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PHYSICS, M6 2023 VCE 7*

Two high-voltage transmission lines span a distance of 260 km between Power Plant A and Town B, as shown in Figure 7. Power Plant A provides 350 MW of power. The potential difference at Power Plant A is 500 kV. The current in the transmission lines has a value of 700 A and the power loss in the transmission lines is 20 MW.
 

   

  1. Show, using calculations, that the total resistance of the two transmission lines is 41 .  (2 marks)
  1. Town B needs a minimum of 480 kV.
  2. Determine whether 480 kV will be available to Town B. Show your working.  (3 marks)
  1. Explain what would happen if the electricity between Power Plant A and Town B were to be transmitted at 50 kV instead of 500 kV. Assume that the resistance of the transmission lines is still 41 .  (2 marks)
Show Answers Only

a.    

b.    The power generated in the power plant is 500 kV.

480V will not be available to Town B.
 

c.    If the voltage was decreased by a factor of 10 to 50 kV:

→ The current through the power lines would increase by a factor of 10.

→ Power remains constant

→ As , this would dramatically increase the power loss and significantly less power would be transmitted to the town.

Show Worked Solution
a.    
 
   
   

 

b.    The power generated in the power plant is 500 kV.

480V will not be available to Town B.

 

c.    If the voltage was decreased by a factor of 10 to 50 kV:

→ Power remains constant

→ The current through the power lines would increase by a factor of 10.

→ As , this would dramatically increase the power loss and significantly less power would be transmitted to the town.

PHYSICS, M6 2023 VCE 6

Kim and Charlie are attempting to create a DC generator and have arranged the magnets along the axis of rotation of the wire loop, J, K, L and M, as shown in Figure 6. They are having some trouble getting it to work. They rotate the loop in the direction of the arrow, as shown in Figure 6.
 

  1. Using physics concepts, explain why this orientation of the magnets will not generate an EMF.  (2 marks)
  1. Kim and Charlie decide to move the magnets so that an EMF is generated. On Figure 6, draw the positions of the magnets to ensure that an EMF is generated.  (1 mark)

Show Answers Only

a.    → The generator has the magnetic field parallel to the plane of the loop. 

→ Therefore, there is no flux cutting through the loop of wire.

→ Further, as the loop rotates there is no change in flux and no current or EMF produced.

b.   → The magnets should be rotated by 90°.
 

Show Worked Solution

a.    → The generator has the magnetic field parallel to the plane of the loop. 

→ Therefore, there is no flux cutting through the loop of wire.

→ Further, as the loop rotates there is no change in flux and no current or EMF produced.

♦ Mean mark (a) 46%.

b.   → The magnets should be rotated by 90°.
 

PHYSICS, M7 2023 VCE 14 MC

Polarisation of visible light provides evidence that electromagnetic radiation can be explained using a

  1. standing wave model for light.
  2. transverse wave model for light.
  3. mechanical wave model for light.
  4. longitudinal wave model for light.
Show Answers Only

Show Worked Solution

→ For polarisation to occur, the plane of vibration of the wave must be perpendicular to direction of motion. 

→ This is a property of the transverse wave model of light.

Calculus, MET1 2023 VCAA 9

The shapes of two walking tracks are shown below.
 

 

Track 1 is described by the function  .

Track 2 is defined by the function  .

The unit of length is kilometres.

  1. Given that   and  , verify that   and  .   (1 mark)
  2. Verify that and both have a turning point at .
  3. Give the co-ordinates of .  (2 marks)
  4. A theme park is planned whose boundaries will form the triangle where is the origin, is at and is at , as shown below, where .
  5. Find the maximum possible area of the theme park, in km².   (3 marks)
     

Show Answers Only

a.   

b.   

c.   

Show Worked Solution
a.   
 

 

 

b.   
   
 

 

 

 

 

 

 

 


♦ Mean mark (b) 48%.

c.  

 
 

 

 

 
 
 
 

♦♦♦ Mean mark (c) 27%.
MARKER’S COMMENT: Many students made arithmetic errors substituting the fractional values of into to find max area.

Calculus, MET1 2023 VCAA 7

Consider . Part of the graph of    is shown below.
 

  1. State the range of .   (1 mark)
  2. Sketch the graph of the inverse function  on the axes above. Label any endpoints and axial intercepts with their coordinates.   (2 marks)
  3. Determine the equation of the domain for the inverse function  .   (2 marks)
  4. Calculate the area of the regions enclosed by the curves of   and  .   (2 marks)
Show Answers Only

a.   

b.   

c.   

d.   

Show Worked Solution

a.   

b.   

c.   


 

 


♦ Mean mark (c) 48%.
MARKER’S COMMENT: Common error → writing the function as .

d.     

 
   
   
   
   

♦♦♦ Mean mark (d) 24%.
MARKER’S COMMENT: Using the symmetry properties of the graph and its inverse helped answer this question efficiently.

