Stage 9 - Q1 - 2 marks
A square sheet has side 30 cm. Cut off a strip of width 6 cm, rotate it and trim to form the illustrated rectangle. Find the new width and height.
Hint
Use the dimensions labelled \(L-w\) and \(L+w\).
Stage 9 - Q2 - 2 marks
In the sheet model, \(L=50\) cm and \(w=10\) cm. Find the area of the discarded square.
Hint
The offcut is a square with side \(w\).
Stage 9 - Q3 - 3 marks
In the sheet model, \(L=70\) cm and \(w=17.5\) cm. Find the area of the new rectangle.
Hint
The new rectangle is narrower but taller.
Stage 9 - Q4 - 3 marks
In the sheet model, the strip width is 25% of the square side. Find the percentage of area retained.
Hint
A percentage of length is not the same percentage of area.
Stage 9 - Q5 - 4 marks
Compare strips 30% and 35% of a square side. By how many percentage points does the wasted area increase?
Hint
Square each length fraction before finding the difference.
Stage 9 - Q6 - 4 marks
Compare strips 35% and 40% of a square side. By how many percentage points does the wasted area increase?
Hint
Square each length fraction before finding the difference.
Stage 9 - Q7 - 5 marks
A square sheet has side 70 cm. The new rectangle must retain 87.75% of its original area. Find the strip width.
Hint
The discarded piece is a square.
Stage 9 - Q8 - 5 marks
For a square of side 90 cm, does doubling a strip width from 15.75 cm to 31.5 cm double the wasted area?
Hint
The waste depends on a square, not directly on the width.
Stage 9 - Q9 - 5 marks
A sheet starts as a square of side 30 cm. After the same cut-and-rotate process, the rectangle is 24 cm longer than it is wide. Find the strip width and retained area.
Hint
The dimension difference is twice the cut width.
Stage 9 - Q10 - 3 marks
A square sheet has side 100 cm. Apply the same cut-and-rotate model. Choose the strip width so the new rectangle is twice as long as it is wide. Find the exact strip width and retained fraction, then give the retained percentage to 1 d.p.
Hint
The long side gains \(w\) while the short side loses \(w\).