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CORE, FUR2 2012 VCAA 4

The wind speeds (in km/h) that were recorded at the weather station at 9.00 am and 3.00 pm respectively on 18 days in November are given in the table below. A scatterplot has been constructed from this data set.
 

CORE, FUR2 2012 VCAA 41
 

Let the wind speed at 9.00 am be represented by the variable ws9.00am and the wind speed at 3.00 pm be represented by the variable ws3.00pm. 

The relationship between ws9.00am and ws3.00pm shown in the scatterplot above is nonlinear. 

A squared transformation can be applied to the variable ws3.00pm to linearise the data in the scatterplot.

  1. Apply the squared transformation to the variable ws3.00pm and determine the equation of the least squares regression line that allows (ws3.00pm)² to be predicted from ws9.00am.

     

    In the boxes provided, write the coefficients for this equation, correct to one decimal place.   (2 marks)

    2012 4-1

  2. Use this equation to predict the wind speed at 3.00 pm on a day when the wind speed at 9.00 am is 24 km/h.

     

    Write your answer, correct to the nearest whole number.   (1 mark)

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a.  

MARKER’S COMMENT: Many students were unable to deal with the squared transformation.


 

b.  

CORE, FUR2 2012 VCAA 3

A weather station records the wind speed and the wind direction each day at 9.00 am. 

The wind speed is recorded, correct to the nearest whole number. 

The parallel boxplots below have been constructed from data that was collected on the 214 days from June to December in 2011.
 

CORE, FUR2 2012 VCAA 3

  1. Complete the following statements.
  2. The wind direction with the lowest recorded wind speed was ________.
  3. The wind direction with the largest range of recorded wind speeds was _______.   (1 mark)

  4. The wind blew from the south on eight days.
  5. Reading from the parallel boxplots above we know that, for these eight wind speeds, the
first quartile
median
third quartile
  1. Given that the eight wind speeds were recorded to the nearest whole number, write down the eight wind speeds.   (1 mark) 
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a.  
 

b.  

♦♦ MARKER’S COMMENT: Although specific data isn’t available, “few” students answered this part correctly.


  

CORE, FUR2 2012 VCAA 2

The maximum temperature and the minimum temperature at this weather station on each of the 30 days in November 2011 are displayed in the scatterplot below.

CORE, FUR2 2012 VCAA 2

The correlation coefficient for this data set is  . 

The equation of the least squares regression line for this data set is

maximum temperature = × minimum temperature

  1. Draw this least squares regression line on the scatterplot above.   (1 mark)

  2. Interpret the vertical intercept of the least squares regression line in terms of maximum temperature and minimum temperature.   (1 mark)

  3. Describe the relationship between the maximum temperature and the minimum temperature in terms of strength and direction.   (1 mark)

  4. Interpret the slope of the least squares regression line in terms of maximum temperature and minimum temperature.   (1 mark)

  5. Determine the percentage of variation in the maximum temperature that may be explained by the variation in the minimum temperature.
  6. Write your answer, correct to the nearest percentage.   (1 mark)

On the day that the minimum temperature was 11.1 °C, the actual maximum temperature was 12.2 °C.

  1. Determine the residual value for this day if the least squares regression line is used to predict the maximum temperature.
  2. Write your answer, correct to the nearest degree.   (2 marks)

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a.  

 CORE, FUR2 2012 VCAA 2 Answer 

b.  

 

♦ Parts (i) to (vi) have an average mean mark of 41%.

c.   

 

d.  

 

 

 

e.   
   
   

 

f.  

MARKER’S COMMENT: Students had particular difficulty with this part, with many using the incorrect calculation of  12.2 – 11.1 = 1.1.
 
 
 

CORE, FUR2 2013 VCAA 4

The time series plot below shows the average pay rate, in dollars per hour, for workers in a particular country for the years 1991 to 2005.
 

CORE, FUR2 2013 VCAA 4

A three median line will be used to model the increasing trend in the average pay rate shown in this time series.

The explanatory variable to be used is year.

  1. Three medians will be used to draw the three median line.

     

    1. On the time series plot above, mark the location of each of the three medians with a cross ().  (2 marks)
    2. Draw the three median line on the time series plot.  (1 mark)
  2. Calculate the slope of the three median line.

