SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Number, NAP-L4-NC01

Mike is downloading a complete hard drive onto his new computer.

It should take 24 minutes to download the full hard drive.

Mike loses his internet connection when    of the hard drive is downloaded.

How many more minutes are needed for Mike to complete the download?

 
 
 
 
Show Answers Only

Show Worked Solution

 

Calculus, MET1 2019 VCAA 9

Consider the functions    and 

  1. State the rule of .  (1 mark) 

  2. Find the values of for which the derivative of is a negative.  (2 marks)

  3. State the rule of .  (1 mark)

  4. Solve  .  (2 marks)

  5. Find the coordinates of the stationary point of the graph of .  (2 marks)

  6. State the number of solutions to  .  (1 mark)

Show Answers Only
Show Worked Solution

a.   
 

b.   

 
c.   
 

d.   

 


 

e.   
   

 

 

 

 

f.   


 


 

Algebra, MET1 2019 VCAA 8

The function    is a polynomial function of degree 4. Part of the graph of    is shown below.

The graph of    touches the -axis at the origin.
 


 

  1. Find the rule of  .   (1 mark) 

Let    be a function with the same rule as  .

Let  , where    is the maximal domain of  .

  1. State  .   (1 mark)

  2. State the range of  .   (2 marks)

Show Answers Only
Show Worked Solution
a.   
   

 

 

b.   
   

 

c.   
   
   

  


 

Measurement, NAP-L4-CA11

This is part of a timetable for the ferry from Apollo Road to West End.
 

 
Skye is catching a ferry from Apollo Road to West End.

She catches the first ferry that leaves Apollo Road after 1 pm.

At what time will Skye arrive at West End?

12:41 pm 1:09 pm 1:12 pm 1:41 pm 2:41 pm
 
 
 
 
 
Show Answers Only

Show Worked Solution

Measurement, NAP-L3-CA17

This is part of a timetable for the ferry from Apollo Road to West End.
 

 
Skye is catching a ferry from Apollo Road to West End.

She catches the first ferry that leaves Apollo Road after 1 pm.

At what time will Skye arrive at West End?

12:41 pm 1:09 pm 1:12 pm 1:41 pm 2:41 pm
 
 
 
 
 
Show Answers Only

Show Worked Solution

Complex Numbers, EXT2 N2 2019 HSC 16b

Let  , where    and    are real numbers.

The roots of    are  .

It is given that    and  .

  1. Show that  .  (3 marks)

  2. The diagram shows the position of  .
     


 

On the diagram, accurately show all possible positions of  .  (2 marks)

Show Answers Only
Show Worked Solution

i.   

♦♦ Mean mark part (i) 26%.

 

 

ii.   
 
 
 
 

 

♦♦♦ Mean mark part (ii) 10%.

Combinatorics, EXT1′ S1 2019 HSC 10 MC

An access code consists of 4 digits chosen from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The code will only work if the digits are entered in the correct order.

Some access codes contain exactly two different digits, for example 3377 or 5155.

How many such access codes can be made using exactly two different digits?

  1. 630
  2. 900
  3. 1080
  4. 2160
Show Answers Only

Show Worked Solution

 

 

 

 

Calculus, EXT1 C2 2019 HSC 14c

The diagram shows the two curves    and  , where    and  . The two curves have a common tangent at where  .
 


 

  1. Explain why   .  (1 mark)

  2. Show that  .  (2 marks)

  3. Hence, or otherwise, find    in terms of  .  (2 marks)

Show Answers Only
Show Worked Solution
i.   
 
 
 

 

♦ Mean mark part (i) 47%.

 

ii.   

♦♦♦ Mean mark part (ii) 19%.

 

iii.   

 
 
 
   
 

 

♦♦ Mean mark part (iii) 21%.

 
 

Algebra, STD1 A2 2019 HSC 33

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)

Show Answers Only
Show Worked Solution

a.   

♦♦♦ Mean mark part (a) 8%.

 

b.   

♦♦ Mean mark part (b) 16%.

 

 

 

 

Financial Maths, STD1 F3 2019 HSC 32

Ashley has a credit card with the following conditions:

  • There is no interest-free period.
  • Interest is charged at the end of each month at 18.25% per annum, compounding daily, from the purchase date (included) to the last day of the month (included).

Ashley's credit card statement for April is shown, with some figures missing.

The minimum payment is calculated as 2% of the closing balance on 30 April.

