4400 Higher June 2008 Paper 3 Q8
8 Here are some patterns made from sticks.
This rule can be used to find the number of sticks in one of these patterns.
| Multiply the pattern number by 2 and then add 1 |
(a) \(n\) is the number of sticks in Pattern number \(p\).
Write down a formula for \(n\) in terms of \(p\). (3)
Write down a formula for \(n\) in terms of \(p\). (3)
(b) Make \(p\) the subject of your formula. (2)
| Scheme | Marks |
|---|---|
| \(n = 2p + 1\) oe | B3 |
| (3) |
Notes
B3: for \(n = 2p + 1\) oe eg \(n = p2 + 1\), \(1 + p \times 2 = n\), \(n = p + p + 1\)
B2 for \(2p + 1\) oe B1 for \(n =\) linear function of \(p\) eg \(n = p + 1\)
| Scheme | Marks |
|---|---|
| \(2p = n - 1\) or \(\dfrac{n}{2} = p + \dfrac{1}{2}\) | M1 |
| \(\dfrac{n - 1}{2}\) oe | A1 |
| (2) | |
| (5 marks) |
Notes
M1: for \(2p = n - 1\) or \(\dfrac{n}{2} = p + \dfrac{1}{2}\)
A1: for \(\dfrac{n - 1}{2}\) oe inc \(\dfrac{n}{2} - \dfrac{1}{2}\)