     

    Write your answer, correct to one decimal place.  (1 mark)

  3. Interpret the slope of the three median line in terms of the relationship between the variables average pay rate and year.  (1 mark)
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  1. i. & ii.

  3.  

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a.i. & ii.   

♦ Mean mark 45%.
MARKER’S COMMENT: Few students found the correct middle point.

 

CORE, FUR2 2013 VCAA 4 Answer

♦♦ Parts (ii) and (iii) produced an overall mean mark of 32%.

 

b.   
   
   
   

 

MARKER’S COMMENT: Answering “an increase of 0.8 each year” received no marks (refer to actul units).

 

c.   

 

CORE, FUR2 2013 VCAA 3

The development index and the average pay rate for workers, in dollars per hour, for a selection of 25 countries are displayed in the scatterplot below.

CORE, FUR2 2013 VCAA 31   

The table below contains the values of some statistics that have been calculated for this data.

     CORE, FUR2 2013 VCAA 32

  1. Determine the standardised value of the development index ( score) for a country with a development index of 91.
  2. Write your answer, correct to one decimal place.   (1 mark)

  3. Use the information in the table to show that the equation of the least squares regression line for a country’s development index, , in terms of its average pay rate, , is given by
  4.           (2 marks)

  5. The country with an average pay rate of $14.30 per hour has a development index of 83.
  6. Determine the residual value when the least squares regression line given in part (b) is used to predict this country’s development index.
  7. Write your answer, correct to one decimal place.   (2 marks)

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MARKER’S COMMENT: Many students made a careless error by using the Average pay rate (-variable).
a.   
   
   
   

 

♦ Parts (b) and (c) had a combined mean mark of 48%.
b.   
   
   

 

 
 

 

 

c.   
   

 

 
 

CORE, FUR2 2014 VCAA 4

The scatterplot below shows the population density, in people per square kilometre, and the area, in square kilometres, of 38 inner suburbs of the same city.

Core, FUR2 2015 VCAA 41

For this scatterplot,

  1. Describe the association between the variables population density and area for these suburbs in terms of strength, direction and form.   (1 mark)

  2. The mean and standard deviation of the variables population density and area for these 38 inner suburbs are shown in the table below.
     
    Core, FUR2 2015 VCAA 42
  3.   i. One of these suburbs has a population density of 3082 people per square kilometre.
  4.     Determine the standard -score of this suburb’s population density.
  5.     Write your answer, correct to one decimal place.   (1 mark)

Assume the areas of these inner suburbs are approximately normally distributed.

  1.  ii. How many of these 38 suburbs are expected to have an area that is two standard deviations or more above the mean?
  2.     Write your answer, correct to the nearest whole number.   (1 mark)

  3. iii. How many of these 38 inner suburbs actually have an area that is two standard deviations or more above the mean?   (1 mark)

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♦♦ Mean mark 30%.
MARKER’S COMMENT: The most common error was to describe the association as positive.
a.   
   

 

 

b.i   
   
   
   

 

b.ii.   

 

b.iii.   

♦♦ Very few students answered this part correctly.

²

 

CORE, FUR2 2014 VCAA 3

The scatterplot and table below show the population, in thousands, and the area, in square kilometres, for a sample of 21 outer suburbs of the same city.
  

Core, FUR2 2015 VCAA 3

In the outer suburbs, the relationship between population and area is non-linear.

A log transformation can be applied to the variable area to linearise the scatterplot.

  1. Apply the log transformation to the data and determine the equation of the least squares regression line that allows the population of an outer suburb to be predicted from the logarithm of its area.
  2. Write the slope and intercept of this regression line in the boxes provided below.
  3. Write your answers, correct to one decimal place.   (1 mark)

  Core, FUR2 2015 VCAA 32

  1. Use this regression equation to predict the population of an outer suburb with an area of 90 km².
  2. Write your answer, correct to the nearest one thousand people.   (1 mark)

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a.   

♦ Mean marks of 43% (part (a)) and 35% (part (b)).
MARKER’S COMMENT: Many students confused the base 10 logarithm with the natural logarithm.

 

b.  

