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Aussie Maths & Science Teachers: Save your time with SmarterEd

ENGINEERING, CS 2022 HSC 23a

The image shows a laminated veneer lumber (LVL) beam that is used to span long distances in buildings.
 

Give reasons for using LVL instead of a steel beam as the supporting member in a building.   (2 marks)

Show Answers Only

Possible reasons include:

→ LVL has higher strength to weight ratio

→ Easier to attach to other timber framing members

→ Uses timber otherwise thrown away as waste

→ Can use defective timber as surrounding layers will support defects

→ Cheaper

→ Easier to colour

Show Worked Solution

Possible reasons include:

→ LVL has higher strength to weight ratio

→ Easier to attach to other timber framing members

→ Uses timber otherwise thrown away as waste

→ Can use defective timber as surrounding layers will support defects

→ Cheaper

→ Easier to colour

CHEMISTRY, M5 2016 HSC 28

A mixture of carbon monoxide, chlorine and phosgene \(\ce{(COCl_2)}\) gases was placed in a closed container. The concentrations of the gases were monitored over time.
 

  1. At what time does the system first reach equilibrium? Justify your answer.   (2 marks)

  2. At four minutes, the temperature of the container was increased.
  3. Explain, with reference to the graph, whether the decomposition of \(\ce{COCl_2}\) into \(\ce{CO}\) and \(\ce{Cl_2}\) is exothermic or endothermic.   (3 marks)

Show Answers Only

a.    At two minutes (where the concentrations stop changing)

b.    \(\ce{CO(g) + Cl2(g) \rightleftharpoons COCl2(g)}\)

→ From the graph, when the temperature is increased, the \(\ce{COCl2}\) concentration decreases while \(\ce{CO}\) and \(\ce{Cl2}\) concentrations increases.

→ The reaction is countering the increase in temperature by shifting to the left and absorbing heat (Le Chatelier’s principle).

→ Therefore the decomposition of \(\ce{COCl2(g)}\) is endothermic.

Show Worked Solution

a.    At two minutes (where the concentrations stop changing)

b.    \(\ce{CO(g) + Cl2(g) \rightleftharpoons COCl2(g)}\)

→ From the graph, when the temperature is increased, the \(\ce{COCl2}\) concentration decreases while \(\ce{CO}\) and \(\ce{Cl2}\) concentrations increases.

→ The reaction is countering the increase in temperature by shifting to the left and absorbing heat (Le Chatelier’s principle).

→ Therefore the decomposition of \(\ce{COCl2(g)}\) is endothermic.

CHEMISTRY, M7 2016 HSC 22

This apparatus was set up to produce methyl butanoate.
 

  1. Identify a safety issue in this experiment.   (1 mark)

  2. Using structural formulae, write the equation for the production of methyl butanoate.   (2 marks)

  3. Justify the use of apparatus `X` in this experiment.   (2 marks)

Show Answers Only

a.   Flame could ignite one of reagents which is flammable.

b.   
     

c.    → Esterification is a relatively slow reaction.

→ Heating the reaction makes it go faster. However, the low boiling points of the reactants make them volatile as they readily convert into gas.

→ The cooling condenser `X` prevents the gas reactants from escaping the experiment by condensing them back into the reaction mixture. This process allows the reaction to proceed at higher temperatures.

Show Worked Solution

a.   Flame could ignite one of reagents which is flammable.
 

b.   
     


 


♦ Mean mark (b) 52%.

c.    → Esterification is a relatively slow reaction.

→ Heating the reaction makes it go faster. However, the low boiling points of the reactants make them volatile as they readily convert into gas.

→ The cooling condenser `X` prevents the gas reactants from escaping the experiment by condensing them back into the reaction mixture. This process allows the reaction to proceed at higher temperatures.


♦♦♦ Mean mark (c) 14%.

CHEMISTRY, M7 2016 HSC 17 MC

A polymer has the following structure.
 

Which of the following represents the monomer from which this polymer can be produced?
 

 

Show Answers Only

`D`

Show Worked Solution

→ Break the polymer at every second \(\ce{C–C}\) bond (yields identical sections)

→ Adjust single carbon bond to \(\ce{C=C}\) bond in monomer

`=>D`

ENGINEERING, AE 2022 HSC 8 MC

It is appropriate to produce a half development of a transition piece when the piece

  1. is very large.
  2. is symmetrical.
  3. is very complex.
  4. needs to be produced quickly.
Show Answers Only

`B`

Show Worked Solution

→ Half development of a transition piece is appropriate when it is symmetrical.

`=>B`

CHEMISTRY, M6 2015 HSC 21

  1. Outline a suitable method to prepare a natural indicator.   (2 marks)

  2. How could a natural indicator be tested?   (2 marks)

Show Answers Only

a.    Methodology:

→ Collect plant material that is a natural indicator of pH. Examples include rose petals and red cabbage.

→ Cut the coloured parts into small pieces.

→ Place material into a beaker with water and boil until the solution becomes coloured.

→ Allow the mixture to cool at room temperature.

→ Decant the liquid into a container, leaving the solid behind.
 

b.    → Prepare test tubes of various acids and bases (pH of each is known).

→ Add some of the indicator to each test tube.

→ Record the natural indicator colour of each example and whether it differentiates between acids and bases and their concentrations.

Show Worked Solution

a.    Methodology:

→ Collect plant material that is a natural indicator of pH. Examples include rose petals and red cabbage.

→ Cut the coloured parts into small pieces.

→ Place material into a beaker with water and boil until the solution becomes coloured.

→ Allow the mixture to cool at room temperature.

→ Decant the liquid into a container, leaving the solid behind.
 

b.    → Prepare test tubes of various acids and bases (pH of each is known).

