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Geometry, NAP-D3-NC25 SA

George creates models of steps using cubes as shown below.
 

 
How many cubes would George need to create a model for 5-steps?
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`45`

Show Worked Solution

`text(1 step = 3 cubes)`

`text(2 steps = 3 + 6 = 9 cubes)`

`text(3 steps = 3 + 6 + 9 = 18 cubes)`

`text(4 steps = 3 + 6 + 9 + 12 = 30 cubes)`

`text(5 steps = 3 + 6 + 9 + 12 + 15 = 45 cubes)`

Geometry, NAP-D3-NC15

Wes made a small staircase by stacking blocks.

There are no gaps between blocks.
 

 
How many blocks in the staircase are not shown at all?

`48` `36` `28` `24`
 
 
 
 
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`36`

Show Worked Solution

`text(Calculate the hidden blocks under each step:)`

`text(1st step = 0)`

`text(2nd step = 6)`

`text(3rd step = 12)`

`text(4th step = 18)`

`:.\ text(36 blocks are not shown.)`

Geometry, NAP-C3-CA23

Sam has these L-shaped tiles.
 

 
One side of the tile is light brown and one side of the tile is dark brown.

The glue only works on one side of the tile (the dark brown side).

Sam wants to glue all the tiles to the floor, so all should have the light brown side facing up.

Which pattern can Sam not make?

 
 
 
 
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Show Worked Solution

`text(No tile can have the same orientation as the)`

`text(black tile.)`

`:.\ text{This pattern can’t be made (due to the bottom}`

`text{left tile).}`

 

Geometry, NAP-E3-NC09

Irene placed three identical tiles together at their edges.

She drew around the outside to make this new shape.
 

 
Which of these could have been the shape of her tiles?

`text(triangles)` `text(rectangles)` `text(trapeziums)` `text(rhombuses)`
 
 
 
 
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`text(rhombuses)`

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`text(rhombuses)`

Geometry, NAP-F3-NC12

Kimoko cut a regular pentagon into several identical pieces with no paper left over.
 

 
Which of these could be the shape of the pieces?

 
 
 
 
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Show Worked Solution

`text(A pentagon can be made up of 5 isosceles)`

`text(triangles as shown below.)`

`:.\ text(The shape of the pieces could only be:)`