords of fibrous connective tissue that connect muscles to bones, transferring force generated by muscle contractions.
The fibrous composition of tendons provides the strength needed to withstand the pulling forces exerted during muscle contractions.
Tendons often extend across joints, helping ligaments maintain joint closure and providing additional stability during movement.
Their limited elasticity ensures efficient transfer of force from muscle to bone with minimal energy loss.
The strategic placement of tendons around joints enables precise control of movement, allowing for complex actions such as fine motor skills in the hands.

Show Worked Solution

Sample Answer

Tendons are tough, inelastic cords of fibrous connective tissue that connect muscles to bones, transferring force generated by muscle contractions.
The fibrous composition of tendons provides the strength needed to withstand the pulling forces exerted during muscle contractions.
Tendons often extend across joints, helping ligaments maintain joint closure and providing additional stability during movement.
Their limited elasticity ensures efficient transfer of force from muscle to bone with minimal energy loss.
The strategic placement of tendons around joints enables precise control of movement, allowing for complex actions such as fine motor skills in the hands.

HMS, BM EQ-Bank 811

Explain the relationship between the structure of a synovial joint and its ability to facilitate movement. (5 marks)

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Sample Answer

Synovial joints contain a joint cavity filled with synovial fluid that lubricates the joint, allowing for smooth movement between bone surfaces.
The joint capsule, reinforced by ligaments, provides stability while still allowing the appropriate range of movement for that specific joint.
Articular cartilage covering the ends of bones reduces friction between moving surfaces, preventing damage and enabling efficient movement.
The synovial membrane secretes synovial fluid in response to movement, providing more lubrication during activity when it’s most needed.
The specific shape of each synovial joint (e.g., ball-and-socket, hinge) determines the type and range of movements possible, optimising function for different body parts.

Show Worked Solution

Sample Answer

Synovial joints contain a joint cavity filled with synovial fluid that lubricates the joint, allowing for smooth movement between bone surfaces.
The joint capsule, reinforced by ligaments, provides stability while still allowing the appropriate range of movement for that specific joint.
Articular cartilage covering the ends of bones reduces friction between moving surfaces, preventing damage and enabling efficient movement.
The synovial membrane secretes synovial fluid in response to movement, providing more lubrication during activity when it’s most needed.
The specific shape of each synovial joint (e.g., ball-and-socket, hinge) determines the type and range of movements possible, optimising function for different body parts.

HMS, BM EQ-Bank 807 MC

A basketballer drops to the floor after landing awkwardly on her foot. The doctor diagnoses a torn structure that connects bone to bone in her ankle. Which structure is most likely injured?

Tendon
Synovial fluid
Ligament
Articular cartilage

Show Answers Only

$C$

Show Worked Solution

Consider Option C:

Ligaments are fibrous bands that connect bone to bone, and when stretched excessively (as in an awkward landing), they can tear, resulting in joint instability.

Other Options:

A is incorrect: Tendons connect muscle to bone, not bone to bone.
B is incorrect: Synovial fluid is a lubricant in joints, not a structure that connects bones.
D is incorrect: Articular cartilage covers the ends of bones to allow smooth movement, but does not connect bone to bone.

$\Rightarrow C$

v1 Financial Maths, STD2 F1 2007 HSC 26b

Isla is in her third year working as a freelance photographer.

Isla purchased photography equipment for $4200.
After 3 years it has depreciated to $3150 using the straight-line method.
Calculate the rate of depreciation per year as a percentage. (2 marks)

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Isla earns $760 per week. Calculate her taxable income for this year if the only allowable deduction is the amount of depreciation of her photography equipment in the third year of use. (1 mark)

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Use this tax table to calculate Isla’s tax payable. (2 marks)

Taxable income	Tax payable
$0 − $11 000	Nil
$11 001 − $42 400	20 cents for each $1 over $11 000
$42 401 − $78 800	$6280 plus 33 cents for each $1 over $42 400
$78 801 − $108 400	$18 292 plus `X` cents for each $1 over $78 800
$108 401 and over	$31 316 plus 48 cents for each $1 over $108 400

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Show Answers Only

`text(8.3%)`
`$38\ 790`
`$5563.00`

Show Worked Solution

i.	`S = V_0 - Dn`
	`S = $3150,\ \ \ V_0 = 4200,\ \ \ n = 3`

`3150`	`= 4200 - D xx 3`
`3D`	`= 1050`
`D`	`= $350`

`:.\ \text{Rate of depreciation per year}`

`= 350 / 4200 xx 100`

`= 8.3 \text{(%)}`

ii.	`\text{Income per year}`	`= 52 xx 760`
		`= $39\ 520`

`\text{Taxable income}`	`= \text{Income - Deduction}`
	`= 39\ 520-350`
	`= $38\ 790`

iii.	`\text{Tax payable}`	`= 0.2(38\,790-11\,000)`
		`= 0.2 xx 27\,790`
		`= $5558.00`

HMS, HIC EQ-Bank 033

Evaluate the ways that cultural background influences an individual's understanding of "good health" and their health behaviours. (5 marks)

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Sample answer (note key word “evaluate” – make a judgement based on criteria; determine the value of).

Cultural background establishes value systems that define “good health.”
Traditional cultures emphasising community wellbeing foster social health but may neglect individual mental health needs.
Evaluating specific cultural health practices shows varying effectiveness. For example, Mediterranean diets offer proven cardiovascular benefits, while some traditional healing practices may harm and/or delay medical intervention.
When assessing health-seeking behaviours, cultures open to medical intervention typically achieve better physical outcomes, while those prioritising community support excel in social health determinants.
Cultural food practices can also vary in effectiveness. For example, some traditional diets provide exceptional nutrition while others contribute to chronic disease when followed exclusively.
The most valuable approach integrates positive cultural traditions with evidence-based health knowledge, suggesting cultural frameworks should be respected but evaluated critically.

Show Worked Solution

Sample answer (note key word “evaluate” – make a judgement based on criteria; determine the value of).

Cultural background establishes value systems that define “good health.”
Traditional cultures emphasising community wellbeing foster social health but may neglect individual mental health needs.
Evaluating specific cultural health practices shows varying effectiveness. For example, Mediterranean diets offer proven cardiovascular benefits, while some traditional healing practices may harm and/or delay medical intervention.
When assessing health-seeking behaviours, cultures open to medical intervention typically achieve better physical outcomes, while those prioritising community support excel in social health determinants.
Cultural food practices can also vary in effectiveness. For example, some traditional diets provide exceptional nutrition while others contribute to chronic disease when followed exclusively.
The most valuable approach integrates positive cultural traditions with evidence-based health knowledge, suggesting cultural frameworks should be respected but evaluated critically.

HMS, HIC EQ-Bank 032

Analyse how an individual's health might change during the transition from high school to university, considering three dimensions of health. (5 marks)

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Sample answer (note key word “analyse” – identify components and the relationship between them; draw out and relate implications).

Physical health may decline initially due to disrupted routines, poor sleep patterns, and potentially unhealthy eating habits as students adapt to independent living and managing their own schedules.
Social health undergoes significant change as established friendship networks are disrupted and new relationships must be formed, potentially causing temporary isolation before new connections develop.
Mental health faces challenges due to academic pressure, financial concerns, and identity development, requiring adjustment to new stressors and development of coping mechanisms.
The interactions between these dimensions create a complex health transition, where challenges in one area (such as social disconnection) can amplify issues in another (such as mental wellbeing).

