4400 Higher November 2006 Paper 4 Q4
4 Here is a pattern of shapes made from centimetre squares.
This rule can be used to find the perimeter of a shape in this pattern.
| Add 1 to the Shape number and then multiply your answer by 2 |
\(P\) cm is the perimeter of Shape number \(n\).
(a) Write down a formula for \(P\) in terms of \(n\). (3)
(b) Make \(n\) the subject of the formula in part (a). (3)
| Scheme | Marks |
|---|---|
| \(P = 2(n + 1)\) | B3 |
| (3) |
Notes
B3: for \(P = 2(n + 1)\) oe
B2 for \(2(n + 1)\) oe or \(n = \frac{P}{2} - 1\) oe
B2 for \(P = 2n + 1\) oe or \(P = n + 1 \times 2\) oe
B1 for \(P\) = any f(\(n\)) (not \(P = n\))
B1 for \(2n + 1\) oe or \(n + 1 \times 2\) oe
B0 for muddle eg \(n + 1 = \times 2 = P\)
(a&b) Ignore units
| Scheme | Marks |
|---|---|
| \(P = 2n + 2\) | M1 |
| \(2n = P - 2\) | M1 |
| \(\dfrac{P - 2}{2}\) or \(\dfrac{P}{2} - 1\) | A1 |
| (3) | |
| (6 marks) |
Notes
M1: \(2n + 2\) seen
or M2 for \(\dfrac{P}{2} = n + 1\) or \(P - 2 \div 2\)
SC ft from \(P = 2n + 1\) or \(2n + 1\) only
M1 for \(2n = P - 1\) or \(P - 1 \div 2\)
A1 ft for \(\dfrac{P - 1}{2}\) oe