Numeracy Higher June 2017 Unit 1 Q4
4. Josef has a job in a workshop that makes decorations.
He has made the following three decorations using small squares of stained glass.
Josef labels these patterns P1, P2 and P3 in order.
Josef continues to make decorations following the pattern he has started.
(a) How many more squares would he need to make pattern P22 than to make pattern P18? [1]
(b)
Josef has 22 squares.
Josef states,
‘I think I can make one complete decoration using all 22 squares, with none left over.’
Is Josef correct?
Yes ☐ No ☐
Give a reason for your answer. [1]
(c)
Each small square of stained glass measures 0·5 cm by 0·5 cm.
The perimeter of one of Josef’s decorations is 10 cm.
Complete the label that Josef would use for this decoration. [2]
P …………………
| Scheme | Marks | Comments |
|---|---|---|
| 8 | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| States or implies ‘No’ with a reason, e.g. ‘all Josef’s patterns have an odd number of squares’, ‘same number on each branch from the one top square makes it an odd number’, ‘one square left over’, ‘one square short’, ‘one more needed’, ‘the arms would be unequal (in length)’, ’22 is even’, ‘P10 is (made using) 21 (squares), P11 is (made using) 23 (squares)’, ‘he would only be able to make a pattern with 21 squares’ | E1 | Do not accept ‘No’ with, e.g. ‘too many squares’, ’22 is not part of the pattern’, ‘it is unequal’ |
| Scheme | Marks | Comments |
|---|---|---|
| P4 | B2 | Allow P = 4 B1 for sight of 10÷0.5 or 20 (small square edges) or shows 5 squares on each side (stated or diagram in the answer space for (c)) B0 for P20 unless sight of 10÷0.5 (which is awarded B1) |