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Measurement, STD2 M1 2017 HSC 16 MC

The benchmark for annual greenhouse gas emissions from the residential sector is 3292 kg of carbon dioxide per person per year.

A new building, planned to house 6 people, has been designed to achieve a 25% reduction on this benchmark.

What is the maximum amount of carbon dioxide per year, to the nearest kilogram, that this building is designed to emit when fully occupied?

A.     823 kg

B.     2469 kg

C.     4938 kg

D.     14 814 kg

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Financial Maths, STD2 F1 2017 HSC 11 MC

A new car was bought for $19 900 and one year later its value had depreciated to $16 300.

What is the approximate depreciation, expressed as a percentage of the purchase price?

  1. 18%
  2. 22%
  3. 78%
  4. 82%
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Measurement, STD2 M6 2017 HSC 8 MC

The diagram shows a right-angled triangle.
 


 

What is the value of  , to the nearest minute?

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COMMENT: An angle that has over 30″ (seconds) is rounded up to the next minute (i.e. rounded up to 70°17′).

 

 
 

 

Number and Algebra, NAP-J2-12

Trevor has poured milk into some glasses.

He makes them all exactly one quarter full.

Trevor counts by quarters to find out, in total, how many full cups of milk he has.
 

  Which number does Trevor count next?

 
 
 
 
 
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CHEMISTRY, M4 2009 HSC 20

  1. Calculate the mass of ethanol that must be burnt to increase the temperature of 210 g of water by 65°C, if exactly half of the heat released by this combustion is lost to the surroundings.
  2. The heat of combustion of ethanol is 1367 kJ mol −1.  (3 marks)

  3. What are TWO ways to limit heat loss from the apparatus when performing a first-hand investigation to determine and compare heat of combustion of different liquid alkanols?  (1 mark)

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a.    3.85 grams

b.    Answers could include two of the following:

→ Use of an insulated vessel (Styrofoam cup)

→ Place the vessel as close as safely possible to the Bunsen’s flame.

→ Use a lid for the beaker

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a.   

Since half of the heat is lost to environmental surroundings.


 

b.    Answers could include two of the following:

→ Use of an insulated vessel (Styrofoam cup)

→ Place the vessel as close as safely possible to the Bunsen’s flame.

→ Use a lid for the beaker

CHEMISTRY, M4 2013 HSC 27

A 0.259 g sample of ethanol is burnt to raise the temperature of 120 g of an oily liquid, as shown in the graph. There is no loss of heat to the surroundings.
 

Using the information shown on the graph, calculate the specific heat capacity of the oily liquid. The heat of combustion of ethanol is 1367 kJ mol–1.   (4 marks)

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Mean mark 59%.
 
 
   
   

GEOMETRY, FUR2 SM-Bank 25

A ship sails due South from Channel-Port-aux-Basques, Canada,  47°N  59°W  to Barbados, 13°N  59°W.

How far did the ship sail, to the nearest kilometre? Assume that the radius of Earth is 6400 km.    (2 marks)

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GEOMETRY, FUR2 SM-Bank 15

Osaka is at  34°N, 135°E, and Denver is at  40°N, 105°W. 

  1. Show that there is a 16-hour time difference between the two cities.
    (Ignore time zones.)    (1 mark)
  2. John lives in Denver and wants to ring a friend in Osaka. In Denver it is 9 pm Monday.     

     

    What time and day is it in Osaka then?   (1 mark)

  3. John’s friend in Osaka sent him a text message which happened to take 14 hours to reach him. It was sent at 10 am Thursday, Osaka time.

     

    What was the time and day in Denver when John received the text?    (1 mark)

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a.  
   

 

 

 

b. 

 

 

c. 

GEOMETRY, FUR2 SM-Bank 14

Pontianak has a longitude of 109°E, and Jarvis Island has a longitude of 160°W.

Both places lie on the Equator

  1. Find the shortest great circle distance between these two places, to the nearest kilometre. You may assume that the radius of the Earth is 6400 km.    (2 marks)
  2. The position of Rabaul is 4° to the south and 48° to the west of Jarvis Island. What is the latitude and longitude of Rabaul?     (1 mark)
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a.  
   

 

 

 

 
 
 

 

b.  
 
 
 
   
 
 
 
 

 

 

 

GEOMETRY, FUR2 SM-Bank 13

Melbourne is located at (38°S, 145°E) and Dubai is located at (24°N, 55°E).

