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Measurement, NAP-F3-NC13

Lilly went to sleep at 10:50 pm.

She woke up at 8:35 am.

How long did Lilly sleep for?

 
 2 hours 15 minutes
 
 9 hours 45 minutes
 
 9 hours 55 minutes
 
 10 hours 45 minutes
Show Answers Only

`text(9 hours 45 minutes)`

Show Worked Solution

`text(One possible strategy:)`

`text(10:50 pm plus 1:10 gets to 12:00 midnight.)`

`text(12:00 midnight plus 8:35 gets to 8:35 am.)`

 

`:.\ text(1 hour 10 minutes plus 8 hours 35 minutes)`

`=\ text(9 hours 45 minutes)`

Probability, NAP-G3-NC19

A spinner can land in any of 4 sections, labelled 1 to 4.

The spinner is spun 100 times and the results are recorded in the bar chart below.

 

 

Which of these spinners is most likely to give results shown in the graph?
 

 
 
 
 
Show Answers Only

Show Worked Solution

`text(Landing on 3 should be about 50%.)`

`text(Landing on 4 should be about 25%.)`

`text{Landing on 1 and 2 (combined) should be about 25%.}`

 

Probability, NAP-G3-NC16

Francis has a bag of marbles.

The number of marbles of each colour is recorded in the table below.
 

   

 
Francis randomly takes 1 marble out of her bag without looking.

What is the chance it is green?

`1/28` `1/7` `1/4` `1/2`
 
 
 
 
Show Answers Only

`1/2`

Show Worked Solution
`text{Pr (Green)}` `= text(Number of green) / text(Total number)`
  `=14/28`
  `=1/2`

Number, NAP-G3-NC15

4 groups of backpackers picked blueberries over two hours.

The weight of the blueberries collected (in kg) by the groups in each hour is shown in the table below.
 

 
Which group picked the greatest mass over the two hours?

`text(Group 1)` `text(Group 2)` `text(Group 3)` `text(Group 4)`
 
 
 
 
Show Answers Only

`text(Group 3:  5.42 kg)`

Show Worked Solution

`text(A possible strategy:)`

`text(A quick estimate of the 1st 2 options shows that)`

`text(that both sums will be lower than 5 kg.)`

`=>\ text(Evaluate only the last 2 options:)`

`text(Group 3:)\ \ 2.5 + 2.92 = 5.42\ text(kg)`

`text(Group 4:)\ \ 2.87 + 2.53 = 5.40\ text(kg)`

 

`:.\ text(Group 3 picked the greatest mass.)`

Measurement, NAP-G4-NC10

The flask pictured below can hold up to 100 mL of water.
 

 
How much water is in the flask?

`60\ text(mL)` `70\ text(mL)` `80\ text(mL)`  `90\ text(mL)`
 
 
 
 
Show Answers Only

`text(80 mL)`

Show Worked Solution

`text(Flask is fully filled until the 60 mL mark.)`

`text(Flask is half filled between 60-100 mL marks.)`

`:.\ text(Volume of water in the flask)`

`=60 + (1/2 xx 40)`

`=80\ text(mL)`

Number, NAP-G3-NC13

12 people went to Sea World together in a bus.

Entry into Sea World was $44 per person and the total cost of the bus was $120.

Which expression shows the total cost of the trip for everybody?

`(44 + 120) xx 12` `44 + 12 + 120` `(12 xx 44) + 120` `12 xx 44`
 
 
 
 
Show Answers Only

`(12 xx 44) + 120` 

Show Worked Solution

`text(Total cost of entry to Sea World)`

`=12 xx $44`

`text(Total cost of bus)\ = $120\ \ text{(given)}`

`:.\ text(Total cost of the trip for everybody)`

`= (12 xx 44) + 120`

Algebra, NAP-G3-CA15

Kate takes part in a swimathon to raise money for charity.

Her grandmother sponsors her $20 in total.

Her uncle sponsors her $1.25 for each lap of the pool she swims.

In order to raise $100, how many laps does Kate need to swim?

