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Trigonometry, 2ADV T2 2004 HSC 9a

Consider the geometric series  

  1. When the limiting sum exists, find its value in simplest form.  (2 marks)

  2. For what values of    in the interval
     
         does the limiting sum of the series exist?  (2 marks)

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i.  

 
 
 

 

ii.  
 
 
 
 

Trigonometry, 2ADV T1 2005 HSC 9b

Trig Ratios, 2UA 2005 HSC 9b
 

The triangle    has a right angle at and  . The line is drawn perpendicular to . The line is then drawn perpendicular to . This process continues indefinitely as shown in the diagram.

  1. Find the length of the interval , and hence show that the length of the interval    is  .  (2 marks)

  2. Show that the limiting sum 
     

     
    is given by  .  (3 marks)

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i.   Trig Ratios, 2UA 2005 HSC 9b Answer

 

 

 

 

 

ii.


 

 

 

 
 
 
 

Financial Maths, 2ADV M1 2014 HSC 14d

At the beginning of every 8-hour period, a patient is given 10 mL of a particular drug.

During each of these 8-hour periods, the patient’s body partially breaks down the drug. Only    of the total amount of the drug present in the patient’s body at the beginning of each 8-hour period remains at the end of that period.  

  1. How much of the drug is in the patient’s body immediately after the second dose is given?    (1 mark)

  2. Show that the total amount of the drug in the patient’s body never exceeds 15 mL.     (2 marks)

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i.   

 

 

ii.   

 

 

 
 
 

 

 

Financial Maths, 2ADV M1 2008 HSC 5b

Consider the geometric series

  1. For what values of does this series have a limiting sum?    (2 marks)

  2. The limiting sum of this series is .

     

    Find the value of .     (2 marks)

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i.   

   

 

 

ii. 

Financial Maths, 2ADV M1 2012 HSC 15a

Rectangles of the same height are cut from a strip and arranged in a row. The first rectangle has width 10cm. The width of each subsequent rectangle is 96% of the width of the previous rectangle.
 

2012 15a
 

  1. Find the length of the strip required to make the first ten rectangles.     (2 marks)

  2. Explain why a strip of 3m is sufficient to make any number of rectangles.     (1 mark)

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i.   

 

MARKER’S COMMENT: A common error was to find instead of
 
 
 

 

ii.  

 
 

 

Probability, 2ADV S1 2013 HSC 15d

Pat and Chandra are playing a game. They take turns throwing two dice. The game is won by the first player to throw a double six. Pat starts the game.

  1. Find the probability that Pat wins the game on the first throw.     (1 mark)

  2. What is the probability that Pat wins the game on the first or on the second throw?     (2 marks)

  3. Find the probability that Pat eventually wins the game.     (2 marks)

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i.   

 
 

 

ii.  

 

♦♦ Mean mark 33%
MARKER’S COMMENT: Many students did not account for Chandra having to lose when Pat wins on the 2nd attempt.

 

iii. 

 

♦♦♦ Mean mark 8%!
 COMMENT: Be aware that diminishing probabilities and within the Series and Applications are a natural cross-topic combination.

 

 
 
 

 

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