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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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Financial Maths, STD2 F1 2005 HSC 6 MC

Janet’s gross income last year was $60 000. She had allowable tax deductions of $5000. Janet paid 1.5% of her taxable income for the Medicare levy.

How much was Janet’s Medicare levy?

  1.    $750
  2.    $825
  3.    $900
  4.    $975
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Algebra, STD2 A1 2004 HSC 11 MC

If  , what is a possible value of    when  ?

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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 5 MC

A new air-conditioning unit was purchased for $5000 on 1 January 2009.

On 1 January of each year after 2009 its value is depreciated by 20% using the reducing balance method.

The value of the air conditioner will be below $1500 for the first time on 1 January

A.   2012

B.   2013

C.   2014

D.   2015

E.   2016

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CORE*, FUR1 2008 VCAA 6 MC

Sam and Charlie each invest $5000 for three years.

Sam’s investment earns simple interest at the rate of 7.5% per annum.

Charlie’s investment earns interest at the rate of 7.5% per annum compounding annually.

At the conclusion of three years, correct to the nearest cent, Sam will have

A.   $86.48 less than Charlie.

B.   $86.48 more than Charlie.

C.   $132.23 less than Charlie.

D.   $132.23 more than Charlie.

E.   the same as Charlie.

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CORE*, FUR1 2008 VCAA 4-5 MC

Sandra has purchased a $4200 plasma television under a hire-purchase agreement. She paid $600 deposit and will pay the balance in equal monthly instalments over one year.

A flat interest rate of 6% per annum is charged.

Part 1

The amount of each monthly instalment is

 
Part 2

The annual effective interest rate that Sandra pays under this agreement is closest to

  5.  
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CORE*, FUR1 2008 VCAA 2 MC

Pia invests $800 000 in an ordinary perpetuity to provide an ongoing fortnightly pension for her retirement.

The interest rate for this investment is 5.8% per annum.

Assuming there are 26 fortnights per year, the amount she will receive at the end of each fortnight is closest to

A.     $464

B.     $892

C.   $1422

D.   $1785

E.   $3867

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CORE*, FUR1 2007 VCAA 4 MC

The price of a property purchased in 2006 was $200 000.

Stamp duty was paid on this purchase according to the schedule below.

The amount of stamp duty paid was

A.   $2560

B.   $2800

C.   $5100

D.   $7660

E.   $9460

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CORE*, FUR1 2007 VCAA 2 MC

A car is valued at $30 000 when new.

Its value is depreciated by 25 cents for each kilometre it travels.

The number of kilometres the car travels before its value depreciates to $8000 is

A.     32 000

B.     55 000

C.     88 000

D.   120 000

E.   550 000

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CORE*, FUR1 2006 VCAA 5 MC

A photocopier is depreciated by $0.04 for each copy it makes.

Three years ago the photocopier was purchased for $48 000.

Its depreciated value now is $21 000.

The total number of copies made by the photocopier in the three years is

A.  

B.   

C.   

D.  

E.  

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CORE*, FUR1 2006 VCAA 2 MC

A bank statement for the month of October is shown below.

Interest on this account is calculated at a rate of 0.15% per month on the minimum monthly balance.

The interest payment for the month of October will be

A.   $0.19

B.   $0.57

C.   $0.71

D.   $0.92

E.   $1.28

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CORE*, FUR1 2005 VCAA 9 MC

Sally planned to repay a loan fully with six equal monthly repayments of  .

Interest was calculated monthly on the reducing balance.

Sally missed the third payment, but made a double payment of    in the fourth month.

Which of the following statements is true?

A.   The same amount of interest is paid each month.

B.  The amount owing after three months is the same as the amount owed after two months.

C.  The amount owing after three months is less than the amount owed after two months.

D.   To fully repay the loan, Sally will pay less than $4800.

E.   To fully repay the loan, Sally will pay more than $4800. 

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CORE*, FUR1 2011 VCAA 4 MC

Nathan bought a $2500 bedroom suite on a contract that involves no deposit and an interest-free loan for a period of 48 months.

He has to pay an initial set-up fee of $25.

In addition, he pays an administration fee of $3.95 per month.

The total amount that Nathan will have to pay in fees for the entire 48 months, as a percentage of the original price of $2500,  is closest to

A.   1.6%

B.   4.0%

C.   7.6%

D.   8.5%

E.   8.6%

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CORE*, FUR1 2012 VCAA 6 MC

The commission charged by a real estate agent for selling a property is calculated as shown in the table below.

The sale price of a property is $380 000.

The commission charged for this sale is

A.      $6080

B.      $7600

C.      $8580

D.      $9100

E.    $10 980

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CORE*, FUR1 2013 VCAA 7 MC

The graph below shows the growth in value of a $1000 investment over a period of four years.
 

A different amount of money is invested under the same investment conditions for eight years.

In total, the amount of interest earned on this investment is $600.