`5`  `10` `64` `80` `88`
 
 
 
 
 
Show Answers Only

`64\ text(laps)`

Show Worked Solution

`text(Let)\ \ x = text(number of laps that Kate need to swim)`

`100` `= 1.25x + 20`
`1.25x` `= 100 – 20`
`:. x` `= 80/1.25`
  `= 64\ text(laps)`

Number, NAP-G3-CA14

Camilla has only 10-cent, 20-cent and 50-cent coins in her purse.

She buys a coffee that costs her $3.80 and pays the exact price.

What is the smallest number of coins she could use to pay for her coffee?

`7`    `8`   `9` `10` `11`
 
 
 
 
 
Show Answers Only

`9\ text(coins)`

Show Worked Solution

`text(The minimum number of coins are:)`

`7 xx 50 text(-cent)` `= $3.50`
`1 xx 20 text(-cent)` `= $0.20`
`1 xx 10 text(-cent)` `=$0.10` 

 

`:.\ text(Minimum coins to make $3.80 = 9 coins)`

Geometry, NAP-G3-CA11

A ramp rises 1 metre for every 8 metres of its base length.
 


 

If it rises 0.7 metres, what is its base length?

`5.6\ text(metres)` `8.7\ text(metres)` `11.4\ text(metres)` `16\ text(metres)`
 
 
 
 
Show Answers Only

`5.6\ text(metres)`

Show Worked Solution
`text(Base length)` `= 8 xx 0.7`
  `= 5.6\ text(metres)`

Geometry, NAP-G3-CA08

Brianna plotted the points  `A-F`  on a grid paper, as shown below.

She then joined some of the points together with lines.

Which of these pairs of lines are parallel?

`AF and AC` `AD and CF` `AE and BD` `AD and BD`
 
 
 
 
Show Answers Only

`AE and BD`

Show Worked Solution

`AE and BD\ text(are parallel.)`

Algebra, NAP-H3-NC20

Adam is a tile designer. He is repeating 4 symbols as shown in the picture below.

Adam is using this pattern for a line of tiles that is 31 tiles long.

 

 
What will be the symbol on the 31st tile?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(7 repeats of the 4 tile pattern make up)`

`text(the first 28 tiles.)`

`:.\ text(The 31st tile is the third tile in the pattern.)`

Number, NAP-H3-NC18

This table shows the prices of different kinds of nuts sold at a farmers' market.

   

Which one of these are the most expensive nuts per kilogram?

pecans cashews almonds walnuts
 
 
 
 
Show Answers Only

`text(Cashews)`

Show Worked Solution

`text(Consider each option:)`

`$1.80\ text(for 250 g = 4 × $1.80 = $7.20 per kg)`

`$6.00\ text(for 750 g = $2 per 250 g = $8 per kg)`

`$7.60\ text(for 1 kg)`

`$3.90\ text(for 500 g = 2 × $3.90 = $7.80 per kg)`

 

`:.\ text(Cashews are the most expensive)`

Number, NAP-H3-NC16

A chocolate factory packs 200 gram chocolate bars into a box that can hold 3 kg of the chocolate bars.

Which one of these expressions shows how many chocolate bars will be needed to fill the box?

`3 xx 200` `3000 ÷ 200` `3000 xx 200` `200 ÷ 3`
 
 
 
 
Show Answers Only

`3000 ÷ 200`

Show Worked Solution

`text(S)text(ince there are 3000 grams in 3 kilograms,)`

`text(Chocolate bars to fill the box)`

`=3000 ÷ 200`

Statistics, NAP-H3-NC13

Bradley's class were asked to choose their favourite colour among four choices.

  • 5 voted for red
  • 2 voted for orange
  • 6 voted for blue
  • The rest voted for green

 

 

How many students in Bradley's class chose green?

`7` `8` `9` `10`
 
 
 
 
Show Answers Only

`7`

Show Worked Solution

`text(S)text(ince red is one quarter of the pie chart,)`

`=>\ text(there are 20 students in Bradley’s class.)`

`:.\ text(Votes for green)`

`=20-(5+2+6)`

`=7`

Number, NAP-I3-CA19

Nigella needs to buy some olive oil.

The supermarket sells Nigella's favourite oil in a number of different sizes.

Which size costs her the least per mL?