 
 

CORE, FUR2 2014 VCAA 2

The scatterplot below shows the population and area (in square kilometres) of a sample of inner suburbs of a large city.
 

Core, FUR2 2015 VCAA 2

The equation of the least squares regression line for the data in the scatterplot is

population = 5330 + 2680 × area

  1. Write down the response variable.   (1 mark)

  2. Draw the least squares regression line on the scatterplot above.   (1 mark)

  3. Interpret the slope of this least squares regression line in terms of the variables area and population.  (2 marks)

  4. Wiston is an inner suburb. It has an area of 4 km² and a population of 6690.
  5. The correlation coefficient, , is equal to 0.668
  6.  i. Calculate the residual when the least squares regression line is used to predict the population of Wiston from its area.  (1 mark)

  7. ii. What percentage of the variation in the population of the suburbs is explained by the variaton in area.
  8.     Write your answer, correct to one decimal place.  (1 mark)

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  2.  
          Core, FUR2 2015 VCAA 2 Answer

  3. ²
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a.  
 

♦ Mean mark 36%.
MARKER’S COMMENT: Use the equation to draw the line and use points at the extremities.
b.   

Core, FUR2 2015 VCAA 2 Answer

 

c.   

♦ Mean mark 41% (part (iii)).

²
 

d.i. 


 

♦ Part (iv) in total had a mean mark 42%.
d.ii.   
 
   

 

CORE, FUR2 2014 VCAA 1

The segmented bar chart below shows the age distribution of people in three countries, Australia, India and Japan, for the year 2010.
 

Core, FUR2 2015 VCAA 1

  1. Write down the percentage of people in Australia who were aged 0 – 14 years in 2010.
  2. Write your answer, correct to the nearest percentage.  (1 mark)

  3. In 2010, the population of Japan was 128 000 000.
  4. How many people in Japan were aged 65 years and over in 2010?  (1 mark)

  5. From the graph above, it appears that there is no association between the percentage of people in the 15 – 64 age group and the country in which they live.
  6. Explain why, quoting appropriate percentages to support your explanation.  (1 mark)

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  3.  
     
     

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a.   

 

b.  

 

c.   

♦ Mean mark 41%.

CORE, FUR2 2015 VCAA 5

The time series plot below displays the life expectancy, in years, of people living in Australia and the United Kingdom (UK) for each year from 1920 to 2010.
 

Core, FUR2 2015 VCAA 51

  1. By how much did life expectancy in Australia increase during the period 1920 to 2010?
  2. Write your answer correct to the nearest year.   (1 mark)

  3. In 1975, the life expectancies in Australia and the UK were very similar.
  4. From 1975, the gap between the life expectancies in the two countries increased, with people in Australia having a longer life expectancy than people in the UK.
  5. To investigate the difference in life expectancies, least squares regression lines were fitted to the data for both Australia and the UK for the period 1975 to 2010.
  6. The results are shown below. 

  Core, FUR2 2015 VCAA 52

  1. The equations of the least squares regression lines are as follows.
 

 

  1. Use these equations to predict the difference between the life expectancies of Australia and the UK in 2030.
  2. Give your answer correct to the nearest year.   (2 marks)

  3. Explain why this prediction may be of limited reliability.   (1 mark)

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    2.  

       

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a.   

 

b.i.   
   
     
 
   

 

 
♦ Mean mark 45%.
MARKER’S COMMENT: Relate answers directly to the limitations of the given statistical data rather than future events in (b)(ii).

 

b.ii.   

 

 

CORE, FUR2 2015 VCAA 4

The table below shows male life expectancy (male) and female life expectancy (female) for a number of countries in 2013. The scatterplot has been constructed from this data.
 

Core, FUR2 2015 VCAA 4

  1. Use the scatterplot to describe the association between male life expectancy and female life expectancy in terms of strength, direction and form.   (1 mark)

  2. Determine the equation of a least squares regression line that can be used to predict male life expectancy from female life expectancy for the year 2013.

     

    Complete the equation for the least squares regression line below by writing the intercept and slope in the space provided.

     

    Write these values correct to two decimal places.  (1 mark)

male = ______________ + ______________ ×  female

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a.   