Graphs, MET1 2023 VCAA 3

  1. Sketch the graph of  on the axes below, labelling all asymptotes with their equation and axial intercepts with their coordinates.   (3 marks)
     


  2. Find the values of for which .   (1 mark)
Show Answers Only

a.   

b.   

Show Worked Solution

a.   

b.   


♦♦ Mean mark (b) 38%.
MARKER’S COMMENT: Many students did not use their graph from part (a).

Functions, SPEC1 2023 VCAA 1

Consider the function with rule  .

  1. Show that the rule for the function can be written as  .   (1 mark)
  1. Sketch the graph of on the axes below, labelling any asymptotes with their equations.   (3 marks)

   

Show Answers Only
a.    
   
   

 
b.   

 

Show Worked Solution
a.    
   
   

 
b.   

 

Statistics, SPEC1 2023 VCAA 6

Josie travels from home to work in the city. She drives a car to a train station, waits, and then rides on a train to the city. The time, minutes, taken to drive to the station is normally distributed with a mean of 20 minutes and standard deviation of 6 minutes . The waiting time, minutes, for a train is normally distributed with a mean of 8 minutes and standard deviation of minutes . The time, minutes, taken to ride on a train to the city is also normally distributed with a mean of 12 minutes and standard deviation of 5 minutes . The three times are independent of each other.

  1. Find the mean and standard deviation of the total time, in minutes, it takes for Josie to travel from home to the city.   (2 marks)
  1. Josie's waiting time for a train on each work day is independent of her waiting time for a train on any other work day. The probability that, for 12 randomly chosen work days, Josie's average waiting time is between 7 minutes 45 seconds and 8 minutes 30 seconds is equivalent to , where and and are real numbers.
  2. Find the values of and .   (2 marks)
Show Answers Only

a.   

b.   

Show Worked Solution

a.   

 
   
   

 

 
   
   
 

 
b.   

 
   
   

 

Networks, GEN2 2023 VCAA 12

A country has five states, and .

A graph can be drawn with vertices to represent each of the states.

Edges represent a border shared between two states.

  1. What is the sum of the degrees of the vertices of the graph above?   (1 mark)

  2. Euler's formula, , holds for this graph.
  3. i. Complete the formula by writing the appropriate numbers in the boxes provided below.   (1 mark)


  4. ii. Complete the sentence by writing the appropriate word in the space provided below.   (1 mark)


    Euler’s formula holds for this graph because the graph is connected and ______________.
  5. The diagram below shows the position of state on a map of this country.
  6. The four other states are indicated on the diagram as 1, 2, 3 and 4.
     

  1. Use the information in the graph above to complete the table below. Match the state and with the corresponding state number and 4 given in the map above.   (1 mark)

Show Answers Only

a.   
 

b.i.   


 

b.ii.     
 

c.   

Show Worked Solution

a.   
 

b.i.   


 

b.ii.     
 

c.   

Recursion and Finance, GEN2 2023 VCAA 5

Arthur borrowed $30 000 to buy a new motorcycle.

Interest on this loan is charged at the rate of 6.4% per annum, compounding quarterly.

Arthur will repay the loan in full with quarterly repayments over six years.

  1. How many repayments, in total, will Arthur make?  (1 mark)

The balance of the loan, in dollars, after quarters, , can be modelled by the recurrence relation

  1. Showing recursive calculations, determine the balance of the loan after two quarters.
  2. Round your answer to the nearest cent.   (1 mark)

  3. The final repayment required will differ slightly from all the earlier repayments of $1515.18
  4. Determine the value of the final repayment.
  5. Round your answer to the nearest cent.   (1 mark)

Show Answers Only

a.   

b.   

c.   

Show Worked Solution

a.   

  
b.   

Mean mark (b) 51%.
♦♦ Mean mark (c) 25%

c.    

 
 
 
 
 
 

 

Data Analysis, GEN2 2023 VCAA 3

The scatterplot below plots the average monthly ice cream consumption, in litres/person, against average monthly temperature, in °C. The data for the graph was recorded in the Northern Hemisphere.
 

When a least squares line is fitted to the scatterplot, the equation is found to be:

consumption = 0.1404 + 0.0024 × temperature

The coefficient of determination is 0.7212

  1. Draw the least squares line on the scatterplot graph above.  (1 mark)

  2. Determine the value of the correlation coefficient .
  3. Round your answer to three decimal places.  (1 mark)

  4. Describe the association between average monthly ice cream consumption and average monthly temperature in terms of strength, direction and form.  (1 mark)

  5. Referring to the equation of the least squares line, interpret the value of the intercept in terms of the variables consumption and temperature.  (1 mark)

  6. Use the equation of the least squares line to predict the average monthly ice cream consumption, in litres per person, when the monthly average temperature is –6°C.  (1 mark)

  7. Write down whether this prediction is an interpolation or an extrapolation.  (1 mark)

Show Answers Only

a.    
         

b.   

c.   

 
d.   

 
e.   

 
f.    

