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Measurement, STD2 M1 2005 HSC 23b

A clay brick is made in the shape of a rectangular prism with dimensions as shown.
 

  1. Calculate the volume of the clay brick.  (1 mark)

Three identical cylindrical holes are made through the brick as shown. Each hole has a radius of 1.4 cm.  
 

  1. What is the volume of clay remaining in the brick after the holes have been made? (Give your answer to the nearest cubic centimetre.)  (3 marks)

  2. What percentage of clay is removed by making the holes through the brick? (Give your answer correct to one decimal place.)  (1 mark)

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ii. 

 

 

iii. 

Probability, STD2 S2 2005 HSC 11 MC

The diagram shows a spinner.
 


 

The arrow is spun and will stop in one of the six sections.

What is the probability that the arrow will stop in a section containing a number greater
than 4?

  1.    
  2.    
  3.    
  4.   
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Financial Maths, STD2 F4 2004 HSC 25a

Tai uses the declining balance method of depreciation to calculate tax deductions for her business. Tai’s computer is valued at $6500 at the start of the 2003 financial year. The rate of depreciation is 40% per annum.

  1. Calculate the value of her tax deduction for the 2003 financial year.  (1 mark)

  2. What is the value of her computer at the start of the 2006 financial year?  (2 marks)

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i. 
 

 

ii. 

Algebra, 2UG 2004 HSC 23b

Kirbee is shopping for computer software. Novirus costs more than
Funmaths. Let dollars be the cost of Funmaths.

  1. Write an expression involving for the cost of Novirus.  (1 mark)
  2. Novirus and Funmaths together cost . Write an equation involving
  3. and solve it to find the cost of Funmaths.  (2 marks)
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(i)  

 

(ii) 

Linear Functions, 2UA 2004 HSC 2a

The diagram shows the points    and  .

The line    is drawn perpendicular to the  -axis through the point  .
 

Linear Functions, 2UA 2004 HSC 2a 
 

  1. Calculate the length of the interval  .   (1 mark)
  2. Find the gradient of the line  .   (1 mark)
  3. What is the size of the acute angle between the line    and the line  ?   (1 mark)
  4. Show that the equation of the line    is  .    (1 mark)
  5. Copy the diagram into your writing booklet and shade the region defined by  .   (1 mark)
  6. Write down the equation of the line  .   (1 mark)
  7. The point    is on the line    such that    is perpendicular to  . Find the coordinates of  .   (2 marks)

 

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  5. Linear Functions, 2UA 2004 HSC 2a Answer
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(ii)  
   
   

 

(iii)  

 

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(v)

Linear Functions, 2UA 2004 HSC 2a Answer

 

(vi)  
 

 

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Financial Maths, STD2 F1 2006 HSC 5 MC

A salesman earns $200 per week plus $40 commission for each item he sells.

How many items does he need to sell to earn a total of $2640 in two weeks?

  1. 33
  2. 56
  3. 61
  4. 66
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Measurement, STD2 M6 2006 HSC 3 MC

The angle of depression of the base of the tree from the top of the building is 65°. The height of the building is 30 m.

How far away is the base of the tree from the building, correct to one decimal place?
 


 

  1. 12.7 m
  2. 14.0 m
  3. 33.1 m
  4. 64.3 m
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Probability, STD2 S2 2006 HSC 1 MC

The probability of an event occurring is

Which statement best describes the probability of this event occurring?

  1.    The event is likely to occur.
  2.    The event is certain to occur.
  3.    The event is unlikely to occur.
  4.    The event has an even chance of occurring.
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Probability, STD2 S2 2005 HSC 23a

There are 100 tickets sold in a raffle. Justine sold all 100 tickets to five of her friends. The number of tickets she sold to each friend is shown in the table.
 

  1. Justine claims that each of her friends is equally likely to win first prize.

     

    Give a reason why Justine’s statement is NOT correct.   (1 mark)

  2. What is the probability that first prize is NOT won by Khalid or Herman?   (2 marks)

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ii. 


 

Measurement, STD2 M1 2004 HSC 23a

The diagram shows the shape of Carmel’s garden bed. All measurements are in
metres.

  1. Show that the area of the garden bed is 57 square metres.   (2 marks)

  2. Carmel decides to add a 5 cm layer of straw to the garden bed.

     

    Calculate the volume of straw required. Give your answer in cubic metres.   (2 marks)

  3. Each bag holds 0.25 cubic metres of straw.

     

    How many bags does she need to buy?   (2 marks)

  4. A straight fence is to be constructed joining point A to point B.

     

    Find the length of this fence to the nearest metre.   (2 marks)

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Statistics, STD2 S1 2004 HSC 8 MC

This sector graph shows the distribution of 116 prizes won by three schools: X, Y and Z.
 

 
How many prizes were won by School X?

