Question 1(a) Achieved

A linear-plus-reciprocal integral, a velocity in km hr⁻¹ integrated to a distance from a point 3 km away, an area between a root and a parabola, a separable equation, and an area bounded by three different curves at once.

Find int (3x + 2 + 1/(3x + 2))dx.

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 Take the three terms one at a time. Which one needs care?

   3x and 2 are plain powers of x. The last, 1/(3x + 2), is a number over a linear bracket.

2. 2 What does 1/(3x + 2) integrate to?

   A log, divided by the 3 in front of x: (1/3) ln |3x + 2|.

3. 3 Put the three together, with the constant.

   int (3x + 2 + 1/(3x + 2))dx = 3x²/2 + 2x + (1/3) ln |3x + 2| + c

What the marker wanted

• Achieved The correct integral. This year’s schedule says the + c is not required for it.

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

How did it go?

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