SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Calculus, EXT1 C2 EQ-Bank 1

Given  \(y=\dfrac{\cos 2 x}{x^2}\),  find the gradient of the tangent of its inverse function at  \(\left(\dfrac{8 \sqrt{2}}{\pi^2}, \dfrac{\pi}{4}\right)\).   (3 marks)

Show Answers Only

\(-\dfrac{\pi^2}{32}\)

Show Worked Solution

\(y=\dfrac{\cos2x}{x^2}\)

\(\text{Inverse: Swap} \ \ x \leftrightarrow y\)

\(x=\dfrac{\cos 2 y}{y^2}\)

\(u=\cos 2 y \ \ \quad \quad \quad v=y^2\)

\(v^{\prime}=-2 \sin 2 y \ \ \quad v^{\prime}=2 y\)

\(\dfrac{dx}{dy}=\dfrac{-2 y^2 \sin 2 y-2 y\, \cos 2 y}{y^4}\)

\(\dfrac{dy}{dx}=\dfrac{y^4}{-2 y^2 \sin 2 y-2 y\, \cos 2 y}\)
 

\(\text{At}\ \ y=\dfrac{\pi}{4}:\)

\(\dfrac{d y}{d x}\) \(=\dfrac{\left(\dfrac{\pi}{4}\right)^4}{-2\left(\dfrac{\pi}{4}\right)^2 \sin \left(\dfrac{\pi}{2}\right)-2\left(\dfrac{\pi}{4}\right) \cos \left(\dfrac{\pi}{2}\right)}\)
  \(=-\dfrac{\pi^4}{256} \times \dfrac{8}{\pi^2}\)
  \(=-\dfrac{\pi^2}{32}\)

Trigonometry, EXT1 T2 EQ-Bank 8

Prove that \(\dfrac{\cos \alpha-\cos (\alpha+2 \beta)}{2 \sin \beta}=\sin (\alpha+\beta)\).   (3 marks)

Show Answers Only
\(\text{LHS}\) \(=\dfrac{\cos \alpha-\cos (\alpha+2 \beta)}{2 \sin \beta}\)
  \(=\dfrac{\cos \alpha-[\cos \alpha\, \cos 2 \beta+\sin \alpha\, \sin 2 \beta]}{2 \sin \beta}\)
  \(=\dfrac{\cos \alpha-\left[\cos \alpha\left(\cos ^2 \beta-\sin ^2 \beta\right)+\sin \alpha(2 \sin \beta\, \cos \beta)\right]}{2 \sin \beta}\)
  \(=\dfrac{\cos \alpha-\cos \alpha\, \cos ^2 \beta+\cos \alpha\, \sin ^2 \beta+2 \sin \alpha\, \sin \beta\, \cos \beta}{2 \sin \beta}\)
  \(=\dfrac{\cos \alpha-\cos \alpha\left(1-\sin ^2 \beta\right)+\cos \alpha\, \sin ^2 \beta+2 \sin \alpha\, \sin \beta\, \cos \beta}{2 \sin \beta}\)
  \(=\dfrac{\cos \alpha-\cos \alpha+\cos \alpha\, \sin ^2 \beta+\cos \alpha\, \sin ^2 \beta+2 \sin \alpha\, \sin \beta\, \cos \beta}{2 \sin \beta}\)
  \(=\dfrac{2 \sin \beta(\cos \alpha\, \sin \beta+\sin \alpha\, \cos \beta)}{2 \sin \beta}\)
  \(=\sin (\alpha+\beta)\)
Show Worked Solution
\(\text{LHS}\) \(=\dfrac{\cos \alpha-\cos (\alpha+2 \beta)}{2 \sin \beta}\)
  \(=\dfrac{\cos \alpha-[\cos \alpha\, \cos 2 \beta+\sin \alpha\, \sin 2 \beta]}{2 \sin \beta}\)
  \(=\dfrac{\cos \alpha-\left[\cos \alpha\left(\cos ^2 \beta-\sin ^2 \beta\right)+\sin \alpha(2 \sin \beta\, \cos \beta)\right]}{2 \sin \beta}\)
  \(=\dfrac{\cos \alpha-\cos \alpha\, \cos ^2 \beta+\cos \alpha\, \sin ^2 \beta+2 \sin \alpha\, \sin \beta\, \cos \beta}{2 \sin \beta}\)
  \(=\dfrac{\cos \alpha-\cos \alpha\left(1-\sin ^2 \beta\right)+\cos \alpha\, \sin ^2 \beta+2 \sin \alpha\, \sin \beta\, \cos \beta}{2 \sin \beta}\)
  \(=\dfrac{\cos \alpha-\cos \alpha+\cos \alpha\, \sin ^2 \beta+\cos \alpha\, \sin ^2 \beta+2 \sin \alpha\, \sin \beta\, \cos \beta}{2 \sin \beta}\)
  \(=\dfrac{2 \sin \beta(\cos \alpha\, \sin \beta+\sin \alpha\, \cos \beta)}{2 \sin \beta}\)
  \(=\sin (\alpha+\beta)\)

HMS, BM 2023 HSC 18 MC

Four Year 7 students on a school camp are participating in archery. Each student had five shots at the target. The centre of the target represents the best possible shot.

The location of each student's five shots are represented by X on the targets shown.

Which student is most likely to be at the associative stage of skill acquisition?
 

 

Show Answers Only

\(A\)

Show Worked Solution
  • A is correct: The associative stage shows improved consistency (grouping of shots) but not perfect accuracy, indicating the learner is refining their technique.

Other Options:

  • B is incorrect: Target B shows shots scattered widely across the target (cognitive stage – inconsistent and inaccurate).
  • C is incorrect: Target C shows shots clustered around the centre (late associative/early autonomous).
  • D is incorrect: Target D shows shots widely dispersed (cognitive stage).

♦♦ Mean mark 43%.

HMS, TIP 2023 HSC 17 MC

The following graph represents aerobic and anaerobic threshold training zones.

Which letter on the graph represents the minimum intensity for an athlete to train to produce a physiological improvement in performance?

  1. W
  2. X
  3. Y
  4. Z
Show Answers Only

\(B\)

Show Worked Solution
  • B is correct: Position X represents the aerobic threshold, the minimum intensity required for physiological adaptations.

Other Options:

  • A is incorrect: Position W is below the aerobic threshold and won’t produce significant adaptations.
  • C is incorrect: Position Y is higher intensity than needed for minimum improvement.
  • D is incorrect: Position Z represents anaerobic threshold, beyond minimum requirement.

♦♦♦ Mean mark 36%.

HMS, HAG 2023 HSC 16 MC

Which row of the table correctly matches the type of cancer?

  Carcinoma Leukaemia
A.   Forms only on the skin Originates in bones and
connective tissues
B. Forms from cells that release
hormones into the blood		 Develops in the body’s
infection-fighting organs
C. Forms in epithelial tissue Originates in the blood-forming
tissue of the bone marrow
D. Usually found in the
gastrointestinal system		 Originates in plasma cells
Show Answers Only

\(C\)

Show Worked Solution
  • C is correct: Carcinomas develop in epithelial tissue and leukemia originates in blood-forming tissue of bone marrow.

Other Options:

  • A is incorrect: Carcinomas can form in many tissues, not just skin; leukemia doesn’t originate in bones/connective tissues.
  • B is incorrect: Hormone-releasing cells would be neuroendocrine tumors; infection-fighting organs relates to lymphoma.
  • D is incorrect: Gastrointestinal limitation is incorrect; plasma cells relate to multiple myeloma, not leukemia.

♦ Mean mark 54%.

HMS, BM 2023 HSC 15 MC

Which of the following best describes an athlete who is a skilled performer?

  1. Displays high levels of confidence and natural ability in their chosen sport
  2. Displays superior technique when executing discrete movements autonomously
  3. Possesses inherited physical attributes essential for success in their chosen sport
  4. Possesses instinctive awareness and the ability to adjust movements mid performance
Show Answers Only

\(D\)

Show Worked Solution
  • D is correct: Skilled performers demonstrate kinaesthetic awareness and can make automatic adjustments during performance.

Other Options:

  • A is incorrect: Confidence and natural ability don’t necessarily indicate skilled performance.
  • B is incorrect: Superior technique is important but adaptation is key to skilled performance.
  • C is incorrect: Physical attributes alone don’t define skilled performance.

♦ Mean mark 51%.

HMS, HAG 2023 HSC 13 MC

The following graphs represent the age and biological sex of Australia's population in 2000 (observed) and 2051 (projected).

Which action would the Australian Government need to implement in 2023 to best support the health of Australians in 2051?

  1. Increase the number of staff in aged care facilities
  2. Develop legislation to regulate the use of e-cigarettes
  3. Target strategic planning to improve the health of infants
  4. Increase funding and research into Alzheimer's disease and dementia
Show Answers Only

\(D\)

Show Worked Solution
  • D is correct: The population projections show significant growth in older age brackets by 2051, when conditions like Alzheimer’s and dementia become prevalent.

Other Options:

  • A is incorrect: Staffing aged care addresses current not future needs shown in the projections.
  • B is incorrect: E-cigarette regulation impacts younger populations primarily.
  • C is incorrect: Infant health strategies don’t address the aging population challenge shown in the data.

♦♦ Mean mark 39%.

HMS, HAG 2023 HSC 10 MC

Which of the following incentives was introduced by the Australian Government to encourage individuals to take out private health insurance?

  1. Entitlement to a mental health treatment plan
  2. Guaranteed 50% rebate on all ancillary services
  3. Free admission for treatment in private hospitals
  4. Exemption from paying the Medicare levy surcharge
Show Answers Only

\(D\)

Show Worked Solution
  • D is correct: Medicare levy surcharge exemption introduced as a financial incentive to encourage private health insurance uptake.

Other Options:

  • A is incorrect: Mental health treatment plans are available through Medicare, not linked to private insurance.
  • B is incorrect: No guarantee of 50% rebate on all ancillary services exists.
  • C is incorrect: Private hospitals still charge for admission despite insurance.

♦♦ Mean mark 45%.

HMS HAG 2023 HSC 8 MC

What strategy would be most effective in improving equity of access to health services for Aboriginal and Torres Strait Islander peoples?

  1. Increasing awareness of online health resources
  2. Increasing the funding for child immunisation programs
  3. Providing a telephone or video consultation with a specialist
  4. Implementing training for community members to become health care providers
Show Answers Only

\(D\)

Show Worked Solution
  • D is correct: Training community members addresses cultural barriers and sustainability by building capacity within Aboriginal and Torres Strait Islander communities.

Other Options:

  • A is incorrect: Online resources may not address cultural barriers or internet access issues.
  • B is incorrect: Child immunisation doesn’t address broader healthcare access barriers.
  • C is incorrect: Telehealth helps but doesn’t address cultural barriers comprehensively.

♦♦ Mean mark 39%.

HMS, HAG 2023 HSC 6 MC

The following table represents the number of deaths per 100000 population in males aged 55-64 years in 1980 and again in 2020 for a range of conditions.

Conditions Male deaths per 100 000 population
aged 55–64
1980 2020
J 14 7
K 100 20
L 173 53
M 600 79

Which condition is represented by the letter \(J\) in the table? 

  1. Skin cancer
  2. Lung cancer
  3. Coronary heart disease
  4. Cerebrovascular disease
Show Answers Only

\(A\)

Show Worked Solution
  • A is correct: Data shows condition J had smallest number of deaths per 100,000 in both 1980 and 2020, consistent with skin cancer mortality patterns.

Other Options:

  • B is incorrect: Would show higher mortality rates than displayed for condition J.
  • C is incorrect: Has significantly higher mortality rates than shown.
  • D is incorrect: Higher mortality rate than condition J.

♦♦ Mean mark 41%.

HMS, HIC EQ-Bank 083

Using ONE health-related issue affecting young people, analyse both the causes and protective factors that can protect and enhance young people's health.   (8 marks)

Show Answers Only

*PEEL – Solution is structured using an adjusted PEEL method; [P] Identify components and their relationship, [E] explain the interaction/influence between them, [Ev] provide evidence showing the relationship in action, [L] linking sentence back to question.

Sample Answer – Health issue: Sense of body and self 

  • [P] Social media exposure and peer pressure interact to create body image issues.
  • [E] The relationship between online content and social comparison shows how digital platforms amplify appearance concerns.
  • [Ev] Mission Australia’s 2023 report confirms body image ranks in top four youth concerns, with one-third developing disordered eating.
  • [L] This interaction demonstrates how external influences directly shape health outcomes.
     
  • [P] Unrealistic media beauty standards interact with existing psychological vulnerabilities in young people.
  • [E] This combination directly damages self-worth when edited images trigger personal insecurities about appearance.
  • [Ev] Research shows that as a consequence of viewing perfect bodies daily via social media, teens report significantly higher anxiety about appearance.
  • [L] These elements combine to produce body dissatisfaction among young people.
     
  • [P] Health literacy functions as a primary protective mechanism.
  • [E] The dynamic between education and resilience shows critical thinking skills disrupt harmful messages.
  • [Ev] School programs teaching media analysis reduce young people’s body dissatisfaction significantly within six months.
  • [L] This establishes a cause-effect pattern where knowledge directly counters negative influences.
     
  • [P] Family support can help counteract negative peer influences on body image.
  • [E] While peers provide appearance pressure, families contribute acceptance and unconditional support.
  • [Ev] Young people with supportive families show 50% lower rates of eating disorders despite social pressures.
  • [L] Together, these factors determine whether external messages translate into actual harm.
Show Worked Solution

*PEEL – Solution is structured using an adjusted PEEL method; [P] Identify components and their relationship, [E] explain the interaction/influence between them, [Ev] provide evidence showing the relationship in action, [L] linking sentence back to question.

