SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

v1 Algebra, STD2 A4 2023 HSC 21

Electricity provider charges 30 cents per kilowatt hour (kWh) for electricity, plus a fixed monthly charge of $90.

  1. Complete the table showing Provider 's monthly charges for different levels of electricity usage.   (1 mark)


Provider charges 52.5 cents per kWh, with no fixed monthly charge. The graph shows how Provider 's charges vary with the amount of electricity used in a month.
 

 
  1. On the grid above, graph Provider 's charges from the table in part (a).   (1 mark)
  2. Use the two graphs to determine the number of kilowatt hours per month for which Provider and Provider charge the same amount.   (1 mark)

  3. A customer uses an average of 600 kWh per month.
  4. Which provider, or , would be the cheaper option and by how much?   (2 marks)

Show Answers Only

a.   

b.    
         

c.   

d.   

Show Worked Solution

a.   

b. 
          
 

c.   


 

d.    

v1 Algebra, STD2 A4 2018 HSC 27d

The graph displays the cost () charged by two companies for the hire of a jetski for hours.
 


  

Both companies charge $450 for the hire of a jetski for 5 hours.

  1. What is the hourly rate charged by Company A?  (1 mark)

  2. Company B charges an initial booking fee of $80.

     

    Write a formula, in the of  , for the cost of hiring a jetski from Company B for hours.  (2 marks)

  3. A jetski is hired for 7 hours from Company B.

     

    Calculate how much cheaper this is than hiring from Company A.  (2 marks)

Show Answers Only
Show Worked Solution
i.   
   

 

ii.   


 

iii.   
 

 

v1 Algebra, STD2 A2 2010 HSC 27c

The graph shows tax payable against taxable income, in thousands of dollars.
  

  1. Use the graph to find the tax payable on a taxable income of .  (1 mark)

  2. Use suitable points from the graph to show that the gradient of the section of the graph marked    is  .    (1 mark)

  3. How much of each dollar earned between    and  is payable in tax? Give your answer correct to the nearest whole number.   (1 mark)

  4. Write an equation that could be used to calculate the tax payable, , in terms of the taxable income, , for taxable incomes between    and  .   (2 marks)

Show Answers Only
Show Worked Solution
i.   

  

ii. 

 
 
 

♦♦ Mean mark (ii) 25%.

iii. 

 

♦♦♦ Mean mark (iii) 12%!
MARKER’S COMMENT: Interpreting gradients is an examiner favourite, so make sure you are confident in this area.

iv. 

 
 

♦♦♦ Mean mark (iv) 15%.
STRATEGY: The earlier parts of this question direct students to the most efficient way to solve this question. Make sure earlier parts of a question are front and centre of your mind when devising strategy.

v1 Algebra, STD2 A2 2014 HSC 27b

Clara is comparing the costs of two different ways of travelling to work.

Clara’s motor scooter uses one litre of fuel for every 22 km travelled. The cost of fuel is $2.24/L and the distance from her home to the work car park is 33 km. The cost of travelling by bus and light rail is $35.80 for 10 single trips.

Which way of travelling is cheaper and by how much? Support your answer with calculations.  (2 marks)

Show Answers Only

Show Worked Solution


  


 


  

v1 Algebra, STD2 A2 2016 HSC 29e

The graph shows the life expectancy of people born between 1900 and 2010.
 


  1. According to the graph, what is the life expectancy of a person born in 1968?  (1 mark)

  2. With reference to the value of the gradient, explain the meaning of the gradient in this context.  (2 marks)

Show Answers Only

Show Worked Solution

i.   

ii.   

 
 

 

♦♦ Mean mark (ii) 33%.

v1 Algebra, STD2 A2 2022 HSC 16

Nicole is 38 years old, and likes to keep fit by doing cross-fit classes.

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

Show Answers Only

a.   

b.   

Show Worked Solution
a.    
   

