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Calculus, MET2 2023 VCAA 3

Consider the function .

  1. State the value of .   (1 mark)
  2. The derivative, , can be expressed in the form .
  3. Find the real number .   (1 mark)
  4.  i. Let be a real number. Find, in terms of , the equation of the tangent to at the point .   (1 mark)

    ii. Hence, or otherwise, find the equation of the tangent to that passes through the origin, correct to three decimal places.   (2 marks)

  1.  

Let .

  1. Find the coordinates of the point of inflection for , correct to two decimal places.   (1 mark)
  2. Find the largest interval of values for which is strictly decreasing.
  3. Give your answer correct to two decimal places.   (1 mark)
  4. Apply Newton's method, with an initial estimate of , to find an approximate -intercept of .
  5. Write the estimates and in the table below, correct to three decimal places.   (2 marks)
      


  6. For the function , explain why a solution to the equation should not be used as an initial estimate in Newton's method.   (1 mark)
  7. There is a positive real number for which the function has a local minimum on the -axis.
  8. Find this value of .   (2 marks)
Show Answers Only

a.   

b.   

ci. 

cii.

d.

e.

f. 

g.

h.

Show Worked Solution

a.   


  

b.    
   
   
 
     
 
   
ci. 


♦♦ Mean mark (c)(i) 50%.

cii. 

  

♦♦♦ Mean mark (c)(ii) 30%.
MARKER’S COMMENT: Some students did not substitute (0, 0) into the correct equation or did not find the value of and used .
d.    
 
 

e.   


♦♦ Mean mark (e) 40%.
MARKER’S COMMENT: Round brackets were often used which were incorrect as endpoints were included. Some responses showed the interval where the function was strictly increasing.

f.     

g.   

♦♦♦ Mean mark (g) 20%.

h.   

 


♦♦♦ Mean mark (h) 10%.
MARKER’S COMMENT: Many students showed that but failed to couple it with . Ensure exact values are given where indicated not approximations.

Calculus, MET2 2023 VCAA 1

Let . Part of the graph of is shown below.

  1. State the coordinates of all axial intercepts of .   (1 mark)
  2. Find the coordinates of the stationary points of .   (2 marks)
    1. Let .
    2. Find the values of for which .   (1 mark)
    1. Write down an expression using definite integrals that gives the area of the regions bound by and .  (2 marks)
    2. Hence, find the total area of the regions bound by and , correct to two decimal places.   (1 mark)
  1. Let , where and .
  2. Find the possible values of and .   (4 marks)
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a.   

b.   

c.i. 

c.ii.

 

c.iii.

d.  

Show Worked Solution

a.   
  

b.   


  

ci   

  

cii  


  

ciii 
 

  

d.   

  

 

Data Analysis, GEN2 2023 VCAA 2a

The following data shows the sizes of a sample of 20 oysters rated as small, medium or large.

  1. Use the data above to complete the following frequency table.   (1 mark)

  1. Use the percentages in the table to construct a percentage segmented bar chart below. A key has been provided.   (1 mark)

     

Show Answers Only

i.    

ii.    
     

Show Worked Solution

i.    

 
ii.    
         

Data Analysis, GEN1 2023 VCAA 1-2 MC

The dot plot below shows the times, in seconds, of 40 runners in the qualifying heats of their 800 m club championship.
 

Question 1

The median time, in seconds, of these runners is

  1. 135.5
  2. 136
  3. 136.5
  4. 137
  5. 137

 
Question 2

The shape of this distribution is best described as

  1. positively skewed with one or more possible outliers.
  2. positively skewed with no outliers.
  3. approximately symmetric with one or more possible outliers.
  4. approximately symmetric with no outliers.
  5. negatively skewed with one or more possible outliers.
Show Answers Only

Show Worked Solution


 

ENGINEERING, TE 2023 HSC 3 MC

Why is pure copper preferred over a copper alloy in telecommunications applications?

  1. It has higher stiffness.
  2. It has better conductivity.
  3. It can be precipitation hardened.
  4. It has a better strength to weight ratio.
Show Answers Only

Show Worked Solution

→ Pure copper offers lower stiffness than copper alloys (eliminate A), is work hardened (eliminate C), and generally has lower strength to weight ratios (eliminate D).