Sample Answer – Health issue: Sense of body and self 

  • [P] Social media exposure and peer pressure interact to create body image issues.
  • [E] The relationship between online content and social comparison shows how digital platforms amplify appearance concerns.
  • [Ev] Mission Australia’s 2023 report confirms body image ranks in top four youth concerns, with one-third developing disordered eating.
  • [L] This interaction demonstrates how external influences directly shape health outcomes.
     
  • [P] Unrealistic media beauty standards interact with existing psychological vulnerabilities in young people.
  • [E] This combination directly damages self-worth when edited images trigger personal insecurities about appearance.
  • [Ev] Research shows that as a consequence of viewing perfect bodies daily via social media, teens report significantly higher anxiety about appearance.
  • [L] These elements combine to produce body dissatisfaction among young people.
     
  • [P] Health literacy functions as a primary protective mechanism.
  • [E] The dynamic between education and resilience shows critical thinking skills disrupt harmful messages.
  • [Ev] School programs teaching media analysis reduce young people’s body dissatisfaction significantly within six months.
  • [L] This establishes a cause-effect pattern where knowledge directly counters negative influences.
     
  • [P] Family support can help counteract negative peer influences on body image.
  • [E] While peers provide appearance pressure, families contribute acceptance and unconditional support.
  • [Ev] Young people with supportive families show 50% lower rates of eating disorders despite social pressures.
  • [L] Together, these factors determine whether external messages translate into actual harm.

HMS, HIC EQ-Bank 081

To what extent do the determinants of health influence the health status of young Australians? In your response, consider major determinants that most significantly impact young people's health.   (12 marks)

Show Answers Only

Judgment Statement

  • Determinants of health influence young Australians’ health to a significant extent, with socioeconomic, environmental and biomedical factors playing a critical role in shaping health outcomes.

Socioeconomic Determinants

  • Evidence supporting this significant influence includes family income controlling health opportunities.
  • Wealthy families can access private healthcare and afford gym memberships while poor families cannot.
  • Youth from the lowest income areas have double the obesity rates and relatively limited access to mental health services.
  • Education has a huge influence on health literacy with children of university-educated parents much more likely to make informed and better health choices.

Biomedical Determinants

  • Genetic factors significantly shape youth health regardless of personal choices or behaviours.
  • Biomedical determinants like predisposition to diabetes, asthma or mental illness affect young people regardless of status.
  • Hormonal changes during puberty universally impact young people’s mood and risk-taking.
  • These biological factors establish baseline health that other determinants modify.

Environmental Determinants

  • Geographic location profoundly impacts health access.
  • Examples of this include rural youth facing specialist shortages and often many travelling hours for treatment, and urban youth dealing with air pollution and overcrowding.
  • Built environments can have an oversized effect on youth activity levels through bike paths and sports facilities.

Interactions of Determinants

  • Determinants rarely work in isolation.
  • Poor rural youth face triple disadvantage – low income, limited services and environmental hazards compound together.
  • Wealthy urban youth can overcome genetic predispositions through healthcare access.
  • These determinants can interplay to either magnify or mitigate health risks, demonstrating their profound influence on all Australian young people.

Reaffirmation

  • The significant influence of health determinants becomes undeniable when examining health data.
  • Location, income and genetics predict many outcomes, significantly reducing an individual’s control over their own health.
  • Positively addressing these influences demands system-level interventions targeting root causes rather than expecting young people to overcome structural disadvantages alone.
Show Worked Solution

Judgment Statement

  • Determinants of health influence young Australians’ health to a significant extent, with socioeconomic, environmental and biomedical factors playing a critical role in shaping health outcomes.

Socioeconomic Determinants

  • Evidence supporting this significant influence includes family income controlling health opportunities.
  • Wealthy families can access private healthcare and afford gym memberships while poor families cannot.
  • Youth from the lowest income areas have double the obesity rates and relatively limited access to mental health services.
  • Education has a huge influence on health literacy with children of university-educated parents much more likely to make informed and better health choices.

Biomedical Determinants

  • Genetic factors significantly shape youth health regardless of personal choices or behaviours.
  • Biomedical determinants like predisposition to diabetes, asthma or mental illness affect young people regardless of status.
  • Hormonal changes during puberty universally impact young people’s mood and risk-taking.
  • These biological factors establish baseline health that other determinants modify.

Environmental Determinants

  • Geographic location profoundly impacts health access.
  • Examples of this include rural youth facing specialist shortages and often many travelling hours for treatment, and urban youth dealing with air pollution and overcrowding.
  • Built environments can have an oversized effect on youth activity levels through bike paths and sports facilities.

Interactions of Determinants

  • Determinants rarely work in isolation.
  • Poor rural youth face triple disadvantage – low income, limited services and environmental hazards compound together.
  • Wealthy urban youth can overcome genetic predispositions through healthcare access.
  • These determinants can interplay to either magnify or mitigate health risks, demonstrating their profound influence on all Australian young people.

Reaffirmation

  • The significant influence of health determinants becomes undeniable when examining health data.
  • Location, income and genetics predict many outcomes, significantly reducing an individual’s control over their own health.
  • Positively addressing these influences demands system-level interventions targeting root causes rather than expecting young people to overcome structural disadvantages alone.

HMS, HIC EQ-Bank 066 MC

Which of the following statements accurately reflects the trend in obesity rates among young people in Australia from 1995 to 2017-18?

  1. Rates steadily declined across all age groups of children and young people.
  2. Rates remained stable with minimal fluctuation over the period.
  3. Rates initially increased but more recently show a trend toward fewer young people being overweight.
  4. Rates consistently increased at the same rate for both males and females in the 5-17 age group.
Show Answers Only

\(C\)

Show Worked Solution
  • C is correct as the data shows that although rates of obesity had been rising over time, more recent figures show a slightly declining trend.

Other options:

  • A is incorrect because rates did not steadily decline across the entire period; they initially increased before showing signs of decline more recently.
  • B is incorrect because there were significant fluctuations in the rates over the period rather than stability.
  • D is incorrect because there’s no evidence of this trend.

PHYSICS, M2 EQ-Bank 1

Jordan is trying to push a heavy filing cabinet across the office floor, but it’s not budging. The cabinet has been used by physics students, and someone has stuck a post-it note on it with a “reminder” that reads:

“According to Newton’s third law, the cabinet pushes back with the same force you apply — so you’ll never move it!”

Jordan sighs and tries harder. Another note on the cabinet reads:

“Don’t bother! The law of conservation of momentum says that if the cabinet is at rest, its momentum must stay at zero forever.”

Identify and explain the two misunderstandings about Newton’s third law and the law of conservation of momentum. Use correct physics principles to explain how Jordan can, in fact, move the filing cabinet.    (5 marks)

Show Answers Only

Newton’s third law misconception:

  • Newton’s third law states that every action has an equal and opposite reaction, but these force pairs act on different objects.
  • Jordan pushes the cabinet, and the cabinet pushes back on him with equal force. These forces do not cancel because they act on separate objects.
  • The motion of the cabinet depends on the net force acting on it, according to Newton’s second law:  \(F_{\text{net}} = ma\).

 Conservation of momentum misconception:

  • Momentum is conserved only in a closed system with no external net forces.
  • Since Jordan exerts an external force on the cabinet and the floor provides friction, the cabinet is not a closed system.
  • Therefore, momentum conservation does not prevent Jordan from moving the cabinet.

 How Jordan can move the cabinet:

  • By bracing his feet, Jordan increases backward friction against the floor, allowing him to exert a greater forward force.
  • If this force exceeds static friction, the cabinet accelerates and its momentum changes:  \(\Delta p = F \Delta t\).
Show Worked Solution

Newton’s third law misconception:

  • Newton’s third law states that every action has an equal and opposite reaction, but these force pairs act on different objects.
  • Jordan pushes the cabinet, and the cabinet pushes back on him with equal force. These forces do not cancel because they act on separate objects.
  • The motion of the cabinet depends on the net force acting on it, according to Newton’s second law:  \(F_{\text{net}} = ma\).

 Conservation of momentum misconception:

  • Momentum is conserved only in a closed system with no external net forces.
  • Since Jordan exerts an external force on the cabinet and the floor provides friction, the cabinet is not a closed system.
  • Therefore, momentum conservation does not prevent Jordan from moving the cabinet.

 How Jordan can move the cabinet:

  • By bracing his feet, Jordan increases backward friction against the floor, allowing him to exert a greater forward force.
  • If this force exceeds static friction, the cabinet accelerates and its momentum changes:  \(\Delta p = F \Delta t\).

Functions, EXT1 F1 F2 EQ-Bank 1

The polynomial  \(P(x)=x^3+2 x^2-19 x-20\)  has three distinct roots, where one root is the sum of the other two roots.

Find the values of the three roots.   (3 marks)

Show Answers Only

\(\text{Roots: \(-5,-1\) and  \(4\).}\)

Show Worked Solution

\(P(x)=x^3+2 x^2-19 x-20\)

\(\text{Let roots}=\alpha, \beta, \alpha+\beta\)

\(\alpha+\beta+(\alpha+\beta)\) \(=-\dfrac{b}{a}=-2\)
\(2 \alpha+2 \beta\) \(=-2\)
\(\alpha\) \(=-1-\beta\ \ldots\ (1)\)

\(\alpha \times \beta \times(\alpha+\beta)\) \(=-\dfrac{d}{a}=20\)
\(\alpha^2 \beta+\alpha \beta^2\) \(=20\ \ldots\ (2)\)

 
\(\text{Substitute (1) into (2):}\)

\((-1-\beta)^2 \beta+(-1-\beta) \beta^2\) \(=20\)
\(\left(1+2 \beta+\beta^2\right) \beta+\left(-\beta^2-\beta^3\right)\) \(=20\)
\(\beta+2 \beta^2+\beta^3-\beta^2-\beta^3\) \(=20\)
\(\beta^2+\beta-20\) \(=0\)
\((\beta+5)(\beta-4)\) \(=0\)

 
\(\Rightarrow \ \beta=-5 \ \ \text {or} \ \ 4\)

\(\text{If} \ \ \beta=-5, \alpha=4 \ \ \text {and if} \ \ \beta=4, \alpha=-5\)

\(\therefore \ \text{Roots: \(-5, -1\) and \(4\).}\)

HMS, HIC EQ-Bank 65 MC

Research into youth mental health shows increasing rates of anxiety and depression.

Which of the following most accurately represents the causal factors behind this trend?

  1. Genetic predispositions combined with increased diagnostic awareness in healthcare settings.
  2. Academic pressure, decreased physical activity levels and changing family structures.
  3. Social media influence, performance pressures, reduced community connection and improved diagnostic methods.
  4. Increased screen time, disrupted sleep patterns and changing social interaction styles.
Show Answers Only

\(C\)

Show Worked Solution
  • C is correct as it acknowledges the complex, multifactorial nature of mental health trends, including social, environmental and detection factors.

Other options:

  • A is incorrect because while genetics and increased awareness play roles, this combination doesn’t capture the full complexity of causal factors.
  • B is incorrect because while these are contributing factors, they represent an incomplete view of the multifaceted causes.
  • D is incorrect because while these are relevant factors, they represent a narrower view that doesn’t account for broader social and diagnostic elements.

HMS, HIC EQ-Bank 62 MC

The risk factors and protective factors that influence health outcomes primarily vary according to which of the following?

  1. The biological sex and gender identity of an individual.
  2. The specific health issue or condition being examined.
  3. The income level and educational attainment of individuals.
  4. The ethnic heritage and cultural practices of communities.
Show Answers Only

\(B\)

Show Worked Solution
  • B is correct because each health issue has its own unique set of risk and protective factors.

Other options:

  • A is incorrect because biological sex and gender can influence but are not the primary determinant of all risk and protective factors.
  • C is incorrect because socioeconomic status, while important, is not the primary determinant.
  • D is incorrect because while cultural background can influence health behaviours and outcomes, it is not the primary determinant.

HMS, HIC EQ-Bank 76

The graph below shows the life expectancy of indigenous vs non-indigenous males and females in city and rural locations.
 

Analyse the key trends in this data.   (8 marks)

Show Answers Only

*PEEL – Solution is structured using an adjusted PEEL method; [P] Identify components and their relationship, [E] explain the interaction/influence between them, [Ev] provide evidence showing the relationship in action, [L] linking sentence back to question.

Geographic Disparities Within ATSI Population

  • [P] The data reveals significant geographic disparities in life expectancy within the Aboriginal and Torres Strait Islander (ATSI) population.
  • [E] This pattern demonstrates how location directly influences health outcomes for Indigenous Australians, with rural residence creating additional disadvantage.
  • [Ev] The graph shows rural ATSI people have markedly shorter lives than their urban counterparts, reflecting limited access to healthcare services and preventative programs. For example, city males have a 3-year higher life expectancy than rural males (73 vs 70).
  • [L] This geographic disparity highlights how environmental determinants compound existing health challenges for rural Indigenous communities.

 
ATSI vs Non-Indigenous Life Expectancy Gap

  • [P] A persistent life expectancy gap exists between Indigenous and non-Indigenous populations across all locations.
  • [E] This consistent disparity indicates systemic health inequities affecting ATSI communities regardless of geographic setting.
  • [Ev] The graph demonstrates both urban and rural ATSI populations have lower life expectancies than non-Indigenous Australians in comparable locations. For example, city non-indigenous females have a 7-year higher life expectancy than rural city indigenous females (85 vs 78).
  • [L] These findings suggest addressing Indigenous health requires both location-specific approaches and broader structural reforms.

