SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

v1 Algebra, STD2 A2 2011 HSC 23b

Sticks were used to create the following pattern. 
  

The number of sticks used is recorded in the table.

  1. Draw Shape 4 of this pattern.  (1 mark)

  2. How many sticks would be required for Shape 128?    (1 mark)

  3. Is it possible to create a shape in this pattern using exactly 609 sticks?

     

    Show suitable calculations to support your answer.    (2 marks)

Show Answers Only
Show Worked Solution

  i.   

ii.   

♦ Mean mark 48%.
MARKER’S COMMENT: Students should attempt to find a “rule” in such questions, and use this formula to solve the question, as per the Worked Solution.  
 

 

iii.   
 
 

    

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)

Show Answers Only
Show Worked Solution

a.
  

b.  
 

 

c.  
   

 

♦ Mean mark part d. 44%.

d. 

GRAPHS, FUR1 2018 VCAA 02 MC

Steven is a wedding photographer.

He charges his clients a fixed fee of $500, plus $250 per hour of photography.

The equation that represents the total amount, , Steven charges, for hours of photography is

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

Show Worked Solution

Graphs, EXT2 2018 HSC 12b

A curve has equation  .

  1. Use implicit differentiation to show that  .  (2 marks)
  2. Hence, or otherwise, find the coordinates of the points on the curve where  .  (2 marks)
Show Answers Only
Show Worked Solution

i.   

♦ Mean mark 98%!

 

ii.   

 

 

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)

Show Answers Only
Show Worked Solution

i.   

 

ii.   


 

 

 

Graphs, MET1 2016 VCAA 5

Let  , where    and  , where  .

  1.   i. Find the rule for , where  .   (1 mark)

    ii. State the domain and range of .   (2 marks)

  2. iii. Show that  .   (2 marks)

  3. iv. Find the coordinates of the stationary point of and state its nature.   (2 marks)

     

  4. Let    where  .
  5.  i. Find the rule for  .   (2 marks)

  6. ii. State the domain and range of  .   (2 marks)

Show Answers Only
  1.   i.
  2.  ii.
  3. iii.
  4. iv.
  5.  i.
  6. ii.
  7.    
Show Worked Solution
a.i.   
   

 

a.ii.  

♦♦ Mean mark part (a)(ii) 30%.
 
 

 

MARKER’S COMMENT: Many students were unsure of how to present their working in this question. Note the layout in the solution.
a.iii.  
   
   
   

 

 

 

 

a.iv.  

♦ Mean mark part (a)(iv) 41%.
MARKER’S COMMENT: Solving a fraction is zero

   

 

 

b.i.  

♦ Mean mark (b)(i) 49%.
MARKER’s COMMENT: Many students failed to consider the restrictions on the domain in and only select the negative root.

 

 

♦ Mean mark part (b)(ii) 44%.

 

b.ii.  

 

Statistics, NAP-H1-04

Che's hockey team played 3 games.

The number of goals his team scored in each game is shown in the tally below.

The team scored 6 goals in Game 1.

What was the total number of goals scored by the team in all three games?

 
 
 
 
Show Answers Only

Show Worked Solution
 

Statistics, NAP-I1-04

The graph below shows the number of students that use different ways to get to school.
 

 

Which statement is true?

 
 More students walk to school than ride a skateboard.
 
 Less students ride in a car to school than ride a bike.
 
 The most common way to get to school is by car.
 
 The most common way to get to school is by bus.
Show Answers Only

Show Worked Solution

Measurement, NAP-I1-02

Malcolm and Barnaby were measuring their screwdrivers using paddle pop sticks.
 


 

Which of these statements is true?

 
 Malcolm's screwdriver is longer than Barnaby's screwdriver.
 
 Malcolm's screwdriver is shorter than Barnaby's screwdriver.
 
 Malcolm's screwdriver is the same length as Barnaby's screwdriver.
Show Answers Only

Show Worked Solution

Conics, EXT2 2016 HSC 12a

The diagram shows an ellipse.

ext2-hsc-2016-12a

  1. Write an equation for the ellipse.  (1 mark)
  2. Find the eccentricity of the ellipse.  (1 mark)
  3. Write the coordinates of the foci of the ellipse.  (1 mark)
  4. Write the equations of the directrices of the ellipse.  (1 mark)
Show Answers Only
Show Worked Solution

i.  