→ Add some of the indicator to each test tube.

→ Record the natural indicator colour of each example and whether it differentiates between acids and bases and their concentrations.

CHEMISTRY, M8 2015 HSC 18-19 MC

Question 18

How could the reliability of the analysis of the pond water be improved?

  1. Analyse more samples from the same pond
  2. Use 50 mL of distilled water as a control sample
  3. Analyse samples from different ponds on the site
  4. Remove other contaminants from the sample before the analysis

 
Question 19

What was the concentration of lead ions in the sample?

  1. `5.0 × 10^{-3} \ text{mol L}^(-1)`
  2. `5.8 × 10^{-3} \ text{mol L}^(-1)`
  3. `9.3 × 10^{-3} \ text{mol L}^(-1)`
  4. `10.7 × 10^{-3} \ text{mol L}^(-1)`
Show Answers Only

`18.  A`

`19.  C`

Show Worked Solution

Question 18

`=>A`
 

Question 19

\[\ce{n(PbCl2) = \frac{0.13}{207.2 + 2 \times 35.45} = \frac{0.13}{278.1} = 4.67 \times 10^{-4} mol}\]

\(\ce{n(Pb^2+) = n(PbCl2) = 4.67 \times 10^{-4} mol}\)

\[\ce{[Pb^2+] = \frac{4.67 \times 10^{-4}}{0.050} = 9.3 \times 10^{-3} mol L^{-1}}\]

`=>C`


♦ Mean mark (Q19) 52%.

BIOLOGY, M7 2015 HSC 25

A group of students wanted to test whether water purifying tablets were effective in making creek water free from bacteria.

They conducted an experiment using a water sample collected from the creek and found that the tablets were effective.

  1. Describe a means of addressing ONE identified hazard relevant to this investigation.   (2 marks)

  2. Illustrate the results of this experiment in diagrammatic form.
  3. Use labels to clearly identify the data collected.   (3 marks)
     
     

Show Answers Only

a.   Successful answers could include one of the following:

→ A pathogenic microbe might be cultured during the process.

→ Post experiment, agar plates must be heated under high pressure to kill any microbes cultured before disposal.
  

b.   Results of experiment:

Show Worked Solution

a.   Successful answers could include one of the following:

→ A pathogenic microbe might be cultured during the process.

→ Post experiment, agar plates must be heated under high pressure to kill any microbes cultured before disposal.
  

b.   Results of experiment:

BIOLOGY, M7 2015 HSC 19-20 MC

Refer to the following information to answer Questions 19 and 20 .
 

Question 19

A medical consequence for six-month-old babies that have only been bottle-fed with formula milk and not breastfed is that

  1. they will not develop microflora.
  2. their immune system will be damaged.
  3. their consumption of milk cannot be quantified.
  4. they will be at increased risk of infectious disease.

 
Question 20

Strict hygiene practices are followed in the care of newborns, whereas hygiene practices in the care of older babies are less emphasised.

Which of the following is the best reason for this difference?

  1. Vaccinations render personal hygiene unnecessary for older babies.
  2. Procaryotic cells are not identified as antigens in early development.
  3. Antibiotic treatments kill bacterial populations in the digestive system.
  4. Early exposure to pathogens helps to build a strong immune system.

 

Show Answers Only

Q19.  `D`

Q20.  `B`

Show Worked Solution

Q 19.

→ Bottle fed babies will not have the added immunity that is provided by the mother’s breast milk.

→ They will therefore have immune systems that are more susceptible to infectious disease.

`=>D`
  

Q20.

→ The immune systems of newborns will not work as efficiently as that of older babies as their immune systems are underdeveloped.

`=>B`


♦ Mean mark Q20 45%.

BIOLOGY, M7 2015 HSC 12-13 MC

Refer to the following information to answer Questions 12 and 13.

Question 12

Which reason best explains why the corresponding control measure reduces this problem?
 

 
Question 13

The following measures could be used to prevent the spread of this fruit fly across Australia.

    1. Australia-wide release of infertile fruit flies
    2. Aerial spraying of orchards throughout the country
    3. Spot spraying of newly affected orchards in Western Australia
    4. Stopping the transport of fruit from Western Australia to other states

To prevent the spread of this fruit fly across Australia, which combination of measures would be most practical to use?

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

Q12.  `B`

Q13.  `D`

Show Worked Solution

Q12.

→ Future generations of flies will eventually be reduced in numbers and may even be wiped out altogether.

`=>B`
 

Q13.

→ It may be possible to contain the outbreak to local areas by restricting the movement of affected fruit to other states and countries, thus making it easier to manage.

`=>D`


♦ Mean mark (Q13) 49%.

BIOLOGY, M5 2015 HSC 11 MC

Environment can affect phenotype by altering the sequence of bases in DNA.

Which of the following is an example of this?

  1. High protein diets making children taller than their parents
  2. Stress causing the expression of one set of genes instead of another
  3. Language and music lessons improving intelligence in young children
  4. Nuclear fallout from atomic bombs increasing birth defects in populations
Show Answers Only

`D`

Show Worked Solution

→ Mutation in genes is commonly caused by radiation

`=>D`

BIOLOGY, M8 2015 HSC 7-8 MC

Refer to the following information to answer Questions 7 and 8 .

The diagram shows a homeostatic mechanism in a mammal.
 

Question 7

What does `text{X}` represent in the diagram?

  1. The heart
  2. The brain
  3. A thermoreceptor in the skin
  4. A pressure receptor in a blood vessel

 
Question 8

Which of the following describes what happens to the muscles and the arteriole walls in the skin when the core body temperature is below normal?
 

Show Answers Only

Q7.  `B`
Q8.  `B`

Show Worked Solution

Q7.   `text{X}` = the brain

→ Messages are sent by the brain to the effectors.

