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Mathematics Revision: Standard Deviation, Percentage Appreciation, and Area Calculations

This document covers important mathematical concepts including breaking down expressions, calculating standard deviation, determining percentage appreciation from a property value increase, and finding the area using side lengths and angles in triangles. Step-by-step solutions ensure clarity in understanding complex problems such as expansion of brackets and application of formulas in geometry. Ideal for students seeking to improve their math skills in preparation for exams.

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Mathematics Revision: Standard Deviation, Percentage Appreciation, and Area Calculations

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  1. Prelim Revision No 7

  2. 1. Break the brackets: (x + 5)(x2 – 3x + 4) 2. Calculate the standard deviation. 3 1 9 2 7

  3. 3. Wilbur’s house has risen in value from £184000 to £198000. Calculate the percentage appreciation.

  4. 4. a) Calculate LCAB C 10cm 8cm B A 12cm b) Calculate Area

  5. 1. Break the brackets: (x+ 5)(x2 – 3x + 4) = x(x2 – 3x + 4) + 5(x2 – 3x + 4) = x3 – 3x2 + 4x + 5x2 – 15x + 20 = x3 + 2x2 – 11x + 20

  6. 2. Calculate the standard deviation. 2 ∑x2 – n – 1 (∑x)/n s = 3 1 9 2 7 2 22 144 / – 5 s = 4 n = 5 x x2 47.2 = 3 1 9 2 7 9 1 81 4 49 4 √ = 11.8 = 3.4 ∑x ∑x2 22 144

  7. 3. Wilbur’s house has risen in value from £184000 to £198000. Calculate the percentage appreciation. Appreciation = 198000 – 184000 = £14000 Percentage Appreciation: 14000 = 0.076 = 7.6% 184000

  8. 4. a) Calculate LCAB C 10cm 8cm x 55.80 B A 12cm CosA = b2 + c2 – a2 = 82 + 122 – 102 = 108 2bc 2 X 8 X 12 192 = 0.5625 A = 55.80 b) Area = ½ bcSinA = ½ X 8 X 12 X sin55.80 = 39.7cm2

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