The amount of money invested is

A.     

B.    

C.   

D.   

E.   

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CORE*, FUR1 2013 VCAA 4 MC

The purchase price of a car is $15 000.

A deposit of $3000 is paid and the balance will be repaid with 36 monthly payments of $400.

The annual flat rate of interest charged is closest to

A.     1.3%

B.     4.0%

C.     5.3%

D.     6.7%

E.   20.0%

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♦ Mean mark 49%.
 
 

 

 
 

 

CORE*, FUR1 2013 VCAA 2 MC

The closing price of a share on Monday was $30.

The closing price of the share on Tuesday was 5% more than its closing price on Monday.

The closing price of the share on Wednesday was 5% less than its closing price on Tuesday.

Which one of the following calculations will give the closing price of the share, in dollars, on Wednesday?

A.     

B.     

C.   

D.   

E.   

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GRAPHS, FUR1 2014 VCAA 8 MC

The constraints of a linear programming problem are given by the following set of inequalities.

 

The coordinates of the points that define the boundaries of the feasible region for this linear programming problem are

A.  

B.  

C. 

D. 

E. 

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GRAPHS, FUR1 2014 VCAA 7 MC

Consider the following statements that relate to the solution of linear programming problems.

Which one of the following statements is true?

A.  Only one point can be a solution.

B.  No point outside the feasible region can be a solution.

C.  To have a solution, the feasible region must be bounded.

D.  Only the corner points of a feasible region can be a solution.

E.  Only the corner points with integer coordinates can be a solution. 

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GRAPHS, FUR1 2014 VCAA 5 MC

The distance–time graph below shows a train’s journey between two towns.

During the journey, the train stopped for 30 minutes.

The average speed of the train, in kilometres per hour, for the journey is closest to

A.  

B.  

C.  

D.  

E.  

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CORE*, FUR1 2014 VCAA 8 MC

Robert invested $6000 at 4.25% per annum with interest compounding quarterly.

Immediately after interest is paid at the end of each quarter, he adds $500 to his investment.

The value of Robert’s investment at the end of the third quarter, after his $500 has been added, is closest to

A.   $6193

B.   $7569

C.   $7574

D.   $7709

E.   $8096

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CORE*, FUR1 2014 VCAA 7 MC

New furniture was purchased for an office at a cost of $18 000.

Using flat rate depreciation, the furniture will be valued at $5000 after four years.

The expression that can be used to determine the value of the furniture, in dollars, after one year is

A.  

B.  

C.  

D.  

E.  

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GRAPHS, FUR1 2006 VCAA 8 MC

The cost of manufacturing a number of frying pans consists of a fixed cost of $400 plus a cost of $50 per frying pan.

The manufacturer could break even by selling

A.   10 frying pans at $90 each.

B.   10 frying pans at $45 each.

C.   15 frying pans at $60 each.

D.   15 frying pans at $30 each.

E.   20 frying pans at $50 each.

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GRAPHS, FUR1 2006 VCAA 7 MC

In a linear programming problem involving animal management on a farm
•    represents the number of cows on the farm
•    represents the number of sheep on the farm.

The feasible region (with boundaries included) for the problem is indicated by the shaded region on the diagram below.

GRAPHS, FUR1 2006 VCAA 7 MC

One of the constraints defining the feasible region indicates that

A.   there must be 20 cows and 60 sheep.

B.   there must be 40 cows and 40 sheep.

C.   the number of sheep cannot exceed 40.

D.   the number of cows must be at least 60.

E.   the total number of cows and sheep cannot exceed 80.

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GRAPHS, FUR1 2006 VCAA 2 MC

GRAPHS, FUR1 2006 VCAA 2 MC

The graph above represents the depth of water in a channel (in metres) as it changes over time (in hours).

During the time interval shown, the number of times the depth of the water in the channel is 10 metres is

A.   

B.   

C.   

D.   

E.   

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GRAPHS, FUR1 2006 VCAA 2 MC Answer

Measurement, 2UG MM6 SM-Bank 01 MC

 

Mapupu and Minoha are two towns on the equator.

The longitude of Mapupu is and the longitude of Minoha is .

How far apart are these two towns if the radius of Earth is approximately ?

(A)  

(B)  

(C)  

(D)  

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GRAPHS, FUR1 2007 VCAA 9 MC

The following five constraints apply to a linear programming problem.

In the diagram below, the shaded region (with boundaries included) represents the feasible region for this linear programming problem.

GRAPHS, FUR1 2007 VCAA 9 MC

The aim is to maximise the objective function  .

If the maximum value of occurs only at the point , then a possible value for is

A.   

B.   

C.   

D.   

E.   

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GRAPHS, FUR1 2007 VCAA 8 MC

Which one of the following pairs of simultaneous linear equations has no solution?

A.
 

 

B.
 

 

C.
 

 

D.
 

 

E.
 