 

b.   

v1 Algebra, STD2 A1 2015 HSC 26b

Clark’s formula is used to determine the dosage of medicine for children.
 


 

The adult daily dosage of a medicine contains 1750 mg of a particular drug.

A child who weighs 30 kg is to be given tablets each containing 125 mg of this drug.

How many tablets should this child be given daily?  (2 marks)

Show Answers Only

Show Worked Solution
 

  


  

v1 Algebra, STD2 A1 2007 HSC 24b

The distance in kilometres () of an observer from the centre of a thunderstorm can be estimated by counting the number of seconds () between seeing the lightning and first hearing the thunder.

Use the formula    to estimate the number of seconds between seeing the lightning and hearing the thunder if the storm is 2.1 km away.   (1 mark)

Show Answers Only

Show Worked Solution

EXAMCOPY Functions, MET2 2022 VCAA 4

Consider the function , where

Part of the graph of is shown below.
 

  1. State the range of .   (1 mark)

  2.  i. Find .   (2 marks)

  3. ii. State the maximal domain over which is strictly increasing.   (1 mark)

  4. Show that .   (1 mark)

  5. Find the domain and the rule of , the inverse of .   (3 marks)

  6. Let be the function , where and .
  7. The inverse function of is defined by .
  8. The area of the regions bound by the functions and can be expressed as a function, .
  9. The graph below shows the relevant area shaded.
     

  1. You are not required to find or define .
  1. Determine the range of values of such that .   (1 mark)

  2. Explain why the domain of does not include all values of .   (1 mark)

Show Answers Only
a.    
b.i
b.ii
c.
d.
e.i 
e.ii No bounded area for
Show Worked Solution

a.   is the range.

b.i   
 
   
     
   
     

 
b.ii 

c.    
   

 
d.   To find the inverse swap and in

 
 
 
 
 
 
 

 
    Domain:
  

e.i   The vertical dilation factor of  is 

For ,

   [Using CAS]


♦♦♦♦ Mean mark (e.i) 10%.
MARKER’S COMMENT: Incorrect responses included and .

e.ii  When for  (or for  ) there is no bounded area.

  There will be no bounded area for .


♦♦♦♦ Mean mark (e.ii) 10%.

CHEMISTRY, M8 2013 VCE 8* MC

A forensic chemist tests mud from a crime scene to determine whether the mud contains zinc. Which one of the following analytical techniques would be best suited to this task?

  1. infrared spectroscopy
  2. mass spectroscopy
  3. atomic absorption spectroscopy
  4. nuclear magnetic resonance spectroscopy
Show Answers Only

Show Worked Solution

→ AAS is the only analytical technique that is specific to identifying metals within a solution.

CHEMISTRY, M7 2018 VCE 1a

Organic compounds are numerous and diverse due to the nature of the carbon atom. There are international conventions for the naming and representation of organic compounds.

  1. Draw the structural formula of 2-methyl-propan-2-ol.   (1 mark)

  2. Give the molecular formula of but-2-yne.   (1 mark)

  1. Give the IUPAC name of the compound that has the structural formula shown above.   (1 mark)

Show Answers Only

i.    
         

ii.   

→ Structural or semi-structural formulas are not appropriate.
 

iii.  → Longest carbon chain is 6, hence hexane

→ Number carbons to give functional group lowest possible numbers: 2,3-dibromo, 4-methyl

→ Compound name: 2,3-dibromo-4-methylhexane

Show Worked Solution

i.    
         

ii.   

→ Structural or semi-structural formulas are not appropriate.
 

iii.  → Longest carbon chain is 6, hence hexane

→ Number carbons to give functional group lowest possible numbers: 2,3-dibromo, 4-methyl

→ Compound name: 2,3-dibromo-4-methylhexane

♦♦♦ Mean mark (c) 27%.

CHEMISTRY, M4 2016 VCE 17*

The combustion of hexane takes place according to the equation

Consider the following reaction.

