Many had already complained that this year's mental maths paper was particularly difficult.
The key stage 2 test paper "Fire, Friend or Foe?" included an introduction, a double-page spread on forest fires, a poem, a four-page story and a newspaper article.
Ann Monk, head of Fen Drayton school near Cambridge, said: "The paper was a bit tough. There was a lot of reading on it. Even where you are just ringing answers, you have to keep checking back with the test to see whether the answer is right. Two of our children did not get anywhere near finishing it."
Maureen Martin, head of Cowbit St Mary's C of E primary near Spalding in Lincolnshire, said: "I do not understand why there is a time limit. If we did without it we would get a better picture of a child's abilities."
Steve Arnold, head at Radcliffe-on-Trent juniors, Nottinghamshire, said:
"The booklet was well-presented and attractive, but it was too wordy. It is meant to assess levels 3 to 5, but if you are a child at level 3, there is a lot of text to read in order to find the answer."
A TES website contributor said it was "horrid and boring, I couldn't even read the whole thing myself".
The Qualifications and Curriculum Authority said the test was carefully trialled and pre-tested to make sure it was appropriate and stimulating for the age group.