Calculate the minimum payment.  (3 marks)

Show Answers Only

Show Worked Solution
 

♦♦♦ Mean mark 12%.

 

 

 

 
 

Calculus, 2ADV C4 2019 HSC 16c

The diagram shows the region  , bounded by the curve  , where  , the -axis and the tangent to the curve at the point  .
 

  1. Show that the tangent to the curve at    meets the -axis at
     
         .  (2 marks)

  2. Using the result of part (i), or otherwise, show that the area of the region    is
     
         .  (2 marks)

  3. Find the exact value of    for which the area of    is a maximum.  (3 marks)

Show Answers Only
Show Worked Solution
i.   
 

 

♦♦ Mean mark part (i) 31%.

 

 

 

ii.   

♦♦♦ Mean mark part (ii) 21%.

 


 

`= 1/(r + 1) – 1/2(1 – (r – 1)/r)“
 
 
 
 

 

iii.   
 
   
   
   

 

♦♦ Mean mark part (iii) 23%.

 
 

 

 
 

 

Financial Maths, 2ADV M1 2019 HSC 16a

A person wins $1 000 000 in a competition and decides to invest this money in an account that earns interest at 6% per annum compounded quarterly. The person decides to withdraw $80 000 from this account at the end of every fourth quarter. Let    be the amount remaining in the account after the th withdrawal.

  1.  Show that the amount remaining in the account after the withdrawal at the end of the eighth quarter is

     

    .  (2 marks)

  2.  For how many years can the full amount of $80 000 be withdrawn?  (3 marks)

Show Answers Only
Show Worked Solution

i. 

 
 
   
   
   

 

ii.   
   
 
   
   

♦♦♦ Mean mark part (ii) 19%.

 

 

Networks, STD2 N3 2019 HSC 40

A museum is planning an exhibition using five rooms.

The museum manager draws a network to help plan the exhibition. The vertices , , , and represent the five rooms. The number on the edges represent the maximum number of people per hour who can pass through the security checkpoints between the rooms.
 


 

  1. What is the capacity of the cut shown?  (1 mark)

  2. The museum manager is planning for a maximum of 240 visitors to pass through the exhibition each hour. By using the 'minimum cut-maximum flow' theorem, the manager determines that the plan does not provide sufficient flow capacity.

     

    Draw the minimum cut onto the network below and recommend a change that the manager could make to one or more security checkpoints to increase the flow capacity to 240 visitors per hour.   (2 marks)
     
       

Show Answers Only
  2.   

Show Worked Solution
a.   
   

♦♦ Mean mark 32%.
COMMENT: In part (a), edge BC flows from the exit to the entry and is therefore not counted.

b.   

 

♦♦♦ Mean mark 19%.
COMMENT: In part (b), edge BC now flows from entry to exit in the new “minimum” cut and is counted.

Statistics, STD2 S5 2019 HSC 15 MC

The scores on an examination are normally distributed with a mean of 70 and a standard deviation of 6. Michael received a score on the examination between the lower quartile and the upper quartile of the scores.

Which shaded region most accurately represents where Michael's score lies?
 

A. B.
C. D.
Show Answers Only

Show Worked Solution

σ

♦♦♦ Mean mark 17%.

Statistics, EXT1 S1 2012 MET2 3

Steve and Jess are two students who have agreed to take part in a psychology experiment. Each has to answer several sets of multiple-choice questions. Each set has the same number of questions, , where is a number greater than 20. For each question there are four possible options A, B, C or D, of which only one is correct.

  1. Steve decides to guess the answer to every question, so that for each question he chooses A, B, C or D at random.

     

    Let the random variable be the number of questions that Steve answers correctly in a particular set.

    1. What is the probability that Steve will answer the first three questions of this set correctly?  (1 mark)

    2. Use the fact that the variance of is to show that the value of is 25.  (1 mark)

  1. The probability that Jess will answer any question correctly, independently of her answer to any other question, is  . Let the random variable be the number of questions that Jess answers correctly in any set of 25.

    If   , show that the value of  .  (2 marks)

Show Answers Only

a.i. 

a.ii. 

b. 

Show Worked Solution
a.i.   
   

 

a.ii.   
 
 
 

 

b.  

♦♦♦ Mean mark part (c) 19%.

 

Calculus, MET1 2018 VCAA 9

Consider a part of the graph of  , as shown below.

  1.  i. Given that  , evaluate    when is a positive even integer or 0.
      
