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Complex Numbers, EXT2 N2 SM-Bank 10

The polynomial  , where    and  , can also be written as  , where    and  .

  1. State the relationship between and .  (1 mark)

  2. Determine the values of  and , given that    and  .  (3 marks)

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i.   

 

ii.   


 

 

 
 

 

GRAPHS, FUR2 2021 VCAA 2

z

Christy sells blocks of land at the housing estate.

Her pay is based on the number of blocks that she sells each week.

The maximum number of blocks sold each week is 20.

The graph below shows Christy's weekly pay, in dollars, for the number of blocks sold.

  1. What is the minimum number of blocks of land that Chirsty must sell to receive $6000 in one week?   (1 mark)

John also sells blocks of land. He is paid $1000 for each block that he sells.

  1. Write down all values for the number of blocks of land sold for which Christy and John will receive the same weekly pay.  (1 mark)
  2. John sells no more than three blocks of land for every five blocks of land sold by Christy.  (1 mark)
  3. Let    be the number of blocks that Christy sells.
  4. Let    be the number of blocks that John sells.
  5. Write the inequality, written as  in terms of  , that represents this situation.
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a.   
 

b.    
 

c.    

GRAPHS, FUR2 2021 VCAA 1

The graph below shows the height, in metres, of a drone flying above a new housing estate over a six-minute period of time.
 

  1. For what length of time, in minutes, was the height of the drone a least 50 m?   (1 mark)
  2. What was the average rate of change in the height of the drone, in metres per minute, in the first two minutes?  (1 mark)
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a.   
 

b.   


  

GEOMETRY, FUR2 2021 VCAA 1

The game of squash is played with a special ball that has a radius of 2 cm.

  1. Show that the volume of one squash ball, rounded to two decimal places, is 33.51 cm3.  (1 mark)

Squash balls may be sold in cube-shaped boxes.

Each box contains one ball and has a side length of 4.1 cm, as shown in the diagram below.
 

  1. Calculate the empty space, in cubic centimetres, that surrounds the ball in the box.
  2. Round your answer to two decimal places.   (1 mark)
  3. Calculate the total surface area, in square centimetres, of one box.   (1 mark)
  4. Retail shops store the cube-shaped boxes in a space within a display unit.
  5. The space has a length of 17.0 cm and a width of 12.5 cm. Due to the presence of a shelf above, there is a maximum height of 8.5 cm available. This is shown in the diagram below.
     

     

  1. Calculate the maximum number of cube-shaped boxes that can fit into the space within the display unit.   (1 mark)
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a.  
   
   
   

 

b. 

     
 

 

c.  
   

 

d. 


 

 

NETWORKS, FUR2 2021 VCAA 1

Maggie's house has five rooms, and , and eight doors.

The floor plan of these rooms and doors is shown below. The outside area, , is shown shaded on the floor plan.
 

The floor plan is represented by the graph below.

On this graph, vertices represent the rooms and the outside area. Edges represent direct access to the rooms through the doors.

One edge is missing from the graph.
 

  1. On the graph above, draw the missing edge.   (1 mark)

  2. What is the degree of vertex ?   (1 mark)

  3. Maggie hires a cleaner to clean the house.
  4. It is possible for the cleaner to enter the house from the outside area, , and walk through each room only once, cleaning each room as he goes and finishing in the outside area, .
  5.  i. Complete the following to show one possible route that the cleaner could take.   (1 mark)

        
         
    ii. What is the mathematical term for such a journey?   (1 mark)

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  1.  
  3.  i.
  4. ii.
Show Worked Solution

a.

b. 
 

c.i. 

c.ii. 

MATRICES, FUR2 2021 VCAA 2

The main computer system in Elena's office has broken down.

The five staff members, Alex (), Brie (), Chai (), Dex () and Elena (), are having problems sending information to each other.

Matrix below shows the available communication links between the staff members.

In this matrix:

  • the '1' in row , column indicates that Alex can send information to Brie
  • the '0' in row , column indicates that Dex cannot send information to Chai.
  1. Which two staff members can send information directly to each other?   (1 mark)

  2. Elena needs to send documents to Chai.
  3. What is the sequence of communication links that will successfully get the information from Elena to Chai?   (1 mark)

  4. Matrix  below is the square of and shows the number of two-step communication links between each pair of staff members.
     

