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Calculus, 2ADV C3 2020 HSC 21

Hot tea is poured into a cup. The temperature of tea can be modelled by  , where is the temperature of the tea, in degrees Celsius, minutes after it is poured.

  1. What is the temperature of the tea 4 minutes after it has been poured?  (1 mark)

  2. At what rate is the tea cooling 4 minutes after it has been poured?  (2 marks)

  3. How long after the tea is poured will it take for its temperature to reach 55°C?  (3 marks)

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a.   
   
   

 

b.   
   

 

 
 

 

c.   

♦ Mean mark part (c) 44%.
 
 

L&E, 2ADV E1 SM-Bank 14

The spread of a highly contagious virus can be modelled by the function

Where is the number of days after the first case of sickness due to the virus is diagnosed and    is the total number of people who are infected by the virus in the first    days.

  1. Calculate  .  (1 mark)

  2. Find the value of    and interpret it result.  (2 marks)

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i.  
   
   

 

ii.   
   
   

 

Algebra, STD2 A4 2016 HSC 29b

The mass kg of a baby pig at age days is given by    where is a constant. The graph of this equation is shown.
 

2ug-2016-hsc-q29_1

  1. What is the value of ?   (1 mark)

  2. What is the daily growth rate of the pig’s mass? Write your answer as a percentage.   (1 mark)

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i.   

♦ Mean mark (i) 48%.
♦♦♦ Mean mark part (ii) 6%!

 
ii.   

Algebra, STD2 A4 2004 HSC 26a

  1. The number of bacteria in a culture grows from 100 to 114 in one hour.

     

    What is the percentage increase in the number of bacteria?   (1 mark)

  2. The bacteria continue to grow according to the formula  , where    is the number of bacteria after    hours.

     

    What is the number of bacteria after 15 hours?   (1 mark)

  1. Use the values of from    to    to draw a graph of  .

     

    Use about half a page for your graph and mark a scale on each axis.   (4 marks)

  2. Using your graph or otherwise, estimate the time in hours for the number of bacteria to reach 300.   (1 mark)

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i.   

COMMENT: Common ADV/STD2 content in new syllabus.

 

ii. 

 
 

 

iii. 

 

iv.