    Give your answer in simplest form.   (2 marks)

    ii. Given that  , evaluate    when is a positive odd integer.
    Give your answer in simplest form.   (1 mark)

  2.  
  3. Find the equation of the tangent to    at the point  .   (2 marks)

  4. The translation maps the graph of    onto the graph of  , where
  6. and is a real constant.
  7. State the value of .   (1 mark)

  8. Let    and  .
    The line is the tangent to the graph of at the point and the line is the tangent to the graph of at , as shown in the diagram below.
     
         
    Find the total area of the shaded regions shown in the diagram above.   (2 marks)

Show Answers Only
  1.  i.
    ii.
Show Worked Solution

a.i. 

♦♦ Mean mark 31%.

 

a.ii.

♦♦♦ Mean mark 19%.

 

b.   
 

 

♦ Mean mark part (b) 49%.

 
 

 

 

 

♦♦ Mean mark part (c) 34%.

c.   
   

 

 

d.   

♦♦♦ Mean mark 7%.

 

π

 


 

Calculus, SPEC2 2011 VCAA 16 MC

The gradient of the the perpendicular line to a curve at any point    is twice the gradient of the line joining and the point  .

The coordinate of points on the curve satisfy the differential equation

Show Answers Only

Show Worked Solution

♦♦♦ Mean mark 25%.
COMMENT: Easily the lowest mean mark in the 2011 MC section.

 

Graphs, SPEC1 2012 VCAA 10

Consider the functions with rules    and 

    1. Find the maximal domain of     (1 mark)

    2. Find the maximal domain of     (1 mark)

    3. Find the largest set of values of    for which    is defined.   (1 mark)

  2. Given that    and that  , evaluate 

     

    Give your answer in the form     (3 marks)

Show Answers Only
Show Worked Solution

a.i.   

 
 

 
a.ii.   

♦♦ Mean mark part (a)(ii) 33%.

 
 
 

 

a.iii. 

♦♦ Mean mark part (a)(iii) 26%.

 
 

 

b.   
   

 

♦♦♦ Mean mark part (b) 20%.

 
 

Vectors, SPEC2 2017 VCAA 5

On a particular morning, the position vectors of a boat and a jet ski on a lake    minutes after they have started moving are given by    and    respectively for  , where distances are measured in kilometres. The boat and the jet ski start moving at the same time. The graphs of their paths are shown below.

  1. On the diagram above, mark the initial positions of the boat and the jet ski, clearly identifying each of them. Use arrows to show the directions in which they move.   (2 marks)

    1. Find the first time for    when the speeds of the boat and the jet ski are the same.   (2 marks)

    2. State the coordinates of the boat at this time.   (1 mark)

    1. Write down an expression for the distance between the jet ski and the boat at any time .   (1 mark)

    2. Find the minimum distance separating the boat and the jet ski. Give your answer in kilometres, correct to two decimal places.   (1 mark)

  4. On another morning, the boat’s position vector remained the same but the jet skier considered starting from a different location with a new position vector given by  , where is a real constant. Both vessels are to start at the same time.
    Assuming the vessels would collide shortly after starting, find the time of the collision and the value of .   (3 marks)

Show Answers Only
  1.  
  2.   
  3.   
Show Worked Solution
a.   


  

 

b.i.   
 
   

 

♦ Mean mark (b)(ii) 48%.

b.ii.   
   

 

c.i.   
 
   

 

c.ii. 

♦♦♦ Mean mark part (c)(ii) 15%.

 

d.   

 
 
 
 

 

♦ Mean mark part (d) 41%.
 

 

 
 

 

Complex Numbers, SPEC2 2017 VCAA 4

  1. Express    in polar form.  (1 mark)

  2. Show that the roots of    are    and  .  (1 mark)

  3. Express the roots of    in terms of  .  (1 mark)

  4. Show that the cartesian form of the relation    is    (2 marks)

  5. Sketch the line represented by    and plot the roots of    on the Argand diagram below.  (2 marks)

     
       

  6. The equation of the line passing through the two roots of    can be expressed as  , where  .

     

    Find in terms of .  (1 mark)

  7. Find the area of the major segment bounded by the line passing through the roots of    and the major arc of the circle given by  .  (2 marks)

Show Answers Only
  5.  
Show Worked Solution
a.   

 

 
 

 

 

b.   

 

♦♦ Mean mark part (c) 31%.

c.   
 

 

d.
    
   
 
 

 

 

e.   

 

f.   

♦♦♦ Mean mark 1%!


 

  

 
 

 

♦♦ Mean mark 31%.

g.   
   