    Only one pair of individuals has two different two-step communication links.

  5. List each two-step communication link for this pair.   (1 mark)

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a.   


 

b.   
 

c.   

MATRICES, FUR2 2021 VCAA 1

Elena imports three brands of olive oil: Carmani () Linelli () and Ohana ().

The number of 1 litre bottles of these oils sold in January 2021 is shown in matrix below.

  1. What is the order of matrix ?   (1 mark)

  2. Elena expected that in February 2021 the sales of all three brands of olive oil would increase by 5%.
  3. She multiplied matrix by a scalar value, , to determine the expected volume of sales for February.
  4. What is the value of the scalar .   (1 mark)

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a.     
 

b.     

 

CORE, FUR2 2021 VCAA 1

In the sport of heptathlon, athletes compete in seven events.

These events are the 100 m hurdles, high jump, shot-put, javelin, 200 m run, 800 m run and long jump.

Fifteen female athletes competed to qualify for the heptathlon at the Olympic Games.

Their results for three of the heptathlon events – high jump, shot-put and javelin – are shown in Table 1

  1. Write down the number of numerical variables in Table 1.   (1 mark)

  2. Complete Table 2 below by calculating the mean height jumped for the high jump, in metres, by the 15 athletes. Write your answer in the space provided in the table.   (1 mark)

  3. In shot-put, athletes throw a heavy spherical ball (a shot) as far as they can. Athlete number six, Jamilia, threw the shot 14.50 m.
  4. Calculate Jamilia's standardised score (). Round your answer to one decimal place.   (1 mark)

  5. In the qualifying competition, the heights jumped in the high jump are expected to be approximately normally distributed.
  6. Chara's jump in this competition would give her a standardised score of 
  7. Use the 68–95–99.7% rule to calculate the percentage of athletes who would be expected to jump higher than Chara in the qualifying competition.   (1 mark)

  8. The boxplot below was constructed to show the distribution of high jump heights for all 15 athletes in the qualifying competition.

 

  1. Explain why the boxplot has no whisker at its upper end.   (1 mark)

  2. For the javelin qualifying competition (refer to Table 1), another boxplot is used to display the distribution of athlete's results.
  3. An athlete whose result is displayed as an outlier at the upper end of the plot is considered to be a potential medal winner in the event.
  4. What is the minimum distance that an athlete needs to throw the javelin to be considered a potential medal winner?   (2 marks)

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a.   

 
  

b.     


 

c.  
   
   

 
d. 
 

e. 


 

f. 

 
 

 

GRAPHS, FUR1 2021 VCAA 1 MC

The graph below shows the average number of sunlight hours per day for each month of a particular year.
 

The number of months for which the average number of sunlight hours per day was recorded as being below four hours is 

  1. 2
  2. 3
  3. 4
  4. 5
  5. 6
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NETWORKS, FUR1 2021 VCAA 2 MC

Five friends ate fruit for morning tea.

The bipartite graph below shows which types of fruit each friend ate.
 

Which one of the following statements is not true?

  1. Only Lee ate pear.
  2. Eric and Kai each ate apple.
  3. Van ate only strawberry.
  4. Quinn and Kai each ate banana.
  5. Orange was the most eaten type of fruit.
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CORE, FUR1 2021 VCAA 18-19 MC

Deepa invests $500 000 in an annuity that provides an annual payment of $44 970.55

Interest is calculated annually.

The first five lines of the amortisation table are shown below.
 

Part 1

The principal reduction associated with payment number 3 is

  1. $17 962.40
  2. $25 969.37
  3. $27 008.15
  4. $28 088.47
  5. $44 970.55

 

Part 2

The number of years, in total, for which Deepa will receive the regular payment of is closest to

  1. 12
  2. 15
  3. 16
  4. 18
  5. 20
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♦ Mean mark part (2) 44%.


 

 

Measurement, STD1 M4 2021 HSC 23

Sue walks along a trail, starting at 7 am and finishing at 10 am. The travel graph shows Sue’s journey from the start to the finish. The journey has been broken into six sections, , , , , and .
 