Show Worked Solution

Sample answer (note key word “analyse” – identify components and the relationship between them; draw out and relate implications).

Physical health may decline initially due to disrupted routines, poor sleep patterns, and potentially unhealthy eating habits as students adapt to independent living and managing their own schedules.
Social health undergoes significant change as established friendship networks are disrupted and new relationships must be formed, potentially causing temporary isolation before new connections develop.
Mental health faces challenges due to academic pressure, financial concerns, and identity development, requiring adjustment to new stressors and development of coping mechanisms.
The interactions between these dimensions create a complex health transition, where challenges in one area (such as social disconnection) can amplify issues in another (such as mental wellbeing).

Vectors, SPEC2 2024 VCAA 4

A model yacht is sailing on a lake between two buoys. Its path from one buoy to the other, relative to an origin $O$, is given by

${\underset{\sim}{r}}_{\text{Y}}(t)=3 \sec (t) \underset{\sim}{i}+2 \tan (t) \underset{\sim}{j}$, where $\dfrac{2 \pi}{3} \leq t \leq \dfrac{4 \pi}{3}$

Displacement components are measured in metres, and time $t$ is measured in minutes.

Use a trigonometric identity to show that the Cartesian equation of the path is given by $\dfrac{x^2}{9}-\dfrac{y^2}{4}=1$. (1 mark)
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Sketch the path of the yacht on the axes below. Label the endpoints with their coordinates and show the direction of motion. (2 marks)

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1. Write down an expression, in terms of $\sec (t)$, for the square of the speed of the yacht at any time, $t$. (1 mark)
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2. Find the time, in minutes, when the minimum speed occurs. You do not need to justify that this speed is a minimum. (1 mark)
  
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3. State the minimum speed of the yacht in metres per minute. (1 mark)
  
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4. State the coordinates of the yacht when the minimum speed occurs. (1 mark)
  
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1. Write down a definite integral, in terms of $t$, that gives the distance travelled by the yacht along the path given by $\underset{\sim}{ r }(t)$ over the time interval $\dfrac{2 \pi}{3} \leq t \leq \dfrac{4 \pi}{3}$. (1 mark)
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2. Find the distance travelled by the yacht over this time interval.
3. Give your answer in metres correct to one decimal place. (1 mark)
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The position vector of a drone videoing the yacht, relative to the same origin as the yacht, $O$, is given by ${\underset{\sim}{ r }}_{ \text{D} }(t)=(2-3 t) \underset{\sim}{ i }+(4 t-1) \underset{\sim}{ j } +(6-t) \underset{\sim}{ k }$, where $0 \leq t \leq 5$.
Displacement components are measured in metres, and time $t$ is measured in minutes.
What is the shortest distance from the drone to the yacht, as the yacht sails along the path given by ${\underset{\sim}{ r }}_{\text{Y}}(t)=3 \sec (t) \underset{\sim}{ i }+2 \tan (t) \underset{\sim}{ j }$, where $\dfrac{2 \pi}{3} \leq t \leq \dfrac{4 \pi}{3}$ ?
Give your answer in metres, correct to one decimal place. (2 marks)

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Show Answers Only

a. $\left(\dfrac{x}{3}\right)^2-\left(\dfrac{y}{2}\right)^2=1$

c.i. $\abs{\underset{\sim}{\dot{r}}(t)}^2=13 \sec ^4 t-9 \sec ^2 t$

c.ii. $\text{Minimum speed occurs at \( t=\pi$ min.}\)

c.iii. $\abs{\underset{\sim}{\dot{r}(t)}}=2 \ \text{metres/min}$

c.iv $\text{Yacht has coordinates} \ (-3,0) \ \text {when min speed occurs.}$

d.i $\text{Distance }=\displaystyle \int_{\frac{2 \pi}{3}}^{\frac{4 \pi}{3}} \sqrt{(3 \sec \, t\, \tan\, t)^2+4\left(\sec ^2 t\right)}\,dt$

d.ii. $\text{Distance}=9.4 \ \text{metres}$

e. $D_{\min }=11.1 \ \text{m}$

Show Worked Solution

a.	$x$	$=3 \sec t $	$\ \Rightarrow \ \sec t$	$=\dfrac{x}{3}$
	$y$	$=2 \tan t $	$\ \Rightarrow \ \tan t$	$=\dfrac{y}{2}$

$\sec ^2 t+1$	$=\tan ^2 t$
$\left(\dfrac{y}{2}\right)^2+1$	$=\left(\dfrac{x}{3}\right)^2$
$\left(\dfrac{x}{3}\right)^2-\left(\dfrac{y}{2}\right)^2$	$=1$

c.i.	$\underset{\sim}{r}$	$=3 \sec (t)\underset{\sim}{i}+2 \tan (t)\underset{\sim}{j}$
	$\underset{\sim}{\dot{r}}(t)$	$=\dfrac{3 \sin t}{\cos ^2 t}\underset{\sim}{i}+\dfrac{2}{\cos ^2 t} \underset{\sim}{j}$
	$\abs{\underset{\sim}{\dot{r}}(t)}^2$	$=\dfrac{9 \sin ^2 t}{\cos ^4 t}+\dfrac{4}{\cos ^4 t}$
		$=\dfrac{9-9 \cos ^2 t+4}{\cos ^4 t}$
		$=\dfrac{13}{\cos ^4 t}-\dfrac{9}{\cos ^2 t}$
		$=13 \sec ^4 t-9 \sec ^2 t$

♦♦♦ Mean mark c.i. 23%.

c.ii. $\text {Differentiate} \ \ \abs{\underset{\sim}{\dot{r}}(t)}^2: $

$\dfrac{d}{d t}\left(\abs{\underset{\sim}{\dot{r}}(t)}^2\right)=\dfrac{52 \sin t}{\cos ^5 t}-\dfrac{18}{\cos ^3 t}=\dfrac{2 \sin t\left(26-9 \sin t\, \cos ^2 t\right)}{\cos ^5 t}$

$\text{Find } t \text{ where } \ \sin t=0 \ \text { for } \ \dfrac{2 \pi}{3} \leq t \leq \dfrac{4 \pi}{3}:$

$t=\pi$

$\text{Minimum speed occurs at \( t=\pi$ min.}\)

c.iii. $\text{Find} \ \ \abs{\underset{\sim}{\dot{r}}(t)}^2 \text{when} \ \ t=\pi:$

$\abs{\underset{\sim}{\dot{r}}(t)^2}=\dfrac{13}{\cos ^4 \pi}-\dfrac{9}{\cos ^2 \pi}=13-9=4$

$\abs{\underset{\sim}{\dot{r}(t)}}=\sqrt{4}=2 \ \text{metres/min}$

♦ Mean mark c.iii. 48%.

c.iv $\text{Find}\ \underset{\sim}{r}(t) \ \text{when} \ \ t=\pi:$

$\underset{\sim}{r}(\pi)=3 \sec \pi \underset{\sim}{i}+2 \tan \pi \underset{\sim}{j}=-3 \underset{\sim}{i}$

