Question 2(a) Achieved

A parametric derivative, a velocity from a log displacement, a second-derivative verification, an inflection point on (ln x)/x, and a turning point that survives an unknown constant.

A function is defined parametrically by x = 3t² + 1 and y = cos t. Find an expression for dy/dx.

The 2024 paper, page 5 ↗ Marking schedule, page 3 ↗

Work it out

Try it on paper first. Stuck? Take one hint at a time.

1. 1 Differentiate x and y with respect to t.

   dx/dt = 6t and dy/dt = −sin t

2. 2 Divide one by the other.

   dy/dx = (dy/dt)/(dx/dt) = (−sin t)/6t

What the marker wanted

• Achieved A correct dy/dx. Writing it in terms of x and y is accepted too.

In our words, from NZQA’s 2024 marking schedule.

How did it go?

Got it moves it further out. Review brings it back tomorrow.