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Number, NAP-K3-NC04

A hot air balloon is 25.2 metres high.

The length of the balloon section is 21.55 metres.
 

 
What is the height of the basket section?

`text(3.65 metres)` `text(3.75 metres)` `text(4.55 metres)` `text(4.65 metres)`
 
 
 
 
Show Answers Only

`text(3.65 metres)`

Show Worked Solution

`text(Let)\ \ h =\ text(height of basket section)`

`h + 21.55` `= 25.2`
`:. h` `= 25.2 – 21.55`
  `= 25.2 – 22 + 0.45`
  `= 3.65`

Number, NAP-K3-CA37 SA

Bert, Gary and Miles are weighing themselves.

Bert weighs 48.65 kilograms.

Gary weighs 0.3 kilograms more than Bert.

Miles weighs 0.75 kilograms less than Bert.

How many kilograms do the three boys weigh altogether?

    kilograms
Show Answers Only

`text(145.5 kg)`

Show Worked Solution

`text(Bert’s weight = 48.65 kg)`

`text(Gary’s weight = 48.65 + 0.3 = 48.95 kg)`

`text(Miles’ weight = 48.65 − 0.75 = 47.9 kg)`
 

`:.\ text(Total weight)` `= 48.65 + 48.95 + 47.9`
  `= 145.5\ text(kg)`

Number, NAP-K3-CA20

The table below compares the approximate populations of two countries.

Country

Approximate population

(millions)
Cuba 11.475
Benin 11.096

Approximately how many more people live in Cuba than in Benin?

37 900 47 900 379 000 479 000
 
 
 
 
Show Answers Only

`379\ 000`

Show Worked Solution

`text(Extra people living in Cuba)`

`=(11.475-11.096) xx 1\ 000\ 000`

`= 0.379 xx 1\ 000\ 000`

`= 379\ 000`

Number, NAP-J3-NC04 SA

Vivian and Curtly throw a cricket ball from the boundary of the cricket oval to the wicket-keeper.

It takes Vivian's throw 3.48 seconds to reach the wicket-keeper.

It takes Curtly's throw 1.84 seconds.

What is the difference in the time taken to reach the wicket-keeper between the two throws?

  seconds
Show Answers Only

`1.64\ text(seconds)`

Show Worked Solution
`text(Time Difference)` `= 3.48 – 1.84`
  `= 3.48 + (0.16 – 2)`
  `= 1.64\ text(seconds)`

Number, NAP-D3-CA18

Richard is a runner.

The length of his last 4 half marathons are recorded in the table below.
 

  
Which half marathon had the shortest distance?

`1`    `2`   `3`   `4`
 
 
 
 
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`text(half marathon 3)`

Show Worked Solution

`20.295\ text(is the shortest distance.)`

`:.\ text(Half marathon 3 was the shortest.)`

Number, NAP-D3-NC22

Jamie buys a 200 gram bag of pumpkin seeds at the market for making muesli.

Each pumpkin seed has a mass of 0.19 grams.

Which of these is the best estimate for the number of seeds in the 200 gram bag?

`100` `500` `1000` `5000`
 
 
 
 
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`1000`

Show Worked Solution

`text(Mass of 10 seeds = 1.90 g)`

`text(Mass of 100 seeds = 19 g)`

`text(Mass of 1000 seeds = 190 g)`

`:. 1000\ text(is the best estimate.)`

Number, NAP-E3-CA06

Roger had tests to check his health that are summarised in the table below.
 

Test Normal range Roger's result
Resting heart rate 60 to 95 92
Blood sugar 4.2 to 6.1 4.1
Vitamin C 0.4 to 1.7 0.5

 
For which tests were Roger's results within the normal range?

 
 Resting heart rate and blood sugar
 
 Blood sugar and vitamin C only
 
 Resting heart rate only
 
 Resting heart rate and vitamin C only
Show Answers Only

`text(Resting heart rate and vitamin C only)`

Show Worked Solution

`text(Checking each test:)`

`text(92 is within 60 and 95)`

`text(4.1 is not within 4.2 and 6.1)`

`text(0.5 is within 0.4 and 1.7)`

`:.\ text(Resting heart rate and vitamin C only are within the normal range.)`

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).}`

Number, NAP-F3-NC16

A mixture requires an amount of salt to be added.

No more than 0.75 grams of salt is allowed in the mixture.

Which amount below is the heaviest mass of salt that can be added?

`text(0.55 grams)` `text(0.6 grams)` `text(0.8 grams)` `text(1.5 grams)` `text(6 grams)`
 
 
 
 
 
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`0.6\ text(grams)`

Show Worked Solution

`text(0.8 grams, 1.5 grams and 6 grams are all > 0.75 grams.)`

`text(0.6 grams > 0.55 grams and less than 0.75 grams.)`

`:.\ text(0.6 grams is the heaviest mass.)`

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.)`

Number, NAP-I3-NC29 SA

Onions cost $3 per kilogram.

Peter buys 3.35 kilograms of onions.

How much does Peter pay for the onions? 

$  
Show Answers Only

`$10.05` 

Show Worked Solution

`text(C)text(ost of 3 kg) = 3 xx $3 = $9`

`text(C)text(ost of 0.1 kg) = 3/10 = text(30 cents)`

`=>\ text(C)text(ost of 0.35 kg)` `= 3.5 × 30\ text(cents)`
  `= $1.05`

  

`:.\ text(C)text(ost of 3.35 kg)` `= 9 + 1.05`
  `= $10.05`