  1. Calculate the value of , in kJ mol, for this reaction   (2 marks)

  2. Is the reaction exothermic or endothermic?   (1 mark)

Show Answers Only

a.   

b.    Endothermic

Show Worked Solution

a.   

→ Reverse equation:

→ Double equation:

→

b.    Endothermic

CHEMISTRY, M4 2015 VCE 17 MC

The oxidation of sulfur dioxide is an exothermic reaction. The reaction is catalysed by vanadium oxide.

Which one of the following energy profile diagrams correctly represents both the catalysed and the uncatalysed reaction?
 


 

Show Answers Only

Show Worked Solution

→ Exothermic reaction releases energy (eliminate C and D).

→ Catalysts only effect the enthalpy during the chemical reaction by reducing the activation energy required.

CHEMISTRY, M4 2018 VCE 14*

An equation for the complete combustion of methanol is

  1. State whether this reaction exothermic or endothermic.   (1 mark)

  2. Calculate the total enthalpy change of the equation, in kilojoules.   (1 mark)

Show Answers Only

a.    → Combustion is an exothermic reaction.

→   also indicates it is exothermic.
 

b.   →

→ 2 moles of are involved.

→

Show Worked Solution

a.    → Combustion is an exothermic reaction.

→   also indicates it is exothermic.
 

b.   →

→ 2 moles of are involved.

→

PHYSICS, M5 2019 VCE 10

A projectile is launched from the ground at an angle of 39° and at a speed of 25 m s, as shown in Figure 10. The maximum height that the projectile reaches above the ground is labelled .
 

  1. Ignoring air resistance, show that the projectile's time of flight from the launch to the highest point is equal to 1.6 seconds. Give your answer to two significant figures. Show your working and indicate your reasoning.  (2 marks)

  2. Calculate the range, , of the projectile. Show your working.  (2 marks)

Show Answers Only

a.    

b.    

Show Worked Solution

a.    
       

 
 
 
 

 

b.   

.

 

PHYSICS, M6 2019 VCE 7*

Students in a Physics practical class investigate the piece of electrical equipment shown in Figure 5. It consists of a single rectangular loop of wire that can be rotated within a uniform magnetic field. The loop has dimensions 0.50 m × 0.25 m and is connected to the output terminals with slip rings. The loop is in a uniform magnetic field of strength 0.40 T.
 

  1. What name best describes the piece of electrical equipment shown in Figure 5.   (1 mark)

  2. What is the magnitude of the flux through the loop when it is in the position shown in Figure 5? Explain your answer.   (2 marks)

The students connect the output terminals of the piece of electrical equipment to an oscilloscope. One student rotates the loop at a constant rate of 20 revolutions per second.

  1. Calculate the period of the rotation of the loop.  (1 mark)

  2. Calculate the maximum flux through the loop. Show your working.  (1 mark)

  3. The loop starts in the position shown in Figure 5.
  4. What is the average voltage measured across the output terminals for the first quarter turn? Show your working.  (2 marks)

Show Answers Only

a.    Alternator.

b.   →

→ This is because the plane of the area of the coil is parallel to the direction of the magnetic field, not perpendicular.

c.    

d.    

e.    

Show Worked Solution

a.    → The device is an alternator.

→ This is due to the input being mechanical motion and the output being AC current, whereas an AC motor is the opposite.

♦ Mean mark (a) 44%.
COMMENT: Many students incorrectly answered AC motor.

b.   →

→ This is because the plane of the area of the coil is parallel to the direction of the magnetic field, not perpendicular.
 

c.    
 

d.    
 

e.    
   
   
♦ Mean mark (e) 51%.

PHYSICS, M6 2019 VCE 6

A home owner on a large property creates a backyard entertainment area. The entertainment area has a low-voltage lighting system. To operate correctly, the lighting system requires a voltage of 12 V. The lighting system has a resistance of 12 .

