Here is an intelligence test which takes about 15 minutes, and is free. The link to the original project and 16 item test is given here.
This talk is about the testing of the 5 item instrument with Danish schoolchildren, and it contains many interesting findings, out of which I will select one: one of the best items in terms of discriminating students was a question which contained explanations as to how the question should be approached, help which usually makes items easier. Paradoxical, and interesting. Sometimes, explanations make the task a purer measure of ability.
You will need to contact the author for more details about his work in using the test in Denmark and reducing it from 16 to 5 items, so as to achieve time effective testing. His abstract is shown below.
ICAR5: a 5-item public domain cognitive test
Speaker: Julius Daugbjerg Bjerrekær
A 5-item abbreviation of the ICAR (International Cognitive Ability Resource) 16-item sample test was created thru exhaustive search. The 5-item version (ICAR5) was optimized for correlation with the 16-item version and for administration time. To validate the test, it was given to students in 6th to 10th grade in two Danish schools (N=236). Age was used as a criterion variable and showed the expected positive relationship (r=.43). Results furthermore showed that the abbreviated test was too difficult for the younger students (6th and 7th grades), but not for the older students. One item was found not to be very discriminative, so it should be replaced with a more suitable item.
Here is the full lecture: