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Aussie Maths & Science Teachers: Save your time with SmarterEd

Quadratics, SMB-006

  1. Complete the table of values for the equation  .  (1 mark)

  1. Sketch the graph    (2 marks)  
      

      
  2. For what range of -values is the parabola concave up?  (1 mark)

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i.   

ii. 

 

iii.   

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i.   

ii. 

 

iii.   

Quadratics, SMB-005

  1. Complete the table of values for the equation  .  (1 mark)

  1. Sketch the graph    (2 marks) 
      
  2. For what range of -values is the parabola concave down?  (1 mark)

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i.   

ii. 

 

iii.   

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i.   

ii. 

 

iii.   

Quadratics, SMB-004

  1. Complete the table of values for the equation  .  (1 mark)

  1. Sketch the graph    (2 marks)  
      
  2. What are the coordinates of the vertex of the parabola?  (1 mark)

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i.   

ii. 

 

iii.   

Exponentials, SMB-001

In 2004 there were 13.5 million registered motor vehicles in Australia. The number of registered motor vehicles is increasing at a rate of 2.3% per year.

Find an expression that represents the number (in millions) of registered motor vehicles , if represents the number of years after 2004?  (2 marks)

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Linear Applications, SMB-007

Fiona and John are planning to hold a fund-raising event for cancer research.  They can hire a function room for $650 and a band for $850.  Drinks will cost them $25 per person.

  1. Write a formula for the cost ($C) of holding the charity event for    people.  (1 mark)

  2. The graph below shows the planned income and costs if they charge $50 per ticket.  Estimate the number of guests they need to break even.    (1 mark)


     

  3. How much profit will Fiona and John make if 80 people attend their event?   (1 mark)

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i.   
   

 

 

ii.  
 
 

 

iii.   

 
   

 

 

 

 

Linear Applications, SMB-006

The average height, , in centimetres, of a girl between the ages of 6 years and 11 years can be represented by a line with equation

where is the age in years. For this line, the gradient is 6.

  1. What does this indicate about the heights of girls aged 6 to 11?   (1 mark)

  2. Give ONE reason why this equation is not suitable for predicting heights of girls older than 12.   (1 mark)

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i.   


 

ii.   

Linear Applications, SMB-004

The prices at an ice cream shop can be seen below.
  

  

Each extra scoop of ice cream costs the same amount of money.

How much will an ice cream with 5 scoops cost?  (2 marks)

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Linear Applications, SMB-001 MC

Jeremy sold ice creams out of his ice cream truck.

He drew the graph below to show how the number of ice creams he sells in a week is related to their price.

 
Which statement best describes the graph?

  1. As the ice cream price goes up, the number sold goes down.
  2. As the ice cream price goes up, the number sold goes up.
  3. As the ice cream price goes down, the number sold goes down.
  4. As the ice cream price goes down, the number sold stays the same.
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Financial Maths, SMB-021

Manou purchased an oven that depreciates in value by 15% per annum. Two years after it was purchased it had depreciated to a value of $6069, using the declining balance method.

What was the purchase price of the oven?   (2 marks)

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Financial Maths, SMB-020

A company purchases a machine for $50 000. The two methods of depreciation being considered are the declining-balance method and the straight-line method.

For the declining-balance method, the salvage value of the machine after years is given by the formula

   

where is the salvage value and is the initial value of the asset.

  1. What is the annual rate of depreciation used in this formula?  (1 mark)

  2. Calculate the salvage value of the machine after 3 years, based on the given formula.  (2 marks)

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  1.  
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a. 
 

b. 

 
   
   

♦♦ Mean mark (a) 24%.
COMMENT: A poor State result in part (a) that warrants attention.

Financial Maths, SMB-019

Alan bought a light aircraft for $76 500. It will depreciate at 14% per annum. 

Using the declining balance method, what will be the salvage value of the light aircraft after 6 years, to the nearest dollar? 

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Financial Maths, SMB-018

Marnus bought a cricket bowling machine two years ago that cost $3400. Its value has depreciated by 10% each year, based on the declining-balance method.