 

 

 

Complex Numbers, SPEC2-NHT 2017 VCAA 2

One root of a quadratic equation with real coefficients is  .

    1. Write down the other root of the quadratic equation.   (1 mark)

    2. Hence determine the quadratic equation, writing it in the form  .   (2 marks)

  1. Plot and label the roots of     on the Argand diagram below.   (3 marks)

  

 

  1. Find the equation of the line that is the perpendicular bisector of the line segment joining the origin and the point  . Express your answer in the form  .   (2 marks)

  1. The three roots plotted in part b. lie on a circle.

     

    Find the equation of this circle, expressing it in the form  ,  where  .   (3 marks)

Show Answers Only
Show Worked Solution

a.i.   

 

 

a.ii.   
 
 
 
 

 

b.   
 

 

 
   
 

 

   

 

c.   

 


 

 
 
 

 

d.   


 


 


 

Calculus, SPEC2-NHT 2018 VCAA 5

A horizontal beam is supported at its endpoints, which are 2 m apart. The deflection metres of the beam measured downwards at a distance metres from the support at the origin is given by the differential equation  .
 


 

  1. Given that both the inclination, , and the deflection, , of the beam from the horizontal at    are zero, use the differential equation above to show that  .   (2 marks)

  2. Find the angle of inclination of the beam to the horizontal at the origin . Give your answer as a positive acute angle in degrees, correct to one decimal place.   (2 marks)

  3. Find the value of , in metres, where the maximum deflection occurs, and find the maximum deflection, in metres.   (3 marks)

  4. Find the maximum angle of inclination of the beam to the horizontal in the part of the beam where  . Give your answer as a positive acute angle in degrees, correct to one decimal place.   (2 marks)

Show Answers Only
Show Worked Solution
a.  
 

 

 

 

 

 

b.   

 
 
 

 

c.   

 

 

 

d.   

 

 

 

Statistics, SPEC2 2018 VCAA 6

The heights of mature water buffaloes in northern Australia are known to be normally distributed with a standard deviation of 15 cm. It is claimed that the mean height of the water buffaloes is 150 cm.

To decide whether the claim about the mean height is true, rangers selected a random sample of 50 mature water buffaloes. The mean height of this sample was found to be 145 cm.

A one-tailed statistical test is to be carried out to see if the sample mean height of 145 cm differs significantly from the claimed population mean of 150 cm.

Let denote the mean height of a random sample of 50 mature water buffaloes.

  1. State suitable hypotheses and for the statistical test.   (1 mark)

  2. Find the standard deviation of .   (1 mark)

  3. Write down an expression for the value of the statistical test and evaluate your answer to four decimal places.   (2 marks)

  4. State with a reason whether should be rejected at the 5% level of significance.   (1 mark)

  5. What is the smallest value of the sample mean height that could be observed for to be not rejected? Give your answer in centimetres, correct to two decimal places.   (1 mark)

  6. If the true mean height of all mature water buffaloes in northern Australia is in fact 145 cm, what is the probability that will be accepted at the 5% level of significance? Give your answer correct to two decimal places.   (1 mark)

  7. Using the observed sample mean of 145 cm, find a 99% confidence interval for the mean height of all mature water buffaloes in northern Australia. Express the values in your confidence interval in centimetres, correct to one decimal place.   (1 mark)

Show Answers Only
  1.  

Show Worked Solution
a.   
 

 

b.   
   
   

 

c.   

 

d.   

 

e. 

♦ Mean mark part (e) 48%.

 

f.   

♦♦♦ Mean mark part (f) 11%.

 
   

 

g.   

Calculus, SPEC1 2015 VCAA 9

Consider the curve represented by 

  1. Find the gradient of the curve at any point    (2 marks)
  2. Find the equation of the tangent to the curve at the point    and find the equation of the tangent to the curve at the point

     

    Write each equation in the form    (2 marks)

  3. Find the acute angle between the tangent to the curve at the point    and the tangent to the curve at the point 

     

    Give your answer in the form  , where is a real constant  (2 marks)

Show Answers Only
Show Worked Solution
a.   
 
 
 

 

b.   

 

 

 
 

 

c.   

 
 
 
 

 

Calculus, SPEC1 2014 VCAA 7

Consider  .

  1.  Write down the range of  .  (1 mark)

  2.  Show that  .  (1 mark)

  3.  Hence evaluate the area enclosed by the graph of  , the -axis and the lines    and  .  (3 marks)

Show Answers Only

Show Worked Solution

a. 