$\text{Yacht has coordinates} \ (-3,0) \ \text {when min speed occurs.}$

d.i $\text{Distance }=\displaystyle \int_{\frac{2 \pi}{3}}^{\frac{4 \pi}{3}} \sqrt{(3 \sec \, t\, \tan\, t)^2+4\left(\sec ^2 t\right)}\,dt$

d.ii. $\text{Distance}=9.4 \ \text{metres}$

e. ${\underset{\sim}{r}}_\text{D}(t)=(2-3 t) \underset{\sim}{i}+(4 t-1) \underset{\sim}{j}+(6-t) \underset{\sim}{k} \quad(0 \leqslant t \leqslant 5)$

$\underset{\sim}{r}(t)=3 \sec (t) \underset{\sim}{i}+2 \tan (t) \underset{\sim}{j} \quad\left(\dfrac{2 \pi}{3} \leqslant t \leqslant \dfrac{4 \pi}{3}\right)$

$D=\sqrt{(3 \sec t-2+3 t)^2+(2 \tan t-4 t+1)^2+(t-6)^2}$

$\text{Find} \ \ D_{\min } \ \text{for} \ \ \dfrac{2 \pi}{3} \leq t \leq \dfrac{4 \pi}{3}:$

$D_{\min }=11.1 \ \text{m}$

♦♦♦ Mean mark (e) 28%.

v1 Financial Maths, STD2 F1 2024 HSC 13 MC

Alicia takes out a loan of $7500. Simple interest is charged on the loan.

The loan and the interest charged will be repaid by making monthly repayments of $250 over 3 years.

What simple interest rate per annum, to the nearest percent, is charged on the loan?

Show Answers Only

$A$

Show Worked Solution

$\text{Number of repayments} = 3 \times 12 = 36$

$\text{Total repayments} = 36 \times 250 = \$9000$

$\text{Interest paid} = 9000 – 7500 = \$1500$

	$I$	$= Prn$
	$1500$	$= 7500 \times r \times 3$
	$r$	$= \dfrac{1500}{7500 \times 3} = 0.0666…$
		$= 6.67\% \approx 7\%$

$\Rightarrow A$

♦ Mean mark 39%.

HMS, BM EQ-Bank 802 MC

Based on the heart rate data shown in the table below, which conclusion is MOST supported by the evidence?

\begin{array}{|l|c|c|c|c|}
\hline \textbf{Training Type} & \textbf{Week 1 RHR} & \textbf{Week 2 RHR} & \textbf{Week 4 RHR} & \textbf{Week 4 RHR} \\
\hline \text{Running} & \text{75 bpm} & \text{72 bpm} & \text{69 bpm} & \text{67 bpm} \\
\hline \text{Cycling} & \text{76 bpm} & \text{73 bpm} & \text{69 bpm} & \text{66 bpm} \\
\hline \text{Swimming} & \text{74 bpm} & \text{73 bpm} & \text{71 bpm} & \text{70 bpm} \\ \hline
\end{array}

Swimming is the most effective activity for reducing resting heart rate
All three training types are equally effective at reducing resting heart rate
Running and cycling produced similar reductions in resting heart rate, both greater than swimming
The training program was too short to draw any meaningful conclusions

Show Answers Only

$C$

Show Worked Solution

Consider Option C:

The data shows running reduced RHR by 8 bpm (75 to 67), cycling by 10 bpm (76 to 66), and swimming by only 4 bpm (74 to 70).

Other Options:

A is incorrect: Swimming actually showed the smallest reduction in RHR.
B is incorrect: The activities clearly show different magnitudes of effect.
D is incorrect: Clear trends are visible across the 4-week period, making meaningful conclusions possible.

$\Rightarrow C$

HMS, BM EQ-Bank 797 MC

During a progressively increasing exercise test, an athlete's blood lactate levels are measured at regular intervals. At which point would blood lactate levels begin to show a significant exponential increase?

When the anaerobic threshold is reached
When exercise intensity exceeds 85% of maximum heart rate
As soon as any exercise begins, regardless of intensity
When the aerobic threshold is reached

Show Answers Only

$A$

Show Worked Solution

Consider Option A:

Blood lactate levels remain relatively stable with small increases until the anaerobic threshold (lactate threshold) is reached.
At this point, lactate production exceeds the body’s ability to clear it, resulting in exponential accumulation in the bloodstream.

Other Options:

B is incorrect: 85% of maximum heart rate approximates the threshold for many, but heart rate doesn’t directly determine lactate accumulation; it varies by individual.
C is incorrect: Lactate is produced during all exercise, but at lower intensities, clearance mechanisms prevent significant accumulation.
D is incorrect: The aerobic threshold causes only a slight increase in lactate levels, not the exponential increase described.

$\Rightarrow A$

HMS, BM EQ-Bank 793

A rugby league player has identified a need to improve anaerobic capacity for the upcoming season. Design and justify an appropriate 4-week anaerobic training program based on the FITT principle, demonstrating how the principle of progressive overload would be applied. (8 marks)

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Sample Answer

Frequency:

Begin with 2 anaerobic sessions per week in Week 1, increasing to 3 sessions by Week 4, allowing adequate recovery between high-intensity sessions while progressively increasing training stimulus throughout the program.

Intensity:

Work intervals should be at 85 – 95% maximum effort to effectively develop the glycolytic energy system, with intensity progression achieved by reducing rest intervals rather than increasing work intensity, which maintains quality while increasing metabolic demand.

Time:

Sessions should last 30 – 40 minutes total (including warm-up and cool-down) with the high-intensity work component being 15 – 20 minutes, as anaerobic training quality diminishes with excessive duration due to accumulated fatigue.

Progressive overload in Week 1:

Work-to-rest ratio of 1:4 (e.g., 15-second sprint with 60-second recovery) for 12 repetitions, focusing on establishing proper technique and maximum effort during work intervals.

Progressive overload in Week 2:

Maintain work duration but decrease recovery to 1 : 3 ratio (15 second sprint with 45 second recovery) for 12 repetitions, increasing metabolic stress while maintaining work quality.

Progressive overload in Week 3:

Increase to 14 repetitions with same 1 : 3 work-to-rest ratio, adding volume while maintaining intensity to further challenge anaerobic capacity.

Progressive overload in Week 4:

Further reduce recovery to 1 : 2 ratio (15 second sprint with 30 second recovery) for 14 repetitions, intensifying the training challenge before reducing volume in preparation for the competitive season.

Show Worked Solution

Sample Answer

Frequency:

Begin with 2 anaerobic sessions per week in Week 1, increasing to 3 sessions by Week 4, allowing adequate recovery between high-intensity sessions while progressively increasing training stimulus throughout the program.

Intensity:

Work intervals should be at 85 – 95% maximum effort to effectively develop the glycolytic energy system, with intensity progression achieved by reducing rest intervals rather than increasing work intensity, which maintains quality while increasing metabolic demand.

Time:

Sessions should last 30 – 40 minutes total (including warm-up and cool-down) with the high-intensity work component being 15 – 20 minutes, as anaerobic training quality diminishes with excessive duration due to accumulated fatigue.

Progressive overload in Week 1:

Work-to-rest ratio of 1 : 4 (e.g., 15 second sprint with 60 second recovery) for 12 repetitions, focusing on establishing proper technique and maximum effort during work intervals.