 

ii.   
 
 
 

 

iii.  

 

iv.  

Complex Numbers, EXT2 N1 2016 HSC 11a

Let  

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

  2.  Show that    is real.  (1 mark)

  3.  Find a positive integer such that    is purely imaginary.  (1 mark)

Show Answers Only
Show Worked Solution

i.  

 
 

 

ii.   
   
   

 

 

iii.  

Probability, 2UA 2016 HSC 2 MC

In a raffle, tickets are sold and there is one prize to be won.

What is the probability that someone buying tickets wins the prize?

(A) 

(B) 

(C) 

(D) 

Show Answers Only

Show Worked Solution

GRAPHS, FUR2 2009 VCAA 2

Luggage over 20 kg in weight is called excess luggage.

Fair Go Airlines charges for transporting excess luggage.

The charges for some excess luggage weights are shown in Table 2.

GRAPHS, FUR2 2009 VCAA 21

  1. Complete this graph by plotting the charge for excess luggage weight of 10 kg. Mark this point with a cross (×).  (1 mark)

    GRAPHS, FUR2 2009 VCAA 22

  2. A graph of the charge against (excess luggage weight)² is to be constructed.

     

    Fill in the missing (excess luggage weight)² value in Table 3 and plot this point with a cross (×) on the graph below.  (1 mark)

    GRAPHS, FUR2 2009 VCAA 23

GRAPHS, FUR2 2009 VCAA 24

  1. The graph above can be used to find the value of in the equation below.

     

          charge = × (excess luggage weight)²

     

    Find .  (1 mark)

  2. Calculate the charge for transporting 12 kg of excess luggage.

     

    Write your answer in dollars correct to the nearest cent.  (1 mark)

Show Answers Only
  1.  
    GRAPHS, FUR2 2009 VCAA 2 Answer
  2.  
    GRAPHS, FUR2 2009 VCAA 2 Answer1
    GRAPHS, FUR2 2009 VCAA 2 Anwer2
Show Worked Solution
a.   

GRAPHS, FUR2 2009 VCAA 2 Answer

 

b.    GRAPHS, FUR2 2009 VCAA 2 Answer1

GRAPHS, FUR2 2009 VCAA 2 Anwer2

 

c.  

 

d.  

NETWORKS, FUR1 2008 VCAA 1 MC

Steel water pipes connect five points underground.

The directed graph below shows the directions of the flow of water through these pipes between these points. 

 

networks-fur1-2008-vcaa-1-mc
 

The directed graph shows that water can flow from

A.   point 1 to point 2.

B.   point 1 to point 4.

C.   point 4 to point 1.

D.   point 4 to point 2.

E.   point 5 to point 2.

Show Answers Only

Show Worked Solution

NETWORKS, FUR2 2014 VCAA 1

Four members of a train club, Andrew, Brianna, Charlie and Devi, have joined one or more interest groups for electric, steam, diesel or miniature trains.

The edges of the bipartite graph below show the interest groups that these four train club members have joined.

 

NETWORKS, FUR2 2014 VCAA 1
 

  1. How many of these four members have joined the steam trains interest group?   (1 mark)

  2. Which interest group have both Brianna and Charlie joined?   (1 mark)

Show Answers Only
Show Worked Solution

a.   

b.  

GRAPHS, FUR1 2011 VCAA 1-2 MC

The charges for posting letters that weigh 100 g or less are shown in the graph below.

Part 1

The charge for posting a 35 g letter is

A.   

B.   

C.   

D.   

E.   

 

Part 2

Two letters are posted.

The total postage charge cannot be

A.   

B.   

C.   

D.   

E.   

Show Answers Only

Show Worked Solution

 

GRAPHS, FUR1 2012 VCAA 2 MC

At a convenience store, one doughnut costs $2.40 and one drink costs $3.00.

A customer purchased five doughnuts and a number of drinks at a total cost of $24.00.

The number of drinks purchased was

A.     

B.     

C.     

D.     