→ In telecommunications, where high conductivity is crucial for transmitting electrical signals, pure copper is the preferred choice to ensure efficient signal transmission.

ENGINEERING, PPT 2023 HSC 24a

Roller coaster support structures can be made from either timber or steel.

Compare the properties of the two materials in roller coaster support structures.  (2 marks)

Show Answers Only

→ Unlike steel, timber has the ability to flex and bend, which can absorb some of the forces exerted by the roller coaster.

→ However, timber has less mechanical strength than steel and is more susceptible to rot and insect damage over time.
 

Answers could include:

→ Steel frames are much more easily fabricated and assembled than timber frames, which can save time and costs in the construction process.

→ Steel is much more resistant to fire than timber, which makes it a safer material to use in roller coasters.

→ Steel has greater mechanical strength and is a more durable material than timber. It is able to withstand the higher stresses and forces exerted on a roller coaster.

Show Worked Solution

→ Unlike steel, timber has the ability to flex and bend, which can absorb some of the forces exerted by the roller coaster.

→ However, timber has less mechanical strength than steel and is more susceptible to rot and insect damage over time.
 

Answers could include:

→ Steel frames are much more easily fabricated and assembled than timber frames, which can save time and costs in the construction process.

→ Steel is much more resistant to fire than timber, which makes it a safer material to use in roller coasters.

→ Steel has greater mechanical strength and is a more durable material than timber. It is able to withstand the higher stresses and forces exerted on a roller coaster.

ENGINEERING, AE 2023 HSC 21b

You are part of a team of engineers working collaboratively on the design of a new aircraft.

Explain the benefits of collaboration when completing the engineering report.   (3 marks)

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→ A collaborative approach allows for the pooling of expert knowledge. This will produce a more comprehensive report with a lower risk of errors within the report.

→ Time efficiency – a division of tasks among team members that utilises their specific skill sets can expedite the writing of the report.

→ Validation of decisions across multiple team members who can independently verify and validate design calculations and recommendations is a more comprehensive approach.

→ Collaboration between engineers with differing years of experience is crucial for professional development and training the next generation of engineers.

Show Worked Solution

→ A collaborative approach allows for the pooling of expert knowledge. This will produce a more comprehensive report with a lower risk of errors within the report.

→ Time efficiency – a division of tasks among team members that utilises their specific skill sets can expedite the writing of the report.

→ Validation of decisions across multiple team members who can independently verify and validate design calculations and recommendations is a more comprehensive approach.

→ Collaboration between engineers with differing years of experience is crucial for professional development and training the next generation of engineers.

ENGINEERING, AE 2023 HSC 21a

How can computer graphics be utilised as a tool in aeronautical engineering?   (2 marks)

Show Answers Only

→ Computer graphics can create a detailed and accurate visual models in three dimensions.

→ This technology can be extremely efficient in the design of aircraft components through simulation, allowing ideas to be tested and adjusted in short time frames.

Answers could also include:

  • The creation of interactive user interfaces
  • The provision of large amounts of data in the analysis of flight dynamics and servicing of aircraft
  • Improving manufacturing and prototyping.

Show Worked Solution

→ Computer graphics can create a detailed and accurate visual models in three dimensions.

→ This technology can be extremely efficient in the design of aircraft components through simulation, allowing ideas to be tested and adjusted in short time frames.

Answers could also include:

  • The creation of interactive user interfaces
  • The provision of large amounts of data in the analysis of flight dynamics and servicing of aircraft
  • Improving manufacturing and prototyping.

PHYSICS, M2 2017 VCE 7 MC

A model car of mass 2.0 kg is propelled from rest by a rocket motor that applies a constant horizontal force of 4.0 N, as shown below. Assume that friction is negligible.
 

Which one of the following best gives the magnitude of the acceleration of the model car?

Show Answers Only

Show Worked Solution
 
   
   

 

PHYSICS, M4 2021 VCE 2 MC

The diagram below shows the electric field lines between four charged spheres: and . The magnitude of the charge on each sphere is the same.
  
 


 

Which of the following correctly identifies the type of charge (+ positive or – negative) that resides on each of the spheres and ?

 
A.  
B.
C.
D.
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Show Worked Solution

→ Electric field lines travel away from positive charges and towards negative charges.