Progressive overload in Week 2:

Maintain work duration but decrease recovery to 1 : 3 ratio (15 second sprint with 45 second recovery) for 12 repetitions, increasing metabolic stress while maintaining work quality.

Progressive overload in Week 3:

Increase to 14 repetitions with same 1 : 3 work-to-rest ratio, adding volume while maintaining intensity to further challenge anaerobic capacity.

Progressive overload in Week 4:

Further reduce recovery to 1 : 2 ratio (15 second sprint with 30 second recovery) for 14 repetitions, intensifying the training challenge before reducing volume in preparation for the competitive season.

HMS, BM EQ-Bank 792

A 16 year old competitive swimmer is preparing for a 1500 metre event. Design an appropriate aerobic training program based on the FITT principle. In your response, explain each component of the FITT principle in relation to the athlete's needs. (5 marks)

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Sample Answer

Frequency:

4 – 5 training sessions per week to allow adequate training stimulus while providing sufficient recovery days, preventing overtraining which is crucial for adolescent athletes still developing physiologically.

Intensity:

70 – 80% of maximum heart rate during the main conditioning phase to develop aerobic capacity appropriate for the 1500m distance, which primarily relies on the aerobic energy system.

Time:

Sessions of 60 – 90 minutes duration with 30 – 45 minutes of continuous swimming to progressively build endurance capacity required for the 1500m event without compromising technique due to excessive fatigue.

Type:

Predominately freestyle swimming with varying drills and techniques (pull buoys, kick sets, pace work) to maintain engagement while specifically training the muscles and movement patterns required for the competitive event.

The program should progressively increase training load by first increasing duration (Time), then Frequency, and finally Intensity, respecting the principle of progressive overload to ensure continued adaptation while minimising injury risk.

Show Worked Solution

Sample Answer

Frequency:

4 – 5 training sessions per week to allow adequate training stimulus while providing sufficient recovery days, preventing overtraining which is crucial for adolescent athletes still developing physiologically.

Intensity:

70 – 80% of maximum heart rate during the main conditioning phase to develop aerobic capacity appropriate for the 1500m distance, which primarily relies on the aerobic energy system.

Time:

Sessions of 60 – 90 minutes duration with 30 – 45 minutes of continuous swimming to progressively build endurance capacity required for the 1500m event without compromising technique due to excessive fatigue.

Type:

Predominately freestyle swimming with varying drills and techniques (pull buoys, kick sets, pace work) to maintain engagement while specifically training the muscles and movement patterns required for the competitive event.

HMS, HIC EQ-Bank 028

Discuss how THREE epidemiological measures are used to explain the health status of Aboriginal and Torres Strait Islander peoples in Australia.

In your response, include specific examples from health reports to illustrate the role of these measures. (5 marks)

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Mortality rates

Mortality rates are used to identify inequities in Aboriginal and Torres Strait Islander health status.
Australia’s Health 2024 reports that cardiovascular disease death rates for Indigenous peoples have declined by 22% in the past 2 decades. Notwithstanding this improvement, a persistent gap compared to non-Indigenous populations remains.

Infant mortality rates

Infant mortality rates provide insight into maternal health services, living conditions and healthcare access.
Data shows a significant but incomplete reduction in Indigenous infant mortality over the past decade, from 6.9 deaths per 1,000 live births in 2012 to 5.4 in 2021, compared to 3.1 for non-Indigenous infants.

Prevalence of disease

Prevalence measures the proportion of a population affected by specific conditions.
For example, the prevalence of diabetes among Indigenous adults (7.9%) is almost double the rate of non-Indigenous Australians (4.1%).
This highlights areas requiring intervention programs and reveals the impact of social determinants of health, including food security and healthcare access in remote communities.

Show Worked Solution

Mortality rates

Mortality rates are used to identify inequities in Aboriginal and Torres Strait Islander health status.
Australia’s Health 2024 reports that cardiovascular disease death rates for Indigenous peoples have declined by 22% in the past 2 decades. Notwithstanding this improvement, a persistent gap compared to non-Indigenous populations remains.

Infant mortality rates

Infant mortality rates provide insight into maternal health services, living conditions and healthcare access.
Data shows a significant but incomplete reduction in Indigenous infant mortality over the past decade, from 6.9 deaths per 1,000 live births in 2012 to 5.4 in 2021, compared to 3.1 for non-Indigenous infants.

Prevalence of disease

Prevalence measures the proportion of a population affected by specific conditions.
For example, the prevalence of diabetes among Indigenous adults (7.9%) is almost double the rate of non-Indigenous Australians (4.1%).
This highlights areas requiring intervention programs and reveals the impact of social determinants of health, including food security and healthcare access in remote communities.

HMS, HIC EQ-Bank 027

Explain how morbidity data is used to assess the health status of Australians and outline TWO limitations of using this data. (3 marks)

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Morbidity data measures the frequency, duration and severity of illnesses in a population, enabling health authorities to identify priority health issues and allocate resources appropriately.
For example, hospital admission rates for cardiovascular disease help prioritise prevention programs in high-risk areas.

Limitations include:

Data may underestimate disease burden as it only captures individuals who access healthcare services, missing those who cannot access care due to geographic, financial or cultural barriers.
Morbidity data often lacks contextual information about social determinants influencing health outcomes, potentially leading to ineffective intervention strategies that don’t address root causes.

Show Worked Solution

Morbidity data measures the frequency, duration and severity of illnesses in a population, enabling health authorities to identify priority health issues and allocate resources appropriately.
For example, hospital admission rates for cardiovascular disease help prioritise prevention programs in high-risk areas.

Limitations include:

Data may underestimate disease burden as it only captures individuals who access healthcare services, missing those who cannot access care due to geographic, financial or cultural barriers.
Morbidity data often lacks contextual information about social issues influencing health outcomes. This can lead to ineffective intervention strategies that don’t address root causes.

HMS, HIC EQ-Bank 020 MC

Researchers are comparing the health status of two regions in Australia using the data below:

\begin{align*}
\begin{array}{|l|l|l|}
\hline
\rule{0pt}{2.5ex}\textbf{Measure}\rule[-1ex]{0pt}{0pt}& \textbf{Region X} & \textbf{Region Y}\\
\hline
\rule{0pt}{2.5ex}\text{Infant mortality rate (per 1,000 live births)}\rule[-1ex]{0pt}{0pt}&\text{4.1}&\text{3.2}\\
\hline
\rule{0pt}{2.5ex}\text{Life expectancy at birth}\rule[-1ex]{0pt}{0pt}& \text{82.3}& \text{84.1}\\
\hline
\rule{0pt}{2.5ex}\text{Prevalence of diabetes (%)}\rule[-1ex]{0pt}{0pt}&\text{5.6}&\text{4.8}\\
\hline
\rule{0pt}{2.5ex}\text{Hospital admissions for respiratory conditions (per 100,000)}\rule[-1ex]{0pt}{0pt}&\text{1,520}&\text{1,320}\\
\hline
\end{array}
\end{align*}

Based on these epidemiological measures, which statement is most accurate?

Region X has better overall health outcomes than Region Y.
Region Y has better overall health outcomes than Region X.
The data shows mixed results with no clear pattern of better health outcomes.
The measures used are insufficient to compare health outcomes between regions.