     

  1. On two occasions Sue stopped to rest. In which sections of the journey did Sue rest?  (1 mark)

  2. In which section of the journey did Sue travel fastest? Justify your answer.  (2 marks)

  3. Kim walked along the same trail, also starting at 7 am and finishing at 10 am. Kim walked at a constant speed for the entire journey.
  4. By showing Kim’s journey on the grid above, determine between what times Sue was ahead of Kim.  (3 marks)

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  3.  
     
       
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a.   

♦ Mean mark part (b) 44%.

 

b.   

♦♦ Mean mark part (c) 30%.

c.

NETWORKS, FUR2 2020 VCAA 1

The Sunny Coast Cricket Club has five new players join its team: Alex, Bo, Cameron, Dale and Emerson.

The graph below shows the players who have played cricket together before joining the team.

For example, the edge between Alex and Bo shows that they have previously played cricket together.
 

  1. How many of these players had Emerson played cricket with before joining the team?   (1 mark)

  2. Who had played cricket with both Alex and Bo before joining the team?   (1 mark)

  3. During the season, another new player, Finn, joined the team.

      

    Finn had not played cricket with any of these players before.

      

    Represent this information on the graph above.   (1 mark)

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  3.  
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a. 
  

b. 

 

c.  

CORE, FUR2 2020 VCAA 7

Samuel owns a printing machine.

The printing machine is depreciated in value by Samuel using flat rate depreciation.

The value of the machine, in dollars, after years, , can be modelled by the recurrence relation

  1. By what amount, in dollars, does the value of the machine decrease each year?   (1 mark)

  2. Showing recursive calculations, determine the value of the machine, in dollars, after two years.   (1 mark)

  3. What annual flat rate percentage of depreciation is used by Samuel?   (1 mark)

  4. The value of the machine, in dollars, after years, , could also be determined using a rule of the form .

     

    Write down this rule for .   (1 mark)

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a.
  

b.  
 

 

c.  
   

 

♦ Mean mark part d. 44%.

d. 

CORE, FUR2 2020 VCAA 4

The age, in years, body density, in kilograms per litre, and weight, in kilograms, of a sample of 12 men aged 23 to 25 years are shown in the table below.
 

          Age       
(years)

        Body density        
(kg/litre)

        Weight        
(kg)
  23 1.07 70.1
  23 1.07 90.4
  23 1.08 73.2
  23 1.08 85.0
  24 1.03 84.3
  24 1.05 95.6
  24 1.07 71.7
  24 1.06 95.0
  25 1.07 80.2
  25 1.09 87.4
  25 1.02 94.9
  25 1.09 65.3
     
  1. For these 12 men, determine
  2.  i. their median age, in years.   (1 mark)

  3. ii. the mean of their body density, in kilograms per litre.   (1 mark)

  4. A least squares line is to be fitted to the data with the aim of predicting body density from weight.
  5.  i. Name the explanatory variable for this least squares line.   (1 mark)

  6. ii. Determine the slope of this least squares line.
  7.     Round your answer to three significant figures.   (1 mark)

  8. What percentage of the variation in body density can be explained by the variation in weight?
  9. Round your answer to the nearest percentage.   (1 mark)

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  1.  i.
  2. ii.
  3. i.
  4. ii.
Show Worked Solution
a.i.    
 
   
   

 

a.ii.  
   

 

b.i.   

♦ Mean mark b.ii. 29%.
MARKER’S COMMENT: Most students did not round correctly.

b.ii.   

 

c.  
 

 

CORE, FUR2 2020 VCAA 3

In a study of the association between BMI and neck size, 250 men were grouped by neck size (below average, average and above average) and their BMI recorded.

Five-number summaries describing the distribution of BMI for each group are displayed in the table below along with the group size.

The associated boxplots are shown below the table.
 

  1. What percentage of these 250 men are classified as having a below average neck size?   (1 mark)

  2. What is the interquartile range (IQR) of BMI for the men with an average neck size?   (1 mark)

  3. People with a BMI of 30 or more are classified as being obese.
  4. Using this criterion, how many of these 250 men would be classified as obese? Assume that the BMI values were all rounded to one decimal place.   (1 mark)

  5. Do the boxplots support the contention that BMI is associated with neck size? Refer to the values of an appropriate statistic in your response.   (2 marks)

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a.   
   