 
 `text(200 mL bottle for $2.50)`
 
 `text(300 mL bottle for $2.50)`
 
 `text(500 mL bottle for $4.50)`
 
 `text(750 mL bottle for $7.50)`
Show Answers Only

`text(300 mL bottle for $2.50)`

Show Worked Solution

`text(Calculate the cost per mL for each option:)`

`text(200 mL for $2.50 = 250/200 = 1.25 c/mL)`

`text(300 mL for $2.50 = 0.83 c/mL)`

`text(500 mL for $4.50 = 0.9 c/mL)`

`text(750 mL for $7.50 = 1 c/mL)`

 

`:. 300\ text(mL bottle for $2.50 costs the least per mL.)`

Number, NAP-I3-CA17

A soft drink factory can make 950 cans of lemonade and 600 cans of ginger ale per hour.

The factory runs non-stop and each can weighs 300 grams.

How many kilograms of soft drink does the factory produce in 1 full day?

 
 `465\ text(kilograms)`
 
 `18\ text(kilograms)`
 
 `285\ text(kilograms)`
 
 `11\ 160\ text(kilograms)`
Show Answers Only

`11\ 160\ text(kilograms per day)`

Show Worked Solution

`text(Total cans made per hour)`

`=950 + 600`

`= 1550`
 

`text(Kilograms made in 1 hour)` 

`=1550 xx 300`

`= 465\ 000\ text(grams)`

`= 465\ text(kilograms)`

`:.\ text(Kilograms made in 1 day)` `=465 xx 24`
  `=11\ 160`

Number, NAP-I3-CA15

Olaf's receipt from a Battery World store was torn and part of it was thrown in the rubbish.
 

naplan-2016-8mc

 
He knew:

  • each AA battery pack cost just under $9.
  • each USB stick cost just under $8.

His credit card statement showed that he spent $83.90 at the Battery World store.

About how much did the hard drive cost?

`$5` `$17` `$28` `$67`
 
 
 
 
Show Answers Only

`$17`

Show Worked Solution

`text(C) text(ost of batteries and USB sticks)`

`~~ 3 xx 9 + 5 xx 8`

`~~ $67\ \ text{(just under)}`

 

`:.\ text(Hard Drive cost)` `~~ 83.90 – 67`
  `~~ $16.9`
  `~~$17`

Algebra, NAP-I3-CA13

Kate is enrolled in an intensive summer swimming program.

Her swimming program is shown in the table below.
 

 
Which statement about Kate's plan is true?

Kate's plan is to swim:

 
 `text(30 laps more than the previous day.)`
 
 `text(20 laps more than the previous day.)`
 
 `text(1.5 times more laps than the previous day.)`
 
 `text(10 times more laps than the previous day.)`
Show Answers Only

`text(1.5 times more laps than the previous day.)`

Show Worked Solution

`text(Day 2 laps = 1.5 times Day 1 laps)`

`text(Day 3 laps = 1.5 times Day 2 laps)`

`:.\ text(1.5 times more laps than the previous day.)`

Number, NAP-H3-CA19 SA

The dog population in five continents can be found in the table below.
 

 
How many more dogs live in Europe than in Africa and South America combined?
Show Answers Only

`36\ 345\ 608`

Show Worked Solution

`text(Number of extra dogs)`

`= 59\ 329\ 647 – (9\ 721\ 457 + 13\ 262\ 582)`

`= 36\ 345\ 608`

Measurement, NAP-H3-CA18

A rectangle has a length of 25 cm and a width of 20 cm.

A square has the same perimeter as this rectangle.

What is the side length of this square in centimetres?

`15` `11.25` `22.5` `125`
 
 
 
 
Show Answers Only

`22.5`

Show Worked Solution
`text(Perimeter of rectangle)` `= (2 xx 25) + (2 xx 20)`
  `=90\ text(cm)`

 

`:.\ text(Side length of square)` `=90/4`
  `=22.5\ text(cm)`

Number, NAP-H3-CA15

Luigi has two large bags of pasta that are identical.

He also has a third, smaller bag of pasta that weighs 225 grams.

Luigi has 1925 grams of pasta in total.

Which expression can be used to calculate the mass of one of the large bags of pasta?