 
Gender Disparities Within ATSI Population

  • [P] Notable gender differences exist in Indigenous life expectancy patterns.
  • [E] This gender disparity reflects different health challenges and risk factors affecting ATSI males and females.
  • [Ev] The graph shows ATSI women consistently outlive ATSI men in both rural and urban settings.
  • [L] This pattern indicates the need for gender-specific approaches within Indigenous health initiatives.
Show Worked Solution

*PEEL – Solution is structured using an adjusted PEEL method; [P] Identify components and their relationship, [E] explain the interaction/influence between them, [Ev] provide evidence showing the relationship in action, [L] linking sentence back to question.

Geographic Disparities Within ATSI Population

  • [P] The data reveals significant geographic disparities in life expectancy within the Aboriginal and Torres Strait Islander (ATSI) population.
  • [E] This pattern demonstrates how location directly influences health outcomes for Indigenous Australians, with rural residence creating additional disadvantage.
  • [Ev] The graph shows rural ATSI people have markedly shorter lives than their urban counterparts, reflecting limited access to healthcare services and preventative programs. For example, city males have a 3-year higher life expectancy than rural males (73 vs 70).
  • [L] This geographic disparity highlights how environmental determinants compound existing health challenges for rural Indigenous communities.

 
ATSI vs Non-Indigenous Life Expectancy Gap

  • [P] A persistent life expectancy gap exists between Indigenous and non-Indigenous populations across all locations.
  • [E] This consistent disparity indicates systemic health inequities affecting ATSI communities regardless of geographic setting.
  • [Ev] The graph demonstrates both urban and rural ATSI populations have lower life expectancies than non-Indigenous Australians in comparable locations. For example, city non-indigenous females have a 7-year higher life expectancy than rural city indigenous females (85 vs 78).
  • [L] These findings suggest addressing Indigenous health requires both location-specific approaches and broader structural reforms.

 
Gender Disparities Within ATSI Population

  • [P] Notable gender differences exist in Indigenous life expectancy patterns.
  • [E] This gender disparity reflects different health challenges and risk factors affecting ATSI males and females.
  • [Ev] The graph shows ATSI women consistently outlive ATSI men in both rural and urban settings.
  • [L] This pattern indicates the need for gender-specific approaches within Indigenous health initiatives.

HMS, HIC EQ-Bank 075

Assess the extent to which socioeconomic and environmental determinants influence the health behaviours and outcomes of young people.   (8 marks)

Show Answers Only

Judgment Statement

  • Socioeconomic and environmental determinants demonstrate significant influence on youth health outcomes.
  • This assessment examines the magnitude of health disparities caused by socioeconomic and environmental determinants and the effectiveness of intervention.

Determinants and Health Disparities

  • These determinants have significant impact on creating health inequalities among young people.
  • Environmental determinants include remoteness. Rural youth may have to travel for hours to access specialist care, producing measurable health delays.
  • Socio-economic determinants can include poor diets where low-income youth face triple the obesity rates due to limited healthy food access.
  • These determinants can also work in combination to compound health disparities. For example, wealthy suburbs offering significantly more sport facilities encourage young people to be active whereas the opposite is true in poor, lower socio-economic areas.
  • This demonstrates how socio-economic and environmental determinants can work in tandem to create highly divergent health pathways.

Intervention Effectiveness

  • Current efforts show limited success in overcoming socioeconomic and environmental determinant-based barriers.
  • While programs exist, rural youth may still have to travel for hours to access specialist care, producing measurable health delays.
  • Environmental improvements prove moderately successful – new bike paths increase activity by 25% but can’t fully compensate for socioeconomic disadvantages.
  • Targeted interventions achieve adequate results in specific areas but fail to address systemic inequalities.
  • On balance, this proves interventions remain insufficient against powerful structural forces.

Overall Assessment

  • When all factors are considered, socioeconomic and environmental determinants exert major influence over youth health.
  • These forces create substantial, persistent health gaps starting early in life.
  • The assessment reveals an urgent need for comprehensive policy changes addressing root causes rather than symptoms.
  • Without systemic intervention, these determinants will continue producing considerable health inequalities across generations.
Show Worked Solution

Judgment Statement

  • Socioeconomic and environmental determinants demonstrate significant influence on youth health outcomes.
  • This assessment examines the magnitude of health disparities caused by socioeconomic and environmental determinants and the effectiveness of intervention.

Determinants and Health Disparities

  • These determinants have significant impact on creating health inequalities among young people.
  • Environmental determinants include remoteness. Rural youth may have to travel for hours to access specialist care, producing measurable health delays.
  • Socio-economic determinants can include poor diets where low-income youth face triple the obesity rates due to limited healthy food access.
  • These determinants can also work in combination to compound health disparities. For example, wealthy suburbs offering significantly more sport facilities encourage young people to be active whereas the opposite is true in poor, lower socio-economic areas.
  • This demonstrates how socio-economic and environmental determinants can work in tandem to create highly divergent health pathways.

Intervention Effectiveness

  • Current efforts show limited success in overcoming socioeconomic and environmental determinant-based barriers.
  • While programs exist, rural youth may still have to travel for hours to access specialist care, producing measurable health delays.
  • Environmental improvements prove moderately successful – new bike paths increase activity by 25% but can’t fully compensate for socioeconomic disadvantages.
  • Targeted interventions achieve adequate results in specific areas but fail to address systemic inequalities.
  • On balance, this proves interventions remain insufficient against powerful structural forces.

Overall Assessment

  • When all factors are considered, socioeconomic and environmental determinants exert major influence over youth health.
  • These forces create substantial, persistent health gaps starting early in life.
  • The assessment reveals an urgent need for comprehensive policy changes addressing root causes rather than symptoms.
  • Without systemic intervention, these determinants will continue producing considerable health inequalities across generations.

HMS, HIC EQ-Bank 72

Explain how the increased accessibility of technology and global events has influenced the health behaviours of young people in Australia. In your answer, provide specific examples.   (5 marks)

Show Answers Only

*Language highlighting the cause-effect relationship is bolded in the answer below.

  • Increased screen time due to smartphone and social media accessibility has reduced physical activity levels among young people. This leads to higher rates of sedentary behaviour and obesity.
  • Global events like COVID-19 pandemic disrupted normal routines. This causes both challenges (increased anxiety and depression) and opportunities (tele-health availability) for young people’s health.
  • Social media platforms expose young people to unrealistic body images and beauty standards. As a result, this contributes to poor body image and eating disorders.
  • Technology provides greater access to health information. This enables young people to become more informed about health issues, though this relationship results in misinformation spreading without critical evaluation skills.
  • Global connectivity through technology allows health trends to spread rapidly. This process ensures both positive (fitness challenges) and negative (dangerous viral challenges) impacts reach young people’s health behaviours quickly.
  • Online communities provide support networks for young people experiencing health issues. This interaction allows reduced isolation and demonstrates why help-seeking behaviours are becoming normalised.
Show Worked Solution

*Language highlighting the cause-effect relationship is bolded in the answer below.

  • Increased screen time due to smartphone and social media accessibility has reduced physical activity levels among young people. This leads to higher rates of sedentary behaviour and obesity.
  • Global events like COVID-19 pandemic disrupted normal routines. This causes both challenges (increased anxiety and depression) and opportunities (tele-health availability) for young people’s health.
  • Social media platforms expose young people to unrealistic body images and beauty standards. As a result, this contributes to poor body image and eating disorders.
  • Technology provides greater access to health information. This enables young people to become more informed about health issues, though this relationship results in misinformation spreading without critical evaluation skills.
  • Global connectivity through technology allows health trends to spread rapidly. This process ensures both positive (fitness challenges) and negative (dangerous viral challenges) impacts reach young people’s health behaviours quickly.
  • Online communities provide support networks for young people experiencing health issues. This interaction allows reduced isolation and demonstrates why help-seeking behaviours are becoming normalised.

PHYSICS, M2 EQ-Bank 12 MC

A 200 g tennis ball is dropped from a height of 2.0 m onto a hard surface. After the first bounce, it reaches a height of 1.4 m. After a second bounce, it reaches a height of 0.98 m.

What is the percentage of mechanical energy lost in the second bounce?

  1. 30%
  2. 42%
  3. 70%
  4. 80%
Show Answers Only

\(A\)

Show Worked Solution
  • Energy lost (2nd bounce) = difference in potential energy before and after the second bounce:
\(\Delta PE\) \(=mgh_1-mgh_2\)  
  \(=0.2 \times 9.8 \times 1.4-0.2 \times 9.8 \times 0.98\)  
  \(=0.8232\ \text{J}\)  

 

\(\text{Energy loss (%)}\) \(=\dfrac{0.8232}{0.2 \times 9.8 \times 1.4} \times 100=30\%\)  

 
\(\Rightarrow A\)

PHYSICS, M2 EQ-Bank 5

Liam is carrying two boxes stacked on top of each other to a customer. The lighter 2.8 kg box is placed on top of the heavier 4.2 kg box.

Liam lifts the stack by applying an upward force of 40 N with each hand to the bottom of the heavier box, as shown below.
 

  1. Calculate the magnitude of the acceleration of the boxes as Liam lifts them.   (2 marks)
  1. Explain why the force that the 4.2 kg box applies to the 2.8 kg box is greater while the boxes are being accelerated than when they are stationary.   (2 marks)
Show Answers Only

a.    \(1.63\ \text{ms}^{-2}\)

b.    When the boxes are at rest:

  • The force that the 4.2 kg box applies to the 2.8 kg box is equal and opposite weight force of the 2.8 kg box.

When the boxes are accelerating:

  • The net force of the system is positive as the system is accelerating.
  • The 4.2 kg box must be applying extra force to the 2.8 kg box to cause it to accelerate at 1.63 ms\(^{-2}\).
Show Worked Solution
a.     \(F_{\text{net}}\) \(=\) total applied force upwards \(-\) weight force of the two boxes
    \(= (2 \times 40)-(7 \times 9.8)\)
    \(=11.4\ \text{N}\)

 
\(a=\dfrac{F_{\text{net}}}{m}=\dfrac{11.4}{7.0}=1.63\ \text{ms}^{-2}\)
  

b.    When the boxes are at rest:

  • The force that the 4.2 kg box applies to the 2.8 kg box is equal and opposite weight force of the 2.8 kg box.

When the boxes are accelerating:

  • The net force of the system is positive as the system is accelerating.
  • The 4.2 kg box must be applying extra force to the 2.8 kg box to cause it to accelerate at 1.63 ms\(^{-2}\).

Recursion, GEN2 2024 NHT 8

Cleo owns equipment that was purchased for $50 000.

She depreciates the value of the equipment using the unit cost method.

Let \(V_n\) be the value of the equipment, in dollars, after \(n\) units of use.

A recurrence relation that can model this value from one unit of use to the next is given by

\(V_0=50\,000, \quad V_{n+1}=V_n-k\)

  1. What does \(k\) represent in this recurrence relation?   (1 mark)

  2. If  \(k=12.50\), determine the value of the equipment after one year if it is used twice per day on all 365 days of the year.   (1 mark)

Another option for Cleo is to depreciate the value of the $50 000 equipment using the reducing balance method.

The value of the equipment, in dollars, after \(n\) months, \(V_n\), can be modelled by a recurrence relation of the form

\(V_0=50\,000, \quad V_{n+1}=R V_n\)

  1. If the depreciation rate per month was 1.5%, what would be the value of \(R\) in this recurrence relation?   (1 mark)

  2. For what value of \(R\) would the equipment be valued at $42 868.75 after three months?   (1 mark)

Show Answers Only

a.   \(k\ \text{represents the depreciation per unit of use.}\)

b.   \(V_{730} =\$40\,875\)

c.   \(R=0.985\)

d.   \(R=0.95\)

Show Worked Solution

a.   \(k\ \text{represents the depreciation per unit of use.}\)
 

b.   \(\text{Units of use}\ = 365 \times 2=730\)

\(V_{730} = 50\,000-(730 \times 12.5)=\$40\,875\)
 

c.   \(R=1-0.015=0.985\)
 

d.   \(\text{Find \(R\) such that:}\)

\(R^{3} \times 50\,000\) \(= 42\,868.75 \)  
\(R\) \(=\sqrt[3]{\dfrac{42\,868.75}{50\,000}}\)  
  \(=0.95\)  

Recursion, GEN2 2024 NHT 7

Cleo took out a reducing balance loan to buy an apartment.

Interest on this loan is charged monthly and the loan is scheduled to be repaid in full with monthly repayments over 20 years.

