Further Mathematics — Hyperbolic Functions

Exam board: AQA  |  Back to subjects

Board-Specific Note

Includes additional Pure plus an optional decision/applied module.

Learning Objectives

• Define sinh, cosh, tanh
• Use their identities
• Solve simple hyperbolic equations

Key Points

• sinh x = (eˣ − e⁻ˣ)/2
• cosh x = (eˣ + e⁻ˣ)/2
• cosh²x − sinh²x = 1

Lesson Plan (50 minutes)

1. Starter (5 min): Recall prior knowledge of hyperbolic functions with quick questions.
2. Teaching (15 min): Work through each of the learning objectives, explaining principles step by step.
3. Key points review (5 min): Revisit the key points together, confirming understanding.
4. Worked example (10 min): Model the example question: Evaluate cosh 0. Solution: cosh 0 = 1
5. Practice (10 min): Students attempt the practice questions independently; circulate and support.
6. Plenary (5 min): Review answers and address misconceptions.

Homework

• Show cosh²x − sinh²x = 1
• Solve sinh x = 2
• Evaluate tanh x for large x

Assessment

Check practice answers against the model answer; use the built-in practice questions as formative assessment.