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Number, NAP-B3-CA05v1

Two places are 3.6 cm apart on a map.

On the map 1 cm represents 3 km.

What is the actual distance between the two places?

`1.2\ text(km)` `6.6\ text(km)` `10.8\ text(km)` `32.4\ text(km)`
 
 
 
 
Show Answers Only

`10.8\ text(km)`

Show Worked Solution
`text(Actual distance)` `=3.6 xx 3`
  `=10.8\ text(km)`

Filed Under: Maps and Directions Tagged With: Band 6, smc-3164-20-Map scales

Geometry, NAP-A3-CA32

Here is a map of Crikey Island.

The shortest distance from Point Nobby to Gilbos is 900 m.
 

 
The shortest distance from Point Nobby to Fire Beach is closest to

`text(1050 m)` `text(1900 m)` `text(2100 m)` `text(2450 m)`
 
 
 
 
Show Answers Only

`text(2100 m)`

Show Worked Solution

`text(Let)\ w =\ text(grid width)`

`text(Distance from Point Nobby to Gilbos) =4.5w`

`:. 4.5 w` `= 900`
`w` `= 200\ text(metres)`

 

`:.\ text(Distance from Point Nobby to Fire Beach)`

`= 10.5 w`

`= 10.5 xx 200`

`= 2100\ text(metres)`

Filed Under: Maps and Directions, Maps and Directions Tagged With: Band 10, smc-3164-20-Map scales, smc-667-20-Map scales

Geometry, NAP-B4-CA22

 
The distance on the map from Hill End to Rouse Hill along the road is 5 cm.

How long will it take to walk from Hill End to Rouse Hill along the road at a speed of 6 kilometres per hour?

 
1 hour 15 minutes
 
1 hour 25 minutes
 
12 hours 5 minutes
 
12 hours 30 minutes
Show Answers Only

`text(1 hour 15 minutes)`

Show Worked Solution
`text(Distance)` `= 5 xx 1500`
  `= 7500\ text(m)`
  `= 7.5\ text(km)`

 

`:.\ text(Walk Time)` `= 7.5/6`
  `= 1.25\ text(hours)`
  `= 1\ text(hour 15 minutes)`

Filed Under: Maps and Bearings, Maps and Bearings, Maps and Directions, Rates and Ratios, Rates and Ratios Tagged With: Band 9, smc-3164-20-Map scales, smc-3177-50-D=SxT, smc-3187-20-Map scales, smc-670-20-Map scales, smc-685-50-D=SxT

Geometry, NAP-D3-CA28 SA

On the map below, York is 60 km from Karkoo.

The town of Cootra is not shown on the map.

Cootra is due east of Barwell and due North of Ungarra.

What is the distance from Ungarra to Cootra?
 

   km
Show Answers Only

`90`

Show Worked Solution

`text(4 grids between Karkoo and York)`

`=> 1\ text(grid interval)` `= 60/4`
  `= 15\ text(km)`

 

`:.\ text(Ungarra to Cootra)` `= 6\ text(grid intervals)`
  `= 6 xx 15`
  `= 90\ text(km)`

Filed Under: Maps and Directions, Maps and Directions Tagged With: Band 9, smc-3164-20-Map scales, smc-667-20-Map scales

Geometry, NAP-F3-CA29 SA

Towns  `A, B and C` are marked on the scale diagram below.

The distance from Town  `A`  to Town  `B`  is 9 km.

What is the distance from Town  `B`  to Town  `C?`

   kilometres
Show Answers Only

`3.6`

Show Worked Solution

`text(Let)\ \ d = text(distance of Town)\ B\ text(to Town)\ \ C`

`text(S)text(ince the diagram is a scale diagram,)`

`d/9` `= 2/5`
`:. d` `= (9 xx 2)/5`
  `= 3.6\ text(km)`

Filed Under: Maps and Directions, Maps and Directions Tagged With: Band 10, smc-3164-20-Map scales, smc-667-20-Map scales

Geometry, NAP-G3-CA20

The distance from Village `A` to Village `C` is 6 cm on the map.
 

 
What is the actual distance from Village `A` to Village `C?`

`50\ text(m)` `180\ text(m)` `500\ text(m)` `1800\ text(m)`
 
 
 
 
Show Answers Only

`1800\ text(m)`

Show Worked Solution
`6\ text(cm) xx 30\ 000` `= 180\ 000\ text(cm)`
  `= 1800\ text(m)`

Filed Under: Maps and Directions, Maps and Directions Tagged With: Band 8, smc-3164-20-Map scales, smc-667-20-Map scales

Geometry, NAP-H3-NC27 SA

Grant was making a scale drawing of a pipeline on grid paper.

The full length of the pipeline is drawn to scale on the grid below. It consists of 8 identical sections joined together (not shown on the diagram).
 

 
What is the length of each section of pipeline?

  metres
Show Answers Only

`25`

Show Worked Solution
`text(S)text(ection length)` `= text(total length)/text(number of sections)`
  `= (5 xx 40)/8`
  `=200/8`
  `= 25\ text(metres)`

Filed Under: Maps and Directions, Maps and Directions Tagged With: Band 9, smc-3164-20-Map scales, smc-667-20-Map scales

Geometry, NAP-H3-CA27 SA

Jana drew a diagram of her tennis racquet.
 

 
The actual length of her racquet is 60 centimetres.

What is the actual width of her racquet head?

   centimetres
Show Answers Only

`26`

Show Worked Solution

`text(Racquet is 30 grid intervals long.)`

`text(30 intervals)` `= 60\ text(cm)`
`:. 1\ text(grid interval)` `= 2\ text(cm)`

 

`text(Racquet head is 13 grid intervals high,)`

`:.\ text(Head width)` `= 13 xx 2`
  `= 26\ text(cm)`

Filed Under: Maps and Directions, Maps and Directions Tagged With: Band 9, smc-3164-20-Map scales, smc-667-20-Map scales

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)`
 
 
 
 
Show Answers Only

`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)`

Filed Under: Maps and Directions, Maps and Directions Tagged With: Band 5, smc-3164-20-Map scales, smc-667-20-Map scales

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)`

Filed Under: Maps and Bearings, Maps and Bearings, Maps and Directions Tagged With: Band 5, smc-3164-20-Map scales, smc-3187-20-Map scales, smc-670-20-Map scales

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