 

b.   
   

 

c.   

♦♦ Mean mark part c. 22%.
COMMENT: Many students incorrectly counted the two “above average” outliers twice.

 

d.   

♦ Mean mark 49%.
MARKER’S COMMENT: General statement of change = 1 mark. Median or IQR values need to be quoted directly for the second mark.

CORE, FUR2 2020 VCAA 2

The neck size, in centimetres, of 250 men was recorded and displayed in the dot plot below.
 

  1. Write down the modal neck size, in centimetres, for these 250 men.   (1 mark)

  2. Assume that this sample of 250 men has been drawn at random from a population of men whose neck size is normally distributed with a mean of 38 cm and a standard deviation of 2.3 cm.
  3.  i. How many of these 250 men are expected to have a neck size that is more than three standard deviations above or below the mean? Round your answer to the nearest whole number.   (1 mark)

  4. ii. How many of these 250 men actually have a neck size that is more than three standard deviations above or below the mean?   (1 mark)

  5. The five-number summary for this sample of neck sizes, in centimetres, is given below.
     

    Use the five-number summary to construct a boxplot, showing any outliers if appropriate, on the grid below.   (2 marks)

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a.   

b.i.   

b.ii.

c.   

Show Worked Solution

a.   

 

♦ Mean mark part b.i. 40%.
b.i.  
   
   

 

♦ Mean mark part b.ii. 42%.
b.ii.  
 
   

 

 

c.   

 

GRAPHS, FUR1 2020 VCAA 2 MC

At a school concert, the entry fee for adults was different from the entry fee for children.

The entry fee for three adults and four children was $67.00

The entry fee for two adults and five children was $57.50

Let    be the entry fee for an adult.

Let    be the entry fee for a child.

A pair of simultaneous equations that could be used to represent the situation above is

A.   B.  
 

 

  

 
C.   D.  
 

 

  

 
E.      
 

 

    
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CORE, FUR1 2020 VCAA 10-12 MC

The data in Table 2 was collected in a study of the association between the variables frequency of nightmares (low, high) and snores (no, yes).
 


 

Part 1

The variables in this study, frequency of nightmares (low, high) and snores (no, yes), are

  1. ordinal and nominal respectively.
  2. nominal and ordinal respectively.
  3. both numerical.
  4. both ordinal.
  5. both nominal.

 
Part 2

The percentage of participants in the study who did not snore is closest to

  1. 42.0%
  2. 43.5%
  3. 49.7%
  4. 52.2%
  5. 56.5%

 
Part 3

Of those people in the study who did snore, the percentage who have a high frequency of nightmares is closest to

  1.   7.5%
  2. 17.1%
  3. 47.8%
  4. 52.2%
  5. 58.0%
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Part 1


 

Part 2

 
 


 

Part 3

 
 

CORE, FUR1 2020 VCAA 1-3 MC

The times between successive nerve impulses (time), in milliseconds, were recorded.

Table 1 shows the mean and the five-number summary calculated using 800 recorded data values.
 


 

Part 1

The difference, in milliseconds, between the mean time and the median time is

  1.  10
  2.  70
  3.  150
  4.  220
  5.  230

 
Part 2

Of these 800 times, the number of times that are longer than 300 milliseconds is closest to

  1. 20
  2. 25
  3. 75
  4. 200
  5. 400

 
Part 3

The shape of the distribution of these 800 times is best described as

  1. approximately symmetric.
  2. positively skewed.
  3. positively skewed with one or more outliers.
  4. negatively skewed.
  5. negatively skewed with one or more outliers.
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Part 1

 


 

Part 2


 

Part 3

♦ Mean mark 50%.

 
 

 

Complex Numbers, EXT2 N1 2004 HSC 2b

Let    and  .

  1. Find  , in the form  .   (1 mark)

  2. Express in modulus-argument form.   (3 marks)

  3. Given that has the modulus-argument form
     
         .
     
    find the modulus-argument form of  .   (1 mark)

  4. Hence find the exact value of     (1 mark)

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i.    
   
   
   

 

ii.  
 

 

iii.  
 
   

 

iv. 

 

Complex Numbers, EXT2 N2 EQ-Bank 1

  is a root of the equation  .

