Stage 8 - Q1 - 2 marks
How many occupied floor squares are shown?
Hint
Count occupied positions, not cube heights.
Stage 8 - Q2 - 2 marks
Find the total number of cubes.
Hint
Each label counts all cubes in that stack.
Stage 8 - Q3 - 2 marks
Find the front-elevation height list from left to right.
Hint
A taller stack hides a shorter one behind it.
Stage 8 - Q4 - 2 marks
Find the right-elevation height list from front to back.
Hint
Look along each row, taking its maximum height.
Stage 8 - Q5 - 3 marks
Draw the front and right elevations of this height plan.
Hint
Use the stated front edge to orient both views.
Stage 8 - Q6 - 3 marks
A full 2 by 3 plan has every stack 4 cubes high. Find the total cubes and both elevation heights.
Hint
The number of stacks and their height play different roles.
Stage 8 - Q7 - 3 marks
In the height plan shown, may the front-left height rise from 1 to 2 without changing either elevation?
Hint
Check the column maximum and the row maximum separately.
Stage 8 - Q8 - 3 marks
Give two full 2 by 2 height plans with front heights 2,2 and right heights 2,2 but different cube totals. List rows from front to back and entries from left to right.
Hint
A lower stack may be hidden behind a taller one in both views.
Stage 8 - Q9 - 4 marks
A full 2 by 2 plan has front heights 2,3 and right heights 3,2. Explain why the front-right stack must have height 3.
Hint
Which row is allowed to contain a stack of height 3?
Stage 8 - Q10 - 5 marks
Challenge: a full 2 by 2 plan has front heights 2,3 from left to right and right heights 3,2 from front to back. Find the minimum and maximum cube totals. Give a plan for each and justify the bounds. List plan rows from front to back and entries in each row from left to right.
Hint
Use row/column maxima to bound each stack, remembering every square is occupied.