The balance of Cleo's loan, in dollars, after \(n\) months, \(C_n\), can be modelled by the recurrence relation

\(C_0=560\,000\ \qquad \ \  C_{n+1}=1.005C_n-4012\)

  1. What amount, in dollars, did Cleo borrow?   (1 mark)

  2. Determine the total value, in dollars, of the repayments made by Cleo in the first year of the loan.   (1 mark)

  3. The interest rate for Cleo's loan is 6% per annum.    
  4. Use this value in a calculation to show that the multiplication factor in the recurrence relation is 1.005   (1 mark)
  5. Complete the next line in the amortisation table.
  6. Write your answers in the spaces provided in the table below.   (1 mark)

\begin{array}{|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Payment} & \text{Repayment} & \quad \text{Interest} \quad & \text{Principal reduction} & \quad \text{Balance} \quad \\
\text{number} \rule[-1ex]{0pt}{0pt}& \text{(\$)} & \text{(\$)} & \text{(\$)} & \text{(\$)}\\
\hline
\rule{0pt}{2.5ex}0 \rule[-1ex]{0pt}{0pt}& 0.00 & 0.00 & 0.00 & 560 \ 000.00\\
\hline
\rule{0pt}{2.5ex}1 \rule[-1ex]{0pt}{0pt}&&&& \\
\hline
\end{array}

  1. The final monthly repayment required to fully repay the loan to the nearest cent will be slightly higher than all previous payments.
  2. Determine the value of this final repayment.
  3. Round your answer to the nearest cent.   (1 mark)

Show Answers Only

a.   \(\$560\,000\)

b.   \(\text{Total repayments}\ = 12 \times 4012=\$48\,144\)

c.   \(\text{Monthly interest rate}\ =\dfrac{0.06}{12}=0.005\)

\(\text{Multiplication factor}\ =1+0.005=1.005\)

d.   

\begin{array}{|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Payment} & \text{Repayment} & \quad \text{Interest} \quad & \text{Principal reduction} & \quad \text{Balance} \quad \\
\text{number} \rule[-1ex]{0pt}{0pt}& \text{(\$)} & \text{(\$)} & \text{(\$)} & \text{(\$)}\\
\hline
\rule{0pt}{2.5ex}1 \rule[-1ex]{0pt}{0pt}& \$4012.00 & \$2800.00 & \$1212.00 & \$558\,788.00 \\
\hline
\end{array}


e.   \(\text{Final repayment}\ = 4012+6.44= \$4018.44\)

Show Worked Solution

a.   \(\$560\,000\)
 

b.   \(\text{Total repayments}\ = 12 \times 4012=\$48\,144\)
 

c.   \(\text{Monthly interest rate}\ =\dfrac{0.06}{12}=0.005\)

\(\text{Multiplication factor}\ =1+0.005=1.005\)
 

d.   

\begin{array}{|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Payment} & \text{Repayment} & \quad \text{Interest} \quad & \text{Principal reduction} & \quad \text{Balance} \quad \\
\text{number} \rule[-1ex]{0pt}{0pt}& \text{(\$)} & \text{(\$)} & \text{(\$)} & \text{(\$)}\\
\hline
\rule{0pt}{2.5ex}1 \rule[-1ex]{0pt}{0pt}& \$4012.00 & \$2800.00 & \$1212.00 & \$558\,788.00 \\
\hline
\end{array}


e.   \(\text{Find number of payments (by TVM Solver):}\)

\(N= \text{SOLVE}\ = 240.0016\)

\(I\%=6.00\%\)

\(PV=560\,000\)

\(PMT = -4012\)

\(FV=0\)

\(P/Y = C/Y = 12\)
 

\(\text{Find \(PV\) (by TVM Solver):}\)

\(N= 240\)

\(I\%=6.00\%\)

\(PV=560\,000\)

\(PMT = -4012\)

\(FV= \text{SOLVE}\ =-6.44\)

\(P/Y = C/Y = 12\)
 

\(\therefore\ \text{Final repayment}\ = 4012+6.44= \$4018.44\)

Data Analysis, GEN2 2024 NHT 6

The time series plot below shows the height, in metres, of the highest high tides \((HHT)\) and lowest low tides \((L L T)\) for Sydney for the first 60 days of 2021.

The thick line for each tide type shows the results of smoothing using a moving median.
 

Complete the sentence below by entering a number in the space provided.   (1 mark)

Both the \(H H T\) data and the \(L L T\) data have been smoothed using ____-median smoothing.

Show Answers Only

\(15\)

Show Worked Solution

\(\text{By trial and error (noting the smoothing line shows significant smoothing i.e. the number will be high).}

\(15\)

Data Analysis, GEN2 2024 NHT 5

The height, in metres, of the maximum highest high tides \((HHT)\) for Sydney Harbour change from month to month during the year. This is shown in the time series plot below for the years 2021, 2022 and 2023.

In this graph, month number 1 is January 2021, month number 2 is February 2021, and so on.
 

The average height, in metres, of the maximum \(H H T\) for each year, rounded to two decimal places, is given in the table below.

Table 5

\begin{array}{|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Year} \rule[-1ex]{0pt}{0pt}&\ \ \ \ 2021\ \ \ \  &\ \ \ \ 2022\ \ \ \ &\ \ \ \ 2023\ \ \ \ \\
\hline
\rule{0pt}{2.5ex}\text{Average height of the} &1.98 &1.99&1.96\\
\rule[-1ex]{0pt}{0pt} \text{maximum \(HTT\) (m)}\\
\hline
\end{array}

The three years of data shown in this graph and in Table 5 will be used to calculate seasonal indices.

Determine the seasonal index for March.

Round your answer to two decimal places.    (2 marks)

Show Answers Only

\(0.97\)

Show Worked Solution

\(\text{March index (2021)}\ = \dfrac{1.89}{1.98}\)

\(\text{March index (2022)}\ = \dfrac{1.92}{1.99}\)

\(\text{March index (2023)}\ = \dfrac{1.93}{1.96}\)

\(\therefore\ \text{Seasonal index (Mar)}\ = \left( \dfrac{1.89}{1.98}+\dfrac{1.92}{1.99}+\dfrac{1.93}{1.96}\right)\ ÷\ 3= 0.97\ \text{(2 d.p.)}\)

HMS, HIC EQ-Bank 71

Explain how both family relationships and peer interactions influence adolescent development during the identity formation stage.    (5 marks)

Show Answers Only

Family relationships provide the foundation for identity development during adolescence (typically ages 12-18) through:

  • Emotional and physical security that allows adolescents to take risks in identity exploration.
  • Parenting styles that balance support with appropriate autonomy.
  • Transmission of initial values and beliefs that form the basis for self-concept.

Peer interactions shape identity formation through:

  • Social comparison processes that help refine self-perception.
  • Opportunities to experiment with different social roles and behaviours.
  • Feedback on identity choices through acceptance or rejection.

The dynamic interplay between these influences creates:

  • Different contexts for identity exploration.
  • Sometimes conflicting messages that adolescents must reconcile.
  • A balanced identity that integrates values from both family and peer spheres.
Show Worked Solution

*PEEL – Solution is structured using an adjusted PEEL method to show cause and effect: [P] State the cause/factor [E] Show how it causes the effect [Ev] Evidence demonstrating why/how [L] Reinforce the causal relationship.

**Language highlighting the cause-effect relationship is bolded in the answer below.

  • [P] Family provides emotional security for identity exploration.
  • [E] This enables adolescents to take risks and try new identities.
  • [Ev] This happens when supportive parents allow teenagers to try new interests like joining drama clubs or make new friend groups without fear of rejection.
  • [L] This shows a clear connection between family stability and confident self-discovery.
     
  • [P] Peer feedback shapes self-perception.
  • [E] This causes adolescents to modify behaviours for acceptance.
  • [Ev] As a result, teenagers adopt clothing styles or music preferences matching their friend group to help them belong.
  • [L] This demonstrates why peer approval directly influences identity choices during adolescence.
     
  • [P] Conflicting family-peer values create identity tension.
  • [E] This leads to adolescents developing independent thinking skills.
  • [Ev] This occurs because teenagers must choose between parents’  expectations and friends’ social priorities, which helps form lasting personal values.
  • [L] These elements work together to produce unique identities balancing both influences through individual decision-making.

Networks, STD2 N3 2024 NHT 38*

The following directed graph represents the one-way paths between attractions at an historical site. The entrance, exit and attractions are represented by vertices.

The numbers on the edges represent the maximum number of visitors allowed along each path per hour.
 

Determine the maximum number of visitors able to walk from the entrance to the exit each hour?   (3 marks)

Show Answers Only

\(\text{Maximum number = 76}\)

Show Worked Solution

\(\text{Max flow = min cut}\)

\(\text{Discounting flows that move from “exit” to “entrance”:}\)

\(\text{Max flow}\ = 13+16+9+17+21 = 76\ \text{visitors}\)

Statistics, STD2 S5 2024 GEN2 3

The time difference between successive high tides and low tides is approximately normally distributed.

Analysis of the 2021 tide chart showed that

  • 99.85% of the time differences are more than 4.88 hours
  • 16% of the time differences are less than 5.76 hours.

Determine the mean and standard deviation for this normal distribution.   (3 marks)

Show Answers Only

\(\sigma=0.44, \ \overline{x}=6.2\)

Show Worked Solution

\(\text{99.85% of the time differences are more than 4.88 hours:}\)

\(-3=\dfrac{4.88-\overline{x}}{\sigma}\ \ \Rightarrow \ -3 \times \sigma=4.88-\overline{x}\ …\ (1)\)

\(\text{16% of the time differences are less than 5.76 hours:}\)

\(-1=\dfrac{5.76-\overline{x}}{\sigma}\ \ \Rightarrow \ -\sigma=5.76-\overline{x}\ …\ (2)\)

\(\text{Subtract}\ (2)-(1):\)

\(2\sigma\) \(=0.88\)  
\(\sigma\) \(=0.44\)  

 
\(\text{Substitute into (2):}\)

\(\overline{x}=5.76+0.44=6.2\)

Data Analysis, GEN2 2024 NHT 3

The time difference between successive high tides and low tides is approximately normally distributed.

Analysis of the 2021 tide chart showed that

  • 99.85% of the time differences are more than 4.88 hours
  • 16% of the time differences are less than 5.76 hours.

Use the 68-95-99.7% rule to determine the mean and standard deviation for this normal distribution.   (2 marks)

Show Answers Only

\(s_x=0.44, \ \overline{x}=6.2\)

Show Worked Solution

\(\text{99.85% of the time differences are more than 4.88 hours:}\)

\(-3=\dfrac{4.88-\overline{x}}{s_x}\ \ \Rightarrow \ -3 \times s_x=4.88-\overline{x}\ …\ (1)\)

\(\text{16% of the time differences are less than 5.76 hours:}\)

\(-1=\dfrac{5.76-\overline{x}}{s_x}\ \ \Rightarrow \ -s_x=5.76-\overline{x}\ …\ (2)\)

\(\text{Subtract}\ (2)-(1):\)

\(2s_x\) \(=0.88\)  
\(s_x\) \(=0.44\)  

 
\(\text{Substitute into (2):}\)

\(\overline{x}=5.76+0.44=6.2\)

HMS, TIP 2024 HSC 31b

To what extent have advancements in sporting technology improved performance?   (12 marks)

Show Answers Only

Judgment Statement

  • Advancements in sporting technology have significantly improved performance across multiple sports disciplines.
  • Key factors include equipment innovation, biomechanical analysis systems, and performance monitoring technologies.

Equipment and Material Innovation

  • Swimming technology demonstrates substantial performance gains through advanced materials.
  • Modern racing suits significantly reduced water resistance, leading to numerous world records and eventual regulation by swimming authorities.
  • Tennis racquet evolution from wooden to graphite composites increased serve speeds and they now achieve speeds up to 200 km/h.
  • Modern equipment enables athletes to achieve previously impossible performance levels.
  • These innovations directly translate to measurable improvements in speed, power and accuracy.

Performance Analysis and Monitoring Systems

  • GPS tracking and biomechanical analysis provide significant advantages in training optimisation.
  • Rugby union teams have achieved marked injury reduction while maintaining peak performance through GPS data management.
  • High-speed cameras and motion sensors allow precise technical refinements in cricket bowling and golf swings.
  • Real-time feedback systems enable immediate corrections during training sessions.
  • Data-driven approaches result in more efficient training programs and reduced injury rates.

Limitations and Access Inequality

  • Technology benefits are not equally distributed across all sports and nations.
  • Financial resources determine access levels to advanced technological systems.
  • Traditional sports may resist technological integration to preserve their character.
  • Wealthier nations with greater technology investment demonstrate higher medal counts at international competitions.
  • Equipment regulations in some sports limit the extent of technological advantages.

Reaffirmation

  • Technology has substantially transformed sporting performance across multiple disciplines.
  • While access inequality moderates the overall impact, the evidence demonstrates significant improvements in speed, accuracy and training efficiency.
  • The extent remains considerable for athletes with access to advanced technological systems.
Show Worked Solution

Judgment Statement

  • Advancements in sporting technology have significantly improved performance across multiple sports disciplines.
  • Key factors include equipment innovation, biomechanical analysis systems, and performance monitoring technologies.

Equipment and Material Innovation

  • Swimming technology demonstrates substantial performance gains through advanced materials.
  • Modern racing suits significantly reduced water resistance, leading to numerous world records and eventual regulation by swimming authorities.
  • Tennis racquet evolution from wooden to graphite composites increased serve speeds and they now achieve speeds up to 200 km/h.
  • Modern equipment enables athletes to achieve previously impossible performance levels.
  • These innovations directly translate to measurable improvements in speed, power and accuracy.

Performance Analysis and Monitoring Systems

  • GPS tracking and biomechanical analysis provide significant advantages in training optimisation.
  • Rugby union teams have achieved marked injury reduction while maintaining peak performance through GPS data management.
  • High-speed cameras and motion sensors allow precise technical refinements in cricket bowling and golf swings.
  • Real-time feedback systems enable immediate corrections during training sessions.
  • Data-driven approaches result in more efficient training programs and reduced injury rates.

Limitations and Access Inequality

  • Technology benefits are not equally distributed across all sports and nations.
  • Financial resources determine access levels to advanced technological systems.
  • Traditional sports may resist technological integration to preserve their character.
  • Wealthier nations with greater technology investment demonstrate higher medal counts at international competitions.
  • Equipment regulations in some sports limit the extent of technological advantages.

Reaffirmation

  • Technology has substantially transformed sporting performance across multiple disciplines.
  • While access inequality moderates the overall impact, the evidence demonstrates significant improvements in speed, accuracy and training efficiency.
  • The extent remains considerable for athletes with access to advanced technological systems.

♦♦ Mean mark 50%.