♦ Mean mark 49%.
MARKER’S COMMENT: Common errors included using the 1st column as the independent () variable and poor rounding.

 

b.  

CORE, FUR2 2015 VCAA 3

The scatterplot below plots male life expectancy (male) against female life expectancy (female) in 1950 for a number of countries. A least squares regression line has been fitted to the scatterplot as shown.
 


 

The slope of this least squares regression line is 0.88

  1. Interpret the slope in terms of the variables male life expectancy and female life expectancy.  (1 mark)

The equation of this least squares regression line is

male = 3.6 + 0.88 × female

  1. In a particular country in 1950, female life expectancy was 35 years.

     

    Use the equation to predict male life expectancy for that country.  (1 mark)

  2. The coefficient of determination is 0.95

     

    Interpret the coefficient of determination in terms of male life expectancy and female life expectancy.  (1 mark)

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a.   

♦ Mean mark 40%.
MARKER’S COMMENT: Many students did not describe the slope, despite being specifically asked about it!

 

b.   

 

c.   

MARKER’S COMMENT: A common error: use of as the basis of the interpretation.

 

CORE, FUR2 2015 VCAA 2

The parallel boxplots below compare the distribution of life expectancy for 183 countries for the years 1953, 1973 and 1993.
 

Core, FUR2 2015 VCAA 2

  1. Describe the shape of the distribution of life expectancy for 1973.   (1 mark)

  2. Explain why life expectancy for these countries is associated with the year. Refer to specific statistical values in your answer.   (2 marks)

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a.   


 

b.   

♦ Mean mark 45%.
MARKER’S COMMENT: Means are typically not discernible from a box plot (unless the data is perfectly symmetrical) and shouldn’t be referred to.

 

GRAPHS, FUR1 2015 VCAA 5 MC

For an overnight school excursion there must be at least one teacher for every 15 students.

Let be the number of students
      be the number of teachers.

The inequality for this constraint is

A.   

B.   

C.   

D.  

E.  

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♦ Mean mark 37%.
MARKER’S COMMENT: Test your answer. 40% of students chose C which means 10 students would be supervised by over 150 teachers!

 

 

Financial Maths, 2ADV M1 SM-Bank 6

A toy train track consists of a number of pieces of track which join together.

The shortest piece of the track is 15 centimetres long and each piece of track after the shortest is 2 centimetres longer than the previous piece.

The total length of the complete track is 7.35 metres.

Find the length of the longest piece of track. (3 marks)

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Statistics, STD2 S5 SM-Bank 2 MC

The pulse rates of a large group of 18-year-old students are approximately normally distributed with a mean of 75 beats/minute and a standard deviation of 11 beats/minute. 

The percentage of 18-year-old students with pulse rates less than 53 beats/minute or greater than 86 beats/minute is closest to

  1.  
  2.  
  3.  
  4.  
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COMMENT: Two applications of the 68-95-99.7% rule are required. A good strategy is to first draw a normal curve and shade the required areas.
   
   
 

core 2008 VCAA 6-7

 

 

Financial Maths, STD2 F4 SM-Bank 1 MC

Ernie took out a reducing balance loan to buy a new family home.

He correctly graphed the amount paid off the principal of his loan each year for the first five years.

The shape of this graph (for the first five years of the loan) is best represented by
 

 

 

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GRAPHS, FUR1 2010 VCAA 9 MC

Two roof sections of a building are separated by a vertical window.

The roof sections are modelled by two straight line graphs as follows.

 

The vertical window has height 1 m.

The value of is

A.   

B.   

C.   

D.   

E.   

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♦ Mean mark 37%.

 

 

GRAPHS, FUR1 2011 VCAA 7-9 MC

Craig plays sport and computer games every Saturday.

Let be the number of hours that he spends playing sport.
Let be the number of hours that he spends playing computer games.

Craig has placed some constraints on the amount of time that he spends playing sport and computer games.

These constraints define the feasible region shown shaded in the graph below. The equations of the lines that define the boundaries of the feasible regions are also shown.

Part 1

One of the constraints that defines the feasible region is

A.  

B.  

C.  

D.  

E.  

 

Part 2

By spending Saturday playing sport and computer games, Craig believes he can improve his health.

