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Number, NAP-B3-CA04

Barry travelled 120 kilometres in 2 hours.

What was his average speed in kilometres per hour?

`50` `60` `80` `240`
 
 
 
 
Show Answers Only

`60\ text(kph)`

Show Worked Solution
`text(Average speed)` `=120/2`
  `=60\ text(km/h)`

Statistics, NAP-E3-CA07

Chris did a survey of the number of female toilets in four shopping centres.

The results were recorded in the table below but the key has been left off the graph?

The total number of female toilets was 44.

How many toilets does represent in the graph?
`1`   `2`  `4`  `5`
 
 
 
 
Show Answers Only

`2`

Show Worked Solution

`text(Total number of female symbols)`

`= 5 + 4.5 + 5.5 + 7`

`= 22`
 

`:.\ text(The number of toilets one symbol represents)`

`=44/22`

`= 2`

Statistics, NAP-E3-CA04

Anne taught a kindergarten class and asked her students what their favorite fruit is.

Their answers were used to draw the pie chart below.
 

 

 
Around a quarter of her students preferred which fruit?

`text(Banana)` `text(Apple)` `text(Mango)` `text(Grapes)`
 
 
 
 
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`text(Apple)`

Show Worked Solution

`text(A quarter of students will represent a sector that)`

`text(is the size of a quarter of the circle.)`

`:.\ text(Apple)`

Measurement, NAP-E3-CA02

The pictures below show a thermometer at two different times.
 

 
By how much has the temperature risen?

`text(4°C)` `text(10°C)` `text(12°C)` `text(16°C)`
 
 
 
 
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`text(16°C)`

Show Worked Solution

`text(Temperature rise)`

`= 4 – (-12)`

`= 4 + 12`

`= 16 text(°C)`

Number, NAP-E3-CA01

The airforce buys 8 new fighter jets for $882.0 million.

Each jet costs the same amount.

What is the cost of 1 fighter jet?

`$110.25\ text(million)` `$441.0\ text(million)` `$874.0\ text(million)` `$7056\ text(million)`
 
 
 
 
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`$110.25\ text(million)`

Show Worked Solution

`{$882.0\ text(million)}/ 8 = $110.25\ text(million)`

Number, NAP-D3-NC07

Leo took $72 to the 2nd hand book shop and bought a number of books.

All the books cost the same amount.

Leo paid for all the books and had no money left.

Which of these could be the amount that one book cost?

`$11` `$9` `$7` `$5`
 
 
 
 
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`$9`

Show Worked Solution

`$72 ÷ 8 = $9`

`text($9 is the only amount that can be evenly)`

`text(divided into $72 with no remainder.)`

Probability, NAP-D3-NC05

A spinner is spun once.
 

 

 
Each shape on the wheel has an equal chance.

What is the chance that the spinner lands on the triangle .

 
 `text(5 chances in 6)`
 
 `text(6 chances in 6)`
 
 `text(1 chance in 5)`
 
 `text(1 chance in 6)`
Show Answers Only

`text(1 chance in 6)`

Show Worked Solution

`text(S)text(ince all shapes have an equal chance,)`​

`Ptext{(triangle)}` `= 1/6`

Number, NAP-D3-NC04

The results from 400 metres running race final was recorded in the table below.
 

 
The time of the runner who came in 3rd place could be

 
 `text(52.57 seconds.)`
 
 `text(52.71 seconds.)`
 
 `text(53.21 seconds.)`
 
 `text(53.94 seconds.)`
Show Answers Only

`text(52.71 seconds)`

Show Worked Solution

`text{52.71 is slower than 2nd place (52.62)}`

`text{but faster than 4th place (53.19).}`

Probability, NAP-E3-NC06

Jack rolls a standard dice three times.

He rolls a six each time.

Jack then has a forth roll.

Which of the following is true?

 
 He is more likely to roll a six than a four.
 
 He is certain to roll a six.
 
 He has an equal chance of rolling a six as a four.
 
 He is more likely to roll a four then a six.
Show Answers Only

`text(He has an equal chance of rolling a six as a four.)`

Show Worked Solution

`text(S)text(ince all numbers have an equal chance)`

`text(of being rolled,)`

`=>\ text(He has an equal chance of rolling a six as a four.)`

Algebra, NAP-G3-NC01

Mike and Georgia saved $120 together.

Georgia saved twice as much money as Mike.

How much money did Georgia save?

`$20` `$40` `$80` `$240`
 
 
 
 
Show Answers Only

`$80`

Show Worked Solution

`text(Let)\ \ x =\ text(Mike’s savings)`

`2x + x` `=120`
`3x` `=120`
`x` `=40`

 

`:.\ text(Georgia saved $80.)`

Geometry, NAP-G3-CA04

Herb is making an animation of a man running.

The picture shows seven frames of his animation.
 

 
He has accidentally swapped two frames.