HMS, TIP 2024 HSC 31aii

Explain how an athlete could taper to improve performance for a major sporting event.   (5 marks)

Show Answers Only
  • Tapering is a strategic reduction in training load before competition that enables athletes to reach peak performance when it matters most. This occurs because reducing training volume allows the body to recover from built-up fatigue.
  • Athletes preparing for major events systematically reduce training volume by 40-60% whilst maintaining intensity levels during the final 1-3 weeks. This process ensures that fitness adaptations are preserved whilst eliminating residual fatigue. Therefore, the body can fully recover and prepare for optimal competition performance.
  • For example, a marathon runner might decrease weekly kilometres from 100 to 40 in the final two weeks. However, they continue including high-intensity intervals to maintain cardiovascular adaptations and prevent detraining effects. This demonstrates how volume reduction preserves training gains whilst promoting recovery.
  • The significance is that tapering allows both physiological and psychological recovery from intensive training periods. Consequently, athletes arrive at competition in their optimal state, resulting in improved power output, reduced fatigue and enhanced performance outcomes during major sporting events.
Show Worked Solution
  • Tapering is a strategic reduction in training load before competition that enables athletes to reach peak performance when it matters most. This occurs because reducing training volume allows the body to recover from built-up fatigue.
  • Athletes preparing for major events systematically reduce training volume by 40-60% whilst maintaining intensity levels during the final 1-3 weeks. This process ensures that fitness adaptations are preserved whilst eliminating residual fatigue. Therefore, the body can fully recover and prepare for optimal competition performance.
  • For example, a marathon runner might decrease weekly kilometres from 100 to 40 in the final two weeks. However, they continue including high-intensity intervals to maintain cardiovascular adaptations and prevent detraining effects. This demonstrates how volume reduction preserves training gains whilst promoting recovery.
  • The significance is that tapering allows both physiological and psychological recovery from intensive training periods. Consequently, athletes arrive at competition in their optimal state, resulting in improved power output, reduced fatigue and enhanced performance outcomes during major sporting events.

♦♦ Mean mark 45%.

Networks, GEN1 2024 NHT 40 MC

A project has 10 activities, labelled \(A\) to \(J\). The table below shows the immediate predecessor(s) for each activity. Each activity has a duration of at least one day.

\begin{array}{|c|c|}
\hline
\rule{0pt}{2.5ex}\textbf{Activity} & \textbf{Immediate}\\
&\textbf{predecessor(s)} \rule[-1ex]{0pt}{0pt}\\
\hline
\rule{0pt}{2.5ex}A \rule[-1ex]{0pt}{0pt}& - \\
\hline
\rule{0pt}{2.5ex}B \rule[-1ex]{0pt}{0pt}& - \\
\hline
\rule{0pt}{2.5ex}C \rule[-1ex]{0pt}{0pt}& A \\
\hline
\rule{0pt}{2.5ex}D \rule[-1ex]{0pt}{0pt}& B \\
\hline
\rule{0pt}{2.5ex}E \rule[-1ex]{0pt}{0pt}& B \\
\hline
\rule{0pt}{2.5ex}F \rule[-1ex]{0pt}{0pt}& D \\
\hline
\rule{0pt}{2.5ex}G \rule[-1ex]{0pt}{0pt}& D, E \\
\hline
\rule{0pt}{2.5ex}H \rule[-1ex]{0pt}{0pt}& C, F \\
\hline
\rule{0pt}{2.5ex}I \rule[-1ex]{0pt}{0pt}& E \\
\hline
\rule{0pt}{2.5ex}J \rule[-1ex]{0pt}{0pt}& G,H \\
\hline
\end{array}

Which one of the following statements about this project is not true?

  1. The earliest starting time of activity \(H\) could be two days.
  2. In the network for this project, there would be a dummy activity from the end of activity \(D\) to the start of activity \(G\).
  3. One of the paths through the network of this project is \(B D G J\).
  4. The latest starting time of activity \(E\) could be three days.
  5. The network for this project would require two dummy activities.
Show Answers Only

\(A\)

Show Worked Solution

\(\text{One strategy: draw a network diagram:}\)
 

\(\text{Earliest starting time of activity \(H\) = 3 days.}\)

\(\Rightarrow A\)

Networks, GEN1 2024 NHT 38-39 MC

The following directed graph represents the one-way paths between attractions at an historical site. The entrance, exit and attractions are represented by vertices.

The numbers on the edges represent the maximum number of visitors allowed along each path per hour.
 

Question 38

What is the maximum number of visitors able to walk from the entrance to the exit each hour?

  1. 75
  2. 76
  3. 77
  4. 88
  5. 96

 
Question 39

A group of students set out from the entrance and walk to the exit. The students all walk together and travel along the same route. They are the only people visiting the site that hour. What is the maximum number of students that could be in the group?

  1. 9
  2. 15
  3. 16
  4. 20
  5. 31
Show Answers Only

\(\text{Question 38:}\ B\)

\(\text{Question 39:}\ D\)

Show Worked Solution

\(\text{Question 38}\)

\(\text{Max flow = min cut}\)

\(\text{Max flow = 13+16+9+17+21=76\)

\(\Rightarrow B\)
  

\(\text{Question 39}\)

\(\text{Given all students must take the same route:}\)

\(\text{Path for max students is 32 → 20 → 32 → 21}\)

\(\text{Max students = minimum capacity of any edge = 20}\)

\(\Rightarrow D\)

HMS, TIP 2024 HSC 30b

Evaluate the use of specific warm-up and psychological readiness procedures to indicate if an athlete is ready to return to play after an injury.   (12 marks)

Show Answers Only

Evaluation Statement:

  • Specific warm-up and psychological readiness procedures are highly effective indicators for return-to-play decisions when used together. Physical warm-up assessments provide objective movement evaluation whilst psychological readiness addresses crucial mental factors affecting re-injury risk.

Warm-up Procedures Effectiveness:

  • Physical warm-up procedures demonstrate strong effectiveness in assessing movement quality and injury site response through progressive sport-specific activities.
  • These protocols bridge clinical clearance and competitive participation by systematically evaluating functional capacity. For example, a footballer recovering from hamstring strain progresses through jogging, sprinting, directional changes, and ball skills under defensive pressure.
  • Evidence supporting this includes successful protocols that replicate game demands and identify movement compensations. However, warm-up assessments show limitations in replicating competitive intensities and psychological pressure that occur during actual competition.
  • The overall evaluation demonstrates that physical procedures provide valuable objective data but cannot assess complete readiness alone.

Psychological Readiness Assessment:

  • Psychological readiness procedures prove highly valuable in measuring confidence levels, re-injury anxiety, and mental preparedness that significantly influence movement patterns.
  • Research confirms athletes reporting fear of re-injury are 2-5 times more likely to sustain subsequent injuries, highlighting psychological factors’ critical importance.
  • Sports psychologists assess concentration capacity and willingness to perform previously injurious movements through validated questionnaires and interviews.
  • The evidence indicates comprehensive psychological evaluation reduces re-injury rates substantially. A critical weakness is reliance on self-reporting that may be influenced by external pressures to return quickly. The assessment proves psychological procedures address essential factors that physical tests cannot evaluate.

Final Evaluation:

  • Weighing these factors shows both procedures are most effective when integrated rather than used independently. Studies indicate athletes meeting both physical and psychological criteria experience significantly lower re-injury rates than those passing only physical assessments.
  • The strengths outweigh the weaknesses because comprehensive protocols incorporating multiple assessment dimensions provide superior return-to-play decisions that protect athlete welfare whilst optimising performance outcomes.
Show Worked Solution

Evaluation Statement:

  • Specific warm-up and psychological readiness procedures are highly effective indicators for return-to-play decisions when used together. Physical warm-up assessments provide objective movement evaluation whilst psychological readiness addresses crucial mental factors affecting re-injury risk.

Warm-up Procedures Effectiveness:

  • Physical warm-up procedures demonstrate strong effectiveness in assessing movement quality and injury site response through progressive sport-specific activities.
  • These protocols bridge clinical clearance and competitive participation by systematically evaluating functional capacity. For example, a footballer recovering from hamstring strain progresses through jogging, sprinting, directional changes, and ball skills under defensive pressure.
  • Evidence supporting this includes successful protocols that replicate game demands and identify movement compensations. However, warm-up assessments show limitations in replicating competitive intensities and psychological pressure that occur during actual competition.
  • The overall evaluation demonstrates that physical procedures provide valuable objective data but cannot assess complete readiness alone.

Psychological Readiness Assessment:

  • Psychological readiness procedures prove highly valuable in measuring confidence levels, re-injury anxiety, and mental preparedness that significantly influence movement patterns.
  • Research confirms athletes reporting fear of re-injury are 2-5 times more likely to sustain subsequent injuries, highlighting psychological factors’ critical importance.
  • Sports psychologists assess concentration capacity and willingness to perform previously injurious movements through validated questionnaires and interviews.
  • The evidence indicates comprehensive psychological evaluation reduces re-injury rates substantially. A critical weakness is reliance on self-reporting that may be influenced by external pressures to return quickly. The assessment proves psychological procedures address essential factors that physical tests cannot evaluate.

Final Evaluation:

  • Weighing these factors shows both procedures are most effective when integrated rather than used independently. Studies indicate athletes meeting both physical and psychological criteria experience significantly lower re-injury rates than those passing only physical assessments.
  • The strengths outweigh the weaknesses because comprehensive protocols incorporating multiple assessment dimensions provide superior return-to-play decisions that protect athlete welfare whilst optimising performance outcomes.

♦♦ Mean mark 50%.

Networks, GEN1 2024 NHT 37 MC

Euler's formula can be applied to which of the following graphs?
 

  1. Graph 4 only
  2. Graphs 1 and 2 only
  3. Graphs 1, 2, 3 and 4
  4. Graphs 3 and 4 only
  5. Graphs 2, 3 and 4 only
Show Answers Only

\(E\)

Show Worked Solution

\(\text{Euler’s formula applies to planar graphs.}\)

\(\text{Graph 1 has a complete pentagon \(\Rightarrow\) cannot be drawn as a planar graph.}\)

\(\text{Graph 4 is already planar.}\)

\(\text{Graph 2 and 3 can both be drawn as a planar graphs.}\)
 

\(\Rightarrow E\)

Networks, GEN1 2024 NHT 36 MC

Four students, Peggy, Quincy, Radley and Sarah, are grouped together to complete a project. The project is in four parts, labelled \(W, X, Y\) and \(Z\). Each student must complete one part of the project.

The table below shows each student's estimate of the score they will receive if they complete each section.

\begin{array}{|c|c|c|c|c|}
\hline \rule{0pt}{2.5ex}\quad \quad \rule[-1ex]{0pt}{0pt}& \text{Peggy}& \text{Quincy}&\text{Radley}&\text{Sarah} \\
\hline \rule{0pt}{2.5ex}W \rule[-1ex]{0pt}{0pt}& 12 & 19 & 18 & 16 \\
\hline \rule{0pt}{2.5ex}X \rule[-1ex]{0pt}{0pt}& 16 & 15 & 15 & 16 \\
\hline \rule{0pt}{2.5ex}Y \rule[-1ex]{0pt}{0pt}& 10 & 16 & 17 & 15 \\
\hline \rule{0pt}{2.5ex}Z \rule[-1ex]{0pt}{0pt}& 19 & 20 & 18 & 18 \\
\hline
\end{array}

Based on the estimates, which allocation of project parts will maximise the students' group score on the project?


A.  		 \begin{array}{|c|c|}
\hline \rule{0pt}{2.5ex}W\rule[-1ex]{0pt}{0pt} & \text { Quincy } \\
\hline \rule{0pt}{2.5ex}X \rule[-1ex]{0pt}{0pt}& \text { Sarah } \\
\hline \rule{0pt}{2.5ex}Y \rule[-1ex]{0pt}{0pt}& \text { Radley } \\
\hline \rule{0pt}{2.5ex}Z \rule[-1ex]{0pt}{0pt}& \text { Peggy } \\
\hline
\end{array}
     B.  		 \begin{array}{|c|c|}
\hline \rule{0pt}{2.5ex}W \rule[-1ex]{0pt}{0pt}& \text { Radley } \\
\hline \rule{0pt}{2.5ex}X \rule[-1ex]{0pt}{0pt}& \text { Peggy } \\
\hline \rule{0pt}{2.5ex}Y \rule[-1ex]{0pt}{0pt}& \text { Quincy } \\
\hline \rule{0pt}{2.5ex}Z \rule[-1ex]{0pt}{0pt}& \text { Sarah } \\
\hline
\end{array}
     C.  		 \begin{array}{|c|l|}
\hline \rule{0pt}{2.5ex}W \rule[-1ex]{0pt}{0pt}& \text { Sarah } \\
\hline \rule{0pt}{2.5ex}X \rule[-1ex]{0pt}{0pt}& \text { Quincy } \\
\hline \rule{0pt}{2.5ex}Y \rule[-1ex]{0pt}{0pt}& \text { Peggy } \\
\hline \rule{0pt}{2.5ex}Z \rule[-1ex]{0pt}{0pt}& \text { Radley } \\
\hline
\end{array}

D.		 \begin{array}{|c|c|}
\hline \rule{0pt}{2.5ex}W \rule[-1ex]{0pt}{0pt}& \text { Radley } \\
\hline \rule{0pt}{2.5ex}X \rule[-1ex]{0pt}{0pt}& \text { Peggy } \\
\hline \rule{0pt}{2.5ex}Y \rule[-1ex]{0pt}{0pt}& \text { Sarah } \\
\hline \rule{0pt}{2.5ex}Z \rule[-1ex]{0pt}{0pt}& \text { Quincy } \\
\hline
\end{array}
     E.		 \begin{array}{|l|l|}
\hline \rule{0pt}{2.5ex}W \rule[-1ex]{0pt}{0pt}& \text { Sarah } \\
\hline \rule{0pt}{2.5ex}X \rule[-1ex]{0pt}{0pt}& \text { Peggy } \\
\hline \rule{0pt}{2.5ex}Y \rule[-1ex]{0pt}{0pt}& \text { Radley } \\
\hline \rule{0pt}{2.5ex}Z \rule[-1ex]{0pt}{0pt}& \text { Quincy } \\
\hline
\end{array}		  
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Calculate the score for each option:}\)

\(A: 19+16+17+19=71\)

\(B: 18+16+16+18=68\)

\(C: 16+15+10+18=59\)

\(D: 18+16+15+20=69\)

\(E: 16+16+17+20=69\)

\(\Rightarrow A\)

PHYSICS, M2 EQ-Bank 4

A 65 kg rider is on a 15 kg bicycle, moving across the top of a 4 metre high hill with a horizontal speed of 3 ms\(^{-1}\).
 

