← Differentiation methods: past papers

AS 91578 · 2023 paper · derivatives, tangents, a proof

Question 1(a) Achieved

Practises The rules & standard derivatives

A chain-rule root, a product rate of change, a second tangent parallel to a given one, a parametric circle tangent to be proved in general form, and an optimisation whose answer is a fraction of a given area.

Differentiate y = √(3x − 2). You do not need to simplify your answer.

The 2023 paper, page 2 ↗ Marking schedule, page 1 ↗

Work it out

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

  1. 1 Write the root as a power.

    y = (3x − 2)1/2

  2. 2 Chain rule: bring the power down, take one off it, and multiply by the derivative of the inside.

    dy/dx = (1/2)(3x − 2)−1/2 × 3 = (3/2)(3x − 2)−1/2
Answer dy/dx = (3/2)(3x − 2)−1/2, which is also 3/(2√(3x − 2)).

What the marker wanted

  • Achieved The correct derivative.

In our words, from NZQA’s 2023 marking schedule.

How did it go?

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