What is the salvage value today, to the nearest dollar?  (2 marks)

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Financial Maths, SMB-015

Hugo is a professional bike rider.

The value of his bike will be depreciated over time using the flat rate method of depreciation.

The graph below shows his bike’s initial purchase price and its value at the end of each year for a period of three years.
 

  1. What was the initial purchase price of the bike?  (1 mark)

  2. Use calculations to show that the bike depreciates in value by $1500 each year.  (1 mark)

  3. Assume that the bike's value continues to depreciate by $1500 each year. Determine its value five years after it was purchased.  (1 mark)

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i.   
 

ii.   

 

 

iii. 

 
 

Financial Maths, SMB-014

Rae paid  $40 000  for new office equipment at the start of the 2019 financial year.

At the start of each following financial year, she used straight-line (flat rate) depreciation to revalue her equipment.

At the start of the 2022 financial year she revalued her equipment at  $22 000.

Calculate the annual straight-line rate of depreciation she used, as a percentage of the purchase price.  (2 marks)

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♦ Mean mark 50%.


 

Statistics, STD1 S3 2022 HSC 23

A teacher surveyed the students in her Year 8 class to investigate the relationship between the average number of hours of phone use per day and the average number of hours of sleep per day.

The results are shown on the scatterplot below.
 

  1. The data for two new students, Alinta and Birrani, are shown in the table below. Plot their results on the scatterplot.  (2 marks)

  1. By first fitting the line of best fit by eye on the scatterplot, estimate the average number of hours of sleep per day for a student who uses the phone for an average of 2 hours per day.  (2 marks)

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  1.  
  2. 9 hours (see LOBF in diagram above)
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a.     
 

b.   

Algebra, STD2 A4 2022 HSC 22

The formula    is used to calculate the cost of producing laptops, where is the cost in dollars, is the number of laptops produced and is the fixed cost in dollars.

  1. Find the cost when 1943 laptops are produced and the fixed cost is $20 180.  (1 mark)

  2. Some laptops have some extra features added. The formula to calculate the production cost for these is
  3.      
  4. where is the additional cost in dollars per laptop produced.
  5. Find the number of laptops produced if the additional cost is $26 per laptop and the total production cost is $97 040.  (2 marks)

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a.   

 
   

 

b.   

 
 
 
 
   

Algebra, STD2 A4 2021 HSC 24

A population,  ,  is to be modelled using the function  ,  where is the time in years.

  1. What is the initial population?  (1 mark)

  2. Find the population after 5 years.  (1 mark)

  3. On the axes below, draw the graph of the population against time, showing the points at    and at  .  (2 marks)
      

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a.   
 
   

 

b.   

 
   
   

 

♦ Mean mark (c) 48%.

c. 

Financial Maths, STD2 F4 2021 HSC 26

Nina plans to invest $35 000 for 1 year. She is offered two different investment options.

Option A:  Interest is paid at 6% per annum compounded monthly.

Option B:  Interest is paid at % per annum simple interest.

  1. Calculate the future value of Nina's investment after 1 year if she chooses Option A.  (2 marks)

  2. Find the value of in Option B that would give Nina the same future value after 1 year as for Option A. Give your answer correct to two decimal places.  (2 marks)

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a.  
 

 

 
 

♦♦ Mean mark part (b) 36%.
b.  
 
 
   
   

Financial Maths, STD2 F1 2021 HSC 19

Adam purchased some office furniture five years ago. It depreciated by $2300 each year based on the straight-line method of depreciation. The salvage value of the furniture is now $7500.

Find the initial value of the office furniture.  (2 marks)

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Statistics, STD1 S3 2020 HSC 22

A group of students sat a test at the end of term. The number of lessons each student missed during the term and their score on the test are shown on the scatterplot.
 


 

  1. Describe the strength and direction of the linear association observed in this dataset.  (2 marks)

  2. Calculate the range of the test scores for the students who missed no lessons.  (1 mark)

  3. Draw a line of the best fit in the scatterplot above.  (1 mark)
  4. Meg did not sit the test. She missed five lessons.

