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CORE, FUR1 2016 VCAA 22 MC

The first three lines of an amortisation table for a reducing balance home loan are shown below.

The interest rate for this home loan is 4.8% per annum compounding monthly.

The loan is to be repaid with monthly payments of $1500.
 

 
The amount of payment number 2 that goes towards reducing the principal of the loan is

  1.  $486
  2.  $502
  3.  $504
  4.  $996
  5.  $998
Show Answers Only

`B`

Show Worked Solution
`text(Interest)` `= 249\ 500 xx (4.8text(%))/12`
  `= 249\ 500 xx 0.048/12`
  `= $998`

 

`:.\ text(Amount that reduces principal)`

`= 1500 – 998`

`= $502`

`=> B`

CORE, FUR1 2016 VCAA 21 MC

Juanita invests $80 000 in a perpetuity that will provide $4000 per year to fund a scholarship at a university.

The graph that shows the value of this perpetuity over a period of five years is
 

 

Show Answers Only

`B`

Show Worked Solution

`text(A perpetuity lasts indefinitely by only)`

`text(paying out interest.)`

`:.\ text(The graph should show a value that)`

`text(does not change over the years.)`

`=> B`

CORE, FUR1 2016 VCAA 14-16 MC

The table below shows the long-term average of the number of meals served each day at a restaurant. Also shown is the daily seasonal index for Monday through to Friday.

 

Part 1

The seasonal index for Wednesday is 0.84

This tells us that, on average, the number of meals served on a Wednesday is

  1. 16% less than the daily average.
  2. 84% less than the daily average.
  3. the same as the daily average.
  4. 16% more than the daily average.
  5. 84% more than the daily average.

 

Part 2

Last Tuesday, 108 meals were served in the restaurant.

The deseasonalised number of meals served last Tuesday was closest to

  1.   `93`
  2. `100`
  3. `110`
  4. `131`
  5. `152`

 

Part 3

The seasonal index for Saturday is closest to

  1. `1.22`
  2. `1.31`
  3. `1.38`
  4. `1.45`
  5. `1.49`
Show Answers Only

`text(Part 1:)\ A`

`text(Part 2:)\ E`

`text(Part 3:)\ D`

Show Worked Solution

`text(Part 1)`

`1 – 0.84 = 0.16`

`:.\ text(A seasonal index of 0.84 tell us)`

`text(16% less meals are served.)`

`=> A`

 

`text(Part 2)`

`text{Deseasonalised number (Tues)}`

`= text(actual number)/text(seasonal index)`

`= 108/0.71`

`~~ 152`

`=> E`

 

`text(Part 3)`

`text(S)text(ince the same number of deseasonalised)`

`text(meals are served each day.)`

`text{S.I. (Sat)}/190` `= 1.10/145`
`text{S.I. (Sat)}` `= (1.10 xx 190)/145`
  `= 1.44…`

`=> D`

CORE, FUR1 2016 VCAA 11-12 MC

The table below gives the Human Development Index (HDI) and the mean number of children per woman (children) for 14 countries in 2007.

A scatterplot of the data is also shown. 
 

 

Part 1

The scatterplot is non-linear.

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

With HDI as the explanatory variable, the equation of the least squares line fitted to the linearised data is closest to

  1. log(children) = 1.1 – 0.0095 × HDI
  2. children = 1.1 – 0.0095 × log(HDI)
  3. log(children) = 8.0 – 0.77 × HDI
  4. children = 8.0 – 0.77 × log(HDI)
  5. log(children) = 21 – 10 × HDI

 

Part 2

There is a strong positive association between a country’s Human Development Index and its carbon dioxide emissions.

From this information, it can be concluded that

  1. increasing a country’s carbon dioxide emissions will increase the Human Development Index of the country.
  2. decreasing a country’s carbon dioxide emissions will increase the Human Development Index of the country.
  3. this association must be a chance occurrence and can be safely ignored.
  4. countries that have higher human development indices tend to have higher levels of carbon dioxide emissions.
  5. countries that have higher human development indices tend to have lower levels of carbon dioxide emissions.
Show Answers Only

`text(Part 1:)\ A`

`text(Part 2:)\ D`

Show Worked Solution

`text(Part 1)`

`=>A`

 

`text(Part 2)`

`text(A strong positive association does not mean)`

`text(an increase in one variable causes an increase)`

`text(in the other.)`

`=> D`

CORE, FUR1 2016 VCAA 8 MC

Parallel boxplots would be an appropriate graphical tool to investigate the association between the monthly median rainfall, in millimetres, and the

  1. monthly median wind speed, in kilometres per hour.
  2. monthly median temperature, in degrees Celsius.
  3. month of the year (January, February, March, etc.).
  4. monthly sunshine time, in hours.
  5. annual rainfall, in millimetres.
Show Answers Only

`C`

Show Worked Solution

`text(Parallel boxplots can be used to investigate an)`

♦ Mean mark 45%.