  1. Express    in exponential form.  (2 marks)

  2. Find the value of .  (1 mark)

  3. Find the other 4 roots of the equation in exponential form.  (3 marks)

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i.   

 

ii.   
 
   
   

 

 

iii.   


 

 

Complex Numbers, EXT2 N1 2005 HSC 2b

Let  .

  1. Express    in modulus-argument form.   (2 marks)

  2. Express    in modulus-argument form.   (2 marks)

  3. Hence express    in the form  .   (1 mark)

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i.   
 

 

 

ii.  
   
   

 

iii.  
   
   

Complex Numbers, EXT2 N1 2020 HSC 13d

  1. Show that for any integer ,  .   (1 mark)

  2. By expanding    show that
     
       .   (3 marks)

  3. Hence, or otherwise, find  .   (2 marks)

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i.     
   
   

 

ii.   
   

 


 

 

iii.   
   
   
   
   

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 A4 2020 HSC 33

The graph shows the number of bacteria, , at time minutes. Initially (when ) the number of bacteria is 1000.
 


 

  1. Find the number of bacteria at 40 minutes.   (1 mark)

  2. The number of bacteria can be modelled by the equation  , where and are constants.
    Use the guess and check method to find, to two decimal places, an upper and lower estimate for the value of . The upper and lower estimates must differ by 0.01. (2 marks)

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a.   


 

b.   

♦♦♦ Mean mark 14%.


 

Statistics, EXT1 S1 2020 HSC 12b

When a particular biased coin is tossed, the probability of obtaining a head is .

This coin is tossed 100 times.

Let be the random variable representing the number of heads obtained. This random variable will have a binomial distribution.

  1. Find the expected value, .  (1 mark)

  2. By finding the variance, , show that the standard deviation of is approximately 5.  (1 mark)

  3. By using a normal approximation, find the approximate probability that is between 55 and 65.  (1 mark)

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i.   

 
 

 

ii.   
   
   

 

 

 

iii.   
   

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)

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  1.   
      
Show Worked Solution

a.      
 


 

b.     
 

   

 
c.  


  

Calculus, 2ADV C3 2020 HSC 21

Hot tea is poured into a cup. The temperature of tea can be modelled by  , where is the temperature of the tea, in degrees Celsius, minutes after it is poured.

  1. What is the temperature of the tea 4 minutes after it has been poured?  (1 mark)

  2. At what rate is the tea cooling 4 minutes after it has been poured?  (2 marks)

  3. How long after the tea is poured will it take for its temperature to reach 55°C?  (3 marks)

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a.   
   
   

 

b.   
   

 

 
 

 

c.   

♦ Mean mark part (c) 44%.
 
 

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)

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a.   
   

 

b.   

 
 
 

 
c.

 
   
 
   

 

 

NETWORKS, FUR2-NHT 2019 VCAA 1

A zoo has an entrance, a cafe and nine animal exhibits: bears , elephants , giraffes , lions , monkeys , penguins , seals , tigers and zebras .

The edges on the graph below represent the paths between the entrance, the cafe and the animal exhibits. The numbers on each edge represent the length, in metres, along that path. Visitors to the zoo can use only these paths to travel around the zoo.
  

 
 

  1. What is the shortest distance, in metres, between the entrance and the seal exhibit ?   (1 mark)

  2. Freddy is a visitor to the zoo. He wishes to visit the cafe and each animal exhibit just once, starting and ending at the entrance.
  3. i. What is the mathematical term used to describe this route?   (1 mark)

  4. ii. Draw one possible route that Freddy may take on the graph below.   (1 mark)


 

A reptile exhibit will be added to the zoo.

A new path of length 20 m will be built between the reptile exhibit and the giraffe exhibit .

A second new path, of length 35 m, will be built between the reptile exhibit and the cafe.

  1. Complete the graph below with the new reptile exhibit and the two new paths added. Label the new vertex and write the distances on the new edges.   (1 mark)

     


 

  1. The new paths reduce the minimum distance that visitors have to walk between the giraffe exhibit and the cafe.

     

    By how many metres will these new paths reduce the minimum distance between the giraffe exhibit and the cafe?   (1 mark)

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  1.  
  2. i. 
    ii. 
  3.  
  4.  
Show Worked Solution

a.   
 

b.i.   
 

b.ii.  

