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Year 9 · Term 1

9.1 Surds and Pythagoras

Learning Objectives

Surds

  1. 1. Differentiate between rational and irrational numbers.
  2. 2. Understand the concept of surds and their approximate values.
  3. 3. Simplify surds by extracting the largest square factor.
  4. 4. Multiply and divide surds, and add/subtract like surds.
  5. 5. Rationalise a denominator of the form 1/√a.

Pythagoras' Theorem

  1. 6. Apply Pythagoras' theorem to find a missing side in a right-angled triangle.
  2. 7. Use the converse of Pythagoras' theorem to test whether a triangle is right-angled.
  3. 8. Use Pythagoras' theorem to find distances between two points in 2D.
  4. 9. Use Pythagoras' theorem to find lengths in 3D solids (space diagonals, slant heights).
  5. 10. Give Pythagoras answers in surd form where appropriate.
  6. 11. Apply Pythagoras' theorem to practical problems (ladders, ziplines, triangles in real contexts).