Coordinate geometry in the (x, y) plane (A2 Unit 3: Pure Mathematics B) — WJEC A-Level Mathematics
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Coordinate geometry in the (x, y) plane (A2 Unit 3: Pure Mathematics B) explained
In kinematics and physical modelling, the parameter t naturally represents time, with x(t) and y(t) describing the horizontal and vertical positions of a moving body simultaneously.
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For projectile motion under gravity, x(t) = (V cos θ)t and y(t) = (V sin θ)t − ½gt² parameterise the flight path, with the parameter domain restricted to 0 ≤ t ≤ T, where T is the time of impact. In robotics and planetary orbits, parametric equations model closed loops and spirals that cannot be represented as single-valued Cartesian functions y = f(x). Model analysis determines critical physical events: setting y(t) = 0 finds times of ground contact, while setting dy/dt = 0 finds the time of maximum height, with maximum height evaluated at y(t_max).
Your focus
- Formulate parametric models where the parameter represents time or angular displacement.
- Solve practical kinematic problems involving trajectories, clearances, and collision times.
- Interpret parametric derivatives as physical velocity components dx/dt and dy/dt.
Coordinate geometry in the (x, y) plane (A2 Unit 3: Pure Mathematics B) exam tips
Marking Points
- setting up parametric equations representing motion or geometric trajectories
- calculating specific event times (such as ground impact or peak elevation)
- substituting critical parameter values into coordinate equations to determine physical positions
Examiner Tips
- 💡Remember: vertical velocity is dy/dt; maximum height occurs when dy/dt = 0.
- 💡Calculate the parameter value t first, then substitute back into x and y for position coordinates.
Common Mistakes
- confusing the parameter t (time) with the horizontal coordinate x
- setting dy/dx = 0 instead of dy/dt = 0 when finding the time of maximum vertical height