Foundation June 2017 Paper 1 Q11
11 A sequence of patterns is made from circular tiles ● and square tiles □
Here are the first three patterns in the sequence.
(a) How many square tiles are needed to make pattern number 6? (2)
(b) How many circular tiles are needed to make pattern number 20? (2)
Derek says,
“When the pattern number is odd, an odd number of square tiles is needed to make the pattern.”
(c) Is Derek right?
You must give reasons for your answer. (2)
You must give reasons for your answer. (2)
| Answer | Mark | Notes |
|---|---|---|
| 36 | M1 | demonstrates the start of a method that could lead to the answer, eg recognition of square numbers, or use of differences, or diagrams |
| A1 | cao |
| Answer | Mark | Notes |
|---|---|---|
| 80 | M1 | demonstrates the start of a method that could lead to the answer, eg repeated addition of 4, or \(20 \times 4\) |
| A1 | cao |
| Answer | Mark | Notes |
|---|---|---|
| C2 | conclusion with supportive evidence, eg odd \(\times\) odd = odd, or all odd numbers squared will be odd. | |
| (C1) | (e.g. starts to work with (generate) square numbers for odd patterns or \((2n + 1)^2\) eg \(1 \times 1 = 1\), or generates sequence for squares using differences) |