Let be the health rating Craig achieves by spending a day playing sport and computer games.

The value of is determined by using the rule  .

For the feasible region shown in the graph above, the maximum value of occurs at

A.   point 

B.   point 

C.   point 

D.   point 

E.   point 

 

Part 3

By spending Saturday playing sport and computer games, Craig believes he can improve his mental alertness.

Let be the mental alertness rating Craig achieves by spending a day playing sport and computer games.

For the feasible region shown in the graph above, the maximum value of occurs at any point that lies on the line that joins points and is the feasible region.

The rule for could be

A.  

B.  

C.  

D.  

E.  

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GRAPHS, FUR1 2012 VCAA 6 MC

The oil price (dollars/barrel) over a ten-year period is shown on the graph below.

Which one of the following statements is true?

  1. The highest oil price over the ten-year period is $70.
  2. The oil price decreased for exactly two of the ten years.
  3. The oil price changed most rapidly during the sixth year.
  4. On average, the oil price changed by $4.50 per year over the ten years.
  5. The difference between the highest and lowest oil price during this ten-year period is $45.
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♦ Mean mark 49%.
 
 

 

GRAPHS, FUR1 2012 VCAA 4-5 MC

Part 1

The graph above shows the volume of water, litres, in a tank at time minutes.

The equation of this line between    and    minutes is

A.  

B.  

C.  

D.  

E.  

 

Part 2

During the 85 minutes that it took to empty the tank, the volume of water in the tank first decreased at the rate of 15 litres per minute and then did not change for a period of time.

The period of time, in minutes, for which the volume of water in the tank did not change is

A.   

B.   

C.   

D.   

E.   

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♦ Mean mark 49%.

 
 

 

 

 

 

GRAPHS, FUR1 2013 VCAA 9 MC

A cafe sells the first 200 cups of hot chocolate each day at a special price of $3.00 per cup. After that, a cup of hot chocolate will be sold for $4.50.

The revenue, , in dollars, made from selling cups of hot chocolate each day is given by the rule

The cost, , in dollars, of making cups of hot chocolate each day is

To break even, the number of cups of hot chocolate that must be sold each day is

A.    

B.  

C.  

D.  

E.  

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COMMENT: Selling up to 200 cups at the special price creates a loss, and the breakeven level must be found in the 2nd revenue equation.

 

GRAPHS, FUR1 2013 VCAA 7 MC

The heat intensity of a fire, , is recorded at different distances, , from the fire.

When is plotted against , the data points lie on a straight line, as shown below.

The point lies on the line.

Given this information, the rule that relates the intensity of the fire, , to the distance, , from the fire is closest to

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GEOMETRY, FUR1 2011 VCAA 8 MC

The diagram below shows a cross-section, , of a swimming pool.

The swimming pool is 11 metres long and the depth increases uniformly from 1 metre at the shallow end to 1.8 metres at the deep end.

The depth of the water at a point 8 metres from the shallow end, represented by on the diagram is closest to

A. 

B. 

C. 

D. 

E. 

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♦ Mean mark 40%.
MARKERS’ COMMENT: The most common mistake was to apply the properties of similar triangles to trapeziums, leading to an incorrect answer of B.
 
   

 

GEOMETRY, FUR1 2015 VCAA 9 MC

A wedge of cheese is in the shape of a triangular prism.

The base of the wedge of cheese is 8 cm long, as shown below.
 

GEO & TRIG, FUR1 2015 VCAA 9 MC

A smaller, similar wedge of cheese is cut from the larger wedge of cheese, as shown in the diagram.

The cut is made at a distance of cm from the back edge of the larger wedge.

The volume of the smaller wedge is half the volume of the larger wedge.

The value of , in centimetres, is closest to

A.   

B.   

C.   

D.   

E.   

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CORE*, FUR1 2015 VCAA 9 MC

Ravi borrowed $160 000 at an interest rate of 6.18% per annum.

Interest is calculated monthly on the reducing balance of the loan.

The loan will be fully repaid with monthly payments of $1950.

Which one of the following statements is not true?