→ This promotes a stimulus response.

`=>B`
 


♦♦ Mean mark (Q7) 38%.

Q8.   When body temperature is below normal:

→ Hairs stand on end and arteriole walls of skin contract to prevent the loss of heat.

`=>B`

CHEMISTRY, M8 2017 HSC 22

Atomic absorption spectroscopy was used to determine the concentration of zinc in a water sample. The absorbance of a series of standard solutions of known concentration of zinc was measured. The results are shown in the table.
 

  1. Plot the data on the grid and draw a line of best fit.   (3 marks)
     

  1. In order for water to be considered safe for drinking, the concentration of zinc must be less than 2.80 ppm.
  2. The absorbance of the water sample was 0.58. Explain whether this water is safe for drinking.   (2 marks)

Show Answers Only

a.   

b.   Using the line of best fit above:

→ 0.58 absorbance (y-axis) ~ 3.6 ppm of zinc concentration

→ Since 3.6 ppm > 2.8 ppm (safe level), the water is not safe to drink.

Show Worked Solution

a.   
   

b.   Using the line of best fit above:

→ 0.58 absorbance (y-axis) ~ 3.6 ppm of zinc concentration

→ Since 3.6 ppm > 2.8 ppm (safe level), the water is not safe to drink.

CHEMISTRY, M6 2015 HSC 5 MC

The oxides `\text{CaO}, \text{CO}_2, \text{Na}_2\text{O}` and `\text{N}_2\text{O}_4` are placed in water to form four separate solutions.

Which row of the table correctly indicates the solutions with pH less than 7 and the solutions with pH greater than 7?
 

Show Answers Only

`A`

Show Worked Solution

→ Acidic solutions (pH < 7) – non-metal oxide solutions

→ Basic solutions (pH > 7) – metal oxide solutions

`=>A`

CHEMISTRY, M7 2017 HSC 9 MC

The following equipment was set up to measure the heat of combustion of an alkanol.
 

   
  

Black deposits were observed on the bottom of the conical flask and the heat of combustion measured was lower than the theoretical value.

Which of the following equations could account for these observations?

  1. `2 text{C}_(2) text{H}_(6)(g)+7 text{O}_(2)(g) rarr 4 text{CO}_(2)(g)+ 6 text{H}_(2)text{O}(g)`
  2. `text{C}_(3) text{H}_(8) text{O}(g)+4 text{O}_(2)(g) rarr text{CO}_(2)(g)+ text{CO}(g)+4 text{H}_(2) text{O}(g)`
  3. `2 text{C}_(4) text{H}_(10) text{O} (g)+3 text{O}_(2)(g) rarr 8 text{C}(s)+2 text{H}_(2)(g)+8 text{H}_(2) text{O}(g)`
  4. `2 text{C}_(2) text{H}_(6) text{O}(g)+4 text{O}_(2)(g) rarr 2 text{CO}_(2)(g)+2 text{C}(s)+6 text{H}_(2) text{O}(g)`
Show Answers Only

`D`

Show Worked Solution

The black deposit is carbon (soot).

By Elimination:

A: Ethane is not an alkanol (eliminate A).

B: No soot is formed in this reaction (eliminate B).

C: This reaction is incorrect as no hydrogen gas is produced (eliminate C).

`=>D`

CHEMISTRY, M7 2017 HSC 4 MC

Esterification can be carried out in a school laboratory using the equipment shown.
 


 

How could the safety of the process shown be improved?

  1. Place a stopper on top of the condenser.
  2. Add concentrated sulfuric acid to the flask.
  3. Change the direction of water flow through the condenser.
  4. Replace the Bunsen burner with an electric heating mantle.
Show Answers Only

`D`

Show Worked Solution

Consider each option

A: Resulting pressure build up is dangerous (incorrect)

B: Adds to the catalytic effect but not a safety reduction measure  (incorrect)

C: Direction is optimal as water flow is coolest where vapours are hottest (incorrect)

D: Heating mantle reduces the chance of vapours igniting (correct)

`=>D`

CHEMISTRY, M8 2017 HSC 2 MC

Which row of the table correctly matches an ion with its flame colour during a flame test?
 

Show Answers Only

`D`

Show Worked Solution

Consider each option:

→ Barium ions produce blue-green (incorrect)

→ Calcium ions produce orange-red (incorrect)

→ Carbonate ions produce no colour (incorrect)

→ Copper ions produce blue-green (correct)

`=>D`

PHYSICS, M5 2015 HSC 4 MC

A projectile is launched from a cliff top. The dots show the position of the projectile at equal time intervals.

Assuming negligible air resistance, which diagram best shows the path of the projectile?
 

 

Show Answers Only

`D`

Show Worked Solution

→ There will be a constant horizontal spacing between the dots as the projectile has a constant horizontal velocity.

→ The vertical spacing between the dots will first decrease until the projectile reaches its maximum height then increase as it moves downwards, due to its downwards acceleration due to gravity.

`=>D`

PHYSICS, M6 2016 HSC 22a

When an alternating current is passed through coil `A`, a voltage is observed on the oscilloscope connected to coil `B`.
 
     
 

How could a bar magnet be used, instead of coil A, to produce a similar pattern on the oscilloscope?   (2 marks)

Show Answers Only

Answers could include one of the following:

→ Move the bar magnet repeatedly towards and away from the end of coil `B`.

→ Rotate the bar magnet in the plane of the page.

→ Any other motion which induces an oscillating voltage in coil `B`.

Show Worked Solution

Answers could include one of the following:

→ Move the bar magnet repeatedly towards and away from the end of coil `B`.

→ Rotate the bar magnet in the plane of the page.

