Vectors (AS Unit 2: Applied Mathematics A) — WJEC A-Level Mathematics
Test yourself on Vectors (AS Unit 2: Applied Mathematics A) with WJEC A-Level practice questions.
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Vectors (AS Unit 2: Applied Mathematics A) explained
Two-dimensional vectors can be represented in Cartesian component form as v = xi + yj (or column vector (x, y)ᵀ) or in magnitude-direction form (r, θ).
Read the full explanation
The magnitude is calculated via Pythagoras' theorem: |v| = √(x² + y²). The direction angle θ relative to a reference axis is found using trigonometry: tan α = |y/x|, with α adjusted to the correct quadrant. For bearings, angle is measured clockwise from North (the positive j direction). Conversely, converting from magnitude r and angle θ to component form uses x = r cos θ and y = r sin θ. Candidates must handle negative components accurately when identifying quadrants.
Your focus
- Compute the magnitude of two-dimensional vectors using the Pythagorean formula |v| = √(x² + y²).
- Determine vector direction relative to coordinate axes or as a three-figure compass bearing.
- Convert fluently between Cartesian component form (xi + yj) and magnitude-direction form.
Vectors (AS Unit 2: Applied Mathematics A) exam tips
Marking Points
- calculating vector magnitude using |v| = √(x² + y²)
- calculating the direction angle using trigonometry tan α = |y/x| and adjusting for quadrant
- converting magnitude and direction back to Cartesian components using x = r cos θ and y = r sin θ
- stating vector direction correctly as a three-figure bearing or angle to a specified axis
Examiner Tips
- 💡Always sketch a quick vector triangle to verify which quadrant the vector lies in before calculating direction.
- 💡Express bearings as three-digit numbers (e.g. 045° or 215°) measured clockwise from the positive j direction.
Common Mistakes
- calculating direction angle using arctan(y/x) without checking the quadrant indicated by component signs
- measuring bearings anticlockwise or from the horizontal axis rather than clockwise from North