4MA0 Foundation January 2017 Paper 2 Q6
6 Here is a sequence of shapes drawn on a square grid.
(a) On the grid, draw Shape number 4 (1)
The table shows the number of shaded squares in the first three shapes.
| Shape number | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Number of shaded squares | 8 | 12 | 16 |
(b) Complete the table to show the number of shaded squares in Shape number 4 and Shape number 5 (1)
(c) Work out the number of shaded squares in Shape number 9 (2)
The width of Shape number 1 is 3 squares.
The width of Shape number 2 is 4 squares.
(d) Find the width of Shape number 8 (1)
The width of Shape number \(n\) is \(W\) squares.
(e) Write down a formula for \(W\) in terms of \(n\). (2)
| Scheme | Marks |
|---|---|
| Square width 6 with hole width 4. Answer: correct shape drawn | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| 20, 24 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| Eg 11×11 − 9×9 or 9×4 + 4 or 24 + 4×4 or (8, 12, 16, 20, 24), 28, 32, 36, 40 | M1 |
| 40 | A1 |
| (2) |
Notes
M1: For a complete method or
For a sequence continued to at least the ninth term, following through a single arithmetical error or
For \(4n + 4\)
| Scheme | Marks |
|---|---|
| 10 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(W = n + 2\) | B2 |
| (2) | |
| (7 marks) |
Notes
B2: oe
B1 for \(n + 2\) or \(n = W - 2\)