Chapter 8.1
Pythagoras' Theorem (Exam Mastery)
Find missing sides in right triangles and apply to real-world problems. Foundation and Higher.
Chapters18
Pythagoras, trigonometry, sine/cosine rules, 3D problems.
Time invested16 hrs
Approximate guided learning for GCSE mastery.
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Important: Higher Tier Content
Most of this section is Higher tier content, especially sine/cosine rules and exact trig values. These topics are worth significant marks (4-6 marks per question) and frequently appear in Paper 3. Foundation tier students focus on basic Pythagoras and SOH CAH TOA only.
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Chapter 8.2
Pythagoras in 3D (Higher)
Apply Pythagoras to cuboids, pyramids, and space diagonals. Grade 7-9.
Chapter 8.3
Pythagoras Problem-Solving
Multi-step problems combining Pythagoras with other geometry. Both tiers.
Chapter 8.4
Trigonometry - SOH CAH TOA (Exam Focus)
Master the ratios and apply to right-angled triangles. Essential for Grade 5+.
Chapter 8.5
Finding Sides with Trig (Exam Technique)
Determine which ratio to use and solve accurately. Both tiers.
Chapter 8.6
Finding Angles with Trig (Exam Technique)
Use inverse trigonometric functions (sin⁻¹, cos⁻¹, tan⁻¹) correctly.
Chapter 8.7
Trigonometry in 3D (Higher)
Apply trig to complex 3D shapes and combined problems. Grade 7-9.
Chapter 8.8
Exact Trigonometric Values (Higher - Exam Focus)
Know exact values for 30°, 45°, 60° without a calculator. Paper 1 staple.
Chapter 8.9
Sine Rule (Higher - Finding Sides)
Apply a/sin A = b/sin B = c/sin C for non-right triangles. Grade 6-9.
Chapter 8.10
Sine Rule (Higher - Finding Angles)
Use sine rule to determine missing angles in ambiguous cases. Grade 6-9.
Chapter 8.11
Cosine Rule (Higher - Finding Sides)
Apply a² = b² + c² - 2bc cos A for any triangle type. Grade 6-9.
Chapter 8.12
Cosine Rule (Higher - Finding Angles)
Rearrange to find angles using cos A = (b² + c² - a²) / 2bc. Grade 6-9.
Chapter 8.13
Area of Triangles (Higher - ½ab sin C)
Use alternative area formula - a common exam question worth easy marks!
Chapter 8.14
Sine and Cosine Rule Problem-Solving (Higher)
Combine sine/cosine rules for complex multi-step scenarios. Grade 7-9.
Chapter 8.15
Trigonometry and Bearings
Combine bearings with trig for navigation and position problems. Grade 7-9.
Chapter 8.16
Trigonometric Graphs (Higher - Exam Questions)
Understand period, amplitude, and transformations of sine/cosine curves.
Chapter 8.17
Trigonometry Exam Technique
Master labeling, accuracy, and common pitfalls in trig questions.
Chapter 8.18
Trigonometry Past Paper Practice
Real exam questions combining Pythagoras and all trig techniques. Papers 2 & 3.
Next steps
Continue with Section 9 on Vectors and Transformations, or revisit geometry topics.