Stage 9 - Q1 - 2 marks
Write and simplify the perimeter. All lengths are in cm.
Hint
A rectangle has two sides of each length.
Stage 9 - Q2 - 2 marks
Write and simplify the area. All lengths are in cm.
Hint
Use \(\text{area}=\text{length}\times\text{width}\).
Stage 9 - Q3 - 3 marks
A square has side \((6x+1)\) cm, where \(x\) is positive. Write its perimeter.
Hint
Multiply the whole side expression by four.
Stage 9 - Q4 - 3 marks
A square has area \(3x\) square cm, with \(x\) positive. Write its perimeter.
Hint
Area and side length are different measures.
Stage 9 - Q5 - 4 marks
Write the perimeter as a simplified expression. Let \(x\) be positive; lengths are in cm.
Hint
Each algebraic side occurs twice.
Stage 9 - Q6 - 4 marks
Write the perimeter as a simplified expression. Let \(x\) be positive; lengths are in cm.
Hint
Each algebraic side occurs twice.
Stage 9 - Q7 - 5 marks
A cube has volume \(343x^3\) cubic cm, with \(x\) positive. Write its side length and the total length of its 12 edges.
Hint
The edge length is the cube root of the volume.
Stage 9 - Q8 - 5 marks
A rectangle has sides \((x+4)\) cm and \((x+2)\) cm, with \(x\) positive. Write an area expression, then evaluate it at \(x=2\).
Hint
You can evaluate a product without expanding it.
Stage 9 - Q9 - 5 marks
A rectangle has sides \((x-5)\) cm and \(4\) cm. Is every positive \(x\) a possible value?
Hint
A geometric length must be strictly positive.
Stage 9 - Q10 - 3 marks
A rectangle and a square have equal perimeters. The square side is \((3x+2)\) cm and one rectangle side is \((4x+1)\) cm, where \(x\) is positive. Find the other side, then compare the areas when \(x=2\).
Hint
A rectangle width is half its perimeter minus its length.