In one of the papers for key stage 3 pupils, teenagers needed to score only 21 per cent to get level 5, which is the Government target for their age group.
Papers are set covering a number of levels to encompass a range of performances. This paper was set for pupils judged by their teachers to be working between levels 5 and 7. There was also a low pass mark of 36 per cent for the slightly easier paper covering levels 4 to 6.
On the easiest paper for the age group, covering levels 3 to 5, KS3 pupils needed 64 per cent for a level 5 - lower than an 11-year-old needed to get level 5 at KS2.
Some differences in pass rates should be expected, given that the papers range in difficulty. But maths teachers said they were concerned that the low pass marks mean schools might be tempted to enter weaker pupils in the harder tests in the hope that they might scrape a level 5 by scoring just above 20 per cent or 35 per cent.
Jennie Golding, chair of the teaching committee at the Mathematical Association and head of maths at Woodroffe School in Dorset, said: "The gut feeling in schools is that it is easier to get a level 5 on a 4-6 paper with a low threshold than by getting more questions right on a level 3-5 paper.
"Educationally, what you want is to have pupils taking papers where they can comfortably complete most of the questions. Passing a harder question with a very low proportion of questions right gives them precious little to build on at key stage 4."
The KS2 tests are also set at a difficulty level of 3-5, but to reach level 5 in maths, 78 per cent was required.
The different boundary levels between primary and secondary support back up findings from single-level test trials that some primary pupils are outperforming KS3 pupils on the same papers.
The level threshold grade boundaries are roughly in line with previous years, when some educationists complained about them being so low that pupils gained little from the experience.
The threshold for a level 5 in KS3 English this year was 31 per cent. In science, it was 57 per cent on the easier level 3-6 paper and 32 per cent on the level 5-7 exam.