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MATRICES, FUR1 2016 VCAA 1 MC

The transpose of `[(2,7,10),(13,19,8)]` is
 

A.    `[(13,19,8),(2,7,10)]`
B.    `[(10,7,2),(8,19,13)]`
C.    `[(2,13),(7,19),(10,8)]`
D.    `[(13,2),(19,7),(8,10)]`
E.    `[(8,10),(19,7),(13,2)]`
Show Answers Only

`C`

Show Worked Solution

`text(Transpose is a new matrix where)`

`text(the rows of 1 matrix become the)`

`text(columns.)`

`text(i.e.)\ \ x_(ij) => x_(ji)`

`[(2,7,10),(13,19,8)]^T` `= [(2,13),(7,19),(10,8)]`

`=> C`

CORE, FUR1 2016 VCAA 18 MC

The value of an annuity, `V_n`, after `n` monthly payments of $555 have been made, can be determined using the recurrence relation

`V_0 = 100\ 000,\ \ \ \ \ V_(n + 1) = 1.0025 V_n - 555`

The value of the annuity after five payments have been made is closest to

  1.   `$97\ 225`
  2.   `$98\ 158`
  3.   `$98\ 467`
  4.   `$98\ 775`
  5. `$110\ 224`
Show Answers Only

`C`

Show Worked Solution
`V_0` `= 100\ 000`
`V_1` `= 1.0025 xx 100\ 000 – 555 = 99\ 695`
`V_2` `= 1.0025 xx 99\ 695 – 555 = 99\ 389.23…`
`V_3` `= 1.0025 xx 99\ 389.24 – 555 = 99\ 082.71…`
`V_4` `= 1.0025 xx V_3 = 98\ 775.41…`
`V_5` `= 1.0025 xx V_4 = 98\ 467.35…`

 
`=> C`

CORE, FUR1 2016 VCAA 17 MC

Consider the recurrence relation below.

`A_0 = 2,\ \ \ \ \ A_(n + 1) = 3 A_n + 1`

The first four terms of this recurrence relation are

  1. `0, 2, 7, 22\ …`
  2. `1, 2, 7, 22\ …`
  3. `2, 5, 16, 49\ …`
  4. `2, 7, 18, 54\ …`
  5. `2, 7, 22, 67\ …`
Show Answers Only

`E`

Show Worked Solution
`A_0` `= 2\ \ (text(given))`
`A_1` `= 3(2) + 1 = 7`
`A_2` `= 3(7) + 1 = 22`
`A_3` `= 3(22) + 1 = 67`

 
`=> E`

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 13 MC

Consider the time series plot below.
 


 

The pattern in the time series plot shown above is best described as having

  1. irregular fluctuations only.
  2. an increasing trend with irregular fluctuations.
  3. seasonality with irregular fluctuations.
  4. seasonality with an increasing trend and irregular fluctuations.
  5. seasonality with a decreasing trend and irregular fluctuations.
Show Answers Only

`C`

Show Worked Solution

`text(The graph shows definite seasonality)`

`text(and no noticeable trend.)`

`=> C`

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`

Measurement, NAP-B1-08

The minute hand is missing.
 


 

What time could this clock be showing?

`text(8 o'clock)` `text(half past 8)` `text(9 o'clock)` `text(half past 9)`
 
 
 
 
Show Answers Only

`text(half past 8)`

Show Worked Solution

`text(S)text(ince the hour hand is halfway between the 8 and 9,)`

`text(the clock could be showing half past 8.)`

Measurement, NAP-D1-12

Children at a Summer Camp are split into four colour teams, red, yellow, blue and green.

Which team has archery lessons first?

`text(Red)` `text(Yellow)` `text(Blue)` `text(Green)`
 
 
 
 
Show Answers Only

`text(Blue)`

Show Worked Solution

`text(Archery is earliest at 11:00 am.)`

`:.\ text(Blue has archery first.)`

Number and Algebra, NAP-D1-11

Melinda placed some shells in rows of 8.

She then put the same number of shells into bags of 6 and had some left over.

How many shells were left over?

`4` `3` `2` `1`
 
 
 
 
Show Answers Only

`2`

Show Worked Solution

`text(Total number of shells)`

`=8 xx 4`

`= 32`
 

`32 ÷ 6 = 5\ text(remainder 2)`

`:. 2\ text(shells were left over.)`

Geometry, NAP-D1-09

Kelly has sorted a number of shapes into groups.