Show Worked Solution

a.    
         

b.   

c.   

 
d.   

 
e.   

 
f.    

Proof, EXT2 P1 2023 SPEC2 1 MC

Consider the following statement.

'If my football team plays badly, then they are not training enough.'

Which one of the following statements is the contrapositive of the statement above?

  1. If my football team plays badly, then they need more training.
  2. If they are training enough, then my football team does not play badly.
  3. If my football team doesn't play badly, then they are training enough.
  4. If they are training enough, then my football team will most likely win.
Show Answers Only

Show Worked Solution

Proof, SPEC2 2023 VCAA 1 MC

Consider the following statement.

'If my football team plays badly, then they are not training enough.'

Which one of the following statements is the contrapositive of the statement above?

  1. If they are not training enough, then my football team plays badly.
  2. If my football team plays badly, then they need more training.
  3. If they are training enough, then my football team does not play badly.
  4. If my football team doesn't play badly, then they are training enough.
  5. If they are training enough, then my football team will most likely win.
Show Answers Only

Show Worked Solution

Networks, GEN1 2022 VCAA 1 MC

The network below shows the distances, in kilometres, along a series of roads.

The vertices and represent the intersections of these roads.
 

Prim's algorithm can be used to find the

  1. critical path.
  2. shortest path.
  3. minimum cut.
  4. minimum allocation.
  5. minimum spanning tree.
Show Answers Only

Show Worked Solution

Prim’s algorithm is used to find the minimum spanning tree.

Matrices, GEN1 2022 VCAA 4 MC

The communication matrix below shows the communication links between five people: Steph , Tran ,Ursula , Vinh and Wanda .

In this matrix:

  • the '1' in row , column indicates that Steph can communicate directly with Tran
  • the '0' in row , column indicates that Vinh cannot communicate directly with Wanda.

Ursula needs to communicate with Steph.

The sequence of communication links that will successfully allow Ursula to communicate with Steph is

Show Answers Only

Show Worked Solution

By elimination:

Option A:  (eliminate A)

Option B:  (eliminate B)

Option C:  (correct)

Option D:  (eliminate D)

Option E:  (eliminate E)

Matrices, GEN1 2022 VCAA 1-2 MC

A bike rental business rents road bikes and mountain bikes in three sizes: child , junior and adult .

Matrix shows the daily rental cost, in dollars, for each type of bike.

 
The element in row and column in matrix is .

 
Question 1

The daily cost of renting an adult mountain bike is shown in element

 
Question 2

On Sundays, the business increases the daily rental price for each type of bike by 10%.

To determine the rental cost for each type of bike on a Sunday, which one of the following matrix calculations needs to be completed?

Show Answers Only

Show Worked Solution


 

Recursion and Finance, GEN1 2022 VCAA 18-19 MC

The balance of a loan, , in dollars, after months is modelled by the recurrence relation


 

Question 18

The balance of the loan first falls below $398 000 after how many months?

  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

 
Question 19

With a small change to the final payment, the loan is expected to be repaid in full in

  1. 25 years.
  2. 26 years.
  3. 28 years.
  4. 29 years.
  5. 30 years.
Show Answers Only

Show Worked Solution

 
 
 

  

 

  

 
 
 
 
 
 

 


♦ Mean mark (Q19) 47%.

CHEMISTRY, M7 2016 VCE 7a

Butanoic acid is the simplest carboxylic acid that is also classified as a fatty acid. Butanoic acid may be synthesised as outlined in the following reaction flow chart.
 

  1. Draw the structural formula of but-1-ene in the box provided.  (1 mark)

  2. State the reagent(s) needed to convert but-1-ene to Compound Y in the box provided.  (1 mark)

  3. Write the systematic name of Compound Y in the box provided.  (1 mark)

  4. Write the semi-structural formula of butanoic acid in the box provided.  (1 mark)

  5. Write a balanced half-equation for the conversion of .  (2 marks)

Show Answers Only

i.    
       

ii.    and (catalyst)

iii.   butan-1-ol or 1-butanol

iv.   

v.   

Show Worked Solution

i.    
       

ii.    and (catalyst)

iii.   butan-1-ol or 1-butanol

iv.   

v.   

♦♦ Mean mark (ii) 29%.

CHEMISTRY, M7 2015 VCE 5b

Draw the full structural formula of an isomer of butan-2-ol.   (1 mark)

Show Answers Only

Possible images include:

                
 

Show Worked Solution

Possible images include:

                
 

CHEMISTRY, M7 2015 VCE 5a

A reaction pathway is designed for the synthesis of the compound that has the structural formula shown below.
 

The table below gives a list of available organic reactants and reagents.
 