`text(association between categorical and numerical)`

`text(variables.)`

`text(S)text(ince rainfall is numerical, the other variable must)`

`text(be categorical. Only)\ C\ text(is categorical.)`

`=> C`

CORE, FUR1 2016 VCAA 6-7 MC

Part 1

The histogram below shows the distribution of the number of billionaires per million people for 53 countries.
 

Using this histogram, the percentage of these 53 countries with less than two billionaires per million people is closest to

  1. `text(49%)`
  2. `text(53%)`
  3. `text(89%)`
  4. `text(92%)`
  5. `text(98%)`

 

Part 2

The histogram below shows the distribution of the number of billionaires per million people for the same 53 countries as in Part 1, but this time plotted on a `log_10` scale.
 

Based on this histogram, the number of countries with one or more billionaires per million people is

  1.   `text(1)`
  2.   `text(3)`
  3.   `text(8)`
  4.   `text(9)`
  5. `text(10)`
Show Answers Only

`text(Part 1:)\ D`

`text(Part 1:)\ E`

Show Worked Solution

`text(Part 1)`

`text(Percentage with less than 2)`

`= text(countries with less than 2)/text(total countries)`

`= 49/((49 + 2 + 1 + 1))`

`= 49/53`

`~~ 92.4text(%)`

`=> D`

 

`text(Part 2)`

`text(Let)\ \ x=\ text(number of billionaires per million,)`

`text(Number of countries where)\ \ x >= 1,`

♦ Mean mark 45%.
MARKER’S COMMENT: On a `log_10` scale, 1 is plotted as 0 because `log_10\ 1 = 0`, or `10^0=1`

`=> log_10 x >= 0`

`:.\ text(Number of countries)`

`= 9 + 1`

`= 10`

`=> E`

CORE, FUR1 2016 VCAA 1-2 MC

The blood pressure (low, normal, high) and the age (under 50 years, 50 years or over) of 110 adults were recorded. The results are displayed in the two-way frequency table below.
 

     

Part 1

The percentage of adults under 50 years of age who have high blood pressure is closest to

  1.  11%
  2.  19%
  3.  26%
  4.  44%
  5.  58%

Part 2

The variables blood pressure (low, normal, high) and age (under 50 years, 50 years or over) are

  1. both nominal variables.
  2. both ordinal variables.
  3. a nominal variable and an ordinal variable respectively.
  4. an ordinal variable and a nominal variable respectively.
  5. a continuous variable and an ordinal variable respectively.
Show Answers Only

`text(Part 1:)\ B`

`text(Part 2:)\ B`

Show Worked Solution

`text(Part 1)`

`text(Percentage)` `= text(Under 50 with high BP)/text(Total under 50)`
  `= 11/58`
  `~~ 19text(%)`

 
`=> B`

 

`text(Part 2)`

♦♦ Mean mark of Part 2: 31%.
MARKER’S COMMENT: Many students incorrectly identified the age (under 50, 50 or over) as nominal.

`text(Blood pressure is an ordinal variable)`

`text(because it is categorical data that can)`

`text(have an order.)`

`text(Under 50 and over 50, likewise, is an)`

`text(ordinal variable.)`

`=> B`

Statistics, NAP-F4-NC02

This graph shows the number of bats in a fruit tree at 15 minute intervals over 4 hours.
 

 
At which time were the highest number of bats in the fruit tree?

`5:45` `6:00` `6:15` `6:30`
 
 
 
 
Show Answers Only

`text(6:15 pm)`

Show Worked Solution

`text(The highest data point is one interval past 6:00 pm.)`

`:.\ text(The highest number were in the tree at 6:15 pm.)`

Number and Algebra, NAP-B2-19

Mandy has 46 jelly beans. Jenny has 34 Jelly beans.

How many jelly beans should Mandy give to Jenny if Mandy wanted them both to have the same number of jelly beans?

`6` `12` `40` `80`
 
 
 
 
Show Answers Only

`6\ text(jelly beans)`

Show Worked Solution

`text(If Mandy gives Jenny 6 jelly beans,)`

`text(Mandy’s jelly beans)` `=46-6`
  `=40`
`text(Jenny’s jelly beans)` `=34+6`
  `=40`

 

`:. 6\ text(jelly beans.)`

Measurement, NAP-B2-14 SA

James needs to catch a bus to the city from Greenville. Below is the bus timetable.

