The “impossible” New Zealand geometry test

Saw this tweet yesterday:

Here’s a direct link to the Guardian article:

The Guardian’s article “Impossible New Zealand Maths Exam Even Flummoxes Teachers”

Glancing through the problems, it looked like a challenging but fair test other than the mysterious appearance of a trig problem. Maybe trig is introduced as part of the geometry curriculum in New Zealand, though.

This morning I had my older son (in 8th grade) go through the test. The trig problem and one of the angle problems gave him a bit of trouble. The rest he was able to solve and explain.

Here is his work (in the order that the problems appear on the test – my numbering doesn’t correspond to the numbering on the exam). Also, sorry about the camera not being in perfect focus. I set the focus before zooming in – whoops!

(1) Parallel lines and angles

(2) A problem about right triangles

(3) A problem about arcs in circles

(4) The mysterious trig problem + a problem about similar triangles and scaling

(5) A problem about similar triangles

(6) A problem about parallel lines

(7) A curious problem that seems to be an exact repeat of problem (3)

(8) A problem about arcs and angles in a circle

(9) A problem about arcs and angles that gave him some trouble

(10) An angle problem that he inadvertently solved struggling with the last problem

(11) A problem about angles in a kite