  1. The bicycle descends the hill, dropping a vertical distance of 4.0 meters before reaching level ground. Assuming no energy is lost to friction or air resistance, calculate the speed of the bicycle and rider at the bottom of the hill.   (3 marks)
  1. At the bottom, the rider applies the brakes. The bike skids 15 metres across flat ground before coming to a stop. Calculate the magnitude of the frictional force acting on the bike during this motion.   (2 marks)
Show Answers Only

a.    \(9.35\ \text{ms}^{-1}\)

b.    \(233\ \text{N}\)

Show Worked Solution

a.    By applying the Law of Conservation of Energy:

\(E_{\text{after}}\) \(=E_{\text{before}}\)  
\(\dfrac{1}{2}mv^2\) \(=\dfrac{1}{2}mu^2+mgh\)  
\(v^2\) \(=u^2 +2gh\)  
\(v\) \(=\sqrt{3^2+2 \times 9.8 \times 4}\)  
  \(=9.35\ \text{ms}^{-1}\)  

 

  • The velocity of the rider at the bottom of the hill is 9.35 ms\(^{-1}\).

b.    At the bottom of the hill:

  • Work done to slow rider = change in rider’s kinetic energy
\(W\) \(=\Delta KE\)  
\(Fs\) \(=\dfrac{1}{2}mv^2-\dfrac{1}{2}mu^2\)  
\(F \times 15\) \(=\dfrac{1}{2} \times 80 \times 0^2-\dfrac{1}{2} \times 80 \times 9.35^2\)  
\(F\) \(=-\dfrac{3496.9}{15}\)  
  \(=-233\ \text{N}\)  

 

  • The braking force acting on the bike is \(233\ \text{N}\).

HMS, HIC 2024 HSC 28b

Evaluate the effectiveness of legislation and health promotion initiatives in addressing ONE major health issue affecting young people.   (12 marks)

Show Answers Only

Evaluation Statement

  • Legislation and health promotion initiatives are highly effective in addressing youth road safety when implemented together.
  • This evaluation examines behavioural change impact and long-term sustainability of interventions.

Behavioural Change Impact

  • Graduated licensing systems are highly influential in reducing youth road fatalities.
  • Evidence supporting this includes the 120 supervised hours requirement, passenger limits for P1 drivers and speed restrictions that have coincided with a sizeable reduction in collision rates.
  • The “Plan B” drink-driving campaign has also proven highly effective by promoting practical drink-driving alternatives. Campaign evaluations show a significant percentage decrease in alcohol-related crashes since 2012.
  • A critical strength of these approaches is the combination of addressing specific risk factors while building safe driving habits.
  • In this way, combined approaches can achieve comprehensive behaviour modification.

Long-term Sustainability

  • Legislative measures show excellent sustainability through systematic enforcement.
  • Mobile phone bans partially fulfil objectives due to enforcement challenges. While awareness has increased, detection difficulties limit long-term compliance although this shortcoming is being mitigated by technology developments.
  • Health promotion campaigns like “Speeding. No One Thinks Big of You” achieve moderate sustainability. Research indicates 75% of young males felt discouraged from speeding after viewing.
  • However, campaign effects diminish without ongoing reinforcement. Although effective for immediate impact, promotion requires continuous investment.

Final Evaluation

  • Weighing these factors shows integrated approaches prove most effective.
  • The strengths outweigh limitations because combining external regulation with attitude change can create lasting impact.
  • While legislation provides consistent framework, health promotion addresses cultural motivations.
  • The overall evaluation reveals neither approach alone suffices.
  • Implications suggest continued investment in both legislative and promotional strategies maximises youth road safety outcomes.
Show Worked Solution

Evaluation Statement

  • Legislation and health promotion initiatives are highly effective in addressing youth road safety when implemented together.
  • This evaluation examines behavioural change impact and long-term sustainability of interventions.

Behavioural Change Impact

  • Graduated licensing systems are highly influential in reducing youth road fatalities.
  • Evidence supporting this includes the 120 supervised hours requirement, passenger limits for P1 drivers, and speed restrictions that have coincided with a sizeable reduction in collision rates.
  • The “Plan B” drink-driving campaign has also proven highly effective by promoting practical drink-driving alternatives. Campaign evaluations show a significant percentage decrease in alcohol-related crashes since 2012.
  • A critical strength of these approaches is the combination of addressing specific risk factors while building safe driving habits.
  • In this way, combined approaches can achieve comprehensive behaviour modification.

Long-term Sustainability

  • Legislative measures show excellent sustainability through systematic enforcement.
  • Mobile phone bans partially fulfil objectives due to enforcement challenges. While awareness has increased, detection difficulties limit long-term compliance although this shortcoming is being mitigated by technology developments.
  • Health promotion campaigns like “Speeding. No One Thinks Big of You” achieve moderate sustainability. Research indicates 75% of young males felt discouraged from speeding after viewing.
  • However, campaign effects diminish without ongoing reinforcement. Although effective for immediate impact, promotion requires continuous investment.

Final Evaluation

  • Weighing these factors shows integrated approaches prove most effective.
  • The strengths outweigh limitations because combining external regulation with attitude change can create lasting impact.
  • While legislation provides consistent framework, health promotion addresses cultural motivations.
  • The overall evaluation reveals neither approach alone suffices.
  • Implications suggest continued investment in both legislative and promotional strategies maximises youth road safety outcomes.

♦♦ Mean mark 43%.

HMS, HIC 2024 HSC 28aii

Explain how the developmental stage of a young person’s life can cause their motivation AND values to vary.   (5 marks)

Show Answers Only
  • Brain development during adolescence causes changes in thinking abilities and decision-making capacity.
  • This leads to shifts from concrete to abstract reasoning, where 13-year-olds value immediate rewards like gaming, while 17-year-olds prioritise long-term goals like university entry.
  • This demonstrates how cognitive growth directly transforms what young people find motivating and important.
  • Identity formation triggers increased peer influence during teenage years.
  • The result is values shifting from family-centred to friend group-focused priorities.
  • For instance, when teenagers seek independence, they adopt friends’ music tastes or political views to fit in.
  • This shows a clear connection between developmental need for belonging and changing value systems.
  • Approaching physical maturity creates new motivations through hormonal changes.
  • This occurs because puberty increases interest in romantic relationships and body image concerns.
  • The underlying reason is hormonal changes trigger desires for social acceptance, motivating gym attendance or dieting behaviours.
  • These elements work together to reshape priorities from childhood interests toward adult-focused goals.
Show Worked Solution
  • Brain development during adolescence causes changes in thinking abilities and decision-making capacity.
  • This leads to shifts from concrete to abstract reasoning, where 13-year-olds value immediate rewards like gaming, while 17-year-olds prioritise long-term goals like university entry.
  • This demonstrates how cognitive growth directly transforms what young people find motivating and important.
  • Identity formation triggers increased peer influence during teenage years.
  • The result is values shifting from family-centred to friend group-focused priorities.
  • For instance, when teenagers seek independence, they adopt friends’ music tastes or political views to fit in.
  • This shows a clear connection between developmental need for belonging and changing value systems.
  • Approaching physical maturity creates new motivations through hormonal changes.
  • This occurs because puberty increases interest in romantic relationships and body image concerns.
  • The underlying reason is hormonal changes trigger desires for social acceptance, motivating gym attendance or dieting behaviours.
  • These elements work together to reshape priorities from childhood interests toward adult-focused goals.

♦ Mean mark 53%.

v1 Financial Maths, STD2 F4 2021 HSC 30

Dianne owns 1600 shares in a company. The market price for each share is $30. Dianne's total dividend from these shares is $768.

Calculate the dividend yield for her shares.   (2 marks)

Show Answers Only

`1.6 text(%)`

Show Worked Solution

♦ Mean mark 47%.
`text(Dividend yield)` `= text(Dividend)/text(Value of shares)`  
  `= 768/(1600xx 30)`  
  `=0.016`  
  `= 1.6 text(% yield)`  

Matrices, GEN1 2024 NHT 32 MC

An online shop offers monthly subscriptions for protein powder.

The shop offers protein powder in three flavours: vanilla \((V)\), chocolate \((C)\) and malt \((M)\).

Let \(P_n\) be the state matrix that shows the expected number of subscribers for each flavour \(n\) months after sales of the protein powder began.

The expected number of subscribers for each flavour can be determined by the matrix recurrence rule

\(P_{n+1}=T P_n+K\)

where

\begin{aligned}
& \quad \quad \quad \ \text { this month }\\
& \quad \quad \quad \ V \quad \ \ C \quad \ M \\ 
& T=\begin{bmatrix}0.2 & 0.2 & 0.1 \\
0.4 & 0.2 & 0.1 \\
0.4 & 0.6 & 0.8
\end{bmatrix} \begin{array}{l}
V \\ C\\ M
\end{array}
\ \text{next month} \quad \text { and } \quad K=\begin{bmatrix} 93 \\ 59 \\ 9\end{bmatrix}\begin{array}{l}V \\ C \\ M \end{array}\end{aligned}

The state matrix, \(P_2\), below shows the expected number of subscribers for each flavour two months after sales began.

\begin{align*}
P_2=\begin{bmatrix}
147 \\
137 \\
199
\end{bmatrix}
\end{align*}

The increase in the expected number of subscribers for vanilla \((V)\) between the initial sales, \(P_0\), and the first month after sales began, \(P_1\), is equal to

  1. 27
  2. 54
  3. 60
  4. 87
  5. 93
Show Answers Only

\(C\)

Show Worked Solution

\(P_{n+1} = TP_{n}+K\ \Rightarrow\ P_2=TP_1+K \ \Rightarrow\ P_1=T^{-1}(P_2-K) \) 
 

\(P_1=\begin{bmatrix}0.2 & 0.2 & 0.1 \\ 0.4 & 0.2 & 0.1 \\ 0.4 & 0.6 & 0.8\end{bmatrix}^{-1}\left(\begin{bmatrix}147 \\ 137 \\ 199\end{bmatrix}-\begin{bmatrix}93 \\ 59 \\ 9\end{bmatrix}\right)=\begin{bmatrix} 120 \\ 98 \\ 104\end{bmatrix}\)
 

\(P_0=\begin{bmatrix}0.2 & 0.2 & 0.1 \\ 0.4 & 0.2 & 0.1 \\ 0.4 & 0.6 & 0.8\end{bmatrix}^{-1}\left(\begin{bmatrix}120 \\ 98 \\ 104\end{bmatrix}-\begin{bmatrix}93 \\ 59 \\ 9\end{bmatrix}\right)=\begin{bmatrix}60 \\ 49 \\ 52\end{bmatrix}\)
 

\(\therefore\ \text{Increase in vanilla subscribers}\ =120-60=60\)

\(\Rightarrow C\)

v1 Financial Maths, STD2 F4 2013 HSC 26e

Lucas invests $5000.

Interest is compounded half-yearly at a rate of 3% per half-year.

2013 26e

Use the table to calculate the value of his investment at the end of 4 years.   (2 marks)

 

Show Answers Only

`$6335`

Show Worked Solution
♦ Mean mark 44%
COMMENT: Structure your answer: 1-Find the interest rate per compounding period (same in this case). 2-Find the number of compounding periods..

`r =\ text(3% per half-year)`

`n = 8 \ \ \ \  text{(8 half-years in 4 years)}`

`⇒ \text{Table Factor} = 1.267`

`text(Investment)` `= 5000 × 1.267`
  `= $6335`

`:.\ \text{After 4 years, investment value is } $6335`

Matrices, GEN1 2024 NHT 31 MC

A group of meerkats lives in an enclosure at a zoo.

The meerkats sleep during the night in one of two chambers, chamber A or chamber B.

The transition diagram below shows the proportion of meerkats that stay in the same sleeping location or change sleeping location from night to night.
 

Every night there are \(a\) meerkats in chamber A.

Every night there are \(b\) meerkats in chamber B .

Of the meerkats sleeping in chamber A on Friday night, eight had slept in chamber B on the previous night.

How many meerkats live in the enclosure?

  1. 20
  2. 30
  3. 40
  4. 50
  5. 60
Show Answers Only

\(E\)

Show Worked Solution
\(20\% \times b\) \(=8\)  
\(b\) \(=\dfrac{8}{0.2} = 40\)  

 
\(\text{Since \(a\) and \(b\) remain the same:}\)

\(0.4 \times a\) \(=8\)  
\(a\) \(=\dfrac{8}{0.4} = 20\)  

 
\(\therefore\ \text{Total meercats}\ = 40+20=60\)

\(\Rightarrow E\)

v1 Financial Maths, STD2 F4 2014 HSC 30a

Jordan wants to accumulate $15 000 in a savings account over 10 years to buy a new car.

The account pays interest at 4% per annum compounded monthly.