How did Kelly sort her shapes?

 
 `text(by length of sides)`
 
 `text(by type of pattern)`
 
 `text(by number of sides)`
 
 `text(by height)`
Show Answers Only

`text(by number of sides)`

Show Worked Solution

`text(Every figure in each box has the same number)`

`text(of sides.)`

`=>\ text(Kelly has sorted them by number of sides.)`

Number and Algebra, NAP-D1-04

Chantelle showed this number on her calculator

She changed it so that it became this number.

What did Chantelle do to change 376 to 306?

 
 `text(added 7)`
 
 `text(subtracted 7)`
 
 `text(added 70)`
 
 `text(subtracted 70)`
Show Answers Only

`text(subtracted 70)`

Show Worked Solution

`376 – 70 = 306`

`=>\ text(subtracted 70)`

Measurement, NAP-E1-17

Rose called a restaurant on 3 November.

She booked dinner in exactly 3 weeks.
 

 
 

What date did Rose book the restaurant for?

 
 `text(6 November)`
 
 `text(10 November)`
 
 `text(23 November)`
 
 `text(24 November)`
Show Answers Only

`text(24 November)`

Show Worked Solution

`text(24 November)`

Measurement, NAP-F1-07

Six students line up side by side.

   

The teacher can make a line of shortest to tallest by swapping two students.

Which two students need to swap positions with each other?

 
 `text(Catherine and Justin)`
 
 `text(Catherine and Luke)`
 
 `text(Justin and Luke)`
 
 `text(Paddy and Luke)`
Show Answers Only

`text(Catherine and Luke)`

Show Worked Solution

`text(Catherine and Luke)`

Number and Algebra, NAP-I1-06

A boat hire shop has 5 paddle boats.

Each paddle boat can fit 4 people in it.

If all the paddle boats are hired out and have 4 people in them, how many people are in paddle boats altogether?

`5` `9` `15` `20`
 
 
 
 
Show Answers Only

`20`

Show Worked Solution
`text(Total people)` `=5 xx 4`
  `=20`

Statistics, NAP-I1-15

Cybil and Therese lived in different streets.

They were each counting different coloured cars that drove past their house one morning.

They drew a correct picture graph to show the number of coloured cars they saw altogether.

Which picture graph did they draw?  

 
 
 
 
Show Answers Only

Show Worked Solution

`text(Adding up the columns:)`

`text(White = 3, Blue = 5, Red = 4.)`

Number and Algebra, NAP-I1-14

The world record for the most push-ups ever completed in one hour is three thousand and ninety-two.

The number of push-ups can be written as:

`392` `3092` `3920` `30\ 092`
 
 
 
 
Show Answers Only

`3092`

Show Worked Solution

`text(Three thousand and ninety-two contains:)`

`=>\ text(3 “thousands”)`

`=>\ text(0 “hundreds”)`

`=>\ text(9 “tens”)`

`=>\ text(2 “ones”)`

`:. 3092`

Number and Algebra, NAP-H1-12

Rory played in a soccer team.

At training, 8 players were there but 4 could not make it.

How many players are in Rory's team?

`4` `8` `11` `12`
 
 
 
 
Show Answers Only

`12\ text(players)`

Show Worked Solution
`text(Players in Rory’s team)` `=8+4`
  `=12`

Number and Algebra, NAP-I1-10

Andrew is travelling from Brisbane to Mackay.

He knows that it is more 968 kilometres but less than 986 kilometres.

Which of these could be the number of kilometres that Andrew has to travel?

`946` `964` `984` `988`
 
 
 
 
Show Answers Only

`984`

Show Worked Solution

`text(S)text(ince)\ 968 < 984 < 986,`

`:. 984\ text(km could be the number.)`

Measurement, NAP-B2-01

The minute hand is not shown.
 


 

What time could this clock be displaying?

`text(10 o'clock)` `text(half past 10)` `text(11 o'clock)` `text(half past 11)`
 
 
 
 
Show Answers Only

`text(half past 10)`

Show Worked Solution

`text(The hour hand is halfway between 10 and 11.)`

`:.\ text(The time could be half past 10.)`