Both my children sat for the S-AEIS in February this year and they passed and got into public schools (primary and secondary) in April 2018. I just want to share our experience. They had to learn the sg maths syllabus for the year prior. So if you are applying for P3 level, you must study for P2 syllabus and a bit of P3 for S-AEIS. We used Singapore maths workbook to see the workings to prepare for Paper 2.
You can find the syllabus, practice questions and past year papers here,
https://sg.ixl.com/standards/maths/primary-2
https://sg.ixl.com/math/primary-2
http://www.sgtestpaper.com/
https://www.testpapersfree.com/
https://testpapers.com.sg/
Just google for other grade/secondary levels.
Also there will be IQ test for the Paper 1 multiple-choice questions.
Below you will find some examples of those pictorial IQ test and some simpler number IQ questions,
https://www.iqtestexperts.com/visual-sample.php
https://www.iqtestexperts.com/pattern-r ... sample.php
https://www.quickiqtest.net/trecqen.php
If your child has never used an optical answer sheet, I suggest you get a sample and let your child practise shading the answer for Paper 1.
Above all, give a lot of encouragement. I have heard of some who failed the first time but passed subsequently. Some take tuition. My children studied on their own as they could handle it.
And in the end if it does not work out, you have other options. There are more and more reasonably priced but smaller
International Schools in Singapore now. All the best!