Calculate how much Jordan must deposit now to achieve this goal. (3 marks)

Show Answers Only

`$10\ 110\ \ \text{(nearest $)}`

Show Worked Solution
♦ Mean mark 52%

`FV = 15\ 000,\ \ n = 10 \times 12 = 120,`

`r = 0.04 / 12 = 0.003333…`

`FV` `= PV (1 + r)^n`
`15\ 000` `= PV (1 + 0.003333…)^{120}`
`PV` `= \frac{15\ 000}{(1.003333…)^{120}}`
  `= 10\ 109.88…`

`∴ \ \text{Jordan must deposit} \ $10\ 110\ \text{(nearest $)}`

Matrices, GEN1 2024 NHT 29 MC

Matrix \(J\) is a row matrix of order  \(1 \times n\).

Matrix \(K\) is a column matrix of order  \(n \times 1\).

Matrix \(J^T\) is the transpose of Matrix \(J\).

Matrix \(K^T\) is the transpose of Matrix \(K\).

Consider the following matrix products where \(n\) is a whole number greater than or equal to 2:

    • \(J^2\)
    • \(JK\)
    • \(K J\)
    • \(J^T K^T\)
    • \(K^T J^T\)

How many of the above matrix products are defined?

  1. 1
  2. 2
  3. 3
  4. 4
  5. 5
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Note:}\ J^{T}\ \text{is order}\ (n \times 1), \ K^{T}\ \text{is order}\ (1 \times n) \)

\(J^2: (1 \times n) \times (1 \times n) \Rightarrow \text{Undefined}\)

\(JK: (1 \times n) \times (n \times 1) \Rightarrow \text{Defined}\)

\(KJ: (n \times 1) \times (1 \times n) \Rightarrow \text{Defined}\)

\(J^T K^T: (n \times 1) \times (1 \times n) \Rightarrow \text{Defined}\)

\(K^T J^T: (1 \times n) \times (n \times 1) \Rightarrow \text{Defined}\)

\(\Rightarrow D\)

v1 Financial Maths, STD2 F4 2021 HSC 26

Mila plans to invest $42 000 for 1.5 years. She is offered two different investment options.

Option A:  Interest is paid at 5% per annum compounded monthly.

Option B:  Interest is paid at `r` % per annum simple interest.

  1. Calculate the future value of Mila's investment after 1.5 years if she chooses Option A. (2 marks)
  2. Find the value of `r` in Option B that would give Mila the same future value after 1.5 years as for Option A. Give your answer correct to two decimal places. (2 marks)
Show Answers Only
  1. `$45\ 264.08`
  2. `5.18text(%)`
Show Worked Solution
a.   `r` `= text(5%)/12 = text(0.4167%) = 0.004167\ \text(per month)`
  `n` `= 12 × 1.5 = 18`
`FV` `= PV(1 + r)^n`
  `= 42\ 000(1 + 0.004167)^{18}`
  `= $45\ 264.08`

 

b.   `I` `= Prn`
  `3\ 264.08` `= 42\ 000 × r × 1.5`
  `r` `= 3\ 264.08 / (42\ 000 × 1.5)`
    `= 0.0518…`
    `= 5.18\ \text{% (to 2 d.p.)}`

HMS, HAG 2024 HSC 27

Select ONE of the following groups that experience health inequities:

  • Socioeconomically disadvantaged people
  • People in rural and remote areas
  • Overseas-born people
  • The elderly
  • People with disabilities

To what extent do socioeconomic factors affect the health of this group?   (8 marks)
  

Group selected:............................................................................................

Show Answers Only

Group selected: People with disabilities

Introduction – Overall judgement

  • Socioeconomic factors significantly affect the health of people with disabilities in Australia
  • Create a cycle of disadvantage that severely impacts both physical and mental wellbeing
  • Influence multiple aspects of life including healthcare access, housing, and social participation

Employment barriers – Primary socioeconomic influence

  • Approximately 30% lower employment rates than general population
  • Limited income potential restricts ability to afford:
    • Specialised healthcare services not covered by Medicare
    • Gap payments for NDIS-supported therapies
    • Essential assistive technologies and modifications
  • Directly impacts access to vital treatments, therapies, and medications

Educational disadvantage – Compounding factor

  • Physical access barriers and inadequate support in educational settings
  • Lower completion rates of secondary and tertiary education
  • Results in limited employment options and lower-paying positions
  • Creates cycle of disadvantage affecting ability to afford:
    • Private health insurance
    • Preventative healthcare services
    • Regular health monitoring

Housing challenges – Financial manifestation

  • Limited accessible housing options at premium prices
  • Contributes to housing stress and potential homelessness
  • Associated mental health conditions including anxiety and depression
  • Extended waiting lists for accessible public housing (often several years)
  • Many forced to live in unsuitable accommodation that compromises health and safety

Counter-argument – Other determinants:

  • Environmental barriers exist regardless of socioeconomic status
  • Healthcare system gaps include inaccessible facilities and equipment
  • Societal attitudes and stigma affect quality of care
  • Healthcare professionals’ lack of disability awareness leads to diagnostic overshadowing
  • These factors can affect health independent of financial means

Predominant influence – Financial burden:

  • Gap payments for therapies not fully covered by support systems
  • Specialised equipment costs beyond subsidies
  • Home modifications essential for independence
  • Significant portion of household income consumed by disability-related expenses
  • Disability Support Pension often insufficient, falling below poverty line
  • Forces difficult choices between healthcare needs and other essentials

Conclusion – Final judgment:

  • Socioeconomic factors affect health of people with disabilities to a very large extent
  • While other factors contribute, financial disadvantage creates the most pervasive barriers
  • Long-term cycle of disadvantage significantly impacts:
    • Quality of life
    • Health outcomes
    • Life expectancy for Australians with disabilities
Show Worked Solution

Group selected: People with disabilities

Introduction – Overall judgement

  • Socioeconomic factors significantly affect the health of people with disabilities in Australia
  • Create a cycle of disadvantage that severely impacts both physical and mental wellbeing
  • Influence multiple aspects of life including healthcare access, housing, and social participation

Employment barriers – Primary socioeconomic influence

  • Approximately 30% lower employment rates than general population
  • Limited income potential restricts ability to afford:
    • Specialised healthcare services not covered by Medicare
    • Gap payments for NDIS-supported therapies
    • Essential assistive technologies and modifications
  • Directly impacts access to vital treatments, therapies, and medications

Educational disadvantage – Compounding factor

  • Physical access barriers and inadequate support in educational settings
  • Lower completion rates of secondary and tertiary education
  • Results in limited employment options and lower-paying positions
  • Creates cycle of disadvantage affecting ability to afford:
    • Private health insurance
    • Preventative healthcare services
    • Regular health monitoring

Housing challenges – Financial manifestation

  • Limited accessible housing options at premium prices
  • Contributes to housing stress and potential homelessness
  • Associated mental health conditions including anxiety and depression
  • Extended waiting lists for accessible public housing (often several years)
  • Many forced to live in unsuitable accommodation that compromises health and safety

Counter-argument – Other determinants:

  • Environmental barriers exist regardless of socioeconomic status
  • Healthcare system gaps include inaccessible facilities and equipment
  • Societal attitudes and stigma affect quality of care
  • Healthcare professionals’ lack of disability awareness leads to diagnostic overshadowing
  • These factors can affect health independent of financial means

Predominant influence – Financial burden:

  • Gap payments for therapies not fully covered by support systems
  • Specialised equipment costs beyond subsidies
  • Home modifications essential for independence
  • Significant portion of household income consumed by disability-related expenses
  • Disability Support Pension often insufficient, falling below poverty line
  • Forces difficult choices between healthcare needs and other essentials

Conclusion – Final judgment:

  • Socioeconomic factors affect health of people with disabilities to a very large extent
  • While other factors contribute, financial disadvantage creates the most pervasive barriers
  • Long-term cycle of disadvantage significantly impacts:
    • Quality of life
    • Health outcomes
    • Life expectancy for Australians with disabilities

♦♦ Mean mark 45%.

HMS, HIC EQ-Bank 68

Research indicates that young people's definitions of health evolve as they move through adolescence.

How do young people's health priorities typically change between early adolescence (12-14 years) and late adolescence (17-19 years).   (5 marks)

Show Answers Only

*Cause-and-effect language that directly addresses the “How” (unofficial) keyword is bolded in the answer below.

  • Young adolescents (12-14) typically define health concretely through immediate, observable aspects like physical appearance and energy levels. This occurs because their developmental stage limits abstract thinking abilities.
  • As a result of cognitive development progressing, late adolescents (17-19) shift toward more sophisticated health concepts that include preventive behaviours, long-term wellbeing, and the integration of physical, mental and social dimensions. This demonstrates why maturity changes health understanding.
  • Peer influence on health definitions transforms from early adolescence, where fitting in often dictates health behaviours, to late adolescence. This happens when greater independence enables young people to balance social factors with personal values.
  • Biological changes during puberty initially focus younger adolescents on body-related health concerns. This process leads to increased autonomy in later adolescence, which allows broader consideration of lifestyle choices.
  • These elements work together to require different health approaches: concrete, socially-relevant messaging for younger adolescents versus participatory, autonomy-respecting strategies for older teens. This shows a clear connection between developmental stage and effective health communication.
Show Worked Solution

*Cause-and-effect language that directly addresses the “How” (unofficial) keyword is bolded in the answer below.

  • Young adolescents (12-14) typically define health concretely through immediate, observable aspects like physical appearance and energy levels. This occurs because their developmental stage limits abstract thinking abilities.
  • As a result of cognitive development progressing, late adolescents (17-19) shift toward more sophisticated health concepts that include preventive behaviours, long-term wellbeing, and the integration of physical, mental and social dimensions. This demonstrates why maturity changes health understanding.
  • Peer influence on health definitions transforms from early adolescence, where fitting in often dictates health behaviours, to late adolescence. This happens when greater independence enables young people to balance social factors with personal values.
  • Biological changes during puberty initially focus younger adolescents on body-related health concerns. This process leads to increased autonomy in later adolescence, which allows broader consideration of lifestyle choices.
  • These elements work together to require different health approaches: concrete, socially-relevant messaging for younger adolescents versus participatory, autonomy-respecting strategies for older teens. This shows a clear connection between developmental stage and effective health communication.

HMS, HIC EQ-Bank 59 MC

A researcher compared how young people from different socioeconomic backgrounds define health priorities.

Which combination of factors would most likely influence differences in these definitions?

    1. Access to healthcare resources in their communities
    2. Cultural beliefs and practices around health
    3. Individual genetic predispositions to certain health conditions
    4. Social media representation of health and fitness
  1. 1 and 2
  2. 1 and 3
  3. 2 and 4
  4. 3 and 4
Show Answers Only
\(A\)
Show Worked Solution
  • A is correct because resource access shapes awareness of health options while cultural beliefs fundamentally determine how health is understood within different communities.

Other options:

  • B is incorrect because genetic predispositions don’t systematically influence how different socioeconomic groups conceptualise health.
  • C is incorrect because social media has less fundamental impact than resource access on how different groups define health priorities.
  • D is incorrect because neither genetics nor social media are primary determinants of socioeconomic differences in health definitions.

HMS, HIC EQ-Bank 66

A researcher wants to investigate adolescents' experiences with physical activity and mental wellbeing. They have designed a study using online surveys with multiple-choice and rating scale questions.

Evaluate the validity, reliability and credibility of this data collection method for understanding adolescent health experiences.   (8 marks)

Show Answers Only

Evaluation Statement

  • Online surveys with fixed responses prove partially effective for researching adolescent health experiences.
  • This evaluation examines validity, reliability and credibility of a study using online surveys with multiple-choice and rating scale questions.

Validity

  • The method partially fulfils validity requirements for capturing complex health experiences.
  • The research involves a method that can gather large samples quickly.
  • However, predetermined response options fail to capture nuanced adolescent perspectives, especially for subjective concepts like mental wellbeing.
  • While strong in measuring basic activity levels through quantifiable data, it proves less suitable for exploring personal health experiences that involve deeper meanings.

Reliability

  • The survey approach inadequately fulfils reliability standards without proper testing and diverse sampling.
  • A lack of pilot testing increases the risk of inconsistent question interpretation across age groups.
  • Also, without demographic information about participants, findings cannot reliably apply to all adolescents.

Credibility

  • Single-method data collection severely limits credibility of findings.
  • Online surveys alone prove insufficient for understanding lived experiences of adolescents.
  • A critical weakness is relying solely on quantitative data when health experiences require qualitative exploration.
  • Evidence shows mixed methods combining surveys with interviews produce superior insights.

Final Evaluation

  • Weighing these factors, the data collection method described provides limited insight into adolescent health experiences.
  • All three criteria reveal significant weaknesses in capturing complex teen health realities.
  • The overall evaluation demonstrates urgent need for mixed methods approaches.
  • Implications suggest researchers must combine quantitative surveys with qualitative interviews to achieve credible, valid and reliable understanding of adolescent wellbeing.
Show Worked Solution

Evaluation Statement

  • Online surveys with fixed responses prove partially effective for researching adolescent health experiences.
  • This evaluation examines validity, reliability and credibility of a study using online surveys with multiple-choice and rating scale questions.

Validity

  • The method partially fulfils validity requirements for capturing complex health experiences.
  • The research involves a method that can gather large samples quickly.
  • However, predetermined response options fail to capture nuanced adolescent perspectives, especially for subjective concepts like mental wellbeing.
  • While strong in measuring basic activity levels through quantifiable data, it proves less suitable for exploring personal health experiences that involve deeper meanings.

Reliability

  • The survey approach inadequately fulfils reliability standards without proper testing and diverse sampling.
  • A lack of pilot testing increases the risk of inconsistent question interpretation across age groups.
  • Also, without demographic information about participants, findings cannot reliably apply to all adolescents.

