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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

 

 

 

 

 

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Financial Maths, 2ADV M1 2005 HSC 7a

Anne and Kay are employed by an accounting firm.

Anne accepts employment with an initial annual salary of  $50 000. In each of the following years her annual salary is increased by $2500.

Kay accepts employment with an initial annual salary of  $50 000. In each of the following years her annual salary is increased by 4%.

  1. What is Anne’s annual salary in her thirteenth year?  (2 marks)

  2. What is Kay’s annual salary in her thirteenth year?  (2 marks)

  3. By what amount does the total amount paid to Kay in her first twenty years exceed that paid to Anne in her first twenty years?  (3 marks)

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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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Financial Maths, 2ADV M1 2008 HSC 4b

The zoom function in a software package multiplies the dimensions of an image by 1.2.  In an image, the height of a building is 50 mm. After the zoom function is applied once, the height of the building in the image is 60 mm. After the second application, it is 72 mm.

  1. Calculate the height of the building in the image after the zoom function has been applied eight times. Give your answer to the nearest mm.     (2 marks)

  2. The height of the building in the image is required to be more than 400 mm. Starting from the original image, what is the least number of times the zoom function must be applied?     (2 marks)

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MARKER’S COMMENT: Within this GP, note that is the term where the zoom has been applied 8 times.
 

 

 

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Financial Maths, 2ADV M1 2011 HSC 5a

The number of members of a new social networking site doubles every day. On Day 1 there were 27 members and on Day 2 there were 54 members.

  1. How many members were there on Day 12?     (1 mark)

  2. On which day was the number of members first greater than 10 million?     (2 marks)

  3. The site earns 0.5 cents per member per day. How much money did the site earn in the first 12 days? Give your answer to the nearest dollar.     (2 marks)

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MARKER’S COMMENT: Better responses stated the general term, before any substitution was made, as shown in the worked solutions.

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MARKER’S COMMENT: Many elementary errors were made by students in dealing with logarithms. BE VIGILANT.

 

 

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♦ Mean mark 44%.
NOTE: This question can also be easily solved by making the total sum of members (each day) and then multiplying by 0.5 cents.
 
 
 

 

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

 

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

 

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♦♦♦ 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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Financial Maths, 2ADV M1 2013 HSC 12c

Kim and Alex start jobs at the beginning of the same year. Kim's annual salary in the first year is $30,000 and increases by 5% at the beginning of each subsequent year. Alex's annual salary in the first year is $33,000, and increases by $1,500 at the beginning of each subsequent year.

  1. Show that in the 10th year, Kim's annual salary is higher than Alex's annual salary.     (2 marks)

  2. In the first 10 years how much, in total, does Kim earn?     (2 marks)

  3. Every year, Alex saves of her annual salary. How many years does it take her to save $87,500?     (3 marks)

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♦ Mean mark 45%.
IMPORTANT: Using the AP sum formula to create and then solve a quadratic in is challenging and often examined. Students need to solve and interpret the solutions.