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Financial Maths, STD2 F1 2009 HSC 23d

The tables below show information about fees for MyBank accounts. 

2009 23d

  1. Li has a Cheap Access Account. During September, he made

     

        • five withdrawals using internet banking
        • two cash withdrawals from a MyBank ATM
        • four EFTPOS purchases
        • two cash withdrawals at other ATMs.

     

    What was the total amount that Li paid in bank fees for the month of September?  (3 marks)

  2. In October, what is the maximum that Li could pay in withdrawal fees to ensure that a Cheap Access Account costs him no more than a Free Access Account?    (1 mark)

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i.   
 
 
 
 

 

 

ii.   

♦ Mean mark 47%
MARKER’S COMMENT: Many students misinterpreted this question. Read carefully!

 

Measurement, STD2 M1 2009 HSC 23c

The diagram shows the shape and dimensions of a terrace which is to be tiled.
 

  1. Find the area of the terrace.   (2 marks)

  2. Tiles are sold in boxes. Each box holds one square metre of tiles and costs $55. When buying the tiles, 10% more tiles are needed, due to cutting and wastage.

     

    Find the total cost of the boxes of tiles required for the terrace.   (2 marks)

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i.    ²

ii.   

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i.
 
 
  ²

 

ii.
    ²

 

 

 

Measurement, STD2 M6 2009 HSC 23a

The point is 25 m from the base of a building. The angle of elevation from  to the top of the building is 38°.
 

  1. Show that the height of the building is approximately 19.5 m.   (1 mark)

  2. A car is parked 62 m from the base of the building.

     

    What is the angle of depression from the top of the building to the car?

     

    Give your answer to the nearest minute.   (2 marks)

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i.   

ii.   

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i. 

 
 

 

ii.  

♦♦ Mean mark 33%
MARKER’S COMMENT: If >30 “seconds”, round to the higher “minute”.
 
 
 
 

 

Data, 2UG 2009 HSC 18 MC

Huong used the ‘capture–recapture’ technique to estimate the number of trout living in a dam.

• She caught, tagged and released 20 trout.

• Later she caught 36 trout at random from the same dam.

• She found that 8 of these 36 trout had been tagged.

What estimate should Huong give for the total number of trout living in this dam, based on her use of the ‘capture–recapture’ technique?

(A)    

(B)    

(C)   

(D)   

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TIP: Work out a set structure to answer these types of questions efficiently. One example is shown in the Worked Solution where the Capture and Recapture are both stated as fractions <1 and then equated.

 

Measurement, STD2 M1 2009 HSC 11 MC

 What is the area of the shaded part of this quadrant, to the nearest square centimetre?  

  1. 34 cm²
  2. 42 cm²
  3. 50 cm²
  4. 193 cm²
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  ²

Probability, STD2 S2 2009 HSC 9 MC

A wheel has the numbers 1 to 20 on it, as shown in the diagram. Each time the wheel is spun, it stops with the marker on one of the numbers.
 


 

 The wheel is spun 120 times.

 How many times would you expect a number less than 6 to be obtained?

  1.    
  2.    
  3.    
  4.    
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Probability, STD2 S2 2009 HSC 8 MC

Some men and women were surveyed at a football game. They were asked which team they supported. The results are shown in the two-way table.
 

2UG-2009-8MC 
 

What percentage of the women surveyed supported Team B, correct to the nearest percent?

  1. 23%
  2. 45%
  3. 47%
  4. 55%
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Probability, STD2 S2 2010 HSC 12 MC

A group of 347 people was tested for flu and the results were recorded. The flu test  results are not always accurate.

2010 12 MC

A person is selected at random from the tested group.

What is the probability that their test result is accurate, to the nearest per cent?

  1.    21%
  2.    22%
  3.    95%
  4.    96%
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Algebra, STD2 A4 2012 HSC 30c

In 2010, the city of Thagoras modelled the predicted population of the city using the equation

.

That year, the city introduced a policy to slow its population growth. The new predicted population was modelled using the equation

.

In both equations, is the predicted population and is the number of years after 2010.  

The graph shows the two predicted populations.
 

