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Geometry and trigonometry

This revision guide focuses on key measurement concepts vital for geometry and trigonometry exams. It covers strategies for working out side lengths using Pythagoras’ theorem, unit conversions for perimeter, area, volume, and capacity, and total surface area calculations for 3D shapes including bins. Learn to utilize scale factors safely and accurately, and understand right-angled triangles with trig ratios (SOH-CAH-TOA). Complete exercises on bearings and navigation to solidify your understanding and prepare effectively for exam questions.

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Geometry and trigonometry

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  1. Geometry and trigonometry revision

  2. MEASUREMENT There may be a question in the exam where you are given a diagram like this and you will need to work out one side length. Remember to use Pythagoras.

  3. Unit conversion • You will need to know unit conversions: perimeter, area, volume and capacity. • Eg:

  4. TOTAL SURFACE AREA THE BIN QUESTION Work out each individual face and then work out the total surface area. This formula includes the lid and base

  5. SCALE FACTORS • k(scale factor) = length of image length of orginal • Always label the original and image diagrams and then determine the scale factor to work out the unknown length.

  6. BE CAUTIOUS!!! • Examiners will always give you the LINEAR scale factor in order to work out the area or even volume for a figure. You must change the scale factor to suit the question by either squaring or cubing.

  7. RIGHT-ANGLED TRIANGLE • CAN ONLY USE: • 1. PYTHAGORAS • 2. TRIG RATIOS (SOH-CAH-TOA)

  8. THREE-DIMENSIONAL PYTHAGORAS THEOREM • This will require you to find a length in a base first before working out the unknown length in question. • Type of questions: a rod in a rectangular prism, a toothpick in a matchbox, a chopstick in a lunchbox etc. • EG: TO THE NEARET CM, WHAT IS THE LONGEST DRUMSTICK THAT COULD FIT IN A RECTANGULAR TOY BOX WHOSE DIMENSIONS ARE 80cm LONG BY 80cm WIDE BY 60cm HIGH?

  9. BEARINGS AND NAVIGATION

  10. CHAPTER REVIEW • COMPLETE Q’S 1-16 SHORT ANSWER PG 471 • COMPLETE Q’S 1-4 EXTENDED RESPONSE PG 473

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