  1. Calculate the difference in longitude between Melbourne and Dubai.  (1 mark)
  2. Show that the time difference between Melbourne and Dubai is 6 hours.  (1 mark)
  3. A plane leaves Melbourne on Friday at 11.30 pm. The flight time to Dubai is 15 hours.

     

    What will be the time and the day in Dubai when the plane is due to land?  (1 marks)

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a.  

 

b.  

 

c.   
   

 

Probability, MET2 2007 VCAA 18 MC

The heights of the children in a queue for an amusement park ride are normally distributed with mean 130 cm and standard deviation 2.7 cm. 35% of the children are not allowed to go on the ride because they are too short.

The minimum acceptable height correct to the nearest centimetre is

  1. 126
  2. 127
  3. 128
  4. 129
  5. 130
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vcaa-2007-meth2-18

 

Graphs, MET2 2008 VCAA 22 MC

The graph of the function   with domain    is shown below.

VCAA 2008 22mc

Which one of the following is not true?

  1. The function is not continuous at    and  
  2. The function exists for all values of between and
  3.  for    and  
  4.  The function is positive for  
  5. The gradient of the function is not defined at  
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Probability, MET2 2008 VCAA 13 MC

According to a survey, 30% of employed women have never been married.

If 10 employed women are selected at random, the probability (correct to four decimal places) that at least 7 have never been married is

A.   

B.   

C.   

D.   

E.   

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Calculus, MET1 SM-Bank 28

The function    has the rule  .

  1. Show that the graph of    cuts the -axis at  .   (1 mark)

  2. Sketch the graph    for    showing where the graph cuts each of the axes.   (2 marks)

  3. Find the area under the curve    between    and  .   (3 marks)

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  1.  
  2.  
       
  3. ²
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a.   

 

 

 

b.   2UA HSC 2006 7b

 

c. 
 
  ­­
 
 
  ²

Graphs, MET1 SM-Bank 27

The graph shown is  .

  1. Write down the value of  .   (1 mark)

  2. Find the value of  .   (1 mark)

  3. Copy or trace the graph into your writing booklet.

     

    On the same set of axes, draw the graph    for  .   (2 marks)

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a.   

b. 

  

 MARKER’S COMMENT: Graphs are consistently drawn too small by many students. Aim to make your diagrams 1/3 to 1/2 of a page. 
c.

Algebra, MET1 SM-Bank 23

The function    with rule    is drawn below.

Inverse Functions, EXT1 2004 HSC 5b

  1. Copy or trace this diagram into your writing booklet.
  2. On the same set of axes, sketch    where   is the inverse function of  .   (1 mark)

  3. Find the domain of the inverse  .   (1 mark)

  4. Find an expression for    in terms of  .   (2 marks)

  5. The graphs of    and    meet at exactly one point  .Let  α  be the -coordinate of  . Explain why  α  is a root of the equation
  6.      .   (1 mark)

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a.  

Inverse Functions, EXT1 2004 HSC 5b Answer

b.  

 

c. 

 

 

 

d.   

 

α

Calculus, MET1 SM-Bank 21

The rule for function   is  .  The diagram shows the graph  .

 Inverse Functions, EXT1 2010 HSC 3b

The graph has two points of inflection. 

  1. Find the coordinates of these points.   (2 marks)

  2. Explain why the domain of must be restricted if is to have an inverse function.    (1 mark)

  3. Find the rule for the inverse function if the domain of is restricted to     (2 marks)

  4. Find the domain for .    (1 mark)

  5. Sketch the curve  .   (1 mark)

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  5. Inverse Functions, EXT1 2010 HSC 3b Answer

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a.   
 
 
   
   

 

 
   
 
   
COMMENT: It is also valid to show that is an even function and if a P.I. exists at , there must be another P.I. at .
 

 


 

 

 

 

b.  
 
 
 

 

c.  

 

 

 

 

d.  

 

e. 

Inverse Functions, EXT1 2010 HSC 3b Answer

Graphs, MET1 SM-Bank 20

The rule for   is    for  .  This function has an inverse,  .

  1. Sketch the graphs of    and    on the same set of axes. (Use the same scale on both axes.)   (2 marks)

  2. Find the rule for the inverse function  .    (2 marks)

  3. Evaluate  .    (1 mark)

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  1.  
    Inverse Functions, EXT1 2008 HSC 5a Answer
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a. 

Inverse Functions, EXT1 2008 HSC 5a Answer
b.  

 

 

 
 
 

 

 

c.