  1. Use the graph to find the predicted population of Thagoras in 2030 if the population policy had NOT been introduced.   (1 mark)

  2. In each of the two equations given, the value of is 3 000 000.

     

    What does represent?   (1 mark)

  3. The guess-and-check method is to be used to find the value of , in  .

     

    (1) Explain, with or without calculations, why 1.05 is not a suitable first estimate for .  (1 mark)

     

    (2) With    and  , use the guess-and-check method and the equation    to estimate the value of to two decimal places. Show at least TWO estimate values for , including calculations and conclusions.  (2 marks)

  4. The city of Thagoras was aiming to have a population under 7 000 000 in 2050. Does the model indicate that the city will achieve this aim?

     

    Justify your answer with suitable calculations.  (2 marks)

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  1.  
  2.  
  3.  

     

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i.   

COMMENT: Common ADV/STD2 content in new syllabus.

 

ii.    


 

♦ Mean mark part (ii) 48%

iii. (1) 

   
 

iii. (2) 

 

 

 

 

 

iv. 

 

 

Algebra, STD2 A4 2012 HSC 30b

A golf ball is hit from point to point , which is on the ground as shown. Point is 30 metres above the ground and the horizontal distance from point to point is  300 m.
 

The path of the golf ball is modelled using the equation 

 

where 

is the height of the golf ball above the ground in metres, and 

is the horizontal distance of the golf ball from point in metres.

The graph of this equation is drawn below.

  

  1. What is the maximum height the ball reaches above the ground?    (1 mark)

  2. There are two occasions when the golf ball is at a height of 35 metres.

     

    What horizontal distance does the ball travel in the period between these two occasions?   (1 mark)

  3. What is the height of the ball above the ground when it still has to travel a horizontal distance of 50 metres to hit the ground at point ?   (1 mark)

  4. Only part of the graph applies to this model.

     

    Find all values of that are not suitable to use with this model, and explain why these values are not suitable.   (2 marks)

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i.   

COMMENT: With a mean mark of 92% in (i), a classic example of low hanging fruit in later questions.

 

ii.  

 

 

iii.   

MARKER’S COMMENT: Responses for (iii) in the range    were deemed acceptable estimates read off the graph.

 

iv.   

♦♦♦ Mean mark (iv) 12%
MARKER’S COMMENT: Many students did not refer to the domain as unsuitable to the model.

Statistics, STD2 S3 2012 HSC 29a*

Tourists visit a park where steam erupts from a particular geyser.

The brochure for the park has a graph of the data collected for this geyser over a period of time.

The graph shows the duration of an eruption and the time until the next eruption, timed from the end of one eruption to the beginning of the next.
 

  

  1. Tony sees an eruption that lasts 4 minutes. Based on the data in the graph, what is the minimum time that he can expect to wait for the next eruption? (1 mark)

  2. Julia saw two consecutive eruptions, one hour apart. Based on the data in the graph, what was the longest possible duration of the first eruption that she saw?    (1 mark)

  3. What does the graph suggest about the association between the duration of an eruption and the time to the next eruption? (1 mark)

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  4.  

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i. 

 

ii. 

♦ Mean mark (b) 47%

 

iii. 

Financial Maths, 2UG 2012 HSC 28e

Matthew bought a laptop priced at  $2800. He paid a 10% deposit and made monthly repayments of  $95.20  for 3 years.

What annual flat rate of interest was Matthew charged? Justify your answer with suitable calculations.   (4 marks)

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Probability, STD2 S2 2012 HSC 27e

A box contains 33 scarves made from two different fabrics. There are 14 scarves made from silk (S) and 19 made from wool (W).
Two girls each select, at random, a scarf to wear from the box.

  1. Complete the probability tree diagram below.   (2 marks) 
      
       

  2. Calculate the probability that the two scarves selected are made from silk.    (1 mark)

  3. Calculate the probability that the two scarves selected are made from different fabrics.   (2 marks)

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  1.  
       
     
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i. 

♦ Mean mark (i) 43%.
ii. 
 
 

 

iii. 
 
 
 
♦ Mean mark (iii) 41%.
MARKER’S COMMENT: In better responses, students multiplied along the branches and then added these two results together

Financial Maths, STD2 F1 2012 HSC 27a

Tai earns a gross weekly wage of  $1024. Each week her deductions are: 

    •    tax instalment of  $296.40 
    •    health fund contribution of  $24.50
    •    union fees of  $15.80.

        She also pays  $3640  over the year as her share of the household expenses.

        What percentage of her net wage does Tai pay for household expenses?    (3 marks)

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MARKER’S COMMENT: The best answers used clear steps in calculating deductions and net wages, and kept wages in their weekly form until the last step.
 