A.   His first payment reduces the loan by less than $1950.

B.   His second payment reduces the loan by more than the first payment.

C.   Repaying more than $1950 per month will reduce the term of the loan.

D.   His final payment will be less than $1760.

E.   His final payment includes interest.

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♦ Mean mark 37%.
STRATEGY: Eliminating A, B and C is clear, and once a decimal month is confirmed for full payment, the last payment must contain interest and E can be eliminated.

 

 

 

CORE*, FUR1 2015 VCAA 6 MC

The transaction details for a savings account for the month of August 2014 are shown in the table below.

The table is incomplete.
 

 

Interest is calculated and paid monthly on the minimum balance for that month.

The annual rate of interest paid on this account is closest to

A.   

B.   

C.   

D.   

E.   

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♦ Mean mark 46%.
 

 

 
 

 

CORE*, FUR1 2015 VCAA 9 MC

Paul has to replace 3000 m of fencing on his farm.

Let be the length, in metres, of fencing left to replace after weeks.

The difference equation

can be used to calculate the length of fencing left to replace after weeks.

In this equation, is a constant.

After one week, Paul still has 2540 m of fencing left to replace.

After three weeks, the length of fencing, in metres, left to replace will be closest to

A.   1310

B.   1380

C.   1620

D.   1690

E.   2100

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♦ Mean mark 47%.
 
 

 

 
 
 
 

 

PATTERNS, FUR1 2015 VCAA 7 MC

A plant was 80 cm tall when planted in a garden.

After it was planted in the garden, its height increased by 16 cm in the first year.

It grew another 12 cm in the second year and another 9 cm in the third year.

Assuming that this pattern of geometric growth continues, the plant will grow to a maximum height of

A.     

B.   

C.   

D.   

E.   

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♦ Mean mark 48%.

 

 
 
 

CORE*, FUR1 2009 VCAA 9 MC

To purchase a house Sam has borrowed $250 000 at an interest rate of 4.45% per annum, fixed for ten years.

Interest is calculated monthly on the reducing balance of the loan. Monthly repayments are set at $1382.50.

After 10 years, Sam renegotiates the conditions for the balance of his loan. The new interest rate will be 4.25% per annum. He will pay $1750 per month.

The total time it will take him to pay out the loan fully is closest to

A.   17 years.

B.   20 years.

C.   21 years.

D.   22 years.

E.   23 years.

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♦ Mean mark 45%.

 

 

 

 

 

CORE*, FUR1 2009 VCAA 8 MC

Robin takes out a reducing balance loan of $100 000 with quarterly repayments of $2150.

After seven years of quarterly repayments, Robin still owes $80 000.

Correct to one decimal place, the interest rate per annum for this loan is

A.     6.3%

B.     8.2%

C.   12.9%

D.   18.9%

E.   24.7%

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♦ Mean mark 45%.

 

CORE*, FUR1 2010 VCAA 9 MC

Rebecca invested $4000 at 5.0% per annum with interest compounding quarterly.

After interest is paid at the end of each quarter, Rebecca adds $800 to her investment.

The value of her investment at the end of the second quarter, after the $800 has been added, is closest to

A.   $4101

B.   $4901

C.   $4911

D.   $5711

E.   $6060

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♦ Mean mark 47%.

 
 

 

 
 

CORE*, FUR1 2010 VCAA 8 MC

Rae paid  $40 000  for new office equipment at the start of the 2007 financial year.

At the start of each following financial year, she used flat rate depreciation to revalue her equipment.

At the start of the 2010 financial year she revalued her equipment at  $22 000.

The annual flat rate of depreciation she used, as a percentage of the purchase price, was

A.   11.25%

B.   15%

C.   17.5%

D.   35%

E.   45%

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♦ Mean mark 50%.

CORE*, FUR1 2010 VCAA 6 MC

The transaction details for an online savings account, for the month of March 2010, are shown below.

The bank pays a simple interest rate of 3.6% per annum on the minimum monthly balance.

The amount of interest that is credited to the account, for the month of March 2010, would be closest to

A.     $4.35

B.     $4.95

C.     $5.20

D.   $43.50

E.   $52.20

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♦ Mean mark 49%.

 
 

 

CORE*, FUR1 2011 VCAA 9 MC

Xavier borrows $45 000 from the bank to buy a car.