  1. Calculate the power drawn by the lighting system.   (1 mark)

To operate the lighting system, the home owner installs an ideal transformer at the house to reduce the voltage from 240 V to 12 V. The home owner then runs a 200 m long heavy-duty outdoor extension lead, which has a total resistance of 3 , from the transformer to the entertainment area.

  1. The lights are a little dimmer than expected in the entertainment area.
  2. Give one possible reason for this and support your answer with calculations.   (4 marks)

  3. Using the same equipment, what changes could the home owner make to improve the brightness of the lights? Explain your answer.   (2 marks)

Show Answers Only

a.   

b.   Potential cause of dimmer lights: 

→ Power loss in the extension lead.

→ The total resistance () in the circuit

→ The new current in the circuit

→ The power loss across the extension lead,

→ Therefore, power supplied to lights .

c.    Changes using the same equipment:

→ The homeowner needs to move the transformer from inside the home (start of the lead) to the outside entertainment area (end of the lead).

→ This would mean a higher voltage/lower current is running through the lead which would decrease the power loss through the lead and improve the brightness of the lights.

Show Worked Solution

a.    


 

b.   Potential cause of dimmer lights: 

→ Power loss in the extension lead.

→ The total resistance () in the circuit

→ The new current in the circuit

→ The power loss across the extension lead,

→ Therefore, power supplied to lights .

♦♦♦ Mean mark (b) 23%.
COMMENT: Many students used 1 Amp in their calculations instead of finding the total current in the system.

c.    Changes using the same equipment:

→ The homeowner needs to move the transformer from inside the home (start of the lead) to the outside entertainment area (end of the lead).

→ This would mean a higher voltage/lower current is running through the lead which would decrease the power loss through the lead and improve the brightness of the lights.

♦♦♦ Mean mark (c) 22%.
COMMENT: Students incorrectly added or changed the equipment used in the question.

PHYSICS, M6 2019 VCE 3

Figure 3 shows a schematic diagram of a DC motor. The motor has a coil, , consisting of 100 turns. The permanent magnets provide a uniform magnetic field of 0.45 T.

The commutator connectors, and , provide a constant DC current, , to the coil. The length of the side is 5.0 cm.

The current flows in the direction shown in the diagram.
 

  1. Which terminal of the commutator is connected to the positive terminal of the current supply?   (1 mark)

  2. Draw an arrow on Figure 3 to indicate the direction of the magnetic force acting on the side .   (1 mark)

  3. Explain the role of the commutator in the operation of the DC motor.   (2 marks)

  4. A current of 6.0 A flows through the 100 turns of the coil .
  5. The side is 5.0 cm in length.
  6. Calculate the size of the magnetic force on the side in the orientation shown in Figure 3. Show your working.   (2 marks)

Show Answers Only

a.    → Current runs from the positive terminal to the negative terminal.

→ is connected to the positive terminal of the current supply.
 

b.    Using the right-hand rule: force on is down the page.

c.    Role of the split-ring commutator:

→ Changes the direction of the current through the arms of the coil every 180.

→ This ensures that the torque through the motor will always be in the same direction so the motor will rotate in the same direction.
 

d.    

Show Worked Solution

a.    → Current runs from the positive terminal to the negative terminal.

→ is connected to the positive terminal of the current supply.
 

b.    Using the right-hand rule: force on is down the page.

c.    Role of the split-ring commutator:

→ Changes the direction of the current through the arms of the coil every 180.

→ This ensures that the torque through the motor will always be in the same direction so the motor will rotate in the same direction.
 

d.    

PHYSICS, M7 2019 VCE 16 MC

Students are conducting a photoelectric effect experiment. They shine light of known frequency onto a metal and measure the maximum kinetic energy of the emitted photoelectron.

The students increase the intensity of the incident light.

