This is a question from an additional maths paper which I have been dwelling on for the past 2 hours or so. I have the mark scheme and hence the answer but I do not understand how it is solved. Please explain if you can make out how. For e.g., why isn't (a)(ii)3.5n or 4n - 1 ?
I understand (a)(i) and (b)(i) since they are really obvious but the rest literally makes me want to strangle a new-born baby.
The question:
(a) An artist makes a sequence of patterns.He uses three types of metal pieces called rods, springs and bobs.He welds them together to make patterns.
In Pattern 2 there are 7 rods, 8 springs and 2 bobs.
In Pattern n there are n bobs.
(i) How many springs are there in Pattern n?
(ii) How many rods are there in Pattern n?
(b) The artist now changes his design to make new patterns with greater widths.The pattern below is called Pattern 3 by 2.In Pattern x by y there are xy bobs.
(i) How many springs are there in Pattern x by y?
(ii) How many rods are there in Pattern x by y?
The answer in accordance to the mark scheme:
(a) (i) 4n
(ii) 3n + 1
(b) (i) 4xy
(ii) Strategy,
e.g. simplify then extend or lookat vertical and horizontal Method leading to correct answer,
e.g. notices 1more row to dimension comparison (x+1)y + x(y+1) ISW (2xy+x+y)