Show Answers Only

$ B$

Show Worked Solution

B is correct because all four measures indicate better health in Region Y: lower infant mortality, higher life expectancy, lower diabetes prevalence, and fewer hospital admissions for respiratory conditions.

$\Rightarrow B$

HMS, BM EQ-Bank 791

Explain the macronutrient and micronutrient requirements for active people, and how these nutrients support energy system function during exercise. (6 marks)

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Sample Answer

Carbohydrates are the primary macronutrient for active individuals, with requirements ranging from 5 – 7g/kg body weight for moderate training to 8 – 10g/kg for intense training, providing glucose for glycolysis and glycogen storage that fuels both aerobic and anaerobic exercise.
Protein requirements for active people (1.2 – 2.0g/kg body weight) exceed those of sedentary individuals (0.8g/kg) to support muscle repair, enzyme production, and as a secondary energy source during prolonged exercise when glycogen is depleted.
Dietary fat (0.8 – 1.2g/kg body weight) provides essential fatty acids and fat-soluble vitamins, while also serving as the primary energy source during low-intensity aerobic activities and extended exercise beyond 90 minutes.
B-complex vitamins, particularly B1 (thiamine), B2 (riboflavin), B3 (niacin), and B6 (pyridoxine), function as coenzymes in energy metabolism, facilitating the conversion of macronutrients into ATP through all energy pathways.
Iron is a critical micronutrient for active individuals as it forms hemoglobin and myoglobin, enhancing oxygen transport and utilisation in working muscles, directly supporting aerobic energy system function.
Electrolytes (sodium, potassium, magnesium) are essential micronutrients that regulate fluid balance, muscle contraction, and nerve impulse transmission, with requirements increasing proportionally with sweat losses during exercise.

Show Worked Solution

Sample Answer

Carbohydrates are the primary macronutrient for active individuals, with requirements ranging from 5 – 7g/kg body weight for moderate training to 8 – 10g/kg for intense training, providing glucose for glycolysis and glycogen storage that fuels both aerobic and anaerobic exercise.
Protein requirements for active people (1.2 – 2.0g/kg body weight) exceed those of sedentary individuals (0.8g/kg) to support muscle repair, enzyme production, and as a secondary energy source during prolonged exercise when glycogen is depleted.
Dietary fat (0.8 – 1.2g/kg body weight) provides essential fatty acids and fat-soluble vitamins, while also serving as the primary energy source during low-intensity aerobic activities and extended exercise beyond 90 minutes.
B-complex vitamins, particularly B1 (thiamine), B2 (riboflavin), B3 (niacin), and B6 (pyridoxine), function as coenzymes in energy metabolism, facilitating the conversion of macronutrients into ATP through all energy pathways.
Iron is a critical micronutrient for active individuals as it forms hemoglobin and myoglobin, enhancing oxygen transport and utilisation in working muscles, directly supporting aerobic energy system function.
Electrolytes (sodium, potassium, magnesium) are essential micronutrients that regulate fluid balance, muscle contraction, and nerve impulse transmission, with requirements increasing proportionally with sweat losses during exercise.

HMS, BM EQ-Bank 787 MC

A basketball team has been performing the following training session:

4 minutes of high-intensity basketball-specific drills (85 - 90% maximum effort)
2 minutes of active recovery (light jogging)
6 total rounds

Which statement BEST describes this training method and its primary energy system target?

This is HIIT, primarily targeting the ATP-PCr system
This is SIT, primarily targeting the glycolytic system
This is HIIT, primarily targeting the glycolytic and aerobic systems
This is SIT, primarily targeting the ATP-PCr and aerobic systems

Show Answers Only

$C$

Show Worked Solution

Consider Option C:

The session describes High Intensity Interval Training (HIIT) with relatively long work intervals (4 minutes) at high but not maximal intensity (85 – 90%), with a $2:1$ work-to-rest ratio.
This duration and intensity primarily challenges both the glycolytic system during the high-intensity phases and the aerobic system throughout.

Other Options:

A is incorrect: The ATP-PCr system is dominant only in the first 10 – 15 seconds of high-intensity exercise; 4 minute intervals would primarily challenge glycolytic and aerobic systems.
B is incorrect: SIT involves shorter (typically 30 seconds), maximal effort intervals with longer recovery periods, unlike the 4 minute work intervals described.
D is incorrect: SIT uses supramaximal intensities for very short durations, not the 4 minute intervals at 85 – 90% effort described, and would not primarily target the combination of ATP-PCr and aerobic systems.

$\Rightarrow C$

HMS, BM EQ-Bank 784

Jessica is a 17-year-old 800m runner with a personal best time of 2 minutes 18 seconds. Her coach has designed the following anaerobic interval training session:

6 × 200m sprints at 90 - 95% maximum effort
2-minute recovery between repetitions
Target time: 29 - 30 seconds per repetition

Evaluate the appropriateness of this anaerobic interval training session for Jessica's event. In your response, consider energy system involvement, specificity to her event, and potential physiological adaptations. (7 marks)

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Sample Answer

The session effectively targets Jessica’s glycolytic energy system, which provides approximately 60 – 70% of the energy required for her 800m event, making the training physiologically relevant.
The 200m distance at high intensity creates significant lactate accumulation, helping Jessica develop greater lactate tolerance needed for maintaining speed in the second lap of her race.
The 2-minute recovery interval (approximately $4:1$ work-to-rest ratio) is appropriate for incomplete recovery, forcing her to start subsequent repetitions with elevated blood lactate levels that simulate the physiological state she will experience during the latter portion of her race.
The prescribed intensity (90 – 95% effort) appropriately develops the speed component required for 800m performance while respecting the principle of specificity.
Six repetitions totaling 1200m provides an appropriate training volume when compared to her competitive distance (800m), offering sufficient stimulus without excessive fatigue.
The target times (29 – 30 seconds) would effectively develop Jessica’s ability to maintain race pace, particularly if they align with her goal 800m pace (approximately 34 – 35 seconds per 200m for a $2:18$ performer).
A complementary suggestion would be to occasionally vary the distance of intervals (e.g., incorporating 300m and 400m repetitions) to further enhance event-specific endurance and pacing strategy development.

Show Worked Solution

Sample Answer

The session effectively targets Jessica’s glycolytic energy system, which provides approximately 60 – 70% of the energy required for her 800m event, making the training physiologically relevant.
The 200m distance at high intensity creates significant lactate accumulation, helping Jessica develop greater lactate tolerance needed for maintaining speed in the second lap of her race.
The 2-minute recovery interval (approximately $4:1$ work-to-rest ratio) is appropriate for incomplete recovery, forcing her to start subsequent repetitions with elevated blood lactate levels that simulate the physiological state she will experience during the latter portion of her race.
The prescribed intensity (90 – 95% effort) appropriately develops the speed component required for 800m performance while respecting the principle of specificity.
Six repetitions totaling 1200m provides an appropriate training volume when compared to her competitive distance (800m), offering sufficient stimulus without excessive fatigue.
The target times (29 – 30 seconds) would effectively develop Jessica’s ability to maintain race pace, particularly if they align with her goal 800m pace (approximately 34 – 35 seconds per 200m for a $2:18$ performer).
A complementary suggestion would be to occasionally vary the distance of intervals (e.g., incorporating 300m and 400m repetitions) to further enhance event-specific endurance and pacing strategy development.