→ Therefore, and must be positive charges.

CHEMISTRY, M3 2012 HSC 3 MC

What effect does a catalyst have on a reaction?

  1. It increases the rate.
  2. It increases the yield.
  3. It increases the heat of reaction.
  4. It increases the activation energy.
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Show Worked Solution

→ A catalyst is a substance that increases the rate of a chemical reaction without itself undergoing any permanent chemical change.

CHEMISTRY, M3 2017 VCE 1 MC

A catalyst

  1. slows the rate of reaction.
  2. ensures that a reaction is exothermic.
  3. moves the chemical equilibrium of a reaction in the forward direction.
  4. provides an alternative pathway for the reaction with a lower activation energy.
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Show Worked Solution

→ A catalyst increases the rate of a chemical reaction by reducing the activation energy of the reaction. Thus, by collision theory, particles require less energy than normal to react to form products.

CHEMISTRY, M2 2016 VCE 9a

Standard solutions of sodium hydroxide, , must be kept in airtight containers. This is because is a strong base and absorbs acidic oxides, such as carbon dioxide, , from the air and reacts with them. As a result, the concentration of is changed to an unknown extent.

in the air reacts with water to form carbonic acid, . This can react with to form sodium carbonate, .

  1. Write a balanced overall equation for the reaction between gas and water to form .   (1 mark)

  2. Write a balanced equation for the complete reaction between and to form .   (1 mark)

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i.   

ii.   

Show Worked Solution

i.   

ii.   

PHYSICS, M2 2014 HSC 3 MC

A pendulum is used to determine the value of acceleration due to gravity. The length of the pendulum is varied, and the time taken for the same number of oscillations is recorded.

Which of the following could increase the reliability of the results?

  1. Changing the mass of the pendulum
  2. Identifying the independent and dependent variables
  3. Recording all measurements to at least four significant figures
  4. Repeating each measurement several times and recording the average
Show Only

Show Worked Solution

→ Reliability of data can be increased by repeating the same experiment numerous times and recording an average from the data as it eliminates random error.

Algebra, STD2 A4 2023 HSC 20

On another planet, a ball is launched vertically into the air from the ground.

The height above the ground, metres, can be modelled using the function  , where is measured in seconds. The graph of the function is shown.

  1. Based on the graph, what is the maximum height reached by the ball?  (1 mark)

  2. Based on the graph, at what TWO times is the ball at of its maximum height?  (2 marks)

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a.   

b.   

Show Worked Solution

a.   

b.   

Measurement, STD2 M7 2023 HSC 16

The graph shows Peta's heart rate, in beats per minute, during the first 60 minutes of a marathon.
 

  1. What was Peta's heart rate 20 minutes after she started her marathon?   (1 mark)

  2. Peta started the marathon at 10 am. At what time would her heart rate first reach 140 beats/minute?   (1 mark)

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a.   

b.   

Show Worked Solution

a.   

b.   

BIOLOGY, M5 EQ-Bank 1 MC

A strawberry plant will send out over the ground runners which will take root and grow a new plant as shown.
 

This method of growing a new plant is an example of

  1. budding.
  2. binary fission.
  3. external fertilisation.
  4. asexual reproduction.
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Show Worked Solution

→ Runners are plant stems which grow and take root to produce a new plant.

→ This does not involve the use of pollen or seeds (sexual reproduction) and the new strawberry plant will be genetically identical to the first.

BIOLOGY, M7 2014 HSC 22a

Explain how TWO specific personal hygiene practices reduce the risk of infection.   (4 marks)

Show Answers Only

“

Show Worked Solution

Answers can include any TWO of the following:

→ Washing hands after handling garbage to remove any pathogens from the skin.

→ Covering your mouth when coughing to reduce the chance of pathogens spreading via water droplets.

→ Covering cuts and sores with bandaids or bandages to reduce the chance of infecting others through the transfer of blood and puss which, as well as covering up potential portals of entry for pathogens, will also protect the individual.

→ Daily showers with body wash and shampoo to remove pathogens from skin and scalp.

BIOLOGY, M7 2014 HSC 22b

Drinking water contaminated with dissolved lead (a heavy metal) can cause a serious disease.