→ Any other motion which induces an oscillating voltage in coil `B`.

PHYSICS, M6 2016 HSC 8 MC

Which movement of the magnet(s) will produce the greatest deflection of the galvanometer?
 

 

 

Show Answers Only

`D`

Show Worked Solution

→ A larger induced current will produce greater deflection of the galvanometer.

→ The induced current is proportional to the total rate of change of magnetic flux through the coil.

→ The faster the movement of the magnet, the greater the rate of change of flux.

`=>D`

PHYSICS, M6 2016 HSC 5 MC

The diagram shows two parallel charged plates `5 × 10^(-3)  text{m}` apart.
 

What is the magnitude of the electric field between the plates in `text{V m}^(-1)` ?

  1. `3.3 × 10^(-4)`
  2. `0.33`
  3. `3`
  4. `3000`
Show Answers Only

`D`

Show Worked Solution
`E` `=(V)/(d)`  
  `=(15)/(0.005)`  
  `=3000\ text{V m}^(-1)`  

 
`=>D`

PHYSICS, M6 2016 HSC 1 MC

Some mobile phones are recharged at a power point using a charger that contains a transformer.

What is the purpose of the transformer?

  1. To convert AC at the power point to DC
  2. To convert DC at the power point to AC
  3. To increase the AC voltage at the power point
  4. To decrease the AC voltage at the power point
Show Answers Only

`D`

Show Worked Solution

→ Transformers cannot convert AC to DC or vice versa, they only change the voltage.

→ As transmission voltages are incredibly high in order to decrease power loss, transformers in the home decrease voltages to a level safe for devices to use.

`=>D`

PHYSICS, M5 2017 HSC 24

The escape velocity from a planet is given by  `v = sqrt((2GM)/(r))`.

  1. The radius of Mars is  `3.39 × 10^(6) \ text{m}`  and its mass is  `6.39 × 10^(23) \ text{kg}`.
  2. Calculate the escape velocity from the surface of Mars.   (2 marks)
  1. Using the law of conservation of energy, show that the escape velocity of an object is independent of its mass.   (3 marks)
Show Answers Only

a.   `v=5010  text{m s}^(-1)`

b.   Applying the law of conservation of energy:

→ The object’s initial mechanical energy must equal its final mechanical energy.

`KE_(i)+U_(i)=KE_(f)+U_(f)`

→ The escape velocity is the minimum velocity required for an object to escape from a central mass and never return.

→ As an object reaches an infinite distance away, `U_(f)=0`

→ When an object has just enough speed to escape, its final speed is zero, hence, `KE_(f)=0`.

→ It follows

`KE_(i)+U_(i)` `=0`  
`(1)/(2)mv^(2)-(GMm)/(r)` `=0`  
`mv^(2)` `=(2GMm)/(r)`  
`∴ v_(esc)` `=sqrt((2GM)/(r))`  

 
→ Which is independent of the object’s mass.

Show Worked Solution
a.    `v` `=sqrt((2xx6.67 xx10^(-11)xx6.39 xx10^(23))/(3.39 xx10^(6)))`
    `=5014.5  text{m s}^(-1)`
    `=5015  text{m s}^(-1)\ \ text{(to 0 d.p.)}`

 

b.   Applying the law of conservation of energy:

→ The object’s initial mechanical energy must equal its final mechanical energy.

`KE_(i)+U_(i)=KE_(f)+U_(f)`

→ The escape velocity is the minimum velocity required for an object to escape from a central mass and never return.

→ As an object reaches an infinite distance away, `U_(f)=0`

→ When an object has just enough speed to escape, its final speed is zero, hence, `KE_(f)=0`.

→ It follows

`KE_(i)+U_(i)` `=0`  
`(1)/(2)mv^(2)-(GMm)/(r)` `=0`  
`mv^(2)` `=(2GMm)/(r)`  
`∴ v_(esc)` `=sqrt((2GM)/(r))`  

 
→ Which is independent of the object’s mass.


Mean mark (b) 53%.

PHYSICS, M6 2017 HSC 22

  1. A torque is applied to a nut, using a wrench, as shown.
     

     
    Suggest TWO ways that the applied torque could be increased.   (2 marks)
  1. A coil consisting of 15 turns is placed in a uniform 0.2 T magnetic field between two magnets. A current of 7.0 amperes flows in the direction shown.
     

Calculate the magnitude and direction of the torque produced by the side `BC` of the 15-turn coil.   (3 marks)

Show Answers Only

a.   The applied torque can be increased by:

→ Increasing the magnitude of the applied force.

→ Increasing the distance between the nut and the point of applied force.
 

b.   0.05 Nm into the page

Show Worked Solution

a.   The applied torque can be increased by:

→ Increasing the magnitude of the applied force.

→ Increasing the distance between the nut and the point of applied force.
 

b.   `F_(BC)` `=BIl sin theta`
    `=0.2 xx7xx0.08 xx sin 90^(@)`
    `=0.112  text{N}`

 
`text{Total force (15 turns)}  =0.112 xx15=1.68\ text{N}`

`:.tau` `=rF sin theta`
  `=1.68 xx0.03 xx sin90^(@)`
  `=0.05  text{Nm into the page}`

Mean mark (b) 58%.

PHYSICS, M5 2017 HSC 12 MC

A satellite orbits Earth with an elliptical orbit that passes through positions `X` and `Y`.
 

Which row of the table correctly identifies the position at which the satellite has greater kinetic energy and the position at which it has greater potential energy?
 

Show Answers Only

`B`

Show Worked Solution

→ `Y`  is at a greater distance from the centre of Earth so it has a greater potential energy at `Y`.

→ As it moves towards `X` its potential energy is converted into kinetic energy, so it has a greater kinetic energy at `X`.

