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L&E, 2ADV E1 2008 HSC 7a

Solve     (3 marks)

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IMPORTANT: Students should recognise this equation as a quadratic, and the best responses substituted with a variable such as .
   
 
MARKER’S COMMENT: Many responses incorrectly stated that there is no solution to or could not find given .

 

Functions, 2ADV F1 2022 HSC 12

A student believes that the time it takes for an ice cube to melt ( minutes) varies inversely with the room temperature . The student observes that at a room temperature of it takes 12 minutes for an ice cube to melt.

  1. Find the equation relating and .    (2 marks)

  2. By first completing this table of values, graph the relationship between temperature and time from to .   (2 marks)
     

 
                   

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a.   

 b.    

       

 

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a.   
 
 
 
   

 

 


♦ Mean mark (a) 49%.

b.   

Functions, EXT1 F2 2020 HSC 11a

Let  .

  1. Show that  .  (1 mark)

  2. Hence, factor the polynomial    as  , where    is a quadratic polynomial.  (2 marks)

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i.   
   

 

ii.   

Algebra, STD2 A2 2019 HSC 34

The relationship between British pounds and Australian dollars on a particular day is shown in the graph.
 

  1. Write the direct variation equation relating British pounds to Australian dollars in the form  . Leave as a fraction.  (1 mark)

  2. The relationship between Japanese yen and Australian dollars on the same day is given by the equation  .

     

    Convert 93 100 Japanese yen to British pounds.  (2 marks)

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a.   

♦ Mean mark 42%.

 

b.   

 

 

 

 

Algebra, STD2 A4 2019 HSC 33

The time taken for a car to travel between two towns at a constant speed varies inversely with its speed.

It takes 1.5 hours for the car to travel between the two towns at a constant speed of 80 km/h.

  1. Calculate the distance between the two towns.  (1 mark)

  2. By first plotting four points, draw the curve that shows the time taken to travel between the two towns at different constant speeds.  (3 marks)

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  2.  
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a.   
   
   

 
b.   

Functions, EXT1 F2 2018 HSC 11a

Consider the polynomial  .

  1. Show that    is a zero of  .  (1 mark)

  2. Find the other zeros.  (2 marks)

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i.   

 

ii.   


 

 

 

Functions, EXT1 F2 2007 HSC 2c

The polynomial    has a zero at  . When    is divided by  , the remainder is .

Find the values of    and  .  (3 marks)

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Functions, EXT1 F2 2015 HSC 11f

Consider the polynomials    and  .

  1. Given that    is divisible by  , show that  .  (1 mark)

  2. Find all the zeros of    when  .  (2 marks)

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i.   
 

 

 

ii. 


 

 
 

 

Algebra, STD2 A2 2007 HSC 24c

Sandy travels to Europe via the USA. She uses this graph to calculate her currency conversions.
  
  
 

  1. After leaving the USA she has US$150 to add to the A$600 that she plans to spend in Europe.

     

    She converts all of her money to euros.How many euros does she have to spend in Europe?    (3 marks)

  2. If the value of the euro falls in comparison to the Australian dollar, what will be the effect on the gradient of the line used to convert Australian dollars to euros?   (1 mark)

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  1. €

  3.  

  4.  

  5.  

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i.   

 

 

€

€
  €

 

ii.   

Algebra, STD2 A2 2014 HSC 26f

The weight of an object on the moon varies directly with its weight on Earth.  An astronaut who weighs 84 kg on Earth weighs only 14 kg on the moon.

A lunar landing craft weighs 2449 kg when on the moon. Calculate the weight of this landing craft when on Earth.   (2 marks)

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Functions, EXT1 F2 2010 HSC 2c

Let  , 

where    is a polynomial and    and    are real numbers.

The polynomial    has a factor of  .

When    is divided by    the remainder is  . 

  1. Find the values of    and  .  (2 marks)

  2. Find the remainder when    is divided by  .     (1 mark)

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i. 

 

 

 

 
 
 

ii. 

 

COMMENT: This question requires a fundamental understanding of the remainder theorem.

Functions, EXT1 F2 2011 HSC 2a

Let    be a polynomial, where    is a real number.

When    is divided by    the remainder is  .

Find the remainder when    is divided by  .    (3 marks)

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