Modelling with Parametric Equations (AQA A-Level Mathematics): Quizzes

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Modelling with Parametric Equations
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In parametric equations, what does the parameter tt typically represent?

Time, angle, or another variable

What is the horizontal motion equation for a projectile with initial velocity v0v_0 at angle θ\theta?

x(t)=v0cos⁡(θ)⋅tx(t) = v_0 \cos(\theta) \cdot t

What shape does the path of a projectile trace out?

Parabola

For projectile motion, what does v0sin⁡(θ)v_0 \sin(\theta) represent in the vertical equation?

Vertical component of initial velocity

What is the max height for a projectile with v0=20v_0 = 20 m/s at 30°30°? (Use g=9.8g = 9.8 m/s²)

5.10 metres

In circular motion parametric equations, what does ω\omega represent?

Angular velocity

For circular motion with r=5r=5 and ω=2\omega=2, what is the position at t=π2t = \frac{\pi}{2}?

(-5, 0)

In ellipse parametric equations, what is the semi-major axis denoted by?

aa

What is the horizontal component equation for an ellipse with semi-major axis aa?

x(t)=acos⁡(t)x(t) = a \cos(t)

Why are parametric equations useful for modelling complex curves?

Difficult to describe with single Cartesian equation

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