HMS, BM EQ-Bank 783

A volleyball player has been prescribed the following anaerobic interval training session:

6 sets of 30 second maximum effort vertical jumping drills
90 seconds rest between sets
3 minutes recovery between exercises
4 different movement patterns focusing on explosive power

Analyse the effectiveness of this training session for volleyball performance, suggesting any modifications that would enhance its sport-specificity. (6 marks)

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Sample Answer

The prescribed 30 second work intervals effectively target the glycolytic energy system, which is important for repeated explosive actions in volleyball, particularly during extended rallies.
The 90 second rest periods ($1:3$ work-to-rest ratio) allow partial but not complete recovery of the glycolytic system, developing the player’s ability to perform under increasing fatigue conditions like tournament play.
Vertical jumping focus directly enhances a key performance element in volleyball (blocking and spiking), making the exercise selection highly sport-specific.
A modification would be to incorporate more reactive and decision-based elements during the work intervals, such as responding to coach signals for jump direction, simulating game reading requirements.
Including ball-handling skills during some intervals would enhance sport-specificity by combining technical skill execution with anaerobic conditioning.
The 3 minute recovery between different exercises is appropriate for ensuring quality movement in subsequent exercises, but could be reduced to 2 minutes later in the training cycle to further challenge recovery capacity.

Show Worked Solution

Sample Answer

The prescribed 30 second work intervals effectively target the glycolytic energy system, which is important for repeated explosive actions in volleyball, particularly during extended rallies.
The 90 second rest periods ($1:3$ work-to-rest ratio) allow partial but not complete recovery of the glycolytic system, developing the player’s ability to perform under increasing fatigue conditions like tournament play.
Vertical jumping focus directly enhances a key performance element in volleyball (blocking and spiking), making the exercise selection highly sport-specific.
A modification would be to incorporate more reactive and decision-based elements during the work intervals, such as responding to coach signals for jump direction, simulating game reading requirements.
Including ball-handling skills during some intervals would enhance sport-specificity by combining technical skill execution with anaerobic conditioning.
The 3 minute recovery between different exercises is appropriate for ensuring quality movement in subsequent exercises, but could be reduced to 2 minutes later in the training cycle to further challenge recovery capacity.

HMS, BM EQ-Bank 782

Explain how a soccer coach could design an effective anaerobic interval training session that addresses the specific movement patterns and energy demands of soccer players. (5 marks)

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Sample Answer

Incorporate high-intensity running intervals with rapid directional changes (10 – 15 seconds) followed by active recovery periods (30 – 45 seconds) to simulate the intermittent sprinting patterns in soccer matches.
Include ball skills and decision-making elements during work intervals to ensure training is sport-specific while maintaining the required intensity for anaerobic development.
Design intervals that replicate position-specific movement demands (e.g., shorter, more frequent sprints for midfielders; longer recovery periods for defenders).
Implement progressive work-to-rest ratios throughout a season, beginning with $1:3$ during early preseason and progressing to $1:1$ or $1:2$ as competition approaches to match game demands.
Structure the session duration (20 – 30 minutes of actual interval work) to reflect the accumulated anaerobic load during a typical soccer match while avoiding excessive fatigue that could impact technical skill development.

Show Worked Solution

Sample Answer

Incorporate high-intensity running intervals with rapid directional changes (10 – 15 seconds) followed by active recovery periods (30 – 45 seconds) to simulate the intermittent sprinting patterns in soccer matches.
Include ball skills and decision-making elements during work intervals to ensure training is sport-specific while maintaining the required intensity for anaerobic development.
Design intervals that replicate position-specific movement demands (e.g., shorter, more frequent sprints for midfielders; longer recovery periods for defenders).
Implement progressive work-to-rest ratios throughout a season, beginning with $1:3$ during early preseason and progressing to $1:1$ or $1:2$ as competition approaches to match game demands.
Structure the session duration (20 – 30 minutes of actual interval work) to reflect the accumulated anaerobic load during a typical soccer match while avoiding excessive fatigue that could impact technical skill development.

HMS, BM EQ-Bank 781

Compare the work-to-rest ratios that would be appropriate for anaerobic interval training programs for the following athletes:

A 100m sprinter
A 400m runner
A basketball player. (5 marks)

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Sample Answer

A 100m sprinter would utilise long rest intervals with a work-to-rest ratio of approximately $1:8$ – $1:10$ (e.g., 10 second sprint with 80 – 100 seconds recovery) to ensure complete ATP-PCr replenishment between maximal intensity efforts, simulating the energy system demands of their event.
A 400m runner would implement moderate rest intervals with a work-to-rest ratio of approximately $1:3$ – $1:4$ (e.g., 45 second sprint with 2-3 minutes recovery) to develop lactate tolerance while allowing sufficient but incomplete recovery between intervals.
A basketball player would employ shorter rest intervals with a work-to-rest ratio of approximately $1:1$ – $1:2$ (e.g., 30 second sprint with 30 – 60 seconds recovery) to simulate game conditions where incomplete recovery between high-intensity efforts is common.
These different ratios specifically target the predominant energy systems used in each activity: primarily ATP-PCr for 100m, ATP-PCr and glycolytic for 400m, and a combination of all three energy systems for basketball.
The work-to-rest ratios would be adjusted throughout a season according to the principle of specificity, with ratios becoming more event-specific as competition approaches.

Show Worked Solution

Sample Answer

A 100m sprinter would utilise long rest intervals with a work-to-rest ratio of approximately $1:8$ – $1:10$ (e.g., 10 second sprint with 80 – 100 seconds recovery) to ensure complete ATP-PCr replenishment between maximal intensity efforts, simulating the energy system demands of their event.
A 400m runner would implement moderate rest intervals with a work-to-rest ratio of approximately $1:3$ – $1:4$ (e.g., 45 second sprint with 2 – 3 minutes recovery) to develop lactate tolerance while allowing sufficient but incomplete recovery between intervals.
A basketball player would employ shorter rest intervals with a work-to-rest ratio of approximately $1:1$ – $1:2$ (e.g., 30 second sprint with 30 – 60 seconds recovery) to simulate game conditions where incomplete recovery between high-intensity efforts is common.
These different ratios specifically target the predominant energy systems used in each activity: primarily ATP-PCr for 100m, ATP-PCr and glycolytic for 400m, and a combination of all three energy systems for basketball.
The work-to-rest ratios would be adjusted throughout a season according to the principle of specificity, with ratios becoming more event-specific as competition approaches.

HMS, BM EQ-Bank 777

Katie is a 15-year-old cross-country runner who has been advised by her coach to incorporate continuous training into her program.

Explain the impact of continuous aerobic training on her physiological adaptations and performance. In your response, make reference to relevant energy systems. (5 marks)

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Sample Answer

Continuous aerobic training would primarily develop Katie’s aerobic energy system by increasing mitochondrial density in muscle cells, enhancing ATP production capacity during long events.
Training would increase cardiac stroke volume, resulting in greater oxygen-rich blood being pumped to working muscles with each heartbeat, improving oxygen transport.
Her maximum oxygen uptake (VO2 max) would increase through improved oxygen extraction at the muscle tissue level, resulting from greater capillary development around individual muscle fibres.
Continuous training promotes glycogen storage efficiency and fat utilisation as fuel source, delaying glycogen depletion during longer cross-country events.
The training would improve her body’s ability to clear lactate, increasing her anaerobic threshold, allowing her to maintain higher speeds before significant lactate build-up.
These adaptations collectively allow Katie to sustain higher racing speeds with lower perceived exertion during cross-country competitions.