What is the latest time James can catch the bus to get to the city before 2 pm?
Show Answers Only

`text(12:40)`

Show Worked Solution

`text(The 12:40 pm bus leaving Greenville arrives at)`

`text(Town Hall at 1:55 pm and is the latest bus)`

`text(arriving before 2 pm.)`

Number and Algebra, NAP-C1-24

Cecil is packing away his club's lawn bowls after a practice session.

One bag carries 4 lawn bowls, as shown below.

Cecil needs to pack away 16 bowls.

Which of these shows how Cecil could work out the number of bags he needs?

`16 ÷ 4` `16 xx 4` `16 - 4` `16 + 4`
 
 
 
 
Show Answers Only

`16 ÷ 4`

Show Worked Solution

`text(S)text(ince each bag can carry 4 bowls, and there)`

`text(are 16 bowls in total,)`

`text(The number of bags = 16 ÷ 4)`

Number and Algebra, NAP-B1-21

What is the difference between the most sick days and the least sick days?

`11` `12` `13` `14`
 
 
 
 
Show Answers Only

`13`

Show Worked Solution

`text{Most sick days (Bella) = 15}`

`text{Least sick days (Kim) = 2}`

`:.\ text(Difference)` `= 15 – 2`
  `= 13`

Number and Algebra, NAP-B1-18

4 groups of 6 plums is the same number of plums as 3 groups of

`8` `6` `4` `3`
 
 
 
 
Show Answers Only

`8`

Show Worked Solution
`text(Number of plums)` `= 4 xx 6`
  `= 24`

`text(If 3 groups,)`

`text(Number in each group)`

`= 24 ÷ 3`

`= 8`

Probability, NAP-C1-22

Rudolph takes 4 marbles out of the bag at the same time.

Which of these is impossible?

 
 3 striped marbles and 1 white marble.
 
 3 white marbles and 1 grey marble.
 
 2 star marbles and 2 white marbles.
 
 2 striped marbles and 2 grey marbles.
Show Answers Only

`text(2 striped marbles and 2 grey marbles.)`

Show Worked Solution

`text{S}text{ince there is only 1 grey marble in the bag,}`

`text(2 striped marbles and 2 grey marbles is impossible.)`

Measurement, NAP-C1-19

Simon makes a calendar for March but forgets to label the days of the week.

He knows the 2nd of March is a Thursday.

What day of the week is 20 March?

 
 `text(Wednesday)`
 
 `text(Tuesday)`
 
 `text(Sunday)`
 
 `text(Monday)`
Show Answers Only

`text(Monday)`

Show Worked Solution

`text(Monday)`

Statistics, NAP-C1-16

Some students at a country school were asked to name their favourite animal.

The four most popular choices were put on the graph below.

  • Dogs were the most popular.
  • Sheep were more popular than cats.
  • Horses were less popular than sheep.

Which column shows sheep on the graph?
 

 

`text(A)` `text(B)` `text(C)` `text(D)`
 
 
 
 
Show Answers Only

`text(B)`

Show Worked Solution

`text(Column D is dogs.)`

`text(S)text(ince horses are less popular than sheep)`

`text(and sheep are more popular than cats.)`

`=>\ text(Sheep are more popular than horses and cats.)`

`=>\ text(Column B is sheep.)`

Number and Algebra, NAP-C1-13

Bobby has 76 football cards.

Shania has 117 football cards.

How many football cards do Bobby and Shania have altogether?

`183` `184` `193` `194`
 
 
 
 
Show Answers Only

`193`

Show Worked Solution
`text(Total cards)` `=117+76`
  `=187+6`
  `=193`

Number and Algebra, NAP-D1-23 SA

Kelly is buying tennis balls from the sporting goods shop.

It costs $12 to buy 4 balls.

If each ball costs the same, how many tennis balls can Kelly buy for $60?
Show Answers Only

`20`

Show Worked Solution
`text(C)text(ost of 1 ball)` `= 12 ÷ 4`
  `=$3`

 

`:.\ text(Number of balls she can buy)`

`= 60 ÷ 3`

`= 20`

Number and Algebra, NAP-D1-16

A chocolate bar has a mass of 100 grams.

The dotted line shows where Sharon cuts the chocolate bar.

Sharon takes the larger piece.

About what mass is Sharon's piece of chocolate?

`text(30 grams)` `text(50 grams)` `text(70 grams)` `text(90 grams)`
 
 
 
 
Show Answers Only

`text(70 grams)`

Show Worked Solution

`text(The cut is on a line where the smaller piece is)`

`text{just over one quarter (25 g) of the chocolate bar.}`

`:.\ text(The larger piece is about 70 grams.)`

Number and Algebra, NAP-E1-24

Siri has this much money.

