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(a) Write down the number of cubes that make an \textit{UP staircase} of height 2.
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(b) On the grid below draw an \textit{UP staircase} of height 4.
(c) Complete the table for the number of cubes that make these \textit{UP staircases}.
[Table_1:
| Height | 1 | 2 | 3 | 4 | 5 | 6 |
|---------------|---|---|---|---|---|---|
| Number of cubes | 1 | 6 | | | | |]
(d) Find how many cubes make an \textit{UP staircase} of height 10.
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(e) (i) What is the height of the tallest \textit{UP staircase} that can be made from 100 cubes?
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(ii) Find how many cubes would be left over.
..............................................................
540
595
535
This is an $UP AND DOWN$ staircase of height 3 made using 9 cubes. It is a 3-step $UP AND DOWN$ staircase because it has a height of 3 cubes.
(a) Find how many cubes make an $UP AND DOWN$ staircase of height 4.
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(b) On the grid below draw an $UP AND DOWN$ staircase of height 2.
(c) Complete the table for the number of cubes that make these $UP AND DOWN$ staircases.
[Table_1]
(d) The numbers of cubes form a sequence. Write down the mathematical name of this sequence.
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(e) Find how many cubes make an $UP AND DOWN$ staircase of height 10.
.........................................................................
(f) Find an expression, in terms of $n$, for the number of cubes that make an $UP AND DOWN$ staircase of height $n$.
.........................................................................
536
590
544
This is a DOUBLE staircase of height 3 made using 12 cubes. It is a 3-step DOUBLE staircase because it has a height of 3 cubes.
(a) Find how many cubes make a DOUBLE staircase of height 2.
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(b) Complete the table for the number of cubes that make these DOUBLE staircases.
[Table_1]
| Height | 1 | 2 | 3 | 4 | 5 | 6 |
|--------------|---|----|----|----|----|----|
| Number of cubes | 2 | 12 | | | | |
(c) Find how many cubes make a DOUBLE staircase of height 10.
.................................................................
(d) (i) Find an expression, in terms of $n$, for the number of cubes that make a DOUBLE staircase of height $n$.
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(ii) Find the height of a DOUBLE staircase made from 240 cubes.
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(e) Write down the connection between the number of cubes that make a DOUBLE staircase and the number of cubes that make an UP AND DOWN staircase, when both staircases have the same height.
.......................................................................................................
589
523
503
(a) Write down the connection between the number of cubes that make a \textit{DOUBLE staircase} and the number of cubes that make an \textit{UP staircase}, when both staircases have the same height.
..............................................................................................................................................................
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(b) Find an expression, in terms of \( n \), for the number of cubes that make an \textit{UP staircase} of height \( n \).
..............................................................................................................................................................
508
590
536
