YES that red book was great but know that the info it gives on the writing section is inaccurate as of the September 2015 session. It screwed up my writing score because I was prepping out of this out of date book, and ACT told no one that they were going to do this! Like how the SAT change is hugely publicized? Not ACT. Annoying. The prompts/what they want you to do is really different and actually pretty hard, so I suggest looking up sample prompts and doing a couple practice essays.
So I had the same issue as you: really strong in english/reading/writing, but sucky in math (science was pretty okay). For me it was a confidence issue, so really enforcing the content was important. I used the Barron’s ACT 36: Aiming for the Perfect Score for content review (like math strategies, problems, etc). Barron’s notoriously throws every possible scenario at you, which was good in my case. They have good strategies for all the sections, but I found that the time was too limited to use most of them. But still use them in practice tests because that will enforce it in your mind.
Make flashcards and study them religiously. If you are strong in English, I would not worry about the specific grammar issues that may be like one question on the test (Barron’s really pushed them, unnecessarily). But just hone in on math, make sure you can meet the time goal, etc. I kept running out of time on science, but practice makes perfect. The red book is good because so many practice test! Those were the most important aspect for me studying - THE most.
If you need additional help in math, definitely google around and find the best specific books. There are lists out there, I know. I took the test after I had finished Honors Pre Calc junior year (senior right now) and did not have to study any new math concepts; just had to brush up on old geometry concepts and enforce some pre calc stuff.
Finally, don’t stress on test day. Because I had prepped myself so much with the practice tests, I knew what to expect and got in the mode. That’s also why writing threw me for a loop - I wasn’t prepared! I flew threw everything and finished with an extra minute or so in sections I normally struggled to finish while practicing. I felt confident. Trust yourself. Don’t second guess. Also don’t forget your calculator like I almost did.
I magically got a 34 composite score, which blew me away. I had been averaging low 30s in practice tests, so, you never know! But, I got a 24 on the writing (out of 36), which was disappointing. Be prepared!!! There is A LOT of hype surrounding these tests, but I just bought a book and sat down. But I am normally a really good test taker, so there’s that. Prep classes can get very expensive, but if you think they can bump your score those few points, talk to your parents and explain how important the test is.
Good luck!!!