     

    Use the line of the best fit drawn in part (c) to estimate Meg's score on this test. (1 mark)

  5. John also did not sit the test and he missed 16 lessons.

     

    Is it appropriate to use the line of the best fit to estimate his score on the test? Briefly explain your answer. (1 mark)

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a.   

b.   
 

c.   

d. 


 

e.   

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a.   

♦ Mean mark (a) 45%.
♦♦ Mean mark (b) 31%.

b.   
 

c.   

d. 


 

 

e.   

♦ Mean mark (e) 38%.

Algebra, STD1 A3 2020 HSC 19

Each year the number of fish in a pond is three times that of the year before.

  1. The table shows the number of fish in the pond for four years.

    Complete the table above showing the number of fish in 2021 and 2022.   (2 marks)
     

  2. Plot the points from the  table in part (a) on the grid.   (2 marks)
     
  3. Which model is more suitable for this dataset: linear or exponential? Briefly explain your answer.   (2 marks)

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a.   

b.   
       

c.     The more suitable model is exponential.

A linear dataset would graph a straight line which is not the case here.

An exponential curve can be used to graph populations that grow at an increasing rate, such as this example.

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a.        

b.  

c.     The more suitable model is exponential.

A linear dataset would graph a straight line which is not the case here.

An exponential curve can be used to graph populations that grow at an increasing rate, such as this example.

♦ Mean mark (c) 31%.

Financial Maths, STD2 F4 2020 HSC 21

The inflation rate over the year from January 2019 to January 2020 was 2%.

The cost of a school jumper in January 2020 was $122.

Calculate the cost of the jumper in January 2019 assuming that the only change in the cost of the jumper was due to inflation.   (2 marks)

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Algebra, STD2 A4 2020 HSC 19

A fence is to be built around the outside of a rectangular paddock. An internal fence is also to be built.

The side lengths of the paddock are metres and metres, as shown in the diagram.
 

 
A total of 900 metres of fencing is to be used. Therefore  .
 
The area, , in square metres, of the rectangular paddock is given by  .

The graph of this equation is shown.
  

  1. If the area of the paddock is , what is the largest possible value of ?   (1 mark)

  2. Find the values of and so that the area of the paddock is as large as possible.   (2 marks)

  3. Using your value from part (b), find the largest possible area of the paddock.   (1 mark)

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a.     

♦ Mean mark part (a) 39%.

 


 

b.   

♦♦ Mean mark part (b) 34%.

 

♦ Mean mark part (c) 40%.
c.   
   
   

Statistics, STD1 S3 2019 HSC 27

A set of bivariate data is collected by measuring the height and arm span of eight children. The graph shows a scatterplot of these measurements.
 

  1. On the graph, draw a line of best fit by eye.  (1 mark)

  2. Robert is a child from the class who was absent when the measurements were taken. He has an arm span of 147 cm. Using your line of best fit from part (a), estimate Robert’s height.  (1 mark)

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  1.   
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a.     
       

♦ Mean mark (a) 38%.

b.   

Financial Maths, STD2 F4 2019 HSC 37

A new car is bought for $24 950. Each year the value of the car is depreciated by the same percentage.

The table shows the value of the car, based on the declining-balance method of depreciation, for the first three years.

What is the value of the car at the end of 10 years?  (3 marks)

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Algebra, STD2 A2 2019 HSC 14 MC

Last Saturday, Luke had 165 followers on social media. Rhys had 537 followers. On average, Luke gains another 3 followers per day and Rhys loses 2 followers per day.

If    represents the number of days since last Saturday and    represents the number of followers, which pair of equations model this situation?

A. 

 
B.

 
C.

 
D.

 
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Financial Maths, STD2 F4 2019 HSC 13 MC

The graph show the future values over time of  , invested at three different rates of compound interest.
 


 

Which of the following correctly identifies each graph?

A. B.
C. D.
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Measurement, STD2 M6 2019 HSC 12 MC

An owl is 7 metres above ground level, in a tree. The owl sees a mouse on the ground at an angle of depression of 32°.

How far must the owl fly in a straight line to catch the mouse, assuming the mouse does not move?