Complete the reaction pathway design flow chart below. Write the corresponding letter for the structural formula of all organic reactants in each of the boxes provided. The corresponding letter for the formula of other necessary reagents should be shown in the boxes next to the arrows.   (5 marks)

Show Answers Only

Show Worked Solution

CHEMISTRY, M7 2015 VCE 5 MC

Which one of the following statements best defines a renewable energy resource?

  1. an energy resource that will not be consumed within our lifetime
  2. an energy resource that does not produce greenhouse gases when consumed
  3. an energy resource derived from plants that are grown for the production of liquid biofuels
  4. an energy resource that can be replaced by natural processes within a relatively short time
Show Answers Only

Show Worked Solution

→ Renewable energy sources have the potential to be replenished at the same rate as their consumption.

PHYSICS, M1 EQ-Bank 2

A boy on a bike is travelling at 8 ms north when he sees a girl on a scooter travelling at 6 ms west, relative to the ground. 

  1. Draw a vector diagram to represent the velocity of the girl relative to the boy.   (2 marks)

  2. Use the vector diagram to calculate the velocity of the girl relative to the boy.   (2 marks)

Show Answers Only

10 ms, S36.9W

Show Worked Solution

a.    


 


 

b.   

 
 

 
Velocity of the girl relative to the boy is 10 ms, S36.9°W.

PHYSICS, M1 EQ-Bank 8

By separating the vector, shown below, into its constituent horizontal and vertical elements, express each component in terms of theta .   (2 marks)
 

Show Answers Only

Horizontal component:

Vertical component:

Show Worked Solution

Horizontal component:

Vertical component:

PHYSICS, M1 EQ-Bank 7

Below is a description of the motion of a runner. The motion can be divided into three stages.

Stage 1: Runner travels 120 metres south taking 20 seconds.

Stage 2: Runner turns west and travels at 5 ms for half a minute.

Stage 3: Runner travels directly back to their starting position.

  1. Determine the distance that the runner ran during Stage 2 of their journey.   (1 mark)
  2. Find the displacement of the start point from the runner Stage 2 is completed.   (3 marks)

Show Answers Only

a.   

b.   

Show Worked Solution
a.    
   
   

 

b.    Stage 1 and Stage 2 displacement diagram:
 

Using Pythagoras:

 
   
   

 

 
 
   

 

Displacement of the start point from the runner is 192.1 m, N51.3°E.

Data Analysis, GEN1 2022 VCAA 9-11 MC

Table 1 summarises the results of a study that compared the effectiveness of individual and group instruction (instructional method) when training future basketball referees.
 

In this table, test grade is the response variable and instructional method is the explanatory variable.
 

Question 9

The variables test grade (A, B, C, D, E) and instructional method (individual, group) are

  1. a numerical and a categorical variable respectively.
  2. both nominal variables.
  3. a nominal and an ordinal variable respectively.
  4. both ordinal variables.
  5. an ordinal and a nominal variable respectively.

 
Question 10

Of the students who received an A grade, the percentage who were instructed individually is closest to

  1. 9%
  2. 22%
  3. 36%
  4. 56%
  5. 64%

 
Question 11

To become a qualified referee, a grade of A or B on the test is required. Those who receive a C, a D or an E will not qualify.

Using column percentages, a new two-way percentage frequency table is constructed from the data in Table 1.

In this new table, qualified to be a referee (yes, no) is the response variable and instructional method (individual, group) is the explanatory variable.

Which one of the following tables correctly displays the data from Table 1?
 

Show Answers Only

Show Worked Solution


 


 

Mean mark (Q10) 56%.


 

Data Analysis, GEN1 2022 VCAA 5 MC

The possum population of a large city park is 2498.

The body lengths of this species of possum are known to be approximately normally distributed with a mean of 88 cm and a standard deviation of 4 cm.

Using the 68–95–99.7% rule, the number of possums in this park with a body length between 84 cm and 96 cm is closest to

  1. 2036
  2. 2043
  3. 2047
  4. 2105
  5. 2156
Show Answers Only

Show Worked Solution

Data Analysis, GEN1 2022 VCAA 1-3 MC

The histogram below displays the distribution of skull width, in millimetres, for 46 female possums.
 

Question 1

The shape of the distribution is best described as

  1. negatively skewed.
  2. approximately symmetric.
  3. negatively skewed with a possible outlier.
  4. positively skewed with a possible outlier.
  5. approximately symmetric with a possible outlier.

 
Question 2

The percentage of the 46 possums with a skull width of less than 55 mm is closest to

  1. 12%
  2. 26%
  3. 39%
  4. 61%
  5. 74%

 
Question 3

The third quartile for this distribution, in millimetres, could be

  1. 55.8
  2. 56.2
  3. 56.9
  4. 57.7
  5. 58.3
Show Answers Only

Show Worked Solution

The distribution’s centre is in the 56–57 group and if the possible outlier is disregarded, the tail of the distribution is spread more to the left → i.e. negatively skewed with possible outlier.