Classify this disease as either infectious or non-infectious. Justify your answer.   (2 marks)

Show Answers Only

“

Show Worked Solution

→ This disease is non-infectious as it is not caused by a pathogen and therefore cannot be transferred from host to host.

→ It can only be obtained through digestion of lead.

BIOLOGY, M6 2014 HSC 1 MC

Exposure to radiation such as X-rays may change the sequence of bases in DNA.

What is this called?

  1. Mutation
  2. Translation
  3. Replication
  4. Transcription
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Show Worked Solution

→ Any permanent change to the DNA sequence is referred to as a mutation.

ENGINEERING, PPT 2018 HSC 21a

The diagram shows a self-driving electric vehicle.
 


 

Innovations in global positioning systems (GPS) and sensor technologies are used in the operation of this vehicle.

Describe how both of these innovations are used in the control of the vehicle.   (3 marks)

Show Answers Only

→ Sensors can be used to prevent collisions through the detection of objects in the path or vicinity of the vehicle.

→ GPS shows the vehicle’s position on the Earth’s surface using triangulation.

Show Worked Solution

→ Sensors can be used to prevent collisions through the detection of objects in the path or vicinity of the vehicle.

→ GPS shows the vehicle’s position on the Earth’s surface using triangulation.

BIOLOGY, M8 2017 HSC 2 MC

Which of the following body systems is involved in detecting and responding to environmental changes?

  1. Circulatory
  2. Digestive
  3. Excretory
  4. Nervous
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Show Worked Solution

→ The nervous system detects and responds to environmental change using sensory nerves.

BIOLOGY, M8 2017 HSC 1 MC

What is the name of the process that enables organisms to maintain a relatively stable internal environment?

  1. Osmosis
  2. Adaptation
  3. Homeostasis
  4. Active transport
Show Answers Only

Show Worked Solution

→ Homeostasis is the process of keeping a fairly stable internal environment in response to change.

CHEMISTRY, M8 2018 HSC 4 MC

Which of the following greatly enhanced scientific understanding of the effects of trace elements?

  1. Improved filtration techniques
  2. The development of atomic absorption spectroscopy
  3. The creation of new elements in particle accelerators
  4. The work of Le Chatelier in describing chemical equilibrium
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Show Worked Solution

→ AAS allows trace elements to be detected at much lower concentrations than previous techniques.

ENGINEERING, AE 2022 HSC 17 MC

During routine maintenance, ultrasonic testing is performed on some aircraft components such as aircraft landing gear.

What is the reason for performing this test?

  1. It can be performed quickly.
  2. It reveals any surface defects.
  3. It reveals any hidden internal faults.
  4. It can be carried out using simple techniques.
Show Answers Only

Show Worked Solution

PHYSICS, M5 2015 HSC 21

A projectile is fired horizontally from a platform.
 

Measurements of the distance travelled by the projectile from the base of the platform are made for a range of initial velocities.   

  1. Graph the data on the grid provided and draw the line of best fit.   (2 marks)
     
     
  1. Calculate the height of the platform.   (2 marks)

Show Answers Only

a. 
     

b.   2.5 m

Show Worked Solution

a.   
          

b.   
 

 
Using the line of best fit, gradient = 0.714.

t = 0.714 s.

 
   
   

 
Height = 2.5 m

Measurement, STD1 M4 2022 HSC 15

Tom is 25 years old, and likes to keep fit by exercising.

  1. Use this formula to find his maximum heart rate (bpm).
  2.       Maximum heart rate = 220 – age in years
  3. Tom's maximum heart rate is .................... bpm.  (1 mark)
  4. Tom will get the most benefit from this exercise if his heart rate is between 50% and 85% of his maximum heart rate.
  5. Between what two heart rates should Tom be aiming for to get the most benefit from his exercise?  (2 marks)

Show Answers Only
Show Worked Solution
a.   
   

 

b.   

Calculus, EXT2 C1 2022 HSC 14b

Let  , where "n" is a non-negative integer.

  1. Show that  .  (1  mark)

  2. Show that  .  (2 marks)

  3. Show that  .  (2 marks)

  4. Using parts (i) and (iii), show by mathematical induction, or otherwise, that for all ,
  5.            (2 marks)

  6. Using parts (ii) and (iv) prove that  .  (1  mark)

Show Answers Only
Show Worked Solution
i.   
   
