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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. 

 

 

Statistics, STD2 S1 2009 HSC 21 MC

The mean of a set of ten scores is 14. Another two scores are included and the new mean is 16.

What is the mean of the two additional scores?

  1.    4
  2.    16
  3.    18
  4.    26
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♦♦♦ Mean mark 28%.

 

 

 

 

Statistics, STD2 S5 2012 HSC 29b

A machine produces nails. When the machine is set correctly, the lengths of the nails are normally distributed with a mean of  6.000 cm  and a standard deviation of  0.040 cm.

To confirm the setting of the machine, three nails are randomly selected. In one sample the lengths are  5.950,  5.983 and  6.140.

The setting of the machine needs to be checked when the lengths of two or more nails in a sample lie more than 1 standard deviation from the mean.

Does the setting on the machine need to be checked? Justify your answer with suitable calculations.   (2 marks)

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♦ Mean mark 44%

σ

 

σ

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%

Statistics, STD2 S1 2011 HSC 7 MC

A set of data is displayed in this box-and-whisker plot.
 

Which of the following best describes this set of data?

  1. Symmetrical
  2. Positively skewed
  3. Negatively skewed
  4. Normally distributed
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♦ Mean mark 47%.

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.   

Probability, STD2 S2 2012 HSC 17 MC

A spinner with different coloured sectors is spun 40 times. The results are recorded in the table.

 What is the relative frequency of obtaining the colour orange? 

  1.      
  2.      
  3.      
  4.     
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♦♦ Mean mark 34%
COMMENT: Note that relative frequency is the frequency of an event divided by the total frequencies (i.e. the probability).
 

 

Statistics, STD2 S4 2012 HSC 11 MC

Which of the following relationships would most likely show a negative correlation?

  1. The population of a town and the number of hospitals in that town. 
  2. The hours spent training for a race and the time taken to complete the race. 
  3. The price per litre of petrol and the number of people riding bicycles to work. 
  4. The number of pets per household and the number of computers per household. 
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♦ Mean mark 43%.

Financial Maths, STD2 F4 2012 HSC 9 MC

Tracy invests some money for 2 years at 4% per annum, compounded quarterly. 

2012 9 mc

Which figure from the table should Tracy use to calculate the value of her investment at the end of 2 years?

  1.   1.020 
  2.   1.082
  3.   1.083
  4.   1.369
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♦♦♦ Mean mark 24%. The lowest MC mean mark in the 2012 exam.
COMMENT: A process to follow: 1-convert the annual rate to the rate per compounding period. 2-calculate the number of compounding periods.

 

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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Statistics, STD2 S1 2010 HSC 1 MC

The results of a survey are displayed in the dot plot.

What is the range of this data?
 

2010 1 MC 
 

  1.    7
  2.    8
  3.    9
  4.    10
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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 S5 2013 HSC 20 MC

There are  60 000  students sitting a state-wide examination. If the results form a normal distribution, how many students would be expected to score a result between 1 and 2 standard deviations above the mean?

You may assume for normally distributed data that:

    • 68% of scores have  -scores between  – 1 and 1
    • 95% of scores have  -scores between  – 2 and 2
    • 99.7% of scores have  -scores between  – 3 and 3.
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♦♦ Mean mark 24% 


 

 

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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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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.

Statistics, STD2 S1 2013 HSC 8 MC

A high school has 100 students in each year group, Year 7 to Year 12. A survey is to be conducted to determine the average number of text messages sent per month by students at the school.

Which of the following would provide the most representative sample for this survey?

  1. All Year 7 students
  2. All physics students in Year 11 and 12
  3. 20 students chosen at random from each year group
  4. 120 students chosen at random from the school roll
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Probability, STD2 S2 2013 HSC 7 MC

In an experiment, a standard six-sided die was rolled 72 times. The results are shown in the table.
 

Which number on the die was obtained the expected number of times?

  1.    1
  2.    2
  3.    3
  4.    6
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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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