`=>B`

PHYSICS, M7 2017 HSC 2 MC

Which of the following is an inertial frame of reference?

  1. A rocket during launch
  2. A train travelling at a constant velocity
  3. A car turning a corner at a constant speed
  4. A lift slowing down as it approaches the ground floor
Show Answers Only

`B`

Show Worked Solution

→ An inertial frame of reference is one which is not accelerating.

`=>B`

PHYSICS, M5 2018 HSC 28

The radius of the moon is 1740 km. The moon's mass is `7.35 × 10^(22)` kg. In this question, ignore the moon's rotational and orbital motion.

A 20 kg mass is launched vertically from the moon's surface at a velocity of `1200 \ text{m s}^(-1)`.

  1. Show that the change in potential energy of the mass in moving from the surface to an altitude of 500 km is `1.26 × 10^7 \ text{J}`.   (2 marks)
  1. Calculate the velocity of the 20 kg mass at an altitude of 500 km.   (3 marks)
Show Answers Only

a.   Proof (See Worked Solutions)

b.   `424  text{m s}^-1`

Show Worked Solution
a.       `U_(i)` `=-(GMm)/(r)`
    `=(-6.67 xx10^(-11)xx7.35 xx10^(22)xx20)/(1.74 xx10^(6))`
    `=-5.64 xx10^(7)\ text{J}`
  `U_(f)` `=(-6.67 xx10^(-11)xx7.35 xx10^(22)xx20)/(2.24 xx10^(6))`
    `=-4.38 xx10^(7)\ text{J}`

 

`:.Delta U` `=U_(f)-U_(i)`  
  `=1.26 xx10^(7)\ text{J}`  

 

b.       `KE_(i)` `=(1)/(2)m u^(2)`  
    `=(1)/(2)xx20 xx1200^(2)`  
    `=1.44 xx10^(7)  text{J}`  
     `KE_(f)` `=KE_(i)-DeltaE_(p)\ \ text{(by LCE)}`  
    `=1.44 xx10^(7)-1.26 xx10^(7)`  
    `=1.8 xx10^(6) text{J}`  

 

`(1)/(2)mv^(2)` `=1.8 xx10^(6)`  
`v^2` `=(2xx1.8 xx10^(6))/(20)`  
`:.v` `=sqrt((2xx1.8 xx10^(6))/(20))`  
  `= 424  text{m s}^-1`  

♦♦ Mean mark (b) 32%.

ENGINEERING, AE 2022 HSC 5 MC

Contemporary aircraft construction includes the use of alloys and composite materials.

Which of the following statements is NOT true for composite materials used in aircraft?

  1. They are generally corrosion resistant.
  2. They can be made into complex shapes.
  3. They have a high strength-to-weight ratio.
  4. They generally cost less than other materials.
Show Answers Only

`D`

Show Worked Solution

→ Composite materials have high corrosion resistance and strength to weight ratios.

→ They can also be made into complex shapes, however, they are far more expensive than other materials.

`=>D`

Networks, STD1 N1 2022 HSC 20

The table below shows the distances, in kilometres, between a number of towns.
 

  1. Using the vertices given, draw a weighted network diagram to represent the information shown in the table.  (2 marks)
     

     
  2. A tourist wishes to visit each town.
  3. Draw the minimum spanning tree which will allow for this AND determine its length.  (3 marks)
     

Show Answers Only
  1.  
     
     
  2.   
     
  3. `1015\ text{km}`
Show Worked Solution

a. 

b.   `text{Using Prim’s algorithm (starting at}\ Y):`

`text{1st edge:}\ YC`

`text{2nd edge:}\ CB`

`text{3rd edge:}\ SB`

`text{4th edge:}\ YM`

`text{Length of minimum spanning tree}`

`=275 + 150+60+530`

`=1015\ text{km}`

Probability, STD1 S2 2022 HSC 17

Each number from 1 to 30 is written on a separate card. The 30 cards are shuffled. A game is played where one of these cards is selected at random. Each card is equally likely to be selected.

Ezra is playing the game, and wins if the card selected shows an odd number between 20 and 30.

  1. List the numbers which would result in Ezra winning the game.  (1 mark)

  2. What is the probability that Ezra does NOT win the game?  (2 marks)

Show Answers Only
  1. `21, 23, 25, 27, 29`
  2. `Ptext{(not win)} = 5/6`
Show Worked Solution

a.   `21, 23, 25, 27, 29`
 

b.    `Ptext{(not win)}` `=1-Ptext{(win)}`
    `=1-5/30`
    `=25/30`
    `=5/6`


♦ Mean mark 51%.

BIOLOGY, M5 2019 HSC 27

Yeast is a single-celled fungus that can reproduce by budding.

  1. What type of reproduction is budding?   (1 mark)

  2. Outline a procedure that could be used to test the effect of temperature on reproduction in yeast.   (4 marks)

Show Answers Only

a.   Asexual.

b.   Steps of procedure:

  1. Prepare 4 water baths of 20, 30, 40 and 50 degrees Celsius.
  2. Add 10mL of yeast suspension in 12 different test tubes.
  3. Place 3 test tubes into each of the 4 water baths.
  4. Incubate for 3 hours.
  5. Take a drop from each test tube and inspect under a microscope using a mm grid and recording yeast counts for each.
  6. Compare the number of cells present at each temperature to see which temperature is most optimal for yeast reproduction.
Show Worked Solution

a.   Asexual.

b.   Steps of procedure:

  1. Prepare 4 water baths of 20, 30, 40 and 50 degrees Celsius.
  2. Add 10mL of yeast suspension in 12 different test tubes.
  3. Place 3 test tubes into each of the 4 water baths.
  4. Incubate for 3 hours.
  5. Take a drop from each test tube and inspect under a microscope using a mm grid and recording yeast counts for each.
  6. Compare the number of cells present at each temperature to see which temperature is most optimal for yeast reproduction.