He is offered a reducing balance loan for three years with an interest rate of 9.75% per annum, compounding monthly.

He can repay this loan by making 36 equal monthly payments.

Instead, Xavier decides to repay the loan in 18 equal monthly payments.

If there are no penalties for repaying the loan early, the amount he will save is closest to

A.   $2697

B.   $3530

C.   $3553

D.   $6581

E.   $7083

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♦ Mean mark 44%.

 

 

 

 

 
 

CORE, FUR1 2011 VCAA 8 MC

Teresa borrowed $120 000 at an interest rate of 7.67% per annum, compounding monthly.

The loan is to be repaid with equal monthly payments.

She decides to repay the loan by making monthly payments of $1430.

Which of the following statements is true?

  1. She will pay out the loan fully in less than ten years.
  2. The amount of interest that she pays on the loan will increase each year.
  3. After four years the amount that she owes on the loan will be less than $80 000.
  4. Every monthly payment that she makes reduces the amount that she owes on the loan by the same amount.
  5. Monthly payments of $1560 (instead of $1430) will enable her to repay this loan in less than nine years. 
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CORE, FUR1 2010 VCAA 12 MC

The time series plot below shows the number of calls each month to a call centre over a twelve-month period.
 

CORE, FUR1 2010 VCAA 12 MC
 

The plot is to be smoothed using five-point median smoothing.

The smoothed number of calls for month number 10 is closest to 

A.   

B.   

C.   

D.   

E.   

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♦ Mean mark 43%.

 

CORE, FUR1 2015 VCAA 13 MC

The quarterly seasonal indices for tractor sales for a supplier are displayed in Table 1.

CORE, FUR1 2015 VCAA 13 MC1

The quarterly tractor sales in 2014 for this supplier are displayed in Table 2.

CORE, FUR1 2015 VCAA 13 MC2

The sales data in Table 2 is to be deseasonalised before a least squares regression line is fitted.

The equation of this least squares regression line is closest to

A.   deseasonalised sales = 0.32 + 910 × quarter number

B.   deseasonalised sales = 370 – 2300 × quarter number

C.   deseasonalised sales = 910 + 0.32 × quarter number

D.   deseasonalised sales = 2300 – 370 × quarter number

E.   deseasonalised sales = 2300 – 0.32 × quarter number 

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2015 fur1 core 13

♦ Mean mark 47%.

CORE, FUR1 2015 VCAA 6-7 MC

The following information relates to Parts 1 and 2.

In New Zealand, rivers flow into either the Pacific Ocean (the Pacific rivers) or the Tasman Sea (the Tasman rivers).

The boxplots below can be used to compare the distribution of the lengths of the Pacific rivers and the Tasman rivers.
 

CORE, FUR1 2015 VCAA 6 MC

Part 1

The five-number summary for the lengths of the Tasman rivers is closest to

 

Part 2

Which one of the following statements is not true?

  1. The lengths of two of the Tasman rivers are outliers.
  2. The median length of the Pacific rivers is greater than the length of more than 75% of the Tasman rivers.
  3. The Pacific rivers are more variable in length than the Tasman rivers.
  4. More than half of the Pacific rivers are less than 100 km in length.
  5. More than half of the Tasman rivers are greater than 60 km in length.
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♦ Mean mark 46%.

 

CORE*, FUR1 2006 VCAA 8 MC

Paula started a stamp collection. She decided to buy a number of new stamps every week.

The number of stamps bought in the th week, , is defined by the difference equation

The total number of stamps in her collection after five weeks is

A.     

B.   

C.   

D.   

E.    

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♦♦ Mean mark 33%.
STRATEGY: Always ask if the question wants a term or a sum of terms. This will minimise a very common mistake in this topic area.

 

PATTERNS, FUR1 2006 VCAA 6 MC

A crystal measured 12.0 cm in length at the beginning of a chemistry experiment.

Each day it increased in length by 3%.

The length of the crystal after 14 days growth is closest to

A.   

B.   

C.   

D.   

E.   

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♦♦ Mean mark 25%.
MARKERS’ COMMENT: The question asks for length after 14 days’ growth, not its length on the start of the 14th day.

