Older primary school children, as well as secondary pupils in years 10 and 11, are most likely to view unsuitable internet material, a report suggests.
Computer-related studies are often popular with boys
University of Central Lancashire academics found internet plagiarism peaked in the same year groups.
The report suggests boys more likely to use the internet to cheat than girls.
Many teachers do not feel equipped to deal with misuse of technology, including bullying, and schools need clearer policies on ICT use, it says.
The research on e-safety in schools, commissioned by the Department for Education and Skills, suggests that schools which encourage pupils to use their own mobile phones or laptops report more instances of bullying and accessing unsuitable websites.
Many teachers feel they need more support and guidance to prevent children viewing websites which contain racist, terrorist, violent or sexual content, the report says.
The researchers - Charlotte Barrow and Dr Gary Heywood-Everett - recommend schools draw up a policy on the safe use of information and communication technology, and appoint a dedicated technology safety co-ordinator.
Half of schools surveyed said they did not have a member of staff directly responsible for this area.
Instances of abuse of technology reduced where schools put into place e-safety policies, and considered the contexts in which such equipment was used, the researchers said.
"Educational establishments may be inadvertently increasing their exposure to breaches of e-safety and be compounding the risks pupils face as a result of the lack of clarity surrounding personal equipment use," their report says.
And Becta - the British Educational Communications and Technology Agency - part of the DfES - needs to make itself more visible as an advisory body for schools.
There are "clear gaps" in the strategic management of e-safety in English schools, the report concludes.
The research was based on a survey of 444 schools, 25 local authorities, 5 regional broadband consortia and in-depth interviews with 61 teachers.