`2xx (1925 + 225)` `2 xx (1925 - 225)` `(1925 + 225) ÷ 2` `(1925 - 225) ÷ 2`
 
 
 
 
Show Answers Only

`(1925 – 225) ÷ 2`

Show Worked Solution

`text(Mass of the two larger bags of pasta)`

`=1925 – 225`
 

`:.\ text(Mass of 1 larger bag)`

`= (1925 – 225) ÷ 2`

Number, NAP-H3-CA13

Which of the following lists the numbers in increasing order?

 
 `text(65%), 0.7, 0.72, 3/4`
 
 `3/4, 0.7, text(65%), 0.72`
 
 `text(65%), 3/4, 0.7, 0.72`
 
 `3/4, 0.72, 0.7, text(65%)`
Show Answers Only

`text(65%), 0.7, 0.72, 3/4`

Show Worked Solution

`text(Convert to decimals:)`

`65text(%) = 0.65`

`3/4 = 0.75`
 

`:.\ text(Ascending order is)`

`text(65%), 0.7, 0.72, 3/4`

Measurement, NAP-I3-CA11

A regular hexagon is drawn below.

5 identical hexagons are connected as shown in the diagram below.

What is the perimeter of the larger shape?

`110\ text(cm)` `121\ text(cm)`  `132\ text(cm)`  `165\ text(cm)`
 
 
 
 
Show Answers Only

`121\ text(cm)`

Show Worked Solution
`text(Perimeter)` `= text(Number of sides)\ xx 5.5`
  `=22 xx 5.5`
  `=121\ text(cm)`

Probability, NAP-I3-CA07

Bellamy creates a game with the spinner shown below.
 

 
If the spinner lands on a 3, he wins a prize.

What is the probability that Bellamy will win a prize on his next spin?

`1/4`  `1/3`  `3/8`  `1/2`
 
 
 
 
Show Answers Only

`1/4`

Show Worked Solution
`P text{(landing on a 3)}` `= text(Number of 3’s)/text(Total possibilities)`
  `=2/8`
  `=1/4`

Algebra, NAP-I3-NC21

Stu and Tarly collect sea-shells on the beach.

Tarly collects 3 times as many sea-shells as Stu plus an additional 5.

Let  `s`  be the number of shells Stu collects.

Which expression correctly shows the number of shells Tarly collects?

`(3 × s) + 5` `3 + (5 × s)` `(s ÷ 3) - 5` `3 - (s ÷ 5)`
 
 
 
 
Show Answers Only

`(3 × s) + 5`

Show Worked Solution

`(3 × s) + 5`

Numbers, NAP-I3-NC20

Matt and Libby both bought the same sized box of chocolates.

Matt ate  `5/6`  of his box.

Libby ate more chocolates than Matt.

What fraction of her chocolates could Libby have eaten?

`4/5` `5/7` `6/7` `7/9`
  
 
 
  
Show Answers Only

`6/7`

Show Worked Solution

`6/7 > 5/6`

`=>\ text(All other fractions are smaller than)\ \ 5/6.`

Number, NAP-I3-NC19

Patrick wants to buy some cricket equipment.

The sports shop's prices of the equipment he wants is listed in the table below.
 

 
Patrick buys all 4 items.

Which of these gives the correct range for the cost of this equipment?

`$300 - $330` `$330 - $360` `$360 - $390` `$390 - $420`
 
 
 
 
Show Answers Only

`$360 – $390`

Show Worked Solution

`text(One strategy for getting an estimate is:)`

`$162.80 + $103.10 ~~ $265`

`$265 + $20 ~~ $285`

`$285 + $90 ~~ $375`

`:.\ text(Range is:)\ \ $360 – $390`

Measurement and Geometry, NAP-I3-NC18

Jimmy drew a shape that is pictured below.

He reflected the shape across the dotted line.

He rotated it 90 degrees anticlockwise.

Which shape below shows what it looks like after this?

 
 
 
 
Show Answers Only

Show Worked Solution

Statistics, NAP-I3-NC16

A soccer competition has six teams playing on the same day.

The table below shows the draw.
 

   

 
If no match ends in a draw, which of the following is possible?

 
 Tigers and Lions are the only teams that lose.
 
 Lions and Cheetahs both lose.
 
 Meerkats and Civets both win.
 