Credibility

  • Single-method data collection severely limits credibility of findings.
  • Online surveys alone prove insufficient for understanding lived experiences of adolescents.
  • A critical weakness is relying solely on quantitative data when health experiences require qualitative exploration.
  • Evidence shows mixed methods combining surveys with interviews produce superior insights.

Final Evaluation

  • Weighing these factors, the data collection method described provides limited insight into adolescent health experiences.
  • All three criteria reveal significant weaknesses in capturing complex teen health realities.
  • The overall evaluation demonstrates urgent need for mixed methods approaches.
  • Implications suggest researchers must combine quantitative surveys with qualitative interviews to achieve credible, valid and reliable understanding of adolescent wellbeing.

HMS, TIP 2024 HSC 26

Assess the possible benefits of implementing neural recovery strategies on performance.   (8 marks)

Show Answers Only

Judgement Statement

  • Neural recovery strategies demonstrate highly effective benefits for athletic performance.
  • Assessment based on physiological recovery enhancement and sustained performance capability.

Physiological Recovery Enhancement

  • Hydrotherapy produces measurable results through alternating hot and cold water immersion.
  • This demonstrates high effectiveness in reducing neural fatigue and inflammation while improving circulation.
  • Sports massage strongly meets recovery needs by stimulating the parasympathetic nervous system and reducing muscle tension.
  • Basketball players using ice baths experience faster recovery between games, while tennis players maintain shoulder mobility through massage therapy.
  • These strategies achieve significant physiological benefits that directly translate to improved performance readiness.

Sustained Performance Capability

  • Active recovery sessions adequately fulfil the need for maintaining movement patterns during rest periods.
  • Light cycling or swimming allows continued fitness maintenance while promoting neural system recovery.
  • Evidence supporting this includes track athletes maintaining conditioning through gentle exercise following competition.
  • Prevention of overtraining strongly demonstrates the effectiveness of structured neural recovery protocols.
  • Weightlifters incorporating planned recovery days maintain proper technique and prevent performance breakdown during intensive training cycles.

Overall Assessment

  • When all factors are considered, neural recovery strategies prove highly beneficial for performance enhancement.
  • The strengths outweigh limitations as these methods address both immediate recovery needs and long-term performance sustainability.
  • Implementation produces optimal outcomes for athletes across various sports disciplines.
Show Worked Solution

Judgement Statement

  • Neural recovery strategies demonstrate highly effective benefits for athletic performance.
  • Assessment based on physiological recovery enhancement and sustained performance capability.

Physiological Recovery Enhancement

  • Hydrotherapy produces measurable results through alternating hot and cold water immersion.
  • This demonstrates high effectiveness in reducing neural fatigue and inflammation while improving circulation.
  • Sports massage strongly meets recovery needs by stimulating the parasympathetic nervous system and reducing muscle tension.
  • Basketball players using ice baths experience faster recovery between games, while tennis players maintain shoulder mobility through massage therapy.
  • These strategies achieve significant physiological benefits that directly translate to improved performance readiness.

Sustained Performance Capability

  • Active recovery sessions adequately fulfil the need for maintaining movement patterns during rest periods.
  • Light cycling or swimming allows continued fitness maintenance while promoting neural system recovery.
  • Evidence supporting this includes track athletes maintaining conditioning through gentle exercise following competition.
  • Prevention of overtraining strongly demonstrates the effectiveness of structured neural recovery protocols.
  • Weightlifters incorporating planned recovery days maintain proper technique and prevent performance breakdown during intensive training cycles.

Overall Assessment

  • When all factors are considered, neural recovery strategies prove highly beneficial for performance enhancement.
  • The strengths outweigh limitations as these methods address both immediate recovery needs and long-term performance sustainability.
  • Implementation produces optimal outcomes for athletes across various sports disciplines.

♦♦♦ Mean mark 37%.

HMS, HIC EQ-Bank 57 MC

A researcher is collecting data on adolescent health behaviours through an anonymous online survey.

Which combination of approaches best addresses ethical requirements when studying sensitive topics?

    1. Obtaining both parental consent and adolescent assent before participation
    2. Including only questions that parents have pre-approved
    3. Providing contact information for relevant support services
    4. Clearly explaining the limits of confidentiality in the consent process
  1. 1 and 2
  2. 1 and 3
  3. 1 and 4
  4. 3 and 4
Show Answers Only
\(D\)
Show Worked Solution
  • Option 1 (obtaining parental consent and adolescent assent) is generally good practice but may not be feasible or appropriate for truly anonymous online surveys.
  • Option 2 (only including parent-approved questions) could compromise research validity and adolescent autonomy.
  • Option 3 ensures participants have access to appropriate support resources.
  • Option 4 ensures transparency about confidentiality limitations in the consent process.

\(\Rightarrow D\)

HMS, HIC EQ-Bank 64

Describe THREE ethical considerations that are present when collecting data from adolescents about their meaning of health.

Include a way in which researchers can address each ethical consideration in your answer.   (5 marks)

Show Answers Only

Sample Answer

  • When collecting data from adolescents about health, researchers must get informed consent from both the teenagers and their parents.
    • Researchers should make sure the participant (and parents) understand what the research involves and that they can withdraw at any time.
  • Confidentiality is essential, so researchers should keep all personal information private.
    • Researchers should use anonymous surveys where possible to protect participants’ identities.
  • Researchers should also be careful that their questions about health aren’t too personal or sensitive.
    • Where appropriate, researchers should provide support resources in case talking about health issues causes any emotional distress.
Show Worked Solution

Sample Answer

  • When collecting data from adolescents about health, researchers must get informed consent from both the teenagers and their parents.
    • Researchers should make sure the participant (and parents) understand what the research involves and that they can withdraw at any time.
  • Confidentiality is essential, so researchers should keep all personal information private.
    • Researchers should use anonymous surveys where possible to protect participants’ identities.
  • Researchers should also be careful that their questions about health aren’t too personal or sensitive.
    • Where appropriate, researchers should provide support resources in case talking about health issues causes any emotional distress.

HMS, HIC EQ-Bank 56 MC

A researcher collected the following sets of data while investigating young people's health behaviours:

    1. The percentage of adolescents who exercised at least three times per week
    2. Patient identification numbers from a youth mental health clinic database
    3. Daily caloric intake recorded by teenagers in a nutrition study
    4. BMI measurements of all individual participants

Which combination correctly identifies all the quantitative data sets?

  1. 1 and 2
  2. 1, 2 and 3
  3. 1, 3 and 4
  4. 3 and 4
Show Answers Only
\(C\)
Show Worked Solution
  • C is correct as all statements listed provide a numerical percentage that can be statistically analysed, which is characteristic of quantitative data.

Explanation:

  • 1 – Quantitative data (numerical measurement that can be mathematically analysed).
  • 2 – Qualitative data. Even though these are numbers, they function as labels or identifiers rather than measurements.
  • 3 – Quantitative data (numerical measurements of food consumption).
  • 4 – Quantitative data. BMI (Body Mass Index) is a numerical measurement calculated from height and weight that can be used for statistical analysis.

PHYSICS, M2 EQ-Bank 2

Consider the information in the diagram below.
  
  1. Calculate the acceleration of the blocks as a result of the applied forces acting on them.   (2 marks)
  1. What forces does block \(Y\) apply to block \(X\).   (2 marks)
Show Answers Only

a.    \(0.5\ \text{ms}^{-2}\)

b.    \(1500\ \text{N}\)

Show Worked Solution

a.    Total system mass \(= 1000 + 2000 = 3000\ \text{kg}\)

Applied force on system \(= 2250\ \text{N}\)

Frictional force on system \(= 0.25 \times 3000 = 750\ \text{N}\)

Net force \(=\) the applied force \(-\) the frictional force \(=2250-750 =1500\ \text{N}\)

Find acceleration using \(F_{\text{net}}= ma\):

\(a=\dfrac{F_{\text{net}}}{m} =\dfrac{1500}{3000} = 0.5\ \text{ms}^{-2}\)

 

b.    Net force on \(X = ma = 1000 \times 0.5 = 500\ \text{N}\) 

Net force on \(X\)  \(=\)  applied force on \(X -\) force of \(Y\) on \(X -\) the frictional force on \(X\).  
\(500\) \(=2250-F_{Y → X}-(1000 \times 0.25)\)  
\(F_{Y → X}\) \(=2250-500-250=1500\ \text{N}\)  

v1 Financial Maths, STD2 F4 2018 HSC 19 MC

The table shows the compounded values of $1 at different interest rates over different periods.
 

 
Ben hopes to have $18 000 in 2 years to travel. He opens an account today which pays interest of 4% p.a., compounded quarterly.

Using the table, which expression calculates the minimum single sum that Ben needs to invest today to ensure he reaches his savings goal?

  1. 18 000 × 1.0816
  2. 18 000 ÷ 1.0816
  3. 18 000 × 1.0829
  4. 18 000 ÷ 1.0829
Show Answers Only

`text(D)`

Show Worked Solution

`text(4% annual)`

`= (4%)/4 = 1% per quarter`

`2 \ text(years) = 8 \ text(periods)`

`\text(From the table: at 8 periods and 1%, compounded value) = 1.0829`.

`:.\ text(Minimum sum) = 18\ 000 ÷ 1.0829`

`=>\ text(D)`

Financial Maths, 2ADV M1 2024 NHT1 24*

Jarryd invested $14 000 into an account earning compound interest at a fixed rate per time period.

The graph below shows the balance of the account for four of the first five time periods after the initial investment. The information for time period 3 is not shown.
 

 

Immediately after the interest was calculated for time period 3, Jarryd added an extra one-off amount into the account.

Determine the value of Jarrod's extra one off amount, giving your answer correct to the nearest cent.   (3 marks)

Show Answers Only

\(\$224.03 \)

Show Worked Solution

\(\text{Increase factor between periods}\ = \dfrac{15\,120}{14\,000}=1.08\)

\(\text{At time period 3:}\)

\(\text{Balance (before extra payment)}\ = 14\,000 \times 1.08^{3} = 17\,635.97 \)

\(\text{Let}\ V = 17\,635.97 +\ \text{extra payment}\)

\(V \times 1.08 = 19\,288.80\ \ \Rightarrow\ \ V=17\,860.00\)

\(\therefore \ \text{Extra payment}\ = 17\,860.00-17\,635.97=\$224.03 \)

Financial Maths, STD2 F1 2024 NHT1 24*

Jarryd invested $14 000 into an account earning compound interest at a fixed rate per time period.

The graph below shows the balance of the account for four of the first five time periods after the initial investment. The information for time period 3 is not shown.
 

 

Immediately after the interest was calculated for time period 3, Jarryd added an extra one-off amount into the account.

Determine the value of Jarrod's extra one off amount, giving your answer correct to the nearest cent.   (3 marks)

Show Answers Only

\(\$224.03 \)

Show Worked Solution

\(\text{Increase factor between periods}\ = \dfrac{15\,120}{14\,000}=1.08\)

\(\text{At time period 3:}\)

\(\text{Balance (before extra payment)}\ = 14\,000 \times 1.08^{3} = 17\,635.97 \)

\(\text{Let}\ V = 17\,635.97 +\ \text{extra payment}\)

\(V \times 1.08 = 19\,288.80\ \ \Rightarrow\ \ V=17\,860.00\)

\(\therefore \ \text{Extra payment}\ = 17\,860.00-17\,635.97=\$224.03 \)

HMS, BM 2024 HSC 15 MC

The diagram shows the order of three sport skills on a continuum, representing both the precision and size of muscular movement involved in the skill.

Which skills are represented by \(X\), \(Y\) and \(Z\)?

\begin{align*}
\begin{array}{c}
\rule{0pt}{2.5ex} \ \rule[-1ex]{0pt}{0pt}& \\
\rule{0pt}{2.5ex}\textbf{A.}\\
\textbf{}\rule[-1ex]{0pt}{0pt}\\
\rule{0pt}{2.5ex}\textbf{B.}\\
\textbf{}\rule[-1ex]{0pt}{0pt}\\
\rule{0pt}{2.5ex}\textbf{C.}\rule[-1ex]{0pt}{0pt}\\
\rule{0pt}{2.5ex}\textbf{D.}\rule[-1ex]{0pt}{0pt}\\
\end{array}
\begin{array}{|l|l|l|}
\hline
\rule{0pt}{2.5ex} X\rule[-1ex]{0pt}{0pt}& Y & Z \\
\hline
\rule{0pt}{2.5ex}\text{Basketball free-throw}&\text{Pedalling in cycling} &\text{Accelerating from a block }\\
\text{}\rule[-1ex]{0pt}{0pt}&\text{} &\text{start in athletics}\\
\hline
\rule{0pt}{2.5ex}\text{Shooting in archery}& \text{Accelerating from a block} &\text{Paddling in kayaking}\\
\text{}\rule[-1ex]{0pt}{0pt}& \text{start in athletics} &\text{}\\
\hline
\rule{0pt}{2.5ex}\text{Paddling in kayaking}\rule[-1ex]{0pt}{0pt}& \text{Tumble turn in swimming} &\text{Shooting in archery} \\
\hline
\rule{0pt}{2.5ex}\text{Tumble turn in swimming}\rule[-1ex]{0pt}{0pt}& \text{Basketball free-throw}  &\text{Pedalling in cycling}\\
\hline
\end{array}
\end{align*}

Show Answers Only

\(A\)

Show Worked Solution
  • A is correct: Basketball free-throw being the most precise/fine, pedalling intermediate, and block start acceleration the most gross motor movement.

Other Options:

  • B, C and D all incorrect: All ordered incorrectly on the fine-gross continuum.

♦♦♦ Mean mark 33%.