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Geometry and Depreciation Problems: Calculations and Solutions

This document consists of a series of mathematical problems focused on geometry and depreciation. It includes tasks such as breaking down expressions, calculating angles formed by tangents and segments, determining the area of a sector given its dimensions, and understanding the depreciation of a vehicle over the years. Each problem is solved step-by-step to demonstrate the calculations necessary for finding the desired values. Suitable for students looking for practice in algebra and geometry concepts.

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Geometry and Depreciation Problems: Calculations and Solutions

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  1. Prelim Revision

  2. O C A B D 1. Break the brackets (3x – 5)(2x + 7) 2. If AD is a tangent and LDBC = 320, Calculate the size of LCDB

  3. 3. Area of sector is 540cm2 Calculate the radius. 2300

  4. 4. Freddie’s van is worth £20000 It is depreciating at a rate of 24% yearly. During which year will the value drop below £7000?

  5. 1. Break the brackets (3x – 5)(2x + 7) 6x2 + 21x – 10x – 35 6x2 + 11x – 35

  6. O C A B D 2. If AD is a tangent and LDBC = 420, Calculate the size of LCDB 640 580 580 260 320

  7. 3. Area of sector is 540cm2 Calculate the radius. 230/360 X π X r2 = Area 2.007 X r2 = 540 r2 = 540 ÷ 2.007 = 269.058 r = √269.058 = 16.4 2300 540

  8. 4. Freddie’s van is worth £20000 It is depreciating at a rate of 24% yearly. During which year will the value drop below £7000? Year 1 0.76 X 20000 = 15200 Year 2 0.76 X 15200 = 11552 Year 3 0.76 X 11552 = 8779.52 Year 4 0.76 X 8779.52 = 6673.43 Falls below £7000 during the 4th year.

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