 Lions, Leopards, Civets and Tigers all win.
Show Answers Only

`text(Meercats and Civets both win.)`

Show Worked Solution

`=>\ text(3 teams must win and 3 teams must lose.)`

`=>\ text(Teams playing each other cannot both lose).`

`:.\ text(Meerkats and Civets both winning is the)`

`text(only option that is possible.)`

Algebra, NAP-I3-NC15

Lee pays a monthly membership of $36 to have unlimited entry to the local swimming pool.

If she does squad training, she needs to pay an extra $8 per session to the swim coach.

If Lee does `n` squad sessions in a month, which expression represents her monthly bill?

`8n` `36n` `36n + 8` `36 + 8n`
 
 
 
 
Show Answers Only

`36 + 8n`

Show Worked Solution

`text(Monthly membership = $36)`

`text(C)text(ost of)\ n\ text(squad sessions =)\ $8n`

`:.\ text(Total monthly bill)\ = 36 + 8n`

Number, NAP-I3-NC14

Giselle does odd jobs around the house to earn pocket money.

She gets $3 per job.

The table below shows all the jobs she did in one week.
 

 
If Giselle does the same jobs for two weeks, how much money will she earn altogether?

`$12` `$24` `$36` `$72`
 
 
 
 
Show Answers Only

 `$72`

Show Worked Solution

`text(Total jobs in 1 week)`

`= 7 + 3 + 2`

`= 12`

`:.\ text(Money earned in 2 weeks)`

`= 2 xx (12 xx 3)`

`= 2 xx 36`

`= $72`

Measurement, NAP-C3-NC15

Which metric unit would a builder use to measure the area of a courtyard?
 

 
 

  
 cubic centimetres
  
 square centimetres
 
 square metres
  
 cubic metres
Show Answers Only

`text(square metres)`

Show Worked Solution

`text(The courtyard is measured by its area and the most)`

`text(appropriate unit for the size is square metres.)`

Geometry, NAP-C3-NC14

A car is travelling  south-west on Chappell Street.

The car is about to turn onto Second Street.
 

 

 
In which direction will the car be travelling after it turns right?

 
 south-west
 
 north-west
 
 south-east
 
 north-east
Show Answers Only

`text(north-west)`

Show Worked Solution

`text(Readjusting the directions to the compass below:)`

`:.\ text(After turning right, the car is travelling north-west.)`

Number, NAP-C3-NC11

Ben is 4 years old.

His brother Mark is exactly 19 months old.

How many months older than Mark is Ben?

`21` `23` `29` `31`
 
 
 
 
Show Answers Only

`29`

Show Worked Solution
`text(Ben’s age)` `=4 xx 12`
  `=48\ text(months)`

 

`:.\ text(Months that Ben is older than Mark)`

`=48-19`

`=29\ text(months)`

Algebra, NAP-E4-CA10

The rules of a number game are shown in the flowchart below.
 

 
The output number is 21.

What are two possible values for the input number?

`7 and 16` `16 and 63` `7 and 26` `26 and 63`
 
 
 
 
Show Answers Only

`7 and 26`

Show Worked Solution

`text(Input 7 into the flowchart:)`

`7 xx 3 = 21`

`text(Input 26 into the flowchart:)`

`26 – 5 = 21` 
 

`:. 7 and 26\ \ text(are the possible values.)`

Number, NAP-E4-CA08

Which arrow is pointing to the approximate position of `sqrt 600` on a number line?
 

 
 
 
 
Show Answers Only

Show Worked Solution

`sqrt600=24.49…`

Number, NAP-C3-NC08

This picture shows a stone vase.
 

 
The picture is 2 cm high. The actual vase is 40 cm high.

What scale is used in the picture?

 
 `text(2 cm represents 20 cm)`
 
 `text(4 cm represents 40 cm)`
 
 `text(1 cm represents 2 cm)`
 
 `text(1 cm represents 20 cm)`
Show Answers Only

`text(1 cm represents 20 cm)`

Show Worked Solution

`text(Scale:)\ \ 2\ text(cm)\ :\ 40\ text(cm)`

`=>\ text(Divide both sides by 2)`

`text(Scale:)\ \ 1\ text(cm)\ :\ 20\ text(cm)`