4MA0 Foundation January 2014 Paper 1 Q5
5 Here is a sequence of patterns made from white dots and black dots.
(a) Draw Pattern number 4 (1)
(b) Complete the table.
(2)
| Pattern number | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Number of white dots | 2 | 4 | 6 | ||
| Number of black dots | 3 | 5 | 7 |
(c) Work out the number of white dots in Pattern number 19 (1)
(d)
(i) Work out the number of black dots in Pattern number 27
(ii) Explain how you found your answer to part (d)(i).
(2)(e) Work out the Pattern number of the pattern with 65 black dots. (2)
(f) \(W\) is the number of white dots in Pattern number \(n\).
Write down a formula for \(W\) in terms of \(n\). (2)
Write down a formula for \(W\) in terms of \(n\). (2)
| Scheme | Marks |
|---|---|
| Correct pattern | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| 8 10 9 11 | B2 |
| (2) |
Notes
B2: B1 for 8 10
B1 for 9 11
| Scheme | Marks |
|---|---|
| 38 | B1 |
| (1) |
Notes
B1: cao
| Scheme | Marks |
|---|---|
| (i) Answer: 55 | B1 |
| (ii) Answer: eg ‘doubled 27 then added 1’, ‘kept adding 2’ | B1 |
| (2) |
Notes
B1: cao
B1: eg. \(2n + 1\); pattern number add next pattern number
| Scheme | Marks |
|---|---|
| \(\dfrac{65 - 1}{2}\) or \(2x + 1 = 65\) | M1 |
| 32 | A1 |
| (2) |
Notes
A1: cao
| Scheme | Marks |
|---|---|
| \(W = 2n\) | B2 |
| (2) | |
| (Total 10 marks) |
Notes
B2: Also accept \(W = n2\), \(W = 2 \times n\), \(W = n \times 2\), \(W = n + n\)
B1 for \(2n\) oe
or for \(W\) = (expression in \(n\))
or for \(n = W \div 2\) (correct formula with \(n\) the subject)