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Number and Algebra, NAP-B1-29

Iris needs 4 cups of raisins to make a fruit cake.

She measures `1/2` a cup each time.

How many `1/2` cups will she need?

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

`8`

Show Worked Solution
`2 xx 1/2\ text(cup)` `= 1\ text(cup)`
`4 xx 1/2\ text(cup)` `= 2\ text(cups)`
`6 xx 1/2\ text(cup)` `= 3\ text(cups)`
`8 xx 1/2\ text(cup)` `= 4\ text(cups)`

 

`=>\ text(Iris needs 8 half cups.)`

Number and Algebra, NAP-B1-28 SA

Kim is packing 27 plums into boxes to take to the market.

Each box can hold 5 plums.

What is the smallest number of boxes Kim needs to make sure all the plums are packed?
Show Answers Only

`6\ text(boxes)`

Show Worked Solution
`text(Boxes needed)` `=27 -: 5`
  `=5\ \ text(remainder 2)`
  `=6\ text(boxes)`

Number and Algebra, NAP-D1-30

In 5 years time, Megan will be 16.

Brian will then be half Megan's age.

How old is Brian now?

`3` `6` `8` `11`
 
 
 
 
Show Answers Only

`3`

Show Worked Solution

`text(In 5 years time:)`

`text{Megan will be 16 (given)}`

`=>\ text(Brian will be 8.)`

`:.\ text(Brian’s age now)` `= 8-5`
  `= 3`

Measurement, NAP-E1-29 SA

Mandy is cutting out luggage tags from a plastic sheet.

Each luggage tag is identical and is pictured below.

Mandy throws away all pieces of plastic that are not complete tags.

What is the greatest number of luggage tags that Mandy can cut from the plastic sheet?
Show Answers Only

`text(10 luggage tags)`

Show Worked Solution

`text(10 luggage tags is the most that can be cut.)`

Statistics, NAP-G1-30

Peter travels a lot for work.

The table below shows the months when Peter visited different places.

During how many months did Peter visit Adelaide but not New Zealand?

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

`5`

Show Worked Solution

`text(Peter visited Adelaide and not NZ in January,)`

`text(February, September, October and November.)`

`=>5`

Number and Algebra, NAP-G1-29 SA

A shop sells eggs in small and large cartons.

A small carton holds 6 eggs.

A large carton holds 12 eggs.

Alice buys a total of 60 eggs.

She buys 3 large cartons and some small cartons.

How many small cartons does she buy?
Show Answers Only

`4`

Show Worked Solution

`text(Eggs in 3 large cartons)`

`= 3 xx 12`

`= 36`
 

`text(Eggs needed in small cartons)`

`= 60 – 36`

`= 24`
 

`:.\ text(Small cartons needed)`

`= 24 ÷ 6`

`= 4`

Number and Algebra, NAP-G1-27 SA

Marcus hangs 2 pairs of pants on a line.

Any trousers next to each other share a peg.

He uses 3 pegs.

How many pegs would Marcus use to hang 5 pairs of pants?
Show Answers Only

`6`

Show Worked Solution

`text(1 pair of trousers = 2 pegs)`

`text(2 pairs of trousers = 3 pegs)`

`text(3 pairs of trousers = 4 pegs)`

`vdots`

`text(5 pairs of trousers = 6 pegs)`

Number and Algebra, NAP-G1-25 SA

Damon had $1.40 in 5-cent coins in his piggy bank.

How many 5-cent coins does Damon have?
Show Answers Only

`28`

Show Worked Solution

`text(One strategy:)`

`$1.40 = 14 xx 10¢`

`2 xx 5¢\ text(coins)\ = 10¢`

`:.\ text(Number of 5¢ coins)` `= 14 xx 2`
  `= 28`

Statistics, NAP-G1-24

Anne went for a walk everyday.

This graph shows how far Anne went on her walk each day in a week.

On how many days in the week did Anne walk at least 5 kilometres?

