Level 1 maths students would have had to know the formula for quadratic equations to answer one of the questions in yesterday's exam - a formula that maths teachers say is not taught until Level 2.

The exam left some students in tears and has sparked an open letter by maths teachers to the NZ Qualifications Authority complaining that the exam was too hard for Level 1 of the National Certificate of Educational Achievement (NCEA).

The Herald has been inundated with complaints. However, NZQA is standing by the test.

Deputy chief executive Kristine Kilkelly said the authority was still "confident in the quality of the Level 1 Mathematics examination".

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However, Education Minister Chris Hipkins has ordered a full report on the exam, saying no-one wants to see students and their families upset, believing that the exams were "unfair".

One question provided a diagram of a rope swing in the shape of a parabolic curve and asked students to calculate the distance between the holes in the seat of the swing, given other key measurements.

Kāpiti College head of maths Jake Wills said Level 1 students should know how to answer the question when the values involved could be "factorised", or broken into numbers that produced the values when multiplied together. But in this case there was no simple factorisation so students would have had to know the formula.

"That should be at Level 2," he said.

Jake Wills, head of maths at Kāpiti College​, who is organising an open letter to the NZ Qualifications Authority complaining that the 2017 NCEA Level 1 maths exam was too hard. Photo / Supplied
Jake Wills, head of maths at Kāpiti College​, who is organising an open letter to the NZ Qualifications Authority complaining that the 2017 NCEA Level 1 maths exam was too hard. Photo / Supplied

Another teacher commented that the question effectively asked students to ignore everything they knew about how swings work, noting that the seat would pull the rope into a U-shape rather than a parabola.

In another part of the exam, students were given a graph showing how many males and females from various age groups were charged with reckless driving and were asked: "How many more times more likely was it that, chosen at random, a vehicle driver who was charged with reckless driving would be a male rather than a female?"

The answer simply required dividing the total of all males by the total of all females, but Wills said it tested a concept of "relative risk" which was part of the curriculum for Level 2, not Level 1.

On the other hand, he said Level 1 students at "excellence" level should have been able to answer a geometry question asking students to calculate the size of an angle of a kite inside a square.

"It's a difficult question that a number of students would have had difficulty with," he said.

They would have had to choose either a numerical value or an algebraic term such as "a" for the side of the square, then express the answer as a multiple of that value.

"That is the sort of thinking we want students to demonstrate with excellence, joining those ideas in different sorts of ways," Wills said.

Wills provides free resources for maths teachers on his website MathsNZ.com.