  1.   26
  2.   32
  3.   81
  4.   99
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Statistics, STD2 S1 2004 HSC 6-7 MC

Use the set of scores  1, 3, 3, 3, 4, 5, 7, 7, 12  to answer Questions 6 and 7.
 

Question 6

What is the range of the set of scores?

  1. 6
  2. 9
  3. 11
  4. 12

 

Question 7

What are the median and the mode of the set of scores?

  1. Median 3, mode 5
  2. Median 3, mode 3
  3. Median 4, mode 5
  4. Median 4, mode 3
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CORE*, FUR1 2009 VCAA 4 MC

A delivery truck when new was valued at  $65 000.

The truck’s value depreciates at a rate of 22 cents per kilometre travelled.

After it has travelled a total distance of 132 600 km, the value of the truck will be

A.  

B.  

C.   

D.  

E.  

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CORE*, FUR1 2009 VCAA 2 MC

An amount of $6500 is borrowed at a simple interest rate of 3.5% per annum.

The total interest paid over the period of the loan is $910.

The period of the loan is closest to

A.   2.5 years.

B.   3.5 years.

C.   3.8 years.

D.   4 years.

E.   4.9 years.

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CORE*, FUR1 2008 VCAA 1 MC

A plumber quoted $300, excluding GST (Goods and Services Tax), to complete a job.

A GST of 10% is added to the price.

The full price for the job will be

A.       $3

B.     $30

C.   $303

D.   $310

E.   $330

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CORE*, FUR1 2007 VCAA 5 MC

A new kitchen in a restaurant cost $50 000. Its value is depreciated over time using the reducing balance method.

The value of the kitchen in dollars at the end of each year for ten years is shown in the graph below.
 


 

Which one of the following statements is true?

A.  The kitchen depreciates by $4000 annually.

B.  At the end of five years, the kitchen's value is less than $20 000.

C.  The reducing balance depreciation rate is less than 5% per annum.

D.  The annual depreciation rate increases over time.

E.  The amount of depreciation each year decreases over time.

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CORE*, FUR1 2005 VCAA 3 MC

Tamara’s bank statement for September has been damaged by spilt ink as shown below.

2005VCAA-Business -3

Tamara’s Pay/Salary was deposited on 30 September.

What is the value of this deposit?

A.   

B.  

C.  

D.   

E.    

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2005VCAA-Business-Sol-3

 

CORE*, FUR1 2011 VCAA 3 MC

A van is purchased for $56 000.

Its value depreciates at a rate of 42 cents for each kilometre that it travels.

The value of the van after it has travelled 32 000 km is

A.   

B.   

C.   

D.   

E.   

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CORE*, FUR1 2011 VCAA 1 MC

An electrician charges $68 per hour to complete a job.

A Goods and Services Tax (GST) of 10% is added to the charge.

Including GST, the cost of a job that takes three hours is

A.       $6.80

B.     $20.40

C.   $204.00

D.   $210.80

E.   $224.40

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CORE*, FUR1 2012 VCAA 4 MC

Mei’s starting salary is $65 000 per annum.

After the first year her salary will increase by 2.8%.

After the second year her salary will increase by a further 3.5%.

After this second increase, her salary will be closest to

A.   $66 820

B.   $68 690

C.   $69 030

D.   $69 160

E.   $69 630

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CORE, FUR1 2014 VCAA 5 MC

A bank approves a $90 000 loan for a customer.

The loan is to be repaid fully over 20 years in equal monthly payments.

Interest is charged at a rate of 6.95% per annum on the reducing monthly balance.

To the nearest dollar, the monthly payment will be

A.     $478

B.     $692

C.     $695

D.   $1409

E.   $1579

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GRAPHS, FUR1 2014 VCAA 6 MC

The Domestics Cleaning Company provides household cleaning services.

For two hours of cleaning, the cost is $55.

For four hours of cleaning, the cost is $94.

The rule for the cost of cleaning services is

where is a fixed charge, in dollars, and is the charge per hour of cleaning, in dollars per hour.

Using this rule, the cost for five hours of cleaning is

A.  

B.  

C.  

D.  

E.  

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GRAPHS, FUR1 2014 VCAA 1 MC

The graph below shows the altitude, in metres, of a balloon over a six-hour flight.

Over the six-hour period, the length of time, in hours, where the altitude of the balloon was at least 1500 m is

A.   

B.   

C.   

D.   

E.   

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CORE*, FUR1 2014 VCAA 4 MC

The cost of hiring a plasterer is $86.00 per hour plus GST of 10%.

The cost of hiring a plasterer for four hours, including GST, is

A.   $120.40

B.   $309.60

C.   $344.00

D.   $352.60

E.   $378.40

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GRAPHS, FUR1 2007 VCAA 4 MC

Paul makes rulers. There is a fixed cost of $60 plus a manufacturing cost of $0.20 per ruler.