`3` `4` `5` `6`
 
 
 
 
Show Answers Only

`4`

Show Worked Solution

`text(Anne walked 5 km or more on Monday, Wednesday,)`

`text(Thursday and Saturday.)`

`=> 4\ text(days)`

Measurement, NAP-H1-26 SA

This prism is made of cubes of the same size.
 


 

Some cubes have been taken out to form the object shown below.
 


 

How many cubes are in this new object?
Show Answers Only

`27`

Show Worked Solution

`text(There are 16 cubes in each layer)`

`=>\ text(32 cubes in the top image.)`

 

`text(5 cubes have been taken out.)`

`:.\ 32 – 5 = 27\ text(cubes are left)`

Number and Algebra, NAP-I1-29

Bennelong writes a number on a piece of paper and hides it.

He gives his friend the following clues about his number.

  • The number is less than 500.
  • The number has 30 tens.
  • The digit in the ones place is one more than the digit in
    the hundreds place.

What is Bennelong's number?

`30` `34` `300` `304`
 
 
 
 
Show Answers Only

`304`

Show Worked Solution

`text(Consider the following clues,)`

`text(Number has 30 tens,)`

`=>\ text(Number is 3 digits, starting with 30_)`

 

`text(The “ones” digit is one more than the “hundreds” digit,)`

`:.\ text(Number must be 304.)`

Number and Algebra, NAP-I1-28

Clive is using a number line to show a pattern.
 


 

In Clive's pattern, what number comes before 35?

`29` `30` `31` `32`
 
 
 
 
Show Answers Only

`31`

Show Worked Solution

`text(Arrow jumps 4 each time.)`

`:.\ text(Number before 35)`

`= 35 – 4`

`= 31`

Number and Algebra, NAP-H1-30

Andrew kept 3 bird cages.

Each bird cage had 8 birds in it.

He then bought one more bird cage and spread the birds out evenly between the 4 cages.

How many birds were then in each cage?

`5` `6` `8` `9`
 
 
 
 
Show Answers Only

`6`

Show Worked Solution
`text(Total birds)` `= 3 xx 8`
  `= 24`

 

`:.\ text(Birds in each of 4 cages)`

`= 24 ÷ 4`

`= 6`

Statistics, NAP-C2-21

Renee made a pie graph of the cost of things she paid for using her credit card over a month.
 

  
Which information can be found using this pie graph?

The amount of money she spent using her credit card

 
 for going to the cinemas in the month.
 
 on electricity each week.
 
 on shopping each day.
 
 on rent for the month.
Show Answers Only

`text(on rent for the month.)`

Show Worked Solution

`text(S)text(ince the pie chart is for payments over a full)`

`text(month, the only information in the options that)`

`text(can be found is on rent for the month.)`

Probability, NAP-C2-16

Angelina takes 3 marbles out of the bag at the same time.
 

 
Which of these is impossible?

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

`text(2 grey marbles and 1 striped marble.)`

Show Worked Solution

`text(2 grey marbles and 1 striped marble.)`

`text{(since there is only 1 grey marble in the bag)}`

Geometry, NAP-F2-29

This grid map shows the names of some places along a hiking track.

The distance between The Terrace and Karuah is about 40 km.
 

 
Which of these is closest to the distance from Rees to Janis along the track?

`text(30 km)` `text(40 km)` `text(50 km)` `text(70 km)`
 
 
 
 
Show Answers Only

`text(50 km)`

Show Worked Solution

`text(Using the distance of The Terrace to Rees as 40 km,)`

`text(the best estimate for Rees to Janis is closest to 50 km)`

`text(among the options.)`

Number and Algebra, NAP-F2-26 SA

Ivan and Novik receive pocket money each week.

Ivan gets $3 and Novik gets $7.

After 12 weeks, how much more pocket money has Novik received than Ivan?

$  
Show Answers Only

`$48`

Show Worked Solution

`text(Novik receives $4 more each week.)`

`:.\ text(Extra money after 12 weeks)`

`= 12 xx 4`

`= $48`

Geometry, NAP-F2-24

4 angles are labelled on the triangle pictured below.
 

 
Which angle is closest in size to 45°?