♦♦ Mean mark (b) 45%.

Measurement, STD1 M5 2022 HSC 11

The floor plan of a home unit has been drawn to scale.
 


 

  1. How many doors are shown on the plan?  (1 mark)

  2. What is the total floor area of the home unit in square metres?  (2 marks)

Show Answers Only
  1. `5`
  2. `text{55.5 m²}`
Show Worked Solution

a.    `5`

b.   `text{Conversion: 1000 mm = 1 metre}`

`text{Calculate area by splitting into 2 rectangles}`

`text{Area}`  `=  5.5 × 5 + (4.5 +2.5) xx 4`  
   `=  55.5\ text{m²}`  

♦♦ Mean mark part (b) 26%.

Algebra, STD1 A2 2022 HSC 6 MC

A water tank holds 6000 litres when full.

The tank is full when water starts to flow out of it at a constant rate of 3 litres per minute until the tank is empty.

Which expression represents the volume (`V` litres) of water in the tank after `t` minutes?

  1. `V=6000-3t`
  2. `V=6000 t-3`
  3. `V=3-6000 t`
  4. `V=3t-6000`
Show Answers Only

`A`

Show Worked Solution

`text{When}\ \ t=0,  \ V=6000-0 xx 3 =6000`
 
`text{When}\ \ t=1,  \ V=6000-1 xx 3 =5997`

`vdots`

`text{After}\ t\ text{minutes}, \ V=6000-t xx 3 =6000-3t`

`=> A`

Calculus, EXT1 C3 2022 HSC 12a

A direction field is to be drawn for the differential equation

`(dy)/(dx)=(x-2y)/(x^(2)+y^(2)). `

On the diagram, clearly draw the correct slopes of the direction field at the points `P, Q` and `R`.  (2 marks)
  

           

Show Answers Only

Show Worked Solution

`text{At (–1, 1):}\ \ dy/dx=(-1-2)/(1+1)=-3/2`

`text{At (1, 1):}\ \ dy/dx=(1-2)/(1+1)=-1/2`

`text{At (2, 1):}\ \ dy/dx=(2-2)/(4+1)=0`
 

Calculus, EXT2 C1 2022 HSC 14b

Let  `J_(n)=int_(0)^(1)x^(n)e^(-x)\ dx`, where "n" is a non-negative integer.

  1. Show that  `J_(0)=1-(1)/(e)`.  (1  mark)

  2. Show that  `J_(n) <= (1)/(n+1)`.  (2 marks)

  3. Show that  `J_(n)=nJ_(n-1)-(1)/(e)`.  (2 marks)

  4. Using parts (i) and (iii), show by mathematical induction, or otherwise, that for all `n >= 1`,
  5.        `J_(n)=n!-(n!)/(e)sum_(r=0)^(n)(1)/(r!)`    (2 marks)

  6. Using parts (ii) and (iv) prove that  `e=lim_(n rarr oo)sum_(r=0)^(n)(1)/(r!)`.  (1  mark)

Show Answers Only
  1. `text{Proof (See Worked Solutions)}`
  2. `text{Proof (See Worked Solutions)}`
  3. `text{Proof (See Worked Solutions)}`
  4. `text{Proof (See Worked Solutions)}`
  5. `text{Proof (See Worked Solutions)}`
Show Worked Solution
i.    `J_0` `=int_0^1 e^(-x)\ dx`
    `=[-e^(-x)]_0^1`
    `=-e^(-1)+1`
    `=1-1/e`

 


Mean mark (i) 93%.

ii.  `text{Show}\ \ J_n<=1/(n+1)`

`text{Note:}\ e^(-x)<1\ \ text{for}\ \ x in [0,1]`

`J_n` `=int_0^1 x^n e^(-x)\ dx`  
  `leq int_0^1 x^n \ dx`  
  `leq 1/(n+1)[x^(n+1)]_0^1`  
  `leq 1/(n+1)(1^(n+1)-0)`  
  `leq 1/(n+1)\ \ text{… as required}`  

 


♦♦ Mean mark (ii) 28%.
 

iii.  `text{Show}\ \ J_n=nJ_(n-1)-1/e`

`u` `=x^n` `v′` `=e^(-x)`
`u′` `=nx^(n-1)` `v` `=-e^(-x)`
`J_n` `=[-x^n * e^(-x)]_0^1-int_0^1 nx^(n-1)*-e^(-x)\ dx`  
  `=(-1^n * e^(-1)+0^n e^0)+nint_0^1 x^(n-1)*e^(-x)\ dx`  
  `=nJ_(n-1)-1/e`  

 
iv.   `text{Prove}\ \ J_(n)=n!-(n!)/(e)sum_(r=0)^(n)(1)/(r!)\ \ text{for}\ \ n >= 0`

`text{If}\ \ n=0:`

`text{LHS} = 1-1/e\ \ text{(see part (i))}`

`text{RHS} = 0!-0!/e (1/(0!)) = 1-1/e(1)=\ text{LHS}`

`:.\ text{True for}\ \ n=0.`
 

`text{Assume true for}\ \ n=k:`

`J_(k)=k!-(k!)/(e)sum_(r=0)^(k)(1)/(r!)`
   


♦ Mean mark (iv) 50%.