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COMMENT: Realising that simultaneous equations have no solution if their gradients are the same is the key to solving this question efficiently..

 

 

 

GRAPHS, FUR1 2007 VCAA 5 MC

GRAPHS, FUR1 2007 VCAA 5 MC

The cost of hiring one motorbike for up to 4 hours is shown in the graph above.

Two motorbikes were hired.

The total charge for hiring the two motorbikes was $45.

The time for which each motorbike was hired could have been

A.   1 hour and 2 hours.

B.   1 hour and 3 hours.

C.   1.5 hours and 2 hours.

D.   1.5 hours and 3 hours.

E.    2 hours and 3.5 hours. 

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GRAPHS, FUR1 2008 VCAA 6 MC

At the local bakery, the cost of four donuts and six buns is $14.70.

The cost of three donuts and five buns is $11.90.

At this bakery, the cost of one donut and two buns will be

A.   

B.   

C.   

D.   

E.   

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GRAPHS, FUR1 2008 VCAA 3 MC

The graph below shows the time , in hours, taken to travel 100 km at an average speed of km/h.

GRAPHS, FUR1 2008 VCAA 3 MC

Which statement is false?

  1. As average speed increases, the time taken to travel 100 km decreases.
  2. It will take 2 hours to travel 100 km at an average speed of 50 km/h.
  3. The relationship between time and average speed is linear.
  4. When travelling at an average speed of 20 km/h, the 100 km journey takes 5 hours to complete.
  5. A formula that relates and is  
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Algebra, STD2 A4 SM-Bank 27

Fiona and John are planning to hold a fund-raising event for cancer research.  They can hire a function room for $650 and a band for $850.  Drinks will cost them $25 per person.

  1. Write a formula for the cost ($C) of holding the charity event for    people.  (1 mark)

  2. The graph below shows the planned income and costs if they charge $50 per ticket.  Estimate the number of guests they need to break even.    (1 mark)

     

  3. How much profit will Fiona and John make if 80 people attend their event?   (1 mark)

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Statistics, STD2 S5 SM-Bank 4 MC

The length of a type of ant is approximately normally distributed with a mean of 4.8 mm and a standard deviation of 1.2 mm.

A standardised ant length of    corresponds to an actual ant length of

A.   

B.   

C.   

D.   

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GRAPHS, FUR1 2009 VCAA 8 MC

Brian, a landscaping contractor, charges by the hour for his company’s services.

To complete a particular job, he will have to use three workers and pay each of them $20 per hour. The fixed costs for the job are $150 and it will take four hours to complete the job.

To break even on this job, his hourly charge to the client should be

A.     

B.     

C.     

D.   

E.    

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GRAPHS, FUR1 2009 VCAA 7 MC

A school’s squash and volleyball teams plan to enter a sports competition.

A squash team requires at least 4 players.

A volleyball team requires at least 6 players.

No more than 25 students from any one school can enter the competition.

Let    be the number of squash players sent by the school to the competition.
Let    be the number of volleyball players sent by the school to the competition.

The constraints above define the feasible region shaded in the graph below.

GRAPHS, FUR1 2009 VCAA 7 MC

 

A fee is charged for all players entering the competition. Squash players are charged $5 and volleyball players are charged $4.

Given the above constraints, the maximum cost for the school’s squash and volleyball teams to enter the competition is

A.     

B.   

C.   

D.   

E.   

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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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GEOMETRY, FUR1 2006 VCAA 6 MC

GEOMETRY, FUR1 2006 VCAA 6 MC

The rectangular box shown in this diagram is closed at the top and at the bottom.

It has a volume of 6 m³.

The base dimensions are 1.5 m × 2 m.

The total surface area of this box is

A.      ²

B.      ²

C.   ²

D.      ²

E.      ²

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²

Measurement, 2UG 2007 HSC 28c

A piece of plaster has a uniform cross-section, which has been shaded, and has dimensions as shown.
 

 
 

  1. Use two applications of Simpson’s rule to approximate the area of the cross-section.    (3 marks)
  2. The total surface area of the piece of plaster is  ².
  3. Calculate the area of the curved surface as shown on the diagram.   (2 marks)

 

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GEOMETRY, FUR1 2006 VCAA 4 MC

GEOMETRY, FUR1 2006 VCAA 4 MC

The building shown in the diagram is 8 m wide and 24 m long.

The side walls are 4 m high.

The peak of the roof is 6 m vertically above the ground.

In cubic metres, the volume of this building is

A.     

B.    

C.     

D.  

E.    

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GEOMETRY, FUR1 2006 VCAA 4 MC Answer 

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GEOMETRY, FUR1 2007 VCAA 4 MC

A steel beam used for constructing a building has a cross-sectional area of 0.048 m2 as shown.

The beam is 12 m long.

GEOMETRY, FUR1 2007 VCAA 4 MC

In cubic metres, the volume of this steel beam is closest to

A.  

B.  

C.   

D.  

E.   

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