 


♦♦ Mean mark (Q1) 36%.
COMMENT: 54% of students chose . The graph distribution however, shows that more than 50% of the data is to the left of the median.

 
   
  %  

 

 

The 34.5th score lies between 57 and 58, therefore, 57.7.

PHYSICS, M1 EQ-Bank 4

A truck travelling in a straight line with a speed of 60 ms slows down and comes to rest over a period of 20 seconds.

  1. Calculate the change in velocity of the truck.   (2 marks)

  2. Determine the average acceleration of the truck across the 20 seconds.   (2 marks)

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a.   

b.   

Show Worked Solution
a.    
   
   

 

b.    
   
   

Networks, GEN1 2023 VCAA 34 MC

A bipartite graph is typically used to display which one of the following?

  1. the allocation of tasks on a construction site
  2. the path used to visit five different construction sites
  3. the total distance travelled between two construction sites
  4. the critical path of activities to be completed in a construction project
  5. the minimum length of cable required to connect six construction sites
Show Answers Only

Show Worked Solution

Consider option A:

Individuals or groups can be represented by a column of nodes and tasks can be represented by a second column, allowing for edges to indicate the allocation of tasks.

Matrices, GEN1 2023 VCAA 25 MC

The daily maximum temperature at a regional town for two weeks is displayed in the table below.

 This information can also be represented by matrix , shown below.

Element indicates that

  1. the temperature was 29 °C on Monday in week 2.
  2. the temperature was 17 °C on Tuesday in week 1.
  3. the lowest temperature for these two weeks was 17 °C.
  4. the highest temperature for these two weeks was 29 °C.
  5. week 2 had a higher average maximum temperature than week 1.
Show Answers Only

Show Worked Solution

Complex Numbers, EXT2 N2 2023 HSC 16a

Let be the complex number  .

  1. Show that  .   (2 marks)

The vertices of a triangle can be labelled and in anticlockwise or clockwise direction, as shown.
 

Three complex numbers and are represented in the complex plane by points and respectively.

  1. Show that if triangle is anticlockwise and equilateral, then  .   (2 marks)

  2. It can be shown that if triangle is clockwise and equilateral, then . (Do NOT prove this.)
  3. Show that if is an equilateral triangle, then

  (2 marks)

Show Answers Only
Show Worked Solution

i.   

 
   
   
   

 
ii.   

 
 
♦♦♦ Mean mark (ii) 18%.

iii.   


 

 
 
 

 

♦♦♦ Mean mark (iii) 11%.

CHEMISTRY, M3 EQ-Bank 4

  1. Write the generalised equation for reactions between metals and dilute acids (1 mark)

  2. Provide one example of the generalised equation from part (i).   (1 mark)

Show Answers Only

i.   

ii.    One example (of many possible answers):

→ Magnesium reacts with hydrochloric acid to produce magnesium chloride and hydrogen gas

Show Worked Solution

i.   
 

ii.    One example (of many possible answers):

→ Magnesium reacts with hydrochloric acid to produce magnesium chloride and hydrogen gas

CHEMISTRY, M3 EQ-Bank 3

  1. Write the generalised equation for reactions between metals and oxygen.   (1 mark)

  2. Provide one example of the generalised equation from part (i).   (1 mark)

Show Answers Only

i.   

ii.   One possible example (of many correct answers):

Show Worked Solution

i.   
 

ii.   One possible example (of many correct answers):

Data Analysis, GEN2 2023 VCAA 1

Data was collected to investigate the use of electronic images to automate the sizing of oysters for sale. The variables in this study were:

    • ID: identity number of the oyster
    • weight: weight of the oyster in grams (g)
    • volume: volume of the oyster in cubic centimetres (cm³)
    • image size: oyster size determined from its electronic image (in megapixels)
    • size: oyster size when offered for sale: small, medium or large

The data collected for a sample of 15 oysters is displayed in the table.
 

  1. Write down the number of categorical variables in the table.   (1 mark)

  2. Determine, in grams:
    1. the mean weight of all the oysters in this sample.   (1 mark)

    2. the median weight of the large oysters in this sample.   (1 mark)
  3. When a least squares line is used to model the association between oyster weight and volume, the equation is: 

    1. Name the response variable in this equation.   (1 mark)

    2. Complete the following sentence by filling in the blank space provided.   (1 mark)

      This equation predicts that, on average, each 10 g increase in the weight of an oyster is associated with a ________________ cm³ increase in its volume.
  1. A least squares line can also be used to model the association between an oyster's volume, in cm³, and its electronic image size, in megapixels. In this model, image size is the explanatory variable.
  2. Using data from the table, determine the equation of this least squares line. Use the template below to write your answer. Round the values of the intercept and slope to four significant figures.   (2 marks)

  3. The number of megapixels needed to construct an accurate electronic image of an oyster is approximately normally distributed.
  4. Measurements made on recently harvested oysters showed that:
    • 97.5% of the electronic images contain less than 4.6 megapixels
    • 84% of the electronic images contain more than 4.3 megapixels.
  1. Use the 68-95-99.7% rule to determine, in megapixels, the mean and standard deviation of this normal distribution.   (2 marks)

Show Answers Only

a.   

b.i. 

b.ii. 

c.i.   

c.ii. 

d.   

e.   