♦♦♦ Mean mark 4%.


 


 
 

 

b.  

 

 

c.   
   
   
   
   
   
   
   
   

Calculus, MET1 2018 VCAA 8

Let  , where is a positive real constant.

  1.  Show that  .   (1 mark)

  2. Find the value of for which the graphs of    and    have exactly one point of intersection.   (3 marks)

Let  . The diagram below shows sections of the graphs of  and for  .
 


 

Let be the area of the region bounded by the curves  and the line  .

  1. Write down a definite integral that gives the value of .   (1 mark)

  2. Using your result from part a., or otherwise, find the value of such that  .   (3 marks)

Show Answers Only
Show Worked Solution

a.   

 

 

b.  

♦♦♦ Mean mark 7%.
MARKER’S COMMENT: Most students found the correct quadratic equation but solved for .

 

 

 

c.   
   
   

♦♦ Mean mark 29%.

 

d.   
 
 
 
 
 
 
 

Algebra, MET2 2018 VCAA 20 MC

The differentiable function    is a probability density function. It is known that the median of the probability density function    is at    and  .

The transformation    maps the graph of    to the graph of  , where    is a probability density function with a median at    and  .

The transformation could be given by

Show Answers Only

Show Worked Solution

♦♦♦ Mean mark 20%.


 


 

Algebra, MET2 2018 VCAA 18 MC

Consider the functions    and  , where and are positive integers, and and are fractions in simplest form.

If    and  , which of the following must be false?

A.  

B.  

C.  

D.  

E.  

Show Answers Only

Show Worked Solution

♦♦♦ Mean mark 14%.

Financial Maths, STD2 2014 HSC 27a

Alex is buying a used car which has a sale price of  $13 380. In addition to the sale price there are the following costs:

2014 27a1

  1. Stamp Duty for this car is calculated at $3 for every $100, or part thereof, of the sale price.  
  2. Calculate the Stamp Duty payable.   (1 mark)
  3.  
  4. Alex wishes to take out comprehensive insurance for the car for 12 months. The cost of comprehensive insurance is calculated using the following: 
    1.  
    2. 2014 27a2
  5. Find the total amount that Alex will need to pay for comprehensive insurance.   (3 marks)
  6.  
  7. Alex has decided he will take out the comprehensive car insurance rather than the less expensive non-compulsory third-party car insurance.
  8. What extra cover is provided by the comprehensive car insurance?   (1 mark)

 

Show Answers Only
  5.  
Show Worked Solution
♦♦♦ Mean mark 12%
IMPORTANT: “or part thereof ..” in the question requires students to round up to 134 to get the right multiple of $3 for their calculation.
(i)   
 

 

(ii)  


 

 
 

 

 
 

 

 

 

♦ Mean mark 34%.
(iii)  
 

GEOMETRY, FUR2 2018 VCAA 3

Frank owns a tennis court.

A diagram of his tennis court is shown below

Assume that all intersecting lines meet at right angles.

Frank stands at point . Another point on the court is labelled point .
 

  1. What is the straight-line distance, in metres, between point and point ?

     

    Round your answer to one decimal place.   (1 mark)

  2. Frank hits a ball when it is at a height of 2.5 m directly above point .

     

    Assume that the ball travels in a straight line to the ground at point .

     

    What is the straight-line distance, in metres, that the ball travels?

     

    Round your answer to the nearest whole number.   (1 mark)

Frank hits two balls from point .

For Frank’s first hit, the ball strikes the ground at point , 20.7 m from point .

For Frank’s second hit, the ball strikes the ground at point .

Point is metres from point .

Point is 10.4 m from point .

The angle, , formed is 23.5°.
 


 

    1. Determine two possible values for angle .

       

      Round your answers to one decimal place.   (1 mark)

    2. If point is within the boundary of the court, what is the value of ?

       

      Round your answer to the nearest metre.  (1 mark)

Show Answers Only
Show Worked Solution
a.   
 
   
   

 

b.
  


 

 
 

 

c.i.  

♦♦ Mean mark 25%.

 

 

♦♦♦ Mean mark 18%.

c.ii.   
 
   
 
 
 
   
   

NETWORKS, FUR1 2018 VCAA 8 MC

Annie, Buddhi, Chuck and Dorothy work in a factory.

Today each worker will complete one of four tasks, 1, 2, 3 and 4.

The usual completion times for Annie, Chuck and Dorothy are shown in the table below.
 