   
   

 


Mean mark (i) 93%.

ii. 

 
   
   
   
   

 


♦♦ Mean mark (ii) 28%.
 

iii. 

 
   
   

 
iv.   


 


   


♦ Mean mark (iv) 50%.

 
   
   
   
   

 


 

v.   

  

 
 
 
   
   
   

♦♦ Mean mark (v) 34%.

BIOLOGY, M8 2019 HSC 1 MC

Which of the following is an example of a non-infectious disease?

  1. Polio caused by a virus
  2. Cholera caused by a bacterium
  3. Wheat rust caused by a fungus
  4. Haemophilia caused by a gene mutation
Show Answers Only

Show Worked Solution

→ Virus, bacteria and fungi are all pathogens; disease carriers which can be transmitted between hosts.

→ Gene mutations are changes in DNA and cannot be transmitted to others by contact or vectors.

BIOLOGY, M7 2022 HSC 21a

Outline ONE way that a pathogen can pass from person to person.  (2 marks)

Show Answers Only

→ A pathogen such as a bacteria, protozoa or fungus can be passed from person to person by direct transmission

→ This involves skin to skin contact, such as sexual intercourse or shaking hands.

 
Other modes of transmission include:

→ Object contamination.

→ Waterborne, foodborne or airborne.

→ Animal faeces or nasal secretions.

→ Bodily fluids/respiratory droplets.

Show Worked Solution

→ A pathogen such as a bacteria, protozoa or fungus can be passed from person to person by direct transmission

→ This involves skin to skin contact, such as sexual intercourse or shaking hands.

 
Other modes of transmission include:

→ Object contamination.

→ Waterborne, foodborne or airborne.

→ Animal faeces or nasal secretions.

→ Bodily fluids/respiratory droplets.

ENGINEERING, TE 2020 HSC 21a

Outline how ONE telecommunications engineering innovation has influenced traditional voice communication systems.   (2 marks)

Show Answers Only

Smartphones:

→ Have replaced landlines, enable constant communication from anywhere.

→ They also support video conferencing and access to information/the internet.

   
Other answers could include:

→ Digital radio: Has less interference and higher sound quality.

→ Videoconferencing: Enables visual as well as audio communication.

→ Cybersecurity: Protects your information when communicating with others.

Show Worked Solution

Smartphones:

→ Have replaced landlines, enable constant communication from anywhere.

→ They also support video conferencing and access to information/the internet.

   
Other answers could include:

→ Digital radio: Has less interference and higher sound quality.

→ Videoconferencing: Enables visual as well as audio communication.

→ Cybersecurity: Protects your information when communicating with others.

ENGINEERING, AE 2020 HSC 10 MC

Which of the following only contains tasks performed by the aeronautical engineer?

  1. Provide technical advice, assemble aircraft, design aircraft
  2. Assist in air traffic control, investigate crashes, pilot aircraft
  3. Make good checklists, read training manuals, schedule flights
  4. Write training manuals, assist in air traffic control, act as a public relations officer
Show Answers Only

Show Worked Solution

By Elimination:

→ Engineers do not assist in air traffic control (eliminate and ).

→ Engineers do not schedule flights (eliminate ).

BIOLOGY, M8 2020 HSC 27

Exposure to arsenic in drinking water has been associated with the onset of many diseases. The World Health Organisation recommends arsenic levels in drinking water should be below 10 g L-1 .

An epidemiological study involving 58 406 young adults was conducted over an 11-year period in one country to investigate young-adult mortality due to chronic exposure to arsenic in local drinking water. Each individual's average exposure and cumulative exposure to arsenic over the time of the study were calculated. Age, sex, education and socioeconomic status were taken into account during the analysis of the results.

The graphs show survival rates for males and females over the 11-year period associated with different average levels of exposure to arsenic in drinking water.
 