 
   
 

 

 
 

Statistics, STD2 S1 2012 HSC 28d

The test results in English and Mathematics for a class were recorded and displayed in the box-and-whisker plots.
 

  1. What is the interquartile range for English?  (1 mark)

  2. Compare and contrast the two data sets by referring to the skewness of the distributions and the measures of location and spread.   (3 marks)

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i.   

ii. 

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i.   

♦ Mean mark (ii) 35%
MARKER’S COMMENT: Markers are looking for students to use the correct language of location and spread such as mean, median, interquartile range, standard deviation and skewness.

ii. 

Statistics, STD2 S1 2011 HSC 11 MC

The sets of data, and , are displayed in the histograms.

2UG 2011 11

Which of these statements is true?

  1.   has a larger mode and has a larger range.
  2.   has a larger mode and the ranges are the same.
  3.   The modes are the same and has a larger range.
  4.   The modes are the same and the ranges are the same.
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♦ Mean mark 47%

Probability, STD2 S2 2010 HSC 8 MC

A bag contains red, green, yellow and blue balls.

The table shows the probability of choosing a red, green, or blue ball from the bag.

If there are 12 yellow balls in the bag, how many balls are in the bag altogether

  1.    16
  2.    36
  3.    48
  4.    60
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Financial Maths, STD2 F1 2010 HSC 5 MC

Minjy invests $2000 for 1 year and 5 months. The simple interest is calculated at a rate of 6% per annum.

What is the total value of the investment at the end of this period?

  1. $2170
  2. $2180
  3. $3003
  4. $3700
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Measurement, STD2 M1 2012 HSC 26g

Bhawana purchases pool chlorine in a new container which holds 35 kg.
 

2012 26g

 
She begins using this new container on the first day of a week.

How many full weeks should this container last?     (2 marks)

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MARKER’S COMMENT: Better answers converted all measurements to grams (rather than use decimals and kgs) and realised the answer should be in full weeks.
 

 

Probability, STD2 S2 2012 HSC 26e

The dot plot shows the number of push-ups that 13 members of a fitness class can do in one minute.

2012 26e

  1.  What is the probability that a member selected at random from the class can do more than 38 push-ups in one minute?   (1 mark)

  2.  A new member who can do 32 push-ups in one minute joins the class.

     

    Does the addition of this new member to the class change the probability calculated in part (i)? Justify your answer.    (1 mark)

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i. 
 

 
ii.   

 
MARKER’S COMMENT: The most successful candidates used the fraction in their part (ii) answer rather than relying solely on words.

Statistics, STD2 S1 2012 HSC 26d

Greg needs to conduct a statistical inquiry into how much time people aged 18–25 years have spent accessing social media websites in the last two weeks. He has decided to survey a sample of students from his university.

The process of statistical inquiry includes the following steps, which are NOT in order.
 

2012 26d 

  1. Using the letters A, B, C, D, E and F, list the steps in the most appropriate order for Greg to conduct his statistical inquiry.   (2 marks)

  2. Greg conducts his statistical inquiry.

     

    At which step in the process would he have drawn this graph?    (1 mark) 

2012 26d2

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i.  

ii.   

Financial Maths, STD2 F1 2012 HSC 18 MC

Jo qualifies for both Rent Assistance and Youth Allowance and receives a fortnightly payment from the government. 

Rent Assistance is  $119.40  per fortnight. 

The maximum Youth Allowance is $402.70 per fortnight. It is reduced by 50 cents in the dollar for any income earned over $236 per fortnight.

Jo earns $300 per fortnight from a part-time job.

What is the total payment Jo receives each fortnight from the government?

  1. $370.70
  2. $372.10
  3. $458.60
  4. $490.10
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Financial Maths, STD2 F4 2012 HSC 16 MC

A machine was bought for $25 000.

Which graph best represents the salvage value of the machine over 10 years using the declining balance method of depreciation?

(A)     (B)  
         
(C)        (D)
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Algebra, STD2 A1 2012 HSC 15 MC

A car takes 6 hours to complete a journey when travelling at 60 km/h.

How long would the same journey take if the car were travelling at 100 km/h?

  1.    36 minutes
  2.      1 hour and 40 minutes
  3.      3 hours and 6 minutes
  4.      3 hours and 36 minutes
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Financial Maths, STD2 F4 2012 HSC 24 MC

A  $400 000 loan can be repaid by making either monthly or fortnightly repayments.