 

Show Worked Solution

a.   
 

b.i. 
 

b.ii. 

 
 

c.i.   
 

c.ii. 
 

d.   


 

e.   

 

PHYSICS, M2 EQ-Bank 2

A block is being dragged along a flat surface with a horizontal force of 30 being applied to it.

The mass of the block is 6 kilograms.

If the block is travelling at a constant velocity, determine the magnitude of the frictional forces acting on the block, giving reasons for your answer.   (2 marks)

Show Answers Only

→ As the block is travelling at a constant velocity, the sum of all the forces acting on the block must add to 0. 

→ The frictional forces must be equal in magnitude and opposite to the applied force.

→ Therefore, the magnitude of the frictional forces is 30 .

Show Worked Solution

→ As the block is travelling at a constant velocity, the sum of all the forces acting on the block must add to 0. 

→ The frictional forces must be equal in magnitude and opposite to the applied force.

→ Therefore, the magnitude of the frictional forces is 30 .

PHYSICS, M4 EQ-Bank 3

List three properties of a bar magnet.  (3 marks)

Show Answers Only

Answers could include three of the following properties:

→ They have a north and a south pole.

→ The magnetic field lines run from north to south.

→ The magnetic field lines leave and enter the magnet at right angles to the surface.

→ They are permanent magnets.

→ Like poles repel and opposite poles attract.

Show Worked Solution

Answers could include three of the following properties:

→ They have a north and a south pole.

→ The magnetic field lines run from north to south.

→ The magnetic field lines leave and enter the magnet at right angles to the surface.

→ They are permanent magnets.

→ Like poles repel and opposite poles attract.

PHYSICS, M4 EQ-Bank 2

The following circuit has 4 resistors and a 24 V DC supply with a switch.
 

  1. Calculate the value of the single resistor that is equivalent to the 5 , 20 , and 40 resistors.   (2 marks)

  2. Determine the potential difference across the 15 resistor when the switch is closed.   (2 mark)

  3. Determine the current through the 5 resistor when the switch is closed.   (2 mark)

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a.    

b.    

c.  

Show Worked Solution
a.    
 
   
 
   

 

b.  

Circuit current:


 

Potential difference across the 15 resistor:


 

c.   Potential difference across the 5 resistor: 


 

Current through the resistor:

PHYSICS, M4 2023 VCE 1

Some physics students are conducting an experiment investigating both electrostatic and gravitational forces. They suspend two equally charged balls, each of mass 4.0 g, from light, non-conducting strings suspended from a low ceiling.

The charged balls repel each other with the strings at an angle of 60°, as shown in Figure 1.
 

There are three forces acting on each ball:

    • a tension force,
    • a gravitational force,
    • an electrostatic force, .
  1. On Figure 1, using the labels and , draw each of the three forces acting on each of the charged balls.  (3 marks)

  2. Show that the tension force, , in each string is . Use  .
  3. Show your working.  (2 marks)

  4. Calculate the magnitude of the electrostatic force, . Show your working.  (2 marks)

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a.   
       

 
b.    System is in an equilibrium state:

→ The sum of the forces must add to zero as seen in the triangle below.
  

→

 
 
   

 
c.   Using the same triangle as part (b): 

 
 
   

Show Worked Solution

a.   
       

 
b.    System is in an equilibrium state:

→ The sum of the forces must add to zero as seen in the triangle below.
  

→

 
 
   

 

c.   Using the same triangle as part (b): 

 
 
   
♦ Mean mark 41%.

PHYSICS, M3 2023 VCE 16 MC

Water waves travelling at constant speed and hitting a barrier can change direction, as shown in the diagram below.
 

Which one of the following best identifies this phenomenon?

  1. diffraction
  2. dispersion
  3. refraction
  4. resonance
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Show Worked Solution

→ Diffraction is the phenomena that can describe when waves bend around a corner after they pass a barrier, as can be observed in the diagram.

PHYSICS, M3 2023 VCE 15 MC

Two ambulances, and , are travelling along a straight road, both with the same constant velocity, . Both ambulances have their sirens on and the sounds produced are identical and have a constant frequency.

Ambulance is travelling directly towards a stationary observer, while ambulance is travelling directly away from the stationary observer, as shown in the diagram below.
 