Show Worked Solution

Sample Answer

Continuous aerobic training would primarily develop Katie’s aerobic energy system by increasing mitochondrial density in muscle cells, enhancing ATP production capacity during long events.
Training would increase cardiac stroke volume, resulting in greater oxygen-rich blood being pumped to working muscles with each heartbeat, improving oxygen transport.
Her maximum oxygen uptake (VO2 max) would increase through improved oxygen extraction at the muscle tissue level, resulting from greater capillary development around individual muscle fibres.
Continuous training promotes glycogen storage efficiency and fat utilisation as fuel source, delaying glycogen depletion during longer cross-country events.
The training would improve her body’s ability to clear lactate, increasing her anaerobic threshold, allowing her to maintain higher speeds before significant lactate build-up.
These adaptations collectively allow Katie to sustain higher racing speeds with lower perceived exertion during cross-country competitions.

HMS, BM EQ-Bank 776

Compare how continuous aerobic training would differ between a marathon runner preparing for a 42.2 km race and a rugby league player during their preseason training. (4 marks)

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Sample Answer

Marathon runner would implement longer continuous training sessions (1-3 hours) at lower intensity (60-70% MHR) to develop specific endurance capacity required for their event.
rugby league player would use shorter continuous sessions (30-45 minutes) at moderate intensity (70-80% MHR) to develop basic aerobic foundation without compromising sport-specific skill development.
Marathon runner focuses on steady pace maintenance with minimal variation to simulate race conditions, whereas rugby league player may incorporate gradual intensity variations to reflect game demands.
Marathon runner’s continuous training directly simulates competition environment, while rugby league player uses continuous training primarily as foundation before progressing to more sport-specific interval training.

Show Worked Solution

Sample Answer

Marathon runner would implement longer continuous training sessions (1-3 hours) at lower intensity (60-70% MHR) to develop specific endurance capacity required for their event.
rugby league player would use shorter continuous sessions (30-45 minutes) at moderate intensity (70-80% MHR) to develop basic aerobic foundation without compromising sport-specific skill development.
Marathon runner focuses on steady pace maintenance with minimal variation to simulate race conditions, whereas rugby league player may incorporate gradual intensity variations to reflect game demands.
Marathon runner’s continuous training directly simulates competition environment, while rugby league player uses continuous training primarily as foundation before progressing to more sport-specific interval training.

HMS, HIC EQ-Bank 024

The graph below shows the prevalence of diabetes (type 1, type 2 and other diabetes excluding gestational diabetes) in Australia from 2000-2021.

Analyse the trends and discuss what these patterns suggest about the health status of Australians. (6 marks)

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Prevalence measures the proportion of a population who have a specific health condition at a particular point in time.
The graph shows a significant increase in the prevalence of diabetes in Australia from 2000 to approximately 2013, followed by a plateau and slight decrease in the period 2013-2021.
The rising trend during the 2000-2013 period reflects the growing burden of diabetes in Australia, likely influenced by increasing rates of obesity, sedentary lifestyles and an aging population.
The plateau observed after 2013 suggests that prevention strategies, increased awareness, and improvements in early intervention may have begun to show effect, though the high prevalence remains a significant public health concern.
Males consistently show higher prevalence rates than females — growing to approximately 1% higher by the end of the period.
The gender disparity suggests that males may have different risk factor profiles, including potentially higher rates of obesity, poorer diets, or differences in healthcare-seeking behaviour.
Overall, this epidemiological data indicates that while progress may have been made in stabilising diabetes rates, the sustained high prevalence represents a serious ongoing challenge for Australia’s healthcare system.
The health care system must focus on both management of existing cases and prevention of new ones, including some differentiated strategies between males and females.

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Prevalence measures the proportion of a population who have a specific health condition at a particular point in time.
The graph shows a significant increase in the prevalence of diabetes in Australia from 2000 to approximately 2013, followed by a plateau and slight decrease in the period 2013-2021.
The rising trend during the 2000-2013 period reflects the growing burden of diabetes in Australia, likely influenced by increasing rates of obesity, sedentary lifestyles and an aging population.
The plateau observed after 2013 suggests that prevention strategies, increased awareness, and improvements in early intervention may have begun to show effect, though the high prevalence remains a significant public health concern.
Males consistently show higher prevalence rates than females — growing to approximately 1% higher by the end of the period.
The gender disparity suggests that males may have different risk factor profiles, including potentially higher rates of obesity, poorer diets, or differences in healthcare-seeking behaviour.
Overall, this epidemiological data indicates that while progress may have been made in stabilising diabetes rates, the sustained high prevalence represents a serious ongoing challenge for Australia’s healthcare system.
The health care system must focus on both management of existing cases and prevention of new ones, including some differentiated strategies between males and females.

HMS, HIC EQ-Bank 023

Explain how epidemiological data on mortality rates can be used to identify priority health issues in Australia. (3 marks)

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Mortality data identifies the leading causes of death in Australia, allowing health authorities to prioritise resources toward conditions with the highest fatality rates, such as cardiovascular disease and cancers.
Age-standardised mortality rates enable meaningful comparisons across different time periods and population groups, helping to identify which health issues are improving or worsening and which demographic groups are most affected.
Premature mortality measures like potential years of life lost (PYLL) highlight conditions causing death in younger age groups, drawing attention to issues like suicide and road accidents that may not rank as highly in overall mortality statistics but have significant societal impact.

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Mortality data identifies the leading causes of death in Australia, allowing health authorities to prioritise resources toward conditions with the highest fatality rates, such as cardiovascular disease and cancers.
Age-standardised mortality rates enable meaningful comparisons across different time periods and population groups, helping to identify which health issues are improving or worsening and which demographic groups are most affected.
Premature mortality measures like potential years of life lost (PYLL) highlight conditions causing death in younger age groups, drawing attention to issues like suicide and road accidents that may not rank as highly in overall mortality statistics but have significant societal impact.

HMS, BM EQ-Bank 774

An Olympic rower competes in a 2000-metre race lasting approximately 6-7 minutes. Critically analyse how the efficiency of ATP production in different energy systems affects the athlete's pacing strategy and overall performance. (8 marks)

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Sample Answer

During the start of the race (first 30 seconds), the rower relies heavily on the ATP-PCr and glycolytic systems to establish position, despite their relatively lower ATP yield efficiency compared to the aerobic system.
The initial acceleration phase rapidly depletes phosphocreatine stores, necessitating a shift toward the glycolytic system, which produces ATP quickly but inefficiently (2 ATP per glucose molecule).
By the 90-second mark, the aerobic system becomes the predominant energy provider due to its superior efficiency (36-38 ATP per glucose), allowing sustained power output over the middle portion of the race.
The rower must manage the balance between high power output and metabolic efficiency, as rowing at maximum intensity would rely too heavily on the inefficient glycolytic system, leading to premature fatigue.
Optimal race strategy involves establishing an intensity that maximises the contribution of the aerobic system while maintaining sufficient pace, typically working at or slightly above the anaerobic threshold.
In the final 250-500 metres (sprint finish), the rower increases intensity, deliberately sacrificing metabolic efficiency by increasing reliance on the glycolytic system to produce ATP more rapidly.
Highly trained rowers develop metabolic adaptations that improve the efficiency of all three energy systems, particularly enhancing mitochondrial density and enzyme activity in the aerobic system.
Training that specifically targets the power-duration relationship at race pace optimises the efficiency of ATP production at the intensities required during competition, allowing for higher sustainable workloads.
Elite rowers can maintain approximately 70-80% of the energy contribution from the aerobic system even during high-intensity racing, demonstrating the importance of aerobic efficiency to overall performance.