The effect of this increase would most likely be

  1. lower maximum kinetic energy of the emitted photoelectrons.
  2. higher maximum kinetic energy of the emitted photoelectrons.
  3. fewer emitted photoelectrons but of higher maximum kinetic energy.
  4. more emitted photoelectrons but of the same maximum kinetic energy.
Show Answers Only

Show Worked Solution

→ The energy of a photon (which is transferred to the photoelectron) is independent of the intensity of the light.

→ Increasing the intensity of light will not change the maximum kinetic energy of the photoelectrons.

→ However, a higher intensity of light corresponds to more photons and thus more emitted photoelectrons.

PHYSICS, M6 2019 VCE 5-6* MC

A 40 V AC generator and an ideal transformer are used to supply power. The diagram below shows the generator and the transformer supplying 240 V to a resistor with a resistance of 1200 .
 

Question 5

Which of the following correctly identifies the parts labelled and , and the function of the transformer?

Question 6

Which one of the following is closest to the current in the primary circuit?

Show Answers Only

Show Worked Solution

→ The primary coil is connected to the power supply (i.e. Part ).

→ For a step-up transformer, there are more coils in the secondary coil then there are in the primary coil.


 


 
 
   
   

 

Mean mark Q6 57%.

Calculus, MET1 2023 VCAA SM-Bank 6

Newton's method is used to estimate the -intercept of the function  .

  1. Verify that and .  (1 mark)

  2. Using an initial estimate of , find the value of .  (2 marks)

Show Answers Only

a.   

b.   

Show Worked Solution
a.    
 
 

 

b.    
   

   

Functions, MET1 EQ-Bank 2

Consider the functions and , where

  1. State the range of .  (1 mark)

  2. Determine the rule for the equation and state the domain of the function .  (2 marks)

  3. Let be the function .
  4. Determine the maximal domain, , such that exists.  (1 marks)

Show Answers Only

a.   

b.   

c.   

Show Worked Solution

a.   

b.    
   
   

c.    
   

Graphs, MET1 EQ-Bank 1

Let  .

  1. On the axes below, sketch the graph of . Label any asymptotes with their equations, and endpoints and axial intercepts with their coordinates.   (3 marks)

  1. Find the values of for which .   (2 marks)

Show Answers Only

a.
   

b.   

Show Worked Solution

a.
     

b.     

Calculus, MET2 EQ-Bank 2

Jac and Jill have built a ramp for their toy car. They will release the car at the top of the ramp and the car will jump off the end of the ramp.

The cross-section of the ramp is modelled by the function , where

is both smooth and continuous at .

The graph of    is shown below, where is the horizontal distance from the start of the ramp and is the height of the ramp. All lengths are in centimetres.

  1. Find for .   (2 marks)

  2.   i. Find the coordinates of the point of inflection of .   (1 mark)

  3.  ii. Find the interval of for which the gradient function of the ramp is strictly increasing.   (1 mark)

  4. iii. Find the interval of for which the gradient function of the ramp is strictly decreasing.  (1 mark)

Jac and Jill decide to use two trapezoidal supports, each of width . The first support has its left edge placed at and the second support has its left edge placed at . Their cross-sections are shown in the graph below.

  1. Determine the value of the ratio of the area of the trapezoidal cross-sections to the exact area contained between and the -axis between and . Give your answer as a percentage, correct to one decimal place.   (3 marks)

  2. Referring to the gradient of the curve, explain why a trapezium rule approximation would be greater than the actual cross-sectional area for any interval , where .   (1 mark)

  3. Jac and Jill roll the toy car down the ramp and the car jumps off the end of the ramp. The path of the car is modelled by the function , where

  4. is continuous and differentiable at , and is where the car lands on the ground after the jump, such that .
    1. Find the values of and .   (2 marks)

    2. Determine the horizontal distance from the end of the ramp to where the car lands. Give your answer in centimetres, correct to two decimal places.   (1 mark)

Show Answers Only

a.   

b.i   

b.ii 

b.iii

c.   

d.   

e.i   

e.ii 

Show Worked Solution

a.   

b.i   


  

b.ii 

b.iii

c.   