 

Buddhi takes 3 minutes for Task 3.

He takes minutes for each other task.

Today the factory supervisor allocates the tasks as follows

    • Task 1 to Dorothy
    • Task 2 to Annie
    • Task 3 to Buddhi
    • Task 4 to Chuck

This allocation will achieve the minimum total completion time if the value of is at least

  1. 0
  2. 1
  3. 2
  4. 3
  5. 4
Show Answers Only

Show Worked Solution


 


 

NETWORKS, FUR2 2018 VCAA 4

Parcel deliveries are made between five nearby towns, to .

The roads connecting these five towns are shown on the graph below. The distances, in kilometres, are also shown.
 

A road inspector will leave from town to check all the roads and return to town when the inspection is complete. He will travel the minimum distance possible.

  1.  How many roads will the inspector have to travel on more than once?   (1 mark)

  2.  Determine the minimum distance, in kilometres, that the inspector will travel.   (1 mark)

Show Answers Only
Show Worked Solution

a.  

♦♦ Mean mark 31%.

 

b.  

♦♦♦ Mean mark 14%.


 

CORE, FUR2 2018 VCAA 6

 

Julie has retired from work and has received a superannuation payment of $492 800.

She has two options for investing her money.

Option 1

Julie could invest the $492 800 in a perpetuity. She would then receive $887.04 each fortnight for the rest of her life.

  1. At what annual percentage rate is interest earned by this perpetuity?  (1 mark)

Option 2

Julie could invest the $492 800 in an annuity, instead of a perpetuity.

The annuity earns interest at the rate of 4.32% per annum, compounding monthly.

The balance of Julie’s annuity at the end of the first year of investment would be $480 242.25

    1. What monthly payment, in dollars, would Julie receive?   (1 mark)
    2. How much interest would Julie’s annuity earn in the second year of investment?
    3. Round your answer to the nearest cent.    (1 mark)

Show Answers Only

Show Worked Solution

a.   
   

♦ Mean mark 41%.
 

 

 

b.i.   

♦ Mean mark 48%.

 

 

♦♦♦ Mean mark 16%.

b.ii.  
 
 
   

 

 

CORE, FUR2 2018 VCAA 3

Table 3 shows the yearly average traffic congestion levels in two cities, Melbourne and Sydney, during the period 2008 to 2016. Also shown is a time series plot of the same data.

The time series plot for Melbourne is incomplete.

  1. Use the data in Table 3 to complete the time series plot above for Melbourne.   (1 mark)

  2. A least squares line is used to model the trend in the time series plot for Sydney. The equation is

       

  1.   i. Draw this least squares line on the time series plot.   (1 mark)

  2.  ii. Use the equation of the least squares line to determine the average rate of increase in percentage congestion level for the period 2008 to 2016 in Sydney.   (1 mark)

    iii. Use the least squares line to predict when the percentage congestion level in Sydney will be 43%.   (1 mark)

The yearly average traffic congestion level data for Melbourne is repeated in Table 4 below.

  1. When a least squares line is used to model the trend in the data for Melbourne, the intercept of this line is approximately –1514.75556
  2. Round this value to four significant figures.   (1 mark)

  3. Use the data in Table 4 to determine the equation of the least squares line that can be used to model the trend in the data for Melbourne. The variable year is the explanatory variable.
  4. Write the values of the intercept and the slope of this least squares line in the appropriate boxes provided below.
  5. Round both values to four significant figures.   (2 marks)

congestion level = 
 
  + 
 
  × year
  1. Since 2008, the equations of the least squares lines for Sydney and Melbourne have predicted that future traffic congestion levels in Sydney will always exceed future traffic congestion levels in Melbourne.

     

    Explain why, quoting the values of appropriate statistics.   (2 marks)

Show Answers Only
Show Worked Solution
a.   

 

b.i.   

 

b.ii.  

♦ Mean mark (b)(ii) 36%.
COMMENT: Major problems caused by part (b)(ii). Review!

 

 

b.iii.   
 
 
   

 

c. 

 

d.   

 

e.   

♦♦♦ Mean mark 18%.

 

Trigonometry, 2ADV T1 SM-Bank 1

A tower is built on flat ground.

Three tourists, , and are observing the tower from ground level.

is due north of the tower, is due east and is on the line of sight from and and between them.

The angles of elevation to the top of the tower from , and are 26°, 28° and 30°, respectively.

What is the bearing of from the tower?  (4 marks)

Show Answers Only

Show Worked Solution