Psychology is a science course and you need to do statistics. There's a lot of biology in it as well e.g. in physiological psych you need to learn brain structures and there's lots of chemical names for drugs and neurotransmitters in the body. So the chemistry in it is biologically based - none of that extra chemistry stuff that you do in an actual chemistry course.
There are other areas in psych that don't require as much biology e.g. social psych and developmental psych (child and adult development).
If you can't get into BPsych, I think it's better to do psych through BSc instead of BA because psych is a science course afterall. Plus you can avoid the stigma of BA degree being useless and that BA students do jackall.
If you want to do psych and sociology, you can do a double degree - BSc/BA - major in psych in BSc and major in sociology in BA. I heard that sociology can be very fluffy and Englishy and lectures tend to put people to sleep. But there are people who like sociology so don't be discouraged.
I don't know about other unis, but at UNSW in first year BPsych it works like this:
Session 1: Psychology 1A + 3 electives
Session 2: Psychology 1B, Introduction to Psychological Applications + 2 electives
You have to continue one first year course in 2nd year, so you have to continue at least one elective from session 1 to session 2 in first year because most subjects require a 1A and 1B to go onto 2nd year level.
At UNSW, you need a 65 average to get into 4th year honours if you're in BPsych or BSc (Adv) while Bsc students need to get a 75 average. The average is across psych subjects only in 2nd and 3rd year.
You definitely need 4th year honours to get anywhere with your degree. If you get a high enough honours, you can continue onto masters (that's an additional 2 years) - which pretty much guarantees a job because you would have had hands-on training in the field. You can still get a good job with a 4-year degree though.