Which one of the following best describes the frequency of each siren as measured by the stationary observer, compared to the frequency the observer would measure if the ambulances were stationary?

  1. The observer measures each siren's frequency to be lower.
  2. The observer measures each siren's frequency to be higher.
  3. The observer measures the frequency of ambulance 's siren to be lower and the frequency of ambulance 's siren to be higher.
  4. The observer measures the frequency of ambulance 's siren to be higher and the frequency of ambulance 's siren to be lower.
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Show Worked Solution

→ By the doppler effect, as the sound waves move towards the person the frequency of the sound waves increase.

→ As the sound waves move away from the person, the frequency of the sound waves will decrease.

PHYSICS, M3 2023 VCE 13 MC

A physics student hears a clap of thunder shortly after observing a flash of lightning.

Which one of the following statements best describes the sound associated with the clap of thunder and the visible light associated with the flash of lightning?

  1. Both the sound and the visible light are examples of transverse waves.
  2. Both the sound and the visible light are examples of longitudinal waves.
  3. Sound is an example of a transverse wave and visible light is an example of a longitudinal wave.
  4. Sound is an example of a longitudinal wave and visible light is an example of a transverse wave.
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Show Worked Solution

→ Sound is a longitudinal wave where the particles travel parallel to the direction of motion and require a medium.

→ Light is a transverse wave of alternating electric and magnetic fields and therefore doesn’t require a medium.

ENGINEERING, TE 2023 HSC 15 MC

What is the primary benefit of placing a satellite in a low earth orbit rather than a higher earth orbit?

  1. Longer lifespan
  2. Less atmospheric drag
  3. Faster data transmission
  4. Cover larger areas on Earth
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Show Worked Solution

→ Low earth orbit (LEO) satellites’ primary benefit is faster data transmission (low communication latency).

→ Another major benefit of LEO satellites is accessibility for servicing, although this was not given as an option.

ENGINEERING, PPT 2023 HSC 8 MC

Why were steam trains replaced with electric trains in underground rail systems?

  1. Electric trains are faster than steam trains.
  2. Electric trains have better traction than steam trains.
  3. Electric trains produce less emissions than steam trains.
  4. Electric trains require less infrastructure than steam trains.

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Show Worked Solution

→ The use of steam trains in the small, unvented tubular tunnels of deep-level underground systems was impractical due to the lack of ventilation.

BIOLOGY, M4 EQ-Bank 36


 

  1. What is/are the producer(s) in this food web?   (1 mark)

  2. Identify ONE carnivore and ONE herbivore.   (2 marks)

  3. If the grasshopper species became extinct, explain THREE changes that may occur.   (3 marks)

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a.    Grass, carrots and grain.

b.   Carnivore: Owl or fox

Herbivore: Bird

c.   Extinction of the grasshopper effects:

→ Will result in a greater availability of the grass and grain they (previously) ate.

→ Subsequently, there will be less competition for food among the other species which also eat grass and grain. These species will thrive and an increase in the bird, mouse and rabbit populations would be expected.

→ The grasshoppers’ extinction will also cause its consumers, the bird and the owl, to have to find other food sources.

→ Population fluctuations of birds and owls would be expected as they adapt to new hunting or grazing habits to replace their lost food source.

→ The complexity of nature in such extinction events can be seen particularly on birds who benefit from more grain availability but lose grasshoppers as a direct food source.

Show Worked Solution

a.    Grass, carrots and grain.
 

b.   Carnivore: Owl or fox

Herbivore: Bird
 

c.   Extinction of the grasshopper effects:

→ Will result in a greater availability of the grass and grain they (previously) ate.

→ Subsequently, there will be less competition for food among the other species which also eat grass and grain. These species will thrive and an increase in the bird, mouse and rabbit populations would be expected.

→ The grasshoppers’ extinction will also cause its consumers, the bird and the owl, to have to find other food sources.

→ Population fluctuations of birds and owls would be expected as they adapt to new hunting or grazing habits to replace their lost food source.

→ The complexity of nature in such extinction events can be seen particularly on birds who benefit from more grain availability but lose grasshoppers as a direct food source.

ENGINEERING, AE 2023 HSC 26b

A team of engineers is working together to develop a new aeronautical device for a company. An engineer takes the design and produces the device without permission.

Describe the implications for the individual engineer and the company.   (3 marks)

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→ The device design is the intellectual property of the company that created it. 

→ Taking the design without permission is stealing and would have legal implications for the individual.

→ The engineer is also not working ethically from a professional basis.

→ The production of the device will also have serious financial implications for the company involved as they are not the intellectual property owners and would likely be prohibited from selling the product.
 

Other answers could include:

→ Health and safety factors.

→ Financial ramifications, particularly through legal action.

→ Employment ramifications given the ethical breach of the professional.

Show Worked Solution

→ The device design is the intellectual property of the company that created it. 

