Quick questions on Parametric equations: curves, conversion and gradients - WJEC A-Level Maths

In parametric form, both coordinates are functions of a parameter, usually $t$ (or an angle): $x = f(t)$ and $y = g(t)$. As $t$ runs through its values, the point $(x, y)$ traces the curve. This is the natural description for motion (where $t$ is time) and for curves like circles and ellipses.

A curve has $x = 2t$, $y = t^2$. Find the Cartesian equation. [2 marks]

For $x = t + 1$, $y = t^2$, find $\dfrac{dy}{dx}$ in terms of $t$. [2 marks]

A curve has $x = \sin t$, $y = \cos t$. State its Cartesian equation. [2 marks]