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Graphical Solutions and Frequency Calculations in Mathematics

This document contains multiple mathematical problems to be solved graphically, including a system of equations and frequency distributions for pie chart angles. It covers the relative and cumulative frequency calculations, along with an exercise on breaking brackets for polynomials. Detailed examples are provided for graphical solutions of equations such as 2x - 3y = 6 and y = x - 4. Furthermore, instructions are included for calculating angles for pie charts based on given frequency data, ensuring comprehensive understanding and application of mathematical concepts.

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Graphical Solutions and Frequency Calculations in Mathematics

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  1. Prelim revision No 6

  2. E 6cm F 340 1. Area? 2. Solve Graphically 2x – 3y = 6 y = x – 4 7cm G

  3. 3. Fill in relative and cumulative frequency columns. 4. Calculate angles for pie chart.

  4. 5. Break the brackets: (x – 2 )(x2 – 3x + 5)

  5. E 6cm F 340 1. Area? Area = ½ef Sin G = ½ X 7 X 6 X sin340 = 11.7cm2 7cm G

  6. (6 , 2) 2. Solve Graphically 2x – 3y = 6 y = x – 4 2x – 3y = 6 x = 0, y = -2 (0 , -2) y = 0, x = 3 (3 , 0) y = x – 4 x = 4, y = 0 (4 , 0) x = 5, y = 1 (5 , 1) 2x – 3y = 6 y = x – 4 Solution x = 6, y = 2

  7. 19/108 19 35 55 85 108 16/108 20/108 30/108 23/108 108 3. Fill in relative and frequency columns. 4. Calculate angles for pie chart. White 66.70 Espresso: 19/108 X 360 = 63.30 Mocha 1000 Latte: 16/108 X 360 = 53.30 Black 76.70

  8. 5. Break the brackets: (x – 2)(x2 – 3x + 5) = x(x2 – 3x + 5) – 2(x2 – 3x + 5) = x3 – 3x2 + 5x – 2x2+ 6x – 10 = x3 – 5x2 + 11x – 10

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