E.   

Show Answers Only

Show Worked Solution

 

Complex Numbers, EXT2 N1 2015 HSC 11b

Consider the complex numbers    and  

  1. Evaluate     (1 mark)

  2. Evaluate     (1 mark)

  3. Find the argument of     (1 mark)

Show Answers Only
Show Worked Solution
i.   
 

 

ii.   ­
­
­

 

iii.   ­
­
­

Complex Numbers, EXT2 N2 2011 HSC 2b

On the Argand diagram, the complex numbers    and    form a rhombus.
 


 

  1. Find    in the form  , where    and    are real numbers.  (1 mark)

  2. An interior angle, , of the rhombus is marked on the diagram.

     

    Find the value of   (2 marks)

Show Answers Only
Show Worked Solution
i.   
 

 

ii.  


 

 

Complex Numbers, EXT2 N1 2011 HSC 2a

Let    and  

  1.  Find     (1 mark)

  2.  Find     (1 mark)

  3.  Express    in the form  , where    and    are real numbers.   (2 marks)

Show Answers Only
Show Worked Solution

i.   

 

 

ii.   
 

 

 iii.   
 
 
 

Complex Numbers, EXT2 N1 2013 HSC 11a

Let    and 

  1. Find    (1 mark)
  2. Express in modulus–argument form.  (2 marks)
  3. Write in its simplest form.  (2 marks)
Show Answers Only
Show Worked Solution

i.   

 

 

ii.   
 
 
 
MARKER’S COMMENT: The directive “in its simplest form” required students to convert to 1.

 

iii.   
 
 

CORE, FUR1 2012 VCAA 1-2 MC

The following bar chart shows the distribution of wind directions recorded at a weather station at 9.00 am on each of 214 days in 2011.
 

Part 1

According to the bar chart, the most frequently observed wind direction was

A.  south-east.

B.  south.

C.  south-west.

D.  west.

E.  north-west.

 
Part 2

According to the bar chart, the percentage of the 214 days on which the wind direction was observed to be east or south-east is closest to

A. 

B. 

C. 

D. 

E. 

Show Answers Only

Show Worked Solution

 

 
 
 

Combinatorics, EXT1 A1 2011 HSC 2e

Alex’s playlist consists of 40 different songs that can be arranged in any order.  

  1. How many arrangements are there for the 40 songs?    (1 mark)

  2. Alex decides that she wants to play her three favourite songs first, in any order.
  3. How many arrangements of the 40 songs are now possible?   (1 mark)

Show Answers Only
Show Worked Solution
i.   

 

ii.   
   

Financial Maths, STD2 F1 2010 HSC 23d

Warrick has a net income of $590 per week. He has created a budget to help manage his money.

       2010 23d

  1. Find the value of , the amount that Warrick allocates towards electricity each week.    (1 mark)

  2. Warrick has an unexpectedly high telephone and internet bill. For the last three weeks, he has put aside his savings as well as his telephone and internet money to pay the bill.

     

    How much money has he put aside altogether to pay the bill?    (1 mark)

  3. The bill for the telephone and internet is $620. It is due in two weeks time. Warrick realises he has not put aside enough money to pay the bill.

     

    How could Warrick reallocate non-essential funds in his budget so he has enough money to pay the bill? Justify your answer with suitable reasons and calculations.   (3 marks)

Show Answers Only

  4.  

Show Worked Solution
i.   
     
   
   

 

ii.   
   
 

 

 

(iii)  
 
 

 


 


 

 

 

Algebra, STD2 A2 2011 HSC 23b

Sticks were used to create the following pattern. 

The number of sticks used is recorded in the table.

  1. Draw Shape 4 of this pattern.  (1 mark)

  2. How many sticks would be required for Shape 100?    (1 mark)

  3. Is it possible to create a shape in this pattern using exactly 543 sticks?

     

    Show suitable calculations to support your answer.    (2 marks)

Show Answers Only
Show Worked Solution

  i.     

ii.     

♦ Mean mark 48%.
MARKER’S COMMENT: Students should attempt to find a “rule” in such questions, and use this formula to solve the question, as per the Worked Solution.  
,
 

 

iii.