The graph shows the loan balances over time using these two different methods of repayment.
 

2012 24 mc

The monthly repayment is $2796.86 and the fortnightly repayment is $1404.76.

What is the difference in the total interest paid using the two different methods of
repayment, to the nearest dollar?

  1.    $51 596
  2.    $166 823
  3.    $210 000
  4.    $234 936
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Statistics, STD2 S1 2012 HSC 7 MC

The Pi Company has two bakeries. The radar chart displays the monthly sales for the bakeries.
 

2012 7 mc 

  
What was the difference in sales in June between the two bakeries?

  1.   $7.50
  2.   $17.50
  3.   $7500
  4.   $17 500
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Measurement, STD2 M6 2011 HSC 4 MC

The angle of depression from a kookaburra’s feet to a worm on the ground is 40°. The worm is 15 metres from a point on the ground directly below the kookaburra’s feet. 
 

 How high above the ground are the kookaburra's feet, correct to the nearest metre?

  1. 10 m
  2. 11 m
  3. 13 m
  4. 18 m
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Statistics, STD2 S1 2012 HSC 1 MC

A set of 15 scores is displayed in a stem-and-leaf plot.
 

2012 1 mc 
 

 What is the median of these scores?

  1.    7 
  2.    8
  3.   77
  4.   78
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Statistics, STD2 S1 2013 HSC 15 MC

The frequency histogram shows the number of goals scored by a football team in each game in a season.
 

2013 15 mc

 
What is the mean number of goals scored per game by this team?

  1.    4
  2.    4.5
  3.    5
  4.    5.5
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Statistics, STD2 S1 2013 HSC 14 MC

The July sales prices for properties in a suburb were:

$552 000,  $595 000,  $607 000,  $607 000,  $682 000, and  $685 000.

On 1 August, another property in the same suburb was sold for over one million dollars.

If the property had been sold in July, what effect would it have had on the mean and median sale prices for July?

  1.    Both the mean and median would have changed.
  2.    Neither the mean nor the median would have changed.
  3.    The mean would have changed and the median would have stayed the same.
  4.    The mean would have stayed the same and the median would have changed.
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Financial Maths, STD2 F1 2013 HSC 13 MC

Polly borrowed $11 000.  She repaid the loan in full at the end of two years with a lump sum of  $12 000.

What annual simple interest rate was she charged?

  1. 4.17%
  2. 4.55%
  3. 8.33%
  4. 9.09%
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Probability, STD2 S2 2013 HSC 10 MC

Students studying vocational education courses were surveyed about their living arrangements.

One of these students is selected at random.

 What is the probability that this student is male and living with his parent(s)?

  1. 31%
  2. 40%
  3. 56%
  4. 77%
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.

Financial Maths, STD2 F1 2013 HSC 9 MC

Lynne invests $1000 for a term of 15 months. Simple interest is paid on the investment at a rate of 3.75% per annum.

How much will Lynne's investment be worth at the end of the term?

  1. $1046.88
  2. $1047.09
  3. $1296.88
  4. $1468.75
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Statistics, STD2 S1 2013 HSC 6 MC

A survey was conducted where people were asked which of two brands of smartphones they preferred. The results were:

  • 48% preferred Brand X
  • 52% preferred Brand Y

A graph displaying the data is to be included in a magazine article. The editor of the magazine wishes to ensure that the graph is not misleading in any way.

Which graph should the editor choose to include in the article?
 

2013 6 mc1

2013 6 mc2

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Financial Maths, STD2 F1 2013 HSC 3 MC

Luke's normal rate of pay is  $24.80  per hour. In one week he worked 14 hours at the normal rate, 4 hours at time-and-a-half, and 3 .5 hours at double time. He was also paid a wet weather allowance of  $50  for the week.

What was his pay for the week?

  1. $583.20
  2. $620.40
  3. $669.60
  4. $719.60
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Probability, STD2 S2 2013 HSC 1 MC

Which of the following events would be LEAST likely to occur?

  1.    Tossing a fair coin and obtaining a head
  2.    Rolling a standard six-sided die and obtaining a 3
  3.    Randomly selecting the letter 'G' from the 26 letters of the alphabet
  4.    Winning first prize in a raffle of 100 tickets in which you have 4 tickets
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