The course you did look's similar to my university's 154 or 134 mathematics course. (The easier ones )
I know people who have done those courses the previous year and are now doing 114 (the hardest course in maths at my univ), and they pass. Besides that, they've seen many of the things before in the easier course and they have experience with it, albeit a simple foundation. Fact is they have to keep up with the rest of us, and our 114 course demands that you think for yourself more, problems are not as straightforward always, and things happen very fast in the course.
Be careful for the statistics course. We have 2 courses here, one is statistics and one is mathematical statistics which includes probability. (And I find probability a tough nut to crack for a newbie to it like myself.)