NCEA maths exams have been hit with mistakes at every level, the Herald can reveal.

The raft of blunders is already putting some students off taking the subject next year, while others are left worried about their performance and whether errors will pop up in other exams.

It comes after the New Zealand Qualifications Authority (NZQA) admitted on Friday that two maths exams - Level 2 calculus and Level 3 statistics - contained mistakes, and apologised to students for an impossible question in the latter.

Exam botch-up: I lost all confidence
Second NCEA maths exam mistake in one day


Now the Herald can reveal two more exams also contained errors - meaning every level from Level 1 through to Scholarship was affected by a blunder.

The Level 1 maths exam, sat on November 17, contained a "discrepancy" in a graph, while information contained in a table in the Scholarship statistics paper, taken on the same day, did not appear on a graph used to illustrate the data.

More than 1100 students were due to sit the scholarship exam, while slightly more than 40,000 were scheduled to sit the Level 1 maths exam.

It also comes hot on the heels of a major controversy over a Level 1 algebra exam earlier this year, which many said was too difficult and left some students in tears.

Teachers and principals are calling for the qualifications authority to review its processes and investigate how so many mistakes could appear within one subject area in the same exam season.

Maths NZ and secondary school maths teacher Jake Wills said NZQA has strong quality control measures that are supposed to be in place.

"What concerns me is that if that's the process they're using then there are obviously people somewhere who aren't doing their job because you shouldn't be able to get this many mistakes coming through if that's the processes that are being used," he said.

Faith in the local examination system could be put at risk.

"I think it really has undermined the confidence that teachers and students and parents have, and the general public have, in NCEA, which isn't good," he said.

"In general NCEA is an exceptionally good system, like every system it's got its flaws, but in general it's a good qualification.

"This year's been particularly bad and I guess as a maths educator I'd like to see that it doesn't happen again, because it negatively impacted my students and their views on mathematics in general."

His students were "not happy", Wills said. Many had been affected by the Level 3 statistics paper which contained a question that was impossible to answer.

"They spent quite a bit of time trying to work out where they'd gone wrong when they hadn't actually done anything wrong."

Secondary Principals Association of New Zealand (SPANZ) president Sandy Pasley said NZQA needed to review its quality assurance procedures.

"I've certainly spoke to the deputy CEO of NZQA [Kristine Kilkelly] and have expressed the concern that schools have felt over students not being able to actually work out the answers for the maths in particular and the stress that puts students under," she said.

The exams body was "extremely regretful", she said, and she trusted it would take the mistakes seriously.

"I think that it seems to have been unfortunate this year with mathematics in particular."

Pasley added: "Maths is a subject that if something happens, if a different number is popped in, it can suddenly make it not solvable. Whereas perhaps if it's some wording it's not quite as drastic."

She advised students who were not happy with their results to speak to their teachers about getting the paper re-examined.

"There's always reconsideration and recount, and I think they should take advantage of that opportunity if they're not happy with their final mark."

Labour's education spokesman Chris Hipkins said the mistakes raised "some pretty serious questions about NZQA's quality assurance processes".

"As a result I think they need to get on top of it very quickly because confidence in our qualifications system will be compromised if they're not seen to be fixing that problem," he said.

"And if it's seen to be a systemic problem then it undermines the credibility of all the qualifications that our kids have got."

An explanation of the mistake in the Level 2 Calculus paper. Photo / supplied
An explanation of the mistake in the Level 2 Calculus paper. Photo / supplied

He would write to the chair of the education and science select committee to consider a review of NZQA's performance, he said.

"Kids need to know that when they go and sit an exam that exam is going to be accurate, it's going to be fair and it's going to give them an opportunity to demonstrate what they're capable of," Hipkins said.

"That's what the exam process is all about and at the moment we've seen multiple examples of where that hasn't been happened."

He added: "We have enough difficulty getting kids to take maths already and I don't want to see anything discouraging kids from taking maths."

In a statement to the Herald, Kilkelly said the mistake in the scholarship statistics exam and the Level 1 maths exam would not have affected students' ability to answer the questions.

"The only error of significance currently under review that impacts on candidate's ability to complete the question is the Level 3 Statistics exam and we are taking it very seriously," Kilkelly said.

"NZQA will undertake a comprehensive review of the quality assurance processes in these instances to determine how the process failed to identify and correct these errors. NZQA is also commissioning an independent review of the Level 3 Statistics examination."

NZQA could not provide information on how many complaints it had received in relation to mistakes in exams this exam season, she said. However, the exam body had received a total of 35 "items of correspondence" about exams, including phone calls to the call centre.

On Friday, NZQA said it had received five complaints in relation to the L2 calculus paper and 10 in relation to the L3 statistics exam.

The maths papers were developed by a writing team made up of experienced examiners, Kilkelly said.

"Subsequent drafts of the papers are checked by external subject matter experts.

"Subject matter experts examine all aspects of examination materials from a technical point of view to ensure it is technically correct.

"All examination material is revised along the way, as needed, in light of the feedback from these checks and reviews."


• Level 1 Maths, 9.30am November 17: Question 2A contained a discrepancy in a graph, the data in a table did not match the graph.
• Level 2 Maths (calculus paper), 9.30am November 24: A figure given in question 2B was wrong.
• Level 3 Statistics, 2pm November 24: Probabilities in a table provided at question 3B added up to more than 1, rendering the question, and a subsequent question, impossible to answer.
• Scholarship Statistics, 9.30am November 17: Question 1, Figure 2 information contained in a table did not appear in related scatter plot graphs.

'It ruined my self-confidence' - maths student

Worried and scared - two words Jayda McIndoe, 18, repeats a number of times when talking about her Level 3 statistics exam.

The Year 13 Kapiti College pupil was among the 15,000 students who sat the botched exam on Thursday. She was also among the thousands left questioning their abilities, and now their marks, in the subject.

"It ruined my self confidence and I'm scared that it kind of ruined my performance for the rest of the exam," she said of the unanswerable question.

"There was another table later on that we also had to fill in and I just didn't even bother because I was like, 'oh obviously I don't know how to do this'."

It was "very worrying", she said, and while she was relieved that it would be taken into consideration by those marking the exam, she was concerned they would not factor in how it may have affected other answers.

"I'm scared that the rest of my results also aren't going to be reflective of my actual abilities because I'm scared that I maybe didn't do as well as I maybe could have if that hadn't have happened," she said.

"There's no way they can take that into consideration really.

"It's very worrying because when you're going for endorsements in the subject there's a lot riding on the exam."
The mistakes were affecting how other students were looking at maths, she said.

"It's just not looking good for the whole subject and I feel like a lot of other students are also feeling [worried] for their future performance in maths," McIndoe said.

"Maths is really necessary so I think most people are just thinking 'well ok I've got to just try to push through it no matter what NZQA throws at me'."

But the mistakes were adding to the stress many students already felt at this time of year, she said.

"It's definitely worrying because when you go into that exam environment you're kind of worried, 'what if they get something wrong again?', 'what if they make something too hard and then what if I fail it just because they've messed it up again?' kind of thing.

"It just increases I think the overall exam anxiety and a lot of students have enough of that already without the worry of the exam being wrong or being too hard."