 

c.  

 

d. 


 

MATRICES, FUR2-NHT 2019 VCAA 1

A total of six residents from two towns will be competing at the International Games.

Matrix , shown below, contains the number of male and the number of female athletes competing from the towns of Gillen and Haldaw .

 

  1. How many of these athletes are residents of Haldaw?   (1 mark)

Each of the six athletes will compete in one event: table tennis, running or basketball.

Matrices and , shown below, contain the number of male and female athletes from each town who will compete in table tennis and running respectively.
 

            Table tennis                        Running             
 

 

  1. Matrix contains the number of male and female athletes from each town who will compete in basketball.

     

    Complete matrix below.   (1 mark)

Matrix contains the cost of one uniform, in dollars, for each of the three events: table tennis , running and basketball .

    1. For which event will the total cost of uniforms for the athletes be $1030?   (1 mark)

    2. Write a matrix calculation, that includes matrix , to show that the total cost of uniforms for the event named in part c.i. is contained in the matrix answer of [1030].   (1 mark)

  1. Matrix and matrix are two new matrices where    and:
  • matrix is a    matrix
  • element total cost of uniforms for all female athletes from Gillen
  • element total cost of uniforms for all female athletes from Haldaw
  • element total cost of uniforms for all male athletes from Gillen
  • element total cost of uniforms for all male athletes from Haldaw
     
  1. Complete matrix with the missing values.   (1 mark)

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  1.  
  2.  
  3. i. 
    ii.
  4.  
Show Worked Solution

a. 
 

b. 
 

c.i. 
 

c.ii. 
 

d. 

CORE, FUR2-NHT 2019 VCAA 6

Marlon plays guitar in a band.

He paid $3264 for a new guitar.

The value of Marlon's guitar will be depreciated by a fixed amount for each concert that he plays.

After 25 concerts, the value of the guitar will have decreased by $200.

  1. What will be the value of Marlon's guitar after 25 concerts?   (1 mark)

  2. Write a calculation that shows that the value of Marlon's guitar will depreciate by $8 per concert.   (1 mark)

  3. The value of Marlon's guitar after concerts, , can be determined using a rule.

     

    Complete the rule below by writing the appropriate numbers in the boxes provided.   (1 mark)

     
                – ×
     

  4. The value of the guitar continues to be depreciated by $8 per concert.

     

    After how many concerts will the value of Marlon's guitar first fall below $2500?   (2 marks)

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a.   
 

 

b.   
 

c.   
 

d.   

 

 

CORE, FUR2-NHT 2019 VCAA 1

The table below displays the average sleep time, in hours, for a sample of 19 types of mammals.
 

  1. Which of the two variables, type of mammal or average sleep time, is a nominal variable?   (1 mark)

  2. Determine the mean and standard deviation of the variable average sleep time for this sample of mammals.
  3. Round your answer to one decimal place.   (1 mark)

  4. The average sleep time for a human is eight hours.
  5. What percentage of this sample of mammals has an average sleep time that is less than the average sleep time for a human.
  6. Round your answer to one decimal place.   (1 mark)

  7. The sample is increase in size by adding in the average sleep time of the little brown bat.
  8. Its average sleep time is 19.9 hours.
  9. By how many many hours will the range for average sleep time increase when the average sleep time for the little brown bat is added to the sample?   (1 mark)

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  2.  

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a.   

 
b.   


 

c.   
 
 

 

d.   
 

GRAPHS, FUR1-NHT 2019 VCAA 1 MC

The graph below shows the temperature, in degrees Celsius, over 24 hours.
 


 

The difference between the highest and lowest temperatures on this day, in degrees Celsius, is closest to

  1. 16
  2. 20
  3. 24
  4. 28
  5. 32
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GRAPHS, FUR2 2019 VCAA 1

The graph below shows the membership numbers of the Wombatong Rural Women’s Association each year for the years 2008–2018.
 


 

  1. How many members were there in 2009?  (1 mark)
    1. Show that the average rate of change of membership numbers from 2013 to 2018 was − 6 members per year.  (1 mark)
    2. If the change in membership numbers continues at this rate, how many members will there be in 2021?  (1 mark)
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a. 

 

b.i.  
 
 
   

 

b.ii.