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Sample Answer

During the start of the race (first 30 seconds), the rower relies heavily on the ATP-PCr and glycolytic systems to establish position, despite their relatively lower ATP yield efficiency compared to the aerobic system.
The initial acceleration phase rapidly depletes phosphocreatine stores, necessitating a shift toward the glycolytic system, which produces ATP quickly but inefficiently (2 ATP per glucose molecule).
By the 90-second mark, the aerobic system becomes the predominant energy provider due to its superior efficiency (36-38 ATP per glucose), allowing sustained power output over the middle portion of the race.
The rower must manage the balance between high power output and metabolic efficiency, as rowing at maximum intensity would rely too heavily on the inefficient glycolytic system, leading to premature fatigue.
Optimal race strategy involves establishing an intensity that maximises the contribution of the aerobic system while maintaining sufficient pace, typically working at or slightly above the anaerobic threshold.
In the final 250-500 metres (sprint finish), the rower increases intensity, deliberately sacrificing metabolic efficiency by increasing reliance on the glycolytic system to produce ATP more rapidly.
Highly trained rowers develop metabolic adaptations that improve the efficiency of all three energy systems, particularly enhancing mitochondrial density and enzyme activity in the aerobic system.
Training that specifically targets the power-duration relationship at race pace optimises the efficiency of ATP production at the intensities required during competition, allowing for higher sustainable workloads.
Elite rowers can maintain approximately 70-80% of the energy contribution from the aerobic system even during high-intensity racing, demonstrating the importance of aerobic efficiency to overall performance.

HMS, BM EQ-Bank 773

Evaluate how the efficiency of ATP production impacts the performance of a soccer midfielder who must perform repeated high-intensity efforts throughout a 90-minute match. (6 marks)

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Sample Answer

During explosive sprints and jumps, the midfielder relies on the ATP-PCr system, which efficiently regenerates ATP for immediate energy needs but has limited capacity lasting only 10-15 seconds.
High-intensity runs rely predominantly on the glycolytic system, which produces ATP relatively inefficiently (2 ATP per glucose molecule) but can sustain energy production for 30-45 seconds.
Lower intensity jogging and walking between high-intensity efforts allow the aerobic system to become the primary ATP provider, using its high efficiency (36-38 ATP per glucose) to support recovery processes.
The efficiency of the aerobic system enables the midfielder to recover phosphocreatine stores during low-intensity periods, with approximately 50% recovery occurring within 30 seconds and near-complete recovery within 3-5 minutes.
As the match progresses, the midfielder’s ability to switch efficiently between energy systems becomes crucial for maintaining performance, particularly in the later stages when glycogen stores become partially depleted.
Training that increases the number of energy-producing structures in muscle cells improves how efficiently the aerobic system makes ATP, helping athletes recover faster between sprints and maintain better performance throughout the game.
Tactical awareness that allows strategic rest periods enables the midfielder to maximise the efficiency of ATP regeneration, particularly of the ATP-PCr system, contributing to sustained performance in crucial late-game situations.
Players with greater metabolic efficiency can maintain higher work rates with lower glycogen utilisation, preserving energy stores for critical game moments in the final stages of the match.

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Sample Answer

During explosive sprints and jumps, the midfielder relies on the ATP-PCr system, which efficiently regenerates ATP for immediate energy needs but has limited capacity lasting only 10-15 seconds.
High-intensity runs rely predominantly on the glycolytic system, which produces ATP relatively inefficiently (2 ATP per glucose molecule) but can sustain energy production for 30-45 seconds.
Lower intensity jogging and walking between high-intensity efforts allow the aerobic system to become the primary ATP provider, using its high efficiency (36-38 ATP per glucose) to support recovery processes.
The efficiency of the aerobic system enables the midfielder to recover phosphocreatine stores during low-intensity periods, with approximately 50% recovery occurring within 30 seconds and near-complete recovery within 3-5 minutes.
As the match progresses, the midfielder’s ability to switch efficiently between energy systems becomes crucial for maintaining performance, particularly in the later stages when glycogen stores become partially depleted.
Training that increases the number of energy-producing structures in muscle cells improves how efficiently the aerobic system makes ATP, helping athletes recover faster between sprints and maintain better performance throughout the game.
Tactical awareness that allows strategic rest periods enables the midfielder to maximise the efficiency of ATP regeneration, particularly of the ATP-PCr system, contributing to sustained performance in crucial late-game situations.
Players with greater metabolic efficiency can maintain higher work rates with lower glycogen utilisation, preserving energy stores for critical game moments in the final stages of the match.

	\(X + X \times 0.1\)	\(= 275\)
	\(1.1X\)	\(= 275\)
	\(X\)	\(= 250\)

a.	\(x\)	\(=3 \sec t \)	\(\ \Rightarrow \ \sec t\)	\(=\dfrac{x}{3}\)
	\(y\)	\(=2 \tan t \)	\(\ \Rightarrow \ \tan t\)	\(=\dfrac{y}{2}\)

\(\sec ^2 t+1\)	\(=\tan ^2 t\)
\(\left(\dfrac{y}{2}\right)^2+1\)	\(=\left(\dfrac{x}{3}\right)^2\)
\(\left(\dfrac{x}{3}\right)^2-\left(\dfrac{y}{2}\right)^2\)	\(=1\)

c.i.	\(\underset{\sim}{r}\)	\(=3 \sec (t)\underset{\sim}{i}+2 \tan (t)\underset{\sim}{j}\)
	\(\underset{\sim}{\dot{r}}(t)\)	\(=\dfrac{3 \sin t}{\cos ^2 t}\underset{\sim}{i}+\dfrac{2}{\cos ^2 t} \underset{\sim}{j}\)
	\(\abs{\underset{\sim}{\dot{r}}(t)}^2\)	\(=\dfrac{9 \sin ^2 t}{\cos ^4 t}+\dfrac{4}{\cos ^4 t}\)
		\(=\dfrac{9-9 \cos ^2 t+4}{\cos ^4 t}\)
		\(=\dfrac{13}{\cos ^4 t}-\dfrac{9}{\cos ^2 t}\)
		\(=13 \sec ^4 t-9 \sec ^2 t\)

	\(I\)	\(= Prn\)
	\(1500\)	\(= 7500 \times r \times 3\)
	\(r\)	\(= \dfrac{1500}{7500 \times 3} = 0.0666…\)
		\(= 6.67\% \approx 7\%\)