`text{Prove true for}\ \ n=k+1:`

`text{i.e.}\ \ J_(k+1)=(k+1)!-((k+1!))/(e)sum_(r=0)^(k+1)(1)/(r!)`

`J_(k+1)` `=(k+1)J_k-1/e\ \ text{(using part (iii))}`  
  `=(k+1)(k!-(k!)/(e)sum_(r=0)^(k)(1)/(r!))-1/e`  
  `=(k+1)!-((k+1)!)/(e)sum_(r=0)^(k)(1)/(r!)-1/e xx ((k+1)!)/((k+1)!)`  
  `=(k+1)!-((k+1)!)/e(\ sum_(\ r=0)^(k)(1)/(r!)+1/((k+1)!))`  
  `=(k+1)!-((k+1)!)/e(\ sum_(\ r=0)^(k+1)(1)/(r!))`  

 
`=>\ text{True for}\ \ n=k+1`

`:.\ text{S}text{ince true for}\ n=1,\ text{by PMI, true for integers}\ n>=1`
 

v.   `0<=J_n<= 1/(n+1)\ \ \ text{(part (ii))}`

`lim_(n->oo) 1/(n+1)=0\ \ => \ lim_(n->oo) J_n=0`

  
`text{Using part (iv):}`

`J_n/(n!)` `=1-1/e sum_(r=0)^(n)(1)/(r!)`  
`1/e sum_(r=0)^(n)(1)/(r!)` `=1-J_n/(n!)`  
`sum_(r=0)^(n)(1)/(r!)` `=e-(eJ_n)/(n!)`  
`lim_(n->oo)(\ sum_(\ r=0)^(n)(1)/(r!))`  `=lim_(n->oo)(e-(eJ_n)/(n!))`  
  `=e-0`  
  `=e`  

♦♦ Mean mark (v) 34%.

BIOLOGY, M5 2019 HSC 14 MC

The following DNA base sequence is used to code for a sequence of four amino acids.

`text{CGC  ATC  ATG  CTA}`

Which of the following correctly represents the anticodons on the transfer RNA during synthesis of this string of amino acids?

  1. `text{GCG  UAG  UAC  GAU}`
  2. `text{CGC  AUC  AUG  CUA}`
  3. `text{CGC  ATC  ATG  CTA}`
  4. `text{GCG  TAG  TAC  GAT}`
Show Answers Only

`B` or `A`

Show Worked Solution

By Elimination:

→ RNA has Uracil (U) in replace of Thymine (T) (eliminate C and D).

→ The DNA segment above must be copied into mRNA with complementary bases (with U replacing T), then anticodons on tRNA have complementary bases again. Therefore the tRNA associated with he DNA segment above will be the same with U instead of T.

`=>B`

→ `A` –  also considered an acceptable answer due to confusion as to whether the segment above was DNA or RNA.

CHEMISTRY, M7 2019 HSC 23

The following apparatus was used in an experiment to determine the molar enthalpy of combustion of ethanol.
 


 

  1. Calculate the experimental molar enthalpy of combustion `(Delta_(c) H)` of ethanol when 0.370 g ethanol was used to raise the water temperature from 18.5°C to 30.0°C.   (4 marks)

  2. Upon replication, the molar enthalpy of combustion obtained in the experiment was consistently much lower than the accepted value.
  3. Explain ONE change that could be made to the experiment that would improve the accuracy of the obtained value.   (2 marks)

Show Answers Only

a.  `-628\ text{kJ mol}^(-1)`

b.   Improvement to experiment accuracy (one of many possible answers):

→ The molar enthalpy of combustion measured in the experiment was not very accurate due to heat being lost to the surroundings.

→ To improve the accuracy, it would be helpful to move the spirit burner closer to the beaker to reduce heat loss.

Show Worked Solution
a.    `text{n(ethanol)}` `= text{m}/text{MM}`
    `=0.370/46.068`
    `=0.008032\ text{mol}`

 
`q=mC DeltaT = 105\ text{g} xx 4.18\ text{J g}^(-1)\ text{K}^(-1) xx (30-18.5)\ text{K} = 5047.35\ text{J}`

`(Delta_(c) H)` `=-q/n`  
  `=- 5047.35/0.008032`  
  `=-628\ 405\ text{J mol}^(-1)`  
  `=-628\ text{kJ mol}^(-1)\ \ text{(3 sig fig)}`  

 

b.   Improvement to experiment accuracy (one of many possible answers):

→ The molar enthalpy of combustion measured in the experiment was not very accurate due to heat being lost to the surroundings.

→ To improve the accuracy, it would be helpful to move the spirit burner closer to the beaker to reduce heat loss.

CHEMISTRY, M7 2019 HSC 21

  1. The structural formula for 2-methylpropan-2-ol is shown in the table.
  2. Draw one structural isomer of this alcohol and state its name.   (2 marks)

     

     

  3. The structural formulae for two compounds are shown below.
     

   
 

  1. Why are these two compounds classed as functional group isomers?   (2 marks)

  2. A chemical test is required to distinguish between the isomers in part (b).
  3. Identify a suitable test and explain the expected observations.   (3 marks)

Show Answers Only

a.   Successful answers should have one of the following:

 

b.  Functional Group isomers

→ Both isomers have the same number and type of atoms, but they have different arrangements of those atoms and therefore have different functional groups.

→ Isomer A has a ketone functional group, while isomer B has an aldehyde functional group.
 

c.   Tollens’ Test:

→ The Tollens’ test can be used to differentiate between Isomer A (a ketone) and Isomer B (an aldehyde).

→ Isomer B will be readily oxidised to a carboxylic acid, whereas isomer A will not.

→ As a result, Isomer B will reduce the silver-ions in Tollens’ reagent to form a silver mirror inside the test tube, while Isomer A will not react.

Show Worked Solution

a.   Successful answers should have one of the following:

b.  Functional Group isomers

→ Both isomers have the same number and type of atoms, but they have different arrangements of those atoms and therefore have different functional groups.

