SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Measurement, STD2 M6 2020 HSC 32

The diagram shows a regular decagon (ten-sided shape with all sides equal and all interior angles equal). The decagon has centre .
 

The perimeter of the shape is 80 cm.

By considering triangle , calculate the area of the ten-sided shape. Give your answer in square centimetres correct to one decimal place.  (4 marks)

Show Answers Only

²

Show Worked Solution

♦♦ Mean mark 33%.


 

 

 
  ²

Measurement, STD2 M6 2020 HSC 31

Mr Ali, Ms Brown and a group of students were camping at the site located at . Mr Ali walked with some of the students on a bearing of 035° for 7 km to location . Ms Brown, with the rest of the students, walked on a bearing of 100° for 9 km to location .
 


 

  1. Show that the angle is 65°.  (1 mark)

  2. Find the distance .  (2 marks)

  3. Find the bearing of Ms Brown's group from Mr Ali's group. Give your answer correct to the nearest degree.  (2 marks)

Show Answers Only
Show Worked Solution
a.   
   

 

b.   

Mean mark 53%.
 
 
 

 
c.

 

♦♦ Mean mark 22%.

 
   
 
   

 

 

Functions, 2ADV F1 2020 HSC 11

There are two tanks on a property, Tank and Tank . Initially, Tank holds 1000 litres of water and Tank B is empty.

  1.  Tank begins to lose water at a constant rate of 20 litres per minute. The volume of water in Tank is modelled by    where    is the volume in litres and    is the time in minutes from when the tank begins to lose water.   (1 mark)
     
    On the grid below, draw the graph of this model and label it as Tank .
     
       

  2. Tank remains empty until    when water is added to it at a constant rate of 30 litres per minute.

     

    By drawing a line on the grid (above), or otherwise, find the value of    when the two tanks contain the same volume of water.  (2 marks)

  3. Using the graphs drawn, or otherwise, find the value of    (where  ) when the total volume of water in the two tanks is 1000 litres.  (1 mark)

Show Answers Only
  1.   
      
Show Worked Solution

a.      
 


 

b.     
 

   

 
c.  


  

Algebra, STD2 A4 2020 HSC 24

There are two tanks on a property, Tank A and Tank B. Initially, Tank A holds 1000 litres of water and Tank B is empty.

  1. Tank A begins to lose water at a constant rate of 20 litres per minute.

     

    The volume of water in Tank A is modelled by    where is the volume in litres and    is the time in minutes from when the tank begins to lose water.

     

    On the grid below, draw the graph of this model and label it as Tank A.   (1 mark)
     

     

  2. Tank B remains empty until    when water is added to it at a constant rate of 30 litres per minute.
     By drawing a line on the grid (above), or otherwise, find the value of    when the two tanks contain the same volume of water.  (2 marks)

  3. Using the graphs drawn, or otherwise, find the value of    (where  ) when the total volume of water in the two tanks is 1000 litres.  (1 mark)

Show Answers Only
  1.   
      
Show Worked Solution

a.      
 

 

b.     
 

   

 
c.  

♦♦ Mean mark part (c) 22%.


  

Statistics, 2ADV S2 2020 HSC 27

A cricket is an insect. The male cricket produces a chirping sound.

A scientist wants to explore the relationship between the temperature in degrees Celsius and the number of cricket chirps heard in a 15-second time interval.

Once a day for 20 days, the scientist collects data. Based on the 20 data points, the scientist provides the information below.

  • A box-plot of the temperature data is shown.
     
       
  • The mean temperature in the dataset is 0.525°C below the median temperature in the dataset.
  • A total of 684 chirps was counted when collecting the 20 data points.

The scientist fits a least-squares regression line using the data , where is the temperature in degrees Celsius and is the number of chirps heard in a 15-second time interval. The equation of this line is

,

where is the slope of the regression,

The least-squares regression line passes through the point  , where    is the sample mean of the temperature data and    is the sample mean of the chirp data.

Calculate the number of chirps expected in a 15-second interval when the temperature is 19° Celsius. Give your answer correct to the nearest whole number.  (5 marks)

Show Answers Only

Show Worked Solution

♦ Mean mark 46%.

 

 

 
 

 

 

 

 
 

Trigonometry, 2ADV T1 2020 HSC 22

The diagram shows a regular decagon (ten-sided shape with all sides equal and all interior angles equal). The decagon has centre .
 

The perimeter of the shape is 80 cm.

By considering triangle , calculate the area of the ten-sided shape. Give your answer in square centimetres correct to one decimal place.  (4 marks)

Show Answers Only

²

Show Worked Solution


 

 

 
  ²

Financial Maths, STD2 F5 2020 HSC 34

Tina inherits $60 000 and invests it in an account earning interest at a rate of 0.5% per month. Each month, immediately after the interest has been paid, Tina withdraws $800.

The amount in the account immediately after the th withdrawal can be determined using the recurrence relation

,

where   and 

  1. Use the recurrence relation to find the amount of money in the account immediately after the third withdrawal.  (2 marks)

  2. Calculate the amount of interest earned in the first three months.  (2 marks)

Show Answers Only
Show Worked Solution

♦ Mean mark part (a) 41%.
a.   
 
 

 

b.   

♦♦ Mean mark part (b) 33%.


 

Trigonometry, 2ADV T1 2020 HSC 15

Mr Ali, Ms Brown and a group of students were camping at the site located at . Mr Ali walked with some of the students on a bearing of 035° for 7 km to location . Ms Brown, with the rest of the students, walked on a bearing of 100° for 9 km to location .
 


 

  1. Show that the angle is 65°.  (1 mark)

  2. Find the distance .  (2 marks)

  3. Find the bearing of Ms Brown's group from Mr Ali's group. Give your answer correct to the nearest degree.  (2 marks)

Show Answers Only
Show Worked Solution
a.   
   

 

b.   

 
 
 

 
c.

 
   
 
   

 

 

Statistics, 2ADV S3 2020 HSC 3 MC

John recently did a class test in each of three subjects. The class scores on each test were normally distributed.

The table shows the subjects and John's scores as well as the mean and standard deviation of the class scores on each test.
 

 
Relative to the rest of class, which row of the table below shows John's strongest subject and his weakest subject?
 

Show Answers Only

Show Worked Solution

 

Statistics, STD2 S5 2020 HSC 8 MC

John recently did a class test in each of three subjects. The class scores on each test were normally distributed.

The table shows the subjects and John's scores as well as the mean and standard deviation of the class scores on each test.

Relative to the rest of class, which row of the table below shows John's strongest subject and his weakest subject?

Show Answers Only

Show Worked Solution