  1. Identify TWO features of the method used that contributed to the validity of this study.   (2 marks)

  2. The hypothesis put forward was that exposure to arsenic in drinking water increases mortality in young adults.
  3. Discuss the data presented in the graphs in relation to this hypothesis.   (4 marks)

Show Answers Only

a.   Successful answers should include two of the following:

→ The identification of the age and sex of participants

→  Socioeconomic status 

→  Arsenic exposure

→  Large sample size

→  The length of the study period
 

b.   Consider the less than 90 g L-1 group:

→  The survival rate for both males and females was highest in this “control” group. This is despite the group being exposed to more arsenic than recommended by WHO.

→  In both males and females, increased exposure to arsenic led to lower survival rates.

→  This gradual survival decrease is best seen in males.

→  In females, all doses over 90 g L-1 lead to similar survival decrease, suggesting other factors, such as a gene or diet, are interacting with the dosage of arsenic.

→ Over the 11 year period, survival progressively declined, supporting the hypothesis.

→  It is important to note, however, that despite the large sample size and time period the study was conducted, survival only dropped by 0.1%.

Show Worked Solution

a.   Successful answers should include two of the following:

→ The identification of the age and sex of participants

→  Socioeconomic status 

→  Arsenic exposure

→  Large sample size

→  The length of the study period
 

b.   Consider the less than 90 g L-1 group:

→  The survival rate for both males and females was highest in this “control” group. This is despite the group being exposed to more arsenic than recommended by WHO.

→  In both males and females, increased exposure to arsenic led to lower survival rates.

→  This gradual survival decrease is best seen in males.

→  In females, all doses over 90 g L-1 lead to similar survival decrease, suggesting other factors, such as a gene or diet, are interacting with the dosage of arsenic.

→ Over the 11 year period, survival progressively declined, supporting the hypothesis.

→  It is important to note, however, that despite the large sample size and time period the study was conducted, survival only dropped by 0.1%.

ENGINEERING, PPT 2021 HSC 26a

Outline a change in technology that has led to improved fuel efficiency in cars.   (2 marks)

Show Answers Only

Successful answers should discuss one of the following:

→ Lighter/more streamlined cars are generally more fuel efficient. This has been achieved through improved manufacturing methods and improved materials (ie replacing steel bumpers with lighter polymers).

→ Improved materials technology used to produce aluminium engine blocks instead of cast iron to decrease weight.

→ Mathematical modelling to increase aerodynamics of a car.

→ Hybrid cars and regenerative braking.

→ Shift towards fuel injection and higher compression ratio.

→ Cruise control maintains better average fuel economy.

→ Improved efficient gearboxes and differentials with low friction and torque.

→ Improvements to lubrication technology to reduce internal friction.

Show Worked Solution

Successful answers should discuss one of the following:

→ Lighter/more streamlined cars are generally more fuel efficient. This has been achieved through improved manufacturing methods and improved materials (ie replacing steel bumpers with lighter polymers).

→ Improved materials technology used to produce aluminium engine blocks instead of cast iron to decrease weight.

→ Mathematical modelling to increase aerodynamics of a car.

→ Hybrid cars and regenerative braking.

→ Shift towards fuel injection and higher compression ratio.

→ Cruise control maintains better average fuel economy.

→ Improved efficient gearboxes and differentials with low friction and torque.

→ Improvements to lubrication technology to reduce internal friction.

BIOLOGY, M8 2020 HSC 9 MC

A public education campaign was developed with the aim of lowering the incidence of skin cancer in the population.

The campaign was adopted Australia wide and is illustrated in the poster.
 

Which is the best method to measure the effectiveness of the campaign?

  1. By measuring exposure to the sun and skin cancer incidence
  2. By surveying beachgoers, asking if they remember the campaign
  3. By comparing skin cancer incidence before and after the campaign
  4. By counting the number of people on the beach wearing hats and sunglasses
Show Answers Only

Show Worked Solution

A direct measurement of any reduction in cancer incidence would prove campaign effectiveness.

BIOLOGY, M7 2020 HSC 4 MC

Malaria is a disease in humans caused by a single-celled Plasmodium species. It is transmitted by female mosquitoes.

Which of the following is true for malaria?

  1. Both Plasmodium and the mosquito are vectors
  2. Both Plasmodium and the mosquito are pathogens
  3. The mosquito is the vector and Plasmodium is the pathogen
  4. The mosquito is the pathogen and Plasmodium is the vector
Show Answers Only

Show Worked Solution

The Plasmodium is the pathogen that causes malaria disease, while the mosquito transmits the pathogen and is therefore the vector.