Last week Paul was able to break even by selling his rulers for $1 each.

The number of rulers Paul sold last week was

A.     

B.     

C.     

D.   

E.   

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GRAPHS, FUR1 2007 VCAA 2 MC

A builder's fee, dollars, can be determined from the rule  , where represents the number of hours worked.

According to this rule, the builder's fee will be

A.   $60 for 1 hour of work.

B.   $110 for 2 hours of work.

C.   $500 for 8 hours of work.

D.   $550 for 10 hours of work.

E.   $1150 for 10 hours of work. 

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GRAPHS, FUR1 2009 VCAA 5-6 MC

Kathy is a tutor who offers tutorial sessions for English and History students.

Part 1

An English tutorial session takes 1.5 hours.

A History tutorial session take 30 minutes.

Kathy has no more than 15 hours available in a week for tutorial sessions.

Let    represent the number of English tutorial sessions Kathy has each week.
Let    represent the number of History tutorial sessions Kathy has each week.

An inequality representing the constraint on Kathy’s tutorial time each week (in hours) is

A.   

B.   

C.   

D.   

E.   

 

Part 2

Kathy prefers to have no more than 18 tutorial sessions in total each week.

She prefers to have at least 4 English tutorial sessions.

She also prefers to have at least as many History tutorial sessions as English tutorial sessions.

Let    represent the number of English tutorial sessions Kathy has each week.
Let    represent the number of History tutorial sessions Kathy has each week.

The shaded region that satisfies all of these constraints is

GRAPHS, FUR1 2009 VCAA 5-6 MC ab

GRAPHS, FUR1 2009 VCAA 5-6 MC cd

GRAPHS, FUR1 2009 VCAA 5-6 MC e

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GRAPHS, FUR1 2009 VCAA 1-3 MC

The graph below shows the water temperature in a fish tank over a 12-hour period.

GRAPHS, FUR1 2009 VCAA 1-3 MC 1  

Part 1

Over the 12-hour period, the temperature of the tank is increasing most rapidly

A.   during the first 2 hours.

B.   from 2 to 4 hours.

C.   from 4 to 6 hours.

D.   from 6 to 8 hours.

E.   from 8 to 10 hours.

 

Part 2

The fish tank is considered to be a safe environment for a type of fish if the water temperature is maintained between 24°C and 28°C.

Over the 12-hour period, the length of time (in hours) that the environment was safe for this type of fish was closest to

A.     

B.     

C.     

D.     

E.   

 

Part 3

The graph below can be used to determine the cost (in cents) of heating the fish tank during the first five hours of heating.

GRAPHS, FUR1 2009 VCAA 1-3 MC 2

 

The cost of heating the tank for one hour is

A.       

B.       

C.     

D.     

E.   

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FS Comm, 2UG SM-Bank 02

Calculate the cost of a call of duration    minutes and    seconds, given that there is a connection fee of    cents and a call rate of    cents per    second block or part thereof.   (2 marks)

 

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FS Comm, 2UG SM-Bank 04

Murray is a photographer and has recently purchased an external hard drive with a    capacity.

If the average size of his photographic files is  , how many should he expect to fit on the hard drive?   (2 marks)

 

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Algebra, STD2 A4 2007 HSC 27a

   A rectangular playing surface is to be constructed so that the length is 6 metres more than the width.

  1. Give an example of a length and width that would be possible for this playing surface.   (1 mark)

  2. Write an equation for the area () of the playing surface in terms of its length ().   (1 mark)

     

    A graph comparing the area of the playing surface to its length is shown.
     
       
     

  3. Why are lengths of 0 metres to 6 metres impossible?   (1 mark)

  4. What would be the dimensions of the playing surface if it had an area of 135 m²?  (2 marks)

     

    Company constructs playing surfaces.

         

  5. Draw a graph to represent the cost of using Company to construct all playing surface sizes up to and including 200 m².

     

    Use the horizontal axis to represent the area and the vertical axis to represent the cost.   (2 marks)

  6. Company charges a rate of $360 per square metre regardless of size. 
  7. Which company would charge less to construct a playing surface with an area of 135 m²

     

    Justify your answer with suitable calculations.   (1 mark)

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Probability, STD2 S2 2007 HSC 25c

In a stack of 10 DVDs, there are 5 rated PG, 3 rated G and 2 rated M.

  1. A DVD is selected at random. What is the probability that it is rated M?   (1 mark)

Grant chooses two DVDs at random from the stack. Copy or trace the tree diagram into your writing booklet.
 

  1. Complete the tree diagram by writing the correct probability on each branch.   (2 marks)

  2. Calculate the probability that Grant chooses two DVDs with the same rating.   (2 marks)

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