Our worksheets and test papers are mainly based on supplementary exercise books of higher levels (i.e. for p.1 class, we may use p.2 ones) which you can commonly find in bookstores.
Not necessary to get the test papers as long as you bought some supplementary exercises or revise those worksheets from school that will be sufficient. In addition, let your kid read more books both in Chinese and English.
I do not have any old test papers of KTS to practise but the result of my girl's mock test is quite okay.