BIOLOGY, M8 2021 HSC 25

A patient visited an audiologist for a hearing test. The audiologist tested both ears at specific frequencies. The volumes at which each frequency could be heard are shown.
 

  1. Plot the data on the grid provided and include a key.   (3 marks)
     

  1. What conclusions can be drawn about the patient's hearing?   (2 marks)

  2. It is discovered that there is a complete and permanent blockage of the outer ear, but the cochlea is still fully functional.
  3. Justify the use of a suitable technology to assist the patient's hearing.   (3 marks)

Show Answers Only

a.  


 

b.   Right ear is within normal hearing range.

Left ear has a deficit and cannot hear at a normal level.
 

c.    Effective technology: Bone Conduction Implants

Bone conduction implants would prove to be the most effective technology to restore hearing to this patient. 

Bone conduction implants detect sound waves via a microphone, relaying them to a sound processor that converts the waves into vibrations which are then directly transferred to the cochlea. This process bypasses the ear blockage, therefore restoring hearing to the patient.

Show Worked Solution

a.   


 

b.   → Right ear is within normal hearing range.

→ Left ear has a deficit and cannot hear at a normal level.
 

c.    Effective technology: Bone Conduction Implants

→ Bone conduction implants would prove to be the most effective technology to restore hearing to this patient. 

→ Bone conduction implants detect sound waves via a microphone, relaying them to a sound processor that converts the waves into vibrations which are then directly transferred to the cochlea.

→ This process bypasses the ear blockage, therefore restoring hearing to the patient.


♦ Mean mark (c) 43%.

ENGINEERING, CS 2021 HSC 21a

Some large cities, such as Sydney, have bridges which span large bodies of water.

Outline TWO ways in which the construction of such bridges affects society.   (2 marks)

Show Answers Only

→ Bridges spanning large bodies of water allow for faster travel than other existing transport such as ferries.

→ This results in greater work productivity due to faster commuting. People will also have greater opportunity to work and recreate on both sides of the bridge.
  

Other advantages could include:

→ Greater use of major infrastructure like hospitals, schools and stadiums

→ Train lines can be constructed on the bridge to allow for extra mass transit

→ Reduction in existing transport on the harbour such as ferries

→ Potential increase in leisure time

Show Worked Solution

→ Bridges spanning large bodies of water allow for faster travel than other existing transport such as ferries.

→ This results in greater work productivity due to faster commuting. People will also have greater opportunity to work and recreate on both sides of the bridge.
  

Other advantages could include:

→ Greater use of major infrastructure like hospitals, schools and stadiums

→ Train lines can be constructed on the bridge to allow for extra mass transit

→ Reduction in existing transport on the harbour such as ferries

→ Potential increase in leisure time

ENGINEERING, AE 2021 HSC 2 MC

The flight recorder, commonly known as the 'black box', was developed in Australia in the 1950s to assist in air crash investigations.

How does a black box assist in an air crash investigation?

  1. It contains aircraft maintenance history.
  2. It holds passenger details and conversations.
  3. It keeps details of flight data and cockpit conversations.
  4. It retains details of baggage weight and flight crew rosters.
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Calculus, 2ADV C3 2022 HSC 20

A scientist is studying the growth of bacteria. The scientist models the number of bacteria, , by the equation

,

where is the number of hours after starting the experiment.

  1. What is the initial number of bacteria in the experiment?  (1 mark)

  2. What is the number of bacteria 24 hours after starting the experiment?  (1 mark)

  3. What is the rate of increase in the number of bacteria 24 hours after starting the experiment?  (2 marks)

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a.   
   

 

b.   

 
   
   

 

c.   
 
   

 

 
   
   

Financial Maths, 2ADV M1 2022 HSC 17

Cards are stacked to build a 'house of cards'. A house of cards with 3 rows is shown.

A house of cards requires 3 cards in the top row, 6 cards in the next row, and each successive row has 3 more cards than the previous row.

  1. Show that a house of cards with 12 rows has a total of 234 cards.  (2 marks)

  2. Another house of cards has a total of 828 cards.
  3. How many rows are in this house of cards?  (3 marks)

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a.   

 
 
   
   

 
b.