→ Taking the design without permission is stealing and would have legal implications for the individual.

→ The engineer is also not working ethically from a professional basis.

→ The production of the device will also have serious financial implications for the company involved as they are not the intellectual property owners and would likely be prohibited from selling the product.
 

Other answers could include:

→ Health and safety factors.

→ Financial ramifications, particularly through legal action.

→ Employment ramifications given the ethical breach of the professional.

ENGINEERING, TE 2023 HSC 24d

One of several fail-safe systems incorporated into a roller coaster design uses the following safety protocol.

Before a roller coaster car brake can be released to allow the roller coaster to commence its ride, ALL of the following conditions must be met:

    • passenger safety harnesses must be secured into place
    • the sensors must indicate the track is clear of obstructions
    • the ride entry and exit gates are locked.

   A logic gate schematic is shown.

  1. What is the purpose of the NAND gate in this schematic?   (2 marks)

  2. Complete the truth table for the logic gate schematic.   (3 marks)

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i.    NAND gate purpose:

→ Ensures that if any or all of the inputs are zero the output will result in a 1 and thus turn on the warning light.

→ In effect, the warning light will remain ON until all conditions for safe operation are met.

ii.    

Show Worked Solution

i.     NAND gate purpose:

→ Ensures that if any or all of the inputs are zero the output will result in a 1 and thus turn on the warning light.

→ In effect, the warning light will remain ON until all conditions for safe operation are met.

ii.    

BIOLOGY, M4 EQ-Bank 33

Why is it detrimental for a predator to be totally efficient at catching its prey?   (2 marks)

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→ When predators are efficient at hunting and catch too many prey, it leads to a rapid decline in the prey’s population.

→ This can lead to a reduction in available food for the predators, causing their population to decline or their need to migrate somewhere else.

Show Worked Solution

→ When predators are efficient at hunting and catch too many prey, it leads to a rapid decline in the prey’s population.

→ This can lead to a reduction in available food for the predators, causing their population to decline or their need to migrate somewhere else.

ENGINEERING, CS 2023 HSC 22b

The diagram shows a child with a mass of 45 kg hanging 2 metres from the left end of a structure, and an adult with a mass of 85 kg hanging 1 metre from the right end.

 

  1. Calculate the reactions at and .   (3 marks)
      

 

  1. Complete the shear force and bending moment diagrams of the scenario described.   (3 marks)

 

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i.   

  
ii.    

Show Worked Solution

i.   

 
 
 

 

 
 

 
ii.    

BIOLOGY, M2 EQ-Bank 30

Red and white blood cells are critical components of human blood with very different functions.

  1. Describe the structure and role of red blood cells.   (3 marks)

  2. Describe the the role of white blood cells and platelets.   (2 marks)

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a.    Red blood cells:

→ Red blood cells (RBCs) make up 40-50% of total blood volume and transport oxygen and carbon dioxide throughout the body.

→ They are able to achieve this by haemoglobin, a globular protein consisting of 4 polypeptide chains and iron. Haemoglobin’s structure allows each of its proteins to carry 4 molecules of oxygen and 4 molecules of carbon dioxide.

→ RBCs are specialised cells and have no nucleus which allows them to carry more haemoglobin, and therefore more oxygen, around the body.
 

b.   White blood cells and platelets:

→ Platelets are small membrane bound cell fragments derived from bone marrow. They are involved in initiating blood clotting.

→ White blood cells (leucocytes) are involved in internal defence.

→ This can include antibody production (B cells), mediating allergic responses (eosinophils) and fighting inflammation (basophils).

Show Worked Solution

a.    Red blood cells:

→ Red blood cells (RBCs) make up 40-50% of total blood volume and transport oxygen and carbon dioxide throughout the body.

→ They are able to achieve this by haemoglobin, a globular protein consisting of 4 polypeptide chains and iron. Haemoglobin’s structure allows each of its proteins to carry 4 molecules of oxygen and 4 molecules of carbon dioxide.

→ RBCs are specialised cells and have no nucleus which allows them to carry more haemoglobin, and therefore more oxygen, around the body.
 

b.   White blood cells and platelets:

→ Platelets are small membrane bound cell fragments derived from bone marrow. They are involved in initiating blood clotting.

→ White blood cells (leucocytes) are involved in internal defence.

→ This can include antibody production (B cells), mediating allergic responses (eosinophils) and fighting inflammation (basophils).

CHEMISTRY, M3 EQ-Bank 1 MC

According to Collision Theory, to increase the rate of a reaction, which of the following must occur? 

  1. A decrease in temperature
  2. An increase in the concentration of a reactant
  3. An increase in the surface area of a reactant
  4. An increase in the frequency of successful collisions
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Show Worked Solution

→ Options A and C will increase the rate of a reaction but neither “must” occur for the rate of a reaction to increase.

→ The frequency of successful collisions defines the rate of reaction.