Further Mathematics — Vectors

Exam board: AQA  |  Back to subjects

Board-Specific Note

Includes additional Pure plus an optional decision/applied module.

Learning Objectives

• Use vector arithmetic and notation
• Compute scalar and vector products
• Work with lines in 3D

Key Points

• Position vectors r = a + λb
• Dot product for angle cosθ = (a·b)/(|a||b|)
• Scalar product of perpendicular vectors is zero

Lesson Plan (50 minutes)

1. Starter (5 min): Recall prior knowledge of vectors 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: Find cosθ between (1,2) and (3,4). Solution: (1·3+2·4)/(√5·5) = 11/(5√5)
5. Practice (10 min): Students attempt the practice questions independently; circulate and support.
6. Plenary (5 min): Review answers and address misconceptions.

Homework

• Dot (2,−1,3) with (1,0,2)
• Are (1,2) and (−4,2) perpendicular?
• Write the line through two points in vector form

Assessment

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