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GSCE COURSEWORK PART 1 Random Sample 91 92 93 94 95 96 97 98 99 100 81 82 83 84 85 86 87 88 89 90 71 72 73 74 75 76 77 78 79 80 61 62 63 64 65 66 67 68 69 70 51 52 53 54 55 56 57 58 59 60 41 42 43 44 45 46 47 48 49 50 31 32 33 34 35 36 37 38 39 40 21 22 23 24 25 26 27 28 29 30 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 I drew 5 3-step stairs all of them were the same size, but they differed in position. Number Of Shape Calculations Total 1 1+2+3+11+12+21 50 8 8+9+10+18+19+28 92 34 34+35+36+44+45+54 248 71 71+72+73+81+82+91 470 78 78+79+80+88+89+98 512 Comment: 1) Notice how all the totals are even 2) The totals increase the higher up the grid you go 3) Across goes up about 42 (92-50) 4) Up goes up about 420 (470-50) Systematic Sample 91 92 93 94 95 96 97 98 99 100 81 82 83 84 85 86 87 88 89 90 71 72 73 74 75 76 77 78 79 80 61 62 63 64 65 66 67 68 69 70 51 52 53 54 55 56 57 58 59 60 41 42 43 44 45 46 47 48 49 50 31 32 33 34 35 36 37 38 39 40 21 22 23 24 25 26 27 28 29 30 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 I drew 5 stairs all on the bottom line going across, I did this to see if there was a pattern. Number Of Shape Calculations Total 1 1+2+3+11+12+21 50 2 2+3+4+12+13+22 56 3 3+4+5+13+14+23 62 4 4+5+6+14+15+24 68 5 5+6+7+15+16+25 74 Comment: There is clearly a pattern here; the totals are increasing by 6, we call this a linear sequence. From this information I predict that the next total will be 80 and the 8th will be 92. 91 92 93 94 95 96 97 98 99 100 81 82 83 84 85 86 87 88 89 90 71 72 73 74 75 76 77 78 79 80 61 62 63 64 65 66 67 68 69 70 51 52 53 54 55 56 57 58 59 60 41 42 43 44 45 46 47 48 49 50 31 32 33 34 35 36 37 38 39 40 21 22 23 24 25 26 27 28 29 30 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 Results: Number Of Shape Calculations Total 6 6+7+8+16+17+26 80 8 8+9+10+18+19+28 92 Both my predictions were correct. Algebraic Expression X+20 X+10 X+11 X X+1 X+2 I drew 1 stair with Algebra on it. Total: (x)+(x+1) +(x+2) +(x+10) +(x+11) +(x+20) = 6X+44 Comment: The reason it's 6x is because there are 6 stairs (x+x+x+x+x+x) It's 44 because the totals across for these stairs are 4...

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