  1.  3.7 m
  2.  5.9 m
  3.  8.3 m
  4.  13.2 m
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♦ Mean mark 36%.

 

 

Financial Maths, STD2 F4 2019 HSC 3 MC

Chris opens a bank account and deposits $1000 into it. Interest is paid at 3.5% per annum, compounding annually.

Assuming no further deposits or withdrawals are made, what will be the balance in the account at the end of two years?

  1. $1070.00
  2. $1071.23
  3. $1822.50
  4. $2070.00
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Financial Maths, STD2 F4 2018 HSC 26h

A car is purchased for $23 900.

The value of the car is depreciated by 11.5% each year using the declining-balance method.

What is the value of the car after three years?  (2 marks)

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Algebra, STD2 A4 2017 HSC 28e

A movie theatre has 200 seats. Each ticket currently costs $8.

The theatre owners are currently selling all 200 tickets for each session. They decide to increase the price of tickets to see if they can increase the income earned from each movie session.

It is assumed that for each one dollar increase in ticket price, there will be 10 fewer tickets sold.

A graph showing the relationship between an increase in ticket price and the income is shown below.
 


 

  1. What ticket price should be charged to maximise the income from a movie session?  (1 mark)

  2. What is the number of tickets sold when the income is maximised?  (1 mark)

  3. The cost to the theatre owners of running each session is $500 plus $2 per ticket sold.

     

    Calculate the profit earned by the theatre owners when the income earned from a session is maximised.  (2 marks)

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i.   

♦ Mean mark 50%.
 

 

ii.   

♦ Mean mark 45%.
 

 

 
 

 

iii.  
   

 

Measurement, STD2 M6 2017 HSC 26d

A sewer pipe needs to be placed into the ground so that it has a 2° angle of depression. The length of the pipe is 15 000 mm.
 


 

How much deeper should one end of the pipe be compared to the other end? Answer to the nearest mm.  (2 marks)

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Statistics, STD2 S4 2017 HSC 12 MC

Which of the data sets graphed below has the largest positive correlation coefficient value?
 

A.      B.     
C.      D.     
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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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Algebra, STD2 A2 2017 HSC 3 MC

The graph shows the relationship between infant mortality rate (deaths per 1000 live births) and life expectancy at birth (in years) for different countries.
 

What is the life expectancy at birth in a country which has an infant mortality rate of 60?

  1. 68 years
  2. 69 years
  3. 86 years
  4. 88 years
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Algebra, STD2 A2 2015 HSC 27c

Ariana’s parents have given her an interest‑free loan of $4800 to buy a car. She will pay them back by paying immediately and every month until she has repaid the loan in full.

After 18 months Ariana has paid back $1510, and after 36 months she has paid back $2770.

This information can be represented by the following equations.

  1. Graph these equations below and use to solve simultaneously for the values of and .   (2 marks)

         

  2. How many months will it take Ariana to repay the loan in full? (2 marks)

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i.

 

 

ii. 

♦ Mean mark 44%.

 

Financial Maths, STD2 F4 2015 HSC 26d

A family currently pays $320 for some groceries.

Assuming a constant annual inflation rate of 2.9%, calculate how much would be paid for the same groceries in 5 years’ time.  (2 marks)

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Financial Maths, STD2 F4 2015 HSC 17 MC

What amount must be invested now at 4% per annum, compounded quarterly, so that in five years it will have grown to  $60 000?

  1. $8919
  2. $11 156
  3. $49 173
  4. $49 316
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Measurement, STD2 M6 2015 HSC 9 MC

From the top of a cliff 67 metres above sea level, the angle of depression of a buoy is 42°.
  

 

How far is the buoy from the base of the cliff, to the nearest metre?

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♦ Mean mark 49%.
COMMENT: The angle of depression is a regularly examined concept. Make sure you know exactly what it refers to.

 

Financial Maths, STD2 F4 2005 HSC 26a

A sports car worth $150 000 is bought in December 2005.

In December each year, beginning in 2006, the value of the sports car is depreciated by 10% using the declining balance method of depreciation.

In which year will the depreciated value first fall below $120 000?   (2 marks)

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