Which two frames were swapped?

 
 frame 3 and 4
 
 frame 3 and 5
 
 frame 4 and 6
 
 frame 5 and 6
Show Answers Only

`text(frame 4 and 6)`

Show Worked Solution

`text(The correct order is:)`

`:.\ text(Frame 4 and 6 have been swapped.)`

Statistics, NAP-G3-CA02

10 of the tallest mountains in the United States are listed in the table below:
 

 

How much taller than Utah's tallest mountain is Colorado's tallest mountain?

`225\ text(metres)` `227\ text(metres)` `273\ text(metres)` `330\ text(metres)`
 
 
 
 
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`273\ text(metres)`

Show Worked Solution

`text(Mount Massive – Kings Peak)`

`= 4398 – 4125`

`= 273\ text(metres)`

Measurement, NAP-I3-CA05

Roger started work at 7:15 in the morning and finished at 6:35 in the evening.

How many hours did Roger spend working?

 
 `text(40 minutes)`
 
 `text(1 hour 20 minutes)`
 
 `text(10 hours 40 minutes)`
 
 `text(11 hours 20 minutes)`
 
 `text(13 hours 50 minutes)`
Show Answers Only

`text(11 hours and 20 minutes)`

Show Worked Solution

`text(7:15 am to 6:15 pm = 11 hours)`

`text(6:15 pm to 6:35 pm = 20 minutes)`

`:.\ text(11 hours and 20 minutes)`

Number, NAP-I3-CA04 SA

Brian has an orchard with 17 different types of fruit trees.

He has a total of 306 fruit trees.

He has the same number of each type of fruit tree.

How many fruit trees of each type does Brian have?

   trees
Show Answers Only

`18`

Show Worked Solution

`text(Number of trees of each type)`

`= 306 ÷ 17`

`= 18\ text(trees)` 

Geometry, NAP-H3-CA01

This is a street map.
 

 

 
About how far is it from Matt's house to Ali's house?

`40\ text(metres)` `100\ text(metres)` `160\ text(metres)` `200\ text(metres)`
 
 
 
 
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`text(100 metres)`

Show Worked Solution

`text(The distance between Matt and Ali’s house is)`

`text(about 2.5 times the width of the scale interval)`

`text(that is equal to 40 metres.)`

`:.\ text(Distance)\ ~~ 2.5 xx 40 ~~ 100\ text(metres)`

Measurement, NAP-I3-NC05

Dom is measuring long jump at a school athletics carnival.

She measures a jump at 3 metres and 17 centimetres.

Which of these shows how Dom would write this measurement in metres?

`3.017\ text(m)` `3.17\ text(m)` `4.17\ text(m)` `4.2\ text(m)`
 
 
 
 
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`3.17\ text(m)`

Show Worked Solution

`text(3 metres and 17 centimetres)`

`= 3.17\ text(m)`

Statistics, NAP-I3-NC04

Matt was recording the colour of cars that drove past his school in 1 hour.

In the hour, Matt saw 9 blue, 12 silver and 6 white cars.

In the tables below, `text(X)` = 3 cars.

Which table correctly shows the number of cars that Matt saw?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(S)text(ince)\ X = 3\ text(cars,)`

`text(9 Blue cars)` `=\ text(XXX)`
`text(12 Silver cars)` `=\ text(XXXX)`
`text(6 White cars)` `=\ text(XX)`

Algebra, NAP-I3-NC02

George has no money in his bank account.

He deposits $6 in his account in week 1.

He then deposits twice the amount into his account each week than he did the previous week.

The total amount in his account is?

 
 always odd.
 
 always even.
 
 sometimes odd and sometimes even.
Show Answers Only

`text(always even.)`

Show Worked Solution

`text(In each successive week, an even number will)`

`text(be added to an existing even number.)`

`text(even + even = even)`

`:.\ text(His account total will always be even.)`

Geometry, NAP-F4-CA02

The distance between Newcastle and Canberra on the map below is 9 cm.
 

 
The scale of the map is  1 cm = 50 km.

What is the actual distance between Newcastle and Canberra?

`350\ text(km)` `450\ text(km)` `600\ text(km)` `900\ text(km)`
 
 
 
 
Show Answers Only

`450\ text(km)`

Show Worked Solution
`text(Distance)` `= 9 xx 50`
  `= 450\ text(km)`

Statistics, NAP-G4-CA03

10 of the tallest mountains in the United States are listed in the table below:
 

 

How much taller than Utah's tallest mountain is Colorado's tallest mountain?

`225\ text(metres)` `227\ text(metres)` `273\ text(metres)` `330\ text(metres)`
 
 
 
 
Show Answers Only

`273\ text(metres)`

Show Worked Solution

`text(Mount Massive – Kings Peak)`

`= 4398 – 4125`

`= 273\ text(metres)`

Probability, NAP-G4-CA02

Arun flips an unbiased coin 200 times.

Which result is most likely?

`20\ text(tails)` `98\ text(tails)` `108\ text(tails)` `196\ text(tails)`
 
 
 
 
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`98\ text(tails)`

Show Worked Solution

`text(The expected result is 100 tails.)`

`:.\ text(The most likely result is the one closest to 100 tails.)`

`=> 98\ text(tails)`