For primary level Free Exam Papers (Chinese / Higher Chinese), check out the following website:
They do have Free Exam Papers for other subjects (English / Maths / Science) as well, from Primary 1 to Primary 6.
Higher Chinese Free Exam Paper
Another site for Free Higher Chinese Exam Paper: http://www.testpaper.biz/Primary-6-Higher-Chinese-Test-Papers-Singapore-PSLE-Chinese-Exam-Papers.html
All the exam papers are in PDF format.