Not every, but several questions on the SAT math sections can be solved without calculation or using mental math. Understanding of the basic concepts cannot be evaded.
The examples in each category of the book that can be easily solved without calculation or using mental math are shown below. You will require the book to follow through the concepts and examples.
Please note that this not a tutorial. It shows how a student should think after completing the book and quickly solve several questions on the SAT without pencil and paper or a calculator.