She buys a drink for $1.25.

How much money does Siri have left?

`text(75 cents)` `text(85 cents)` `text(90 cents)` `text(95 cents)`
 
 
 
 
Show Answers Only

`text(85 cents)`

Show Worked Solution

`text(Money Siri has at the start)`

`=$1+50¢+20¢+20¢+10¢+10¢`

`=$2.10`

`text(Money left after buying a drink)`

`=$2.10 – $1.25`

`=85\ text(cents)`

Number and Algebra, NAP-E1-23

In Year 3 there are 17 more girls than boys.

Ari knows there are 35 girls.

How can Ari work out the number of boys in Year 3.

 
 `text(add 35 to 17)`
 
 `text(subtract 17 from 35)`
 
 `text(multiply 17 by 35)`
 
 `text(divide 35 by 17)`
Show Answers Only

`text(subtract 17 from 35)`

Show Worked Solution

`text(subtract 17 from 35)`

Statistics, NAP-E1-22

4 friends practiced taking soccer penalty goals.

They took 8 penalty with their right foot and another 8 penalty goals with their left foot.

The results are shown in the graph below.

Who scored the most penalty goals?

`text(Lionel)` `text(Kane)` `text(Tim)` `text(Pele)`
 
 
 
 
Show Answers Only

`text(Pele)`

Show Worked Solution

`text(Consider each player:)`

`text(Lionel = 3 + 7 = 10)`

`text(Kane = 6 + 4 = 10)`

`text(Tim = 7 + 2 = 9)`

`text(Pele = 6 + 5 = 11)`

`:.\ text(Pele scored the mosh penalty goals.)`

Number and Algebra, NAP-F1-27

Eliza took half the chocolates that were in a bowl.

Without any other chocolates being taken, Eliza took two more.

Eight chocolates were left in the bowl.

How many chocolates were in the bowl at the start?

`6` `10` `18` `20`
 
 
 
 
Show Answers Only

`20`

Show Worked Solution

`text(If we add the last 2 chocolates to the 8 left in)`

`text(the bowl, there are 10 in the bowl.)`

`=>\ text(10 is half the chocolates at the start.)`

`:.\ text(20 chocolates were in the bowl.)`

Measurement, NAP-F1-26

Lionel's soccer grand final is on the 4th September.
 


 

Lionel has a grand final breakfast for fans 5 days before the grand final.

What day of the week is Lionel's grand final breakfast for fans?

 
 `text(Thursday)`
 
 `text(Wednesday)`
 
 `text(Tuesday)`
 
 `text(Monday)`
 
 `text(Sunday)`
Show Answers Only

`text(Monday)`

Show Worked Solution

`text(1 day before is Friday.)`

`text(2 days before is Thursday.)`

`vdots`

`text(5 days before is Monday.)`

Measurement and Geometry, NAP-F1-25

Using this measuring tape, how long is the calculator?

`text(5 cm)` `text(11 cm)` `text(13 cm)` `text(18 cm)`
 
 
 
 
Show Answers Only

`text(13 cm)`

Show Worked Solution

`text(Length of calculator)`

`= 18 – 5`

`= 13\ text(cm)`

Statistics, NAP-F1-22

A year 7 class is split into boys and girls and each group collected butterflies in a jar.

The total number of butterflies in each jar is put in the table below.

How many more butterflies did the boys catch than the girls?

`5` `6` `7` `9`
 
 
 
 
Show Answers Only

`9`

Show Worked Solution

`text(Butterflies in the boys’ jar)`

`=7 xx 2 = 14`

`text(Butteflies in the girls’ jar)`

`=2.5 xx 2 = 5`

 

`:.\ text(The boys caught 9 more butterflies.)`

Statistics, NAP-G1-22

This table shows the main sport in Winter for 600 students.

Which of these is true?

 
 Most students played netball.
 
 More students swam than played AFL.
 
 Less students played soccer than netball.
 
 More than half the students played soccer.
Show Answers Only

`text(More students swam than played AFL.)`

Show Worked Solution

`text(More students swam than played AFL.)`

Measurement, NAP-G1-20

Roger's birthday is on the third of June.

Bonnie's birthday is 5 days before Roger's birthday.

On which day of the week is Bonnie's birthday?

`text(Sunday)` `text(Monday)` `text(Tuesday)` `text(Wednesday)` `text(Thursday)`
 
 
 
 
 
Show Answers Only

`text(Tuesday)`

Show Worked Solution

`text(Sunday – Roger’s birthday)`

`text(Saturday – 1 day before)`

`text(Friday – 2 days before)`

`vdots`

`text(Tuesday – 5 days before)`