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Statistical Analysis and Mathematical Calculations for 2009 Solutions

This document presents solutions to math problems from 2009, including equations, gradients, quartiles, and sales comparisons.

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Statistical Analysis and Mathematical Calculations for 2009 Solutions

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  1. This is the formula that we use.

  2. (a) • A • Skewed to the right 2009 Paper 1 Solution Main Grid

  3. Gradient = 3 Intercept = -1 Equation: y = 3x -1 Solution Main Grid

  4. (x + 3)(x - 8) Solution Main Grid

  5. Solution Main Grid

  6. 37 41 43 47 56 58 59 61 66 68 70 75 Median position = (12 + 1)/2 = between 6th and 7th median = 58.5 Lower quartile = (43 + 47)/2 = 45 Upper quartile = (66 + 68)/2 = 67 SIQR = (67 – 45)/2 = 11 • In December, the marks on average are better, 67 > 58.5 • and the range of marks are less spread out, 7 < 11 Solution Main Grid

  7. Cosa positive Tana negative For these three conditions to be met, angle in fourth quadrant Sina negative Sina negative Cosa positive Tana negative 270 < a < 360 Solution Main Grid

  8. Re arranging y = -x + 5 Gradient is -1 Solution Main Grid

  9. Solution Main Grid

  10. (a) x = -3 (b) y = (x + 3)2 - 4 (c) At x = 0 y = (0 + 3)2 – 4 = 9 – 4 = 5 C is (0 , 5) Solution Main Grid

  11. Solution Main Grid

  12. 2009 P2 2007 sales = 3000 x 1.11 = 3330 2008 sales = 3330 x 0.90 = 2997 So sales were less in 2008 than 2006, by 3 copies. Solution Main Grid

  13. Solution Main Grid

  14. Volume of Aluminium = vol outside cylinder – vol inside cylinder = 4 750 506 – 3 868 794 = 881 712 mm3 = 882 000 mm3 (3 sig figs) Solution Main Grid

  15. Substitute into first equation 14 x 11.95 + 60y = 344.30 60y = 344.30 – 167.30 y = 177 ÷ 60 = 2.95 check with other equation Cost of passenger is £2.95 X 2 X 3 (c) 28x + 120y = 688.60 63x + 120y = 1106.85 -35x = -418.25 x = 11.95 Cost of car is £11.95 • 14x + 60y = 344.30 • 21x + 40y = 368.95 Solution Main Grid

  16. Main Grid Solution

  17. Solution Main Grid

  18. Solution Main Grid

  19. Solution Main Grid

  20. Solution Main Grid

  21. S A T C √ √ Solution Main Grid

  22. Solution Main Grid

  23. Dividing by ‘a’ and b4 Solution Main Grid

  24. 17 125 D 14m x 38° C A Main Grid Solution

  25. 1.7m 1.7m 0.9m Height of tunnel = 1.44 + 1.7 = 3.14m Solution Main Grid

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