 

  

 
 

    
d.   


 

e.i   

  


 

e.ii 

PHYSICS, M7 2020 VCE 16 MC

The diagram below shows a plot of maximum kinetic energy, ,  versus frequency, , for various metals capable of emitting photoelectrons.
 

 

Which one of the following correctly ranks these metals in terms of their work function, from highest to lowest in numerical value?

  1. sodium, potassium, lithium, nickel
  2. nickel, potassium, sodium, lithium
  3. potassium, nickel, lithium, sodium
  4. lithium, sodium, potassium, nickel
Show Answers Only

Show Worked Solution

→

→ The threshold frequency occurs when

→ , hence  .

→ The greater the threshold frequency, the greater the work function. Therefore, lithium has the greatest work function.

Statistics, SPEC2 2022 VCAA 6

A company produces soft drinks in aluminium cans.

The company sources empty cans from an external supplier, who claims that the mass of aluminium in each can is normally distributed with a mean of 15 grams and a standard deviation of 0.25 grams.

A random sample of 64 empty cans was taken and the mean mass of the sample was found to be 14.94 grams.

Uncertain about the supplier's claim, the company will conduct a one-tailed test at the 5% level of significance. Assume that the standard deviation for the test is 0.25 grams.

  1. Write down suitable hypotheses and for this test.   (1 mark)

  2. Find the value for the test, correct to three decimal places.   (1 mark)

  3. Does the mean mass of the random sample of 64 empty cans support the supplier's claim at the 5% level of significance for a one-tailed test? Justify your answer.   (1 mark)

  4. What is the smallest value of the mean mass of the sample of 64 empty cans for not to be rejected? Give your answer correct to two decimal places.   (1 mark)

The equipment used to package the soft drink weighs each can after the can is filled. It is known from past experience that the masses of cans filled with the soft drink produced by the company are normally distributed with a mean of 406 grams and a standard deviation of 5 grams.

  1. What is the probability that the masses of two randomly selected cans of soft drink differ by no more than 3 grams? Give your answer correct to three decimal places.   (2 marks)

Show Answers Only

a.   

b.   

c.   

d.   

e. 

Show Worked Solution

a.   
 

b.   


 

c.   


 

d.   


 

e.   

♦ Mean mark (e) 46%.

CHEMISTRY, M2 EQ-Bank 8

  1. Consider the compounds butyraldehyde , lactic acid , and fructose .
  2. Identify which TWO of these compounds have the same empirical formula and justify your choice.    (2 marks)

  3. The empirical formula of a compound is and its molar mass is determined to be 340.32 g mol.
  4. Calculate the molecular formula of this compound.     (3 marks)

Show Answers Only

a.    Determine the empirical formula of each compound.

Butyraldehyde : Empirical formula =

Lactic acid : Empirical formula =

Fructose : Empirical formula =

→ Butyraldehyde and lactic acid have the same empirical formula of .
 

b.   

Show Worked Solution

a.    Determine the empirical formula of each compound.

Butyraldehyde : Empirical formula =

Lactic acid : Empirical formula =

Fructose : Empirical formula =

→ Butyraldehyde and lactic acid have the same empirical formula of .

 

b.    Calculate the molar mass of the empirical formula :

 
 

Ratio of the molar mass of the compound to the molar mass of the empirical formula:

 
 

Multiply the subscripts in the empirical formula by 4 to get the molecular formula:

 

→ Thus, the molecular formula of the compound is .

CHEMISTRY, M2 EQ-Bank 4

A propane tank contains 10.0 kg of propane . How many moles of propane are in the tank?   (2 marks)

Show Answers Only

 

Show Worked Solution

Calculate the number of moles of propane ():

 

→ The number of moles of propane in the tank is 226.8 mol.