CORE, FUR1 2006 VCAA 9 MC

A student uses the following data to construct the scatterplot shown below.

core 2006 VCAA 9i

To linearise the scatterplot, she applies an -squared transformation.

She then fits a least squares regression line to the transformed data with  as the dependent variable.

The equation of this least squares regression line is closest to

A.   

B.   

C.   

D.   

E.   

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♦ Mean mark 42%.

PATTERNS, FUR1 2007 VCAA 9 MC

At the end of the first day of a volcanic eruption, 15 km2 of forest was destroyed.

At the end of the second day, an additional 13.5 km2 of forest was destroyed.

At the end of the third day, an additional 12.15 km2 of forest was destroyed.

The total area of the forest destroyed by the volcanic eruption continues to increase in this way.

In square kilometres, the total amount of forest destroyed by the volcanic eruption at the end of the fourteenth day is closest to

A.   

B.   

C.   

D.   

E.   

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CORE, FUR1 2007 VCAA 11-13 MC

The following information relates to Parts 1, 2 and 3.

The time series plot below shows the revenue from sales (in dollars) each month made by a Queensland souvenir shop over a three-year period.

Part 1

This time series plot indicates that, over the three-year period, revenue from sales each month showed

A.   no overall trend.

B.   no correlation.

C.   positive skew.

D.   an increasing trend only.

E.   an increasing trend with seasonal variation.

 

Part 2

A three median trend line is fitted to this data.

Its slope (in dollars per month) is closest to

A.   

B.   

C.   

D.   

E.   

 

Part 3

The revenue from sales (in dollars) each month for the first year of the three-year period is shown below.

If this information is used to determine the seasonal index for each month, the seasonal index for September will be closest to

A.   

B.   

C.   

D.   

E.   

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♦ Mean mark 37%.
MARKERS’ COMMENT: A common error was to incorrectly use the 6 month and 30 month data points as the median.

 

 

 

CORE, FUR1 2007 VCAA 10 MC

The relationship between the variables

size of car (1 = small, 2 = medium, 3 = large)

and

salary level (1 = low, 2 = medium, 3 = high)

is best displayed using 

A.   a scatterplot.

B.   a histogram.

C.   parallel boxplots.

D.   a back-to-back stemplot.

E.   a percentaged segmented bar chart.

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♦ Mean mark 37%.

CORE, FUR1 2007 VCAA 9 MC

 A student uses the following data to construct the scatterplot shown below.

core 2007 VCAA 9i

To linearise the scatterplot, she applies a log y transformation; that is, a log transformation is applied to the -axis scale.

She then fits a least squares regression line to the transformed data.

With as the explanatory variable, the equation of this least squares regression line is closest to

A.   

B.   

C.   

D.   

E.   

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CORE*, FUR1 2008 VCAA 8 MC

When placed in a pond, the length of a fish was 14.2 centimetres.

During its first month in the pond, the fish increased in length by 3.6 centimetres.

During its th month in the pond, the fish increased in length by centimetres, where  

The maximum length this fish can grow to (in cm) is closest to

A.  14.4

B.  16.9

C.  19.0

D.  28.6

E.  17.2

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♦ Mean mark 45%.

 

 
 

 

Graphs, MET2 2015 VCAA 22 MC

The graphs of the functions with rules    and    are shown below.

 VCAA 2015 22mc

Which one of the following best represents the graph of the function with rule

 VCAA 2015 22mci

 VCAA 2015 22mcii

 VCAA 2015 22mciii

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♦♦ Mean mark 35%.
 

 

Algebra, MET2 2015 VCAA 18 MC

**Won't be asked in METHODS from 2016 onwards due to absolute value signs.

 

For which one of the following functions is the equation    true for all    and  

A.  

B.  

C.  

D.  

E.  

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♦ Mean mark 48%.
 
 
 
 
 

Probability, MET2 2014 VCAA 22 MC

John and Rebecca are playing darts. The result of each of their throws is independent of the result of any other throw. The probability that John hits the bullseye with a single throw is The probability that Rebecca hits the bullseye with a single throw is John has four throws and Rebecca has two throws.

The ratio of the probability of Rebecca hitting the bullseye at least once to the probability of John hitting the bullseye at least once is

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♦ Mean mark 37%.