→ Isomer A has a ketone functional group, while isomer B has an aldehyde functional group.
 

c.   Tollens’ Test:

→ The Tollens’ test can be used to differentiate between Isomer A (a ketone) and Isomer B (an aldehyde).

→ Isomer B will be readily oxidised to a carboxylic acid, whereas isomer A will not.

→ As a result, Isomer B will reduce the silver-ions in Tollens’ reagent to form a silver mirror inside the test tube, while Isomer A will not react.


♦♦ Mean mark (c) 39%.

CHEMISTRY, M5 2019 HSC 16 MC

At equilibrium, a 1.00 L vessel contains 0.0430 mol of \(\ce{H2}\), 0.0620 mol of \(\ce{I2}\), and 0.358 mole of \(\ce{HI}\). The system is represented by the following equation:

\(\ce{H2(g) + I2(g) \rightleftharpoons 2HI(g)}\)

Which of the following is closest to the value of the equilibrium constant, \(K_{eq}\), for this reaction?

  1. 0.0208
  2. 48.1
  3. 134
  4. 269
Show Answers Only

\(B\)

Show Worked Solution
\(K_{eq}\) \(= \dfrac{\ce{[HI]^2}}{\ce{[H_2][I_2]}} \)  
  \(=\dfrac{0.358^2}{(0.0430)(0.0620)}\)  
  \(=48.1\)  

 
\(\Rightarrow B\)

BIOLOGY, M6 2019 HSC 8 MC

A group of four students set out to determine the animal species diversity over an area of one hectare in each of five different habitats. Each student graphed their data as shown.

Which of the graphs produced is the most suitable to represent animal species diversity in the different habitats?
 

Show Answers Only

`B`

Show Worked Solution

By Elimination:

→ The data type is categorical, and a line graph / area under line graph would not be suited (eliminate C and D).

→ A (and D) refers to the number of animals rather than number of species (eliminate A)

→ A column graph is the best graph to show the numerical value of species counts in each category, and would therefore be the most effective way to show this data.

`=>B`

CHEMISTRY, M7 2019 HSC 10 MC

Which class of organic compound must contain at least three carbon atoms?

  1. Aldehydes
  2. Alkenes
  3. Carboxylic acids
  4. Ketones
Show Answers Only

`D`

Show Worked Solution

Consider each option

→ Aldehydes can form methanal (1 carbon atom – eliminate)

→ Alkenes can form ethene (2 carbon atoms – eliminate)

→ Carboxylic acids can form methanoic acid (1 carbon atom – eliminate)

→ Ketones can for propanone (3 carbon atoms)

`=>D`

CHEMISTRY, M6 2019 HSC 5 MC

The diagram represents the titration curve for a reaction between a particular acid and a particular base. 
 

Which indicator would be best for this titration?

Show Answers Only

`C`

Show Worked Solution

→ The pH range at which isopicramic acid exhibits a colour change includes the point at which the acid and base react in equal amounts (equivalence point), which is at approximately pH 5.

→ The colour change can be used to identify when the equivalence point has been reached in a titration.

`=>C`

CHEMISTRY, M5 2019 HSC 3 MC

Which of the following metal carbonates has the highest molar solubility?

  1. Calcium carbonate
  2. Copper`text{(II)}` carbonate
  3. Iron`text{(II)}` carbonate
  4. Lead`text{(II)}` carbonate
Show Answers Only

`A`

Show Worked Solution

→ Calcium carbonate has the greatest solubility product among the listed metal carbonates.

→ Since all of these metal carbonates release the same amount of ions in solutions, their solubility products can be directly compared to determine which substance is most soluble.

`=>A`

ENGINEERING, PPT 2020 HSC 3 MC

Which of the following manufacturing methods can be used to produce complex polymer components?

  1. Sand casting
  2. Blow moulding
  3. Lost wax casting
  4. Injection moulding
Show Answers Only

`D`

Show Worked Solution

By Elimination:

→ Sand casting and lost wax casting are for metals, so not `A` or `C`.

→ Blow moulding can only make simple hollow shapes (eliminate `B`).

`=>D`

ENGINEERING, AE 2020 HSC 2 MC

What is the main purpose of the flaps on the wings of an aircraft?

  1. To make the aircraft safer at higher speeds
  2. To decrease lift to allow faster take-off speeds
  3. To increase lift at lower speeds for take-off and landing
  4. To decrease drag to allow higher take-off and landing speeds
Show Answers Only

`C`

Show Worked Solution

→ The purpose of the flaps is to generate more lift at lower speeds.

→ This enables aircraft to fly at greatly reduced speeds with a lower risk of stalling.

`=>C`

BIOLOGY, M7 2022 HSC 9 MC

A new vaccine against an infectious disease was developed. The effectiveness of the vaccine in preventing infection in humans was plotted over time in three different age groups.
 

Which of the following is a valid conclusion that can be drawn from the data in the graph?

  1. The vaccine is ineffective after six months.
  2. The younger the person the more effective the vaccine.
  3. The younger the person, the faster the immunity to infection declines.
  4. The vaccine offers more protection to younger people than those over 65 .
Show Answers Only

`D`

Show Worked Solution

The graph shows that the vaccine has a lower effectiveness against infection for people aged over 65 than for the younger age groups over the whole period.

`=>D`

BIOLOGY, M8 2022 HSC 5 MC

Data for incidence of notifiable infectious diseases in Australia are shown in the table.
 

Which type of graph should be chosen to best represent these data?

  1. A column graph because percentages are continuous.
  2. A column graph because diseases are categorical.
  3. A line graph because percentages are continuous.
  4. A line graph because diseases are categorical.
Show Answers Only

`B`

Show Worked Solution

A column graph would be the most appropriate as the diseases are divided into categories.

`=>B`