`A` `B` `C` `D`
 
 
 
 
Show Answers Only

`A`

Show Worked Solution

`text(Angles)\ B and C\ text(are closer to 90°.)`

`text(Angle)\ D\ text(is obtuse.)`

`text(Angle)\ A\ text(looks close to half a right angle.)`

`:.\ text(Angle)\ A`

Numbar and Algebra, NAP-F2-20

Ryan is walking a trail that is 3250 metres long.

He has walked 2419 metres so far.

How many metres are left for him to walk?

`831` `839` `841` `1239`
 
 
 
 
Show Answers Only

`831`

Show Worked Solution
STRATEGY: Do this subtraction in bite size pieces by subtracting thousands first, then hundreds, then the balance (as per the solution).
`3250 – 2419` `=1250-419`
  `=850-19`
  `=831`

 

`:.\ 831\ text(metres left to walk.)`

Number and Algebra, NAP-F2-19

Calvin took half the chocolates in a box.

Without any other chocolates being taken, Jeremy took five more.

Seven chocolates were left in the box.

How many chocolates were in the box originally?

`14` `20` `24` `30`
 
 
 
 
Show Answers Only

`24`

Show Worked Solution

`text(If we add back the 5 chocolates to the 7 left in)`

`text(the box, there are 12 in the box.)`

`=>\ text(12 is half the chocolates at the start.)`

`:.\ text(24 chocolates were in the box.)`

Measurement, NAP-F2-18

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

 
Lionel has a grand final week breakfast 5 days before the grand final.

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

 
 `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, NAP-F2-17

Roger went to a movie at the cinema that started at 10:20 am.

The movie finished 1:32 pm.

How long did the movie take?

 
 1 hour 52 minutes
 
 2 hours 52 minutes
 
 3 hours 12 minutes
 
 4 hours 12 minutes
Show Answers Only

`text(3 hours 12 minutes)`

Show Worked Solution

`text(One strategy:)`

`text(10:20 am plus 3 hours)`

`=1:20\ text(pm)`

`text(1:20 pm plus 12 minutes)`

`=1:32\ text(pm)`

`:.\ text(The move took 3 hours 12 minutes)`

Geometry, NAP-C2-19

An orientation course is set up with 4 drinking stations.

Runners start and then progress through the course in the order of the drinking stations labelled 1-4 in the diagram below.

 
At which drinks station do the runners make the greatest change of direction?

Station 1 Station 2 Station 3 Station 4
 
 
 
 
Show Answers Only

`text(Station 2)`

Show Worked Solution

`text(Station 2)`

Number and Algebra, NAP-E2-27

Simon is painting a wall at his home grey.
 

 
About what fraction of the wall does Simon still have to paint grey?

`1/4`    `1/6` `3/4` `5/6`
 
 
 
 
Show Answers Only

`1/6`

Show Worked Solution

`text(The unpainted section is around one third)`

`text(of the right half of the wall.)`

`:.\ text(Fraction still to paint)`

`= 1/3 xx 1/2`

`= 1/6`

Measurement, NAP-E2-28

Tenzing started his trek at 5:30 am.

He arrived at his destination `14 1/2` hours later.

At what time did he arrive at his destination?

`7:30\ text(pm)` `8:00\ text(pm)` `9:30\ text(pm)` `10:00\ text(pm)`
 
 
 
 
Show Answers Only

`text(8:00 pm)`

Show Worked Solution

`text(One strategy:)`

`5:30\ text(am plus)\ 14.5\ text(hours)` `=\ text(5:30 pm plus)\ 2.5\ text(hours)`
  `=\ text(8:00 pm)`

Statistics, NAP-H2-26 SA

The goals scored by 4 players in a season of water polo were recorded in the graph below.

Will scored 8 goals in the season.

Sam scored 5 goals.

How many more goals did Bilbo score than Ginili?
Show Answers Only

`7\ text(more goals)`

Show Worked Solution

`text(S) text(ince Will scored 8 goals,)`

`= 2\ text(goals)`

`=>\ text(Bilbo scored 10 goals)`

`=>\ text(Ginili scored 3 goals)`

`:.\ text(Bilbo scored 7 more goals than Ginili.)`