Self teaching Gcse and A-Level maths

[member 624364]

Hi, I have recently embarked on the journey to do a mathematics degree. I am 16 and homeschooled, although, I self teach myself as I find it easier to read from textbooks and teach myself the material from resources online and the likes.
I have taken a math Gcse a few months ago and was going for the lowest pass mark which is a c just to at-least get the pass. At the time I did not much like mathematics and was only going for a pass. Now however, I have found a new passion for mathematics and want to pursue it to a degree level. Therefore, I am wanting to go for an A and a further maths A at gcse. Once completed(I hope), I wish to do an A-level in maths and further maths.

I read that on the qualifications for entry to the university I am looking at, Queens, I need to either get A*AB at a-level, or AAA. I Am not sure what my third subject would be to study, and depending on the subject I will have to decide whether to go fro the A*AB so that I can get a B for the third subject or get all A's for the three of them.

So to take on this journey I need guidance, I was hoping for advice on books and resources to learn all the way up to completing A-levels in maths and further maths, at either A* or A. Any advice would be helpful :)

Also, has anybody done this before? I feel like I need motivation to know that it is possible to do. Being out of school makes it feel like an almost impossible task to do. If so I would be very happy to hear your story.

 

[fresh_42]

Here's a collection of insight articles available on PF about this subject [self-study]

https://www.physicsforums.com/insights/how-to-study-mathematics/
https://www.physicsforums.com/insights/overcame-learning-challenges-faced-studying-stem/
https://www.physicsforums.com/insights/resources-high-school-math-home/
https://www.physicsforums.com/insights/problems-self-studying/
https://www.physicsforums.com/insights/self-study-basic-high-school-mathematics/
https://www.physicsforums.com/insights/self-study-calculus/
https://www.physicsforums.com/insights/self-study-analysis-part-intro-analysis/
https://www.physicsforums.com/insights/self-study-analysis-part-ii-intermediate-analysis/
https://www.physicsforums.com/insights/self-study-algebra-part-ii-abstract-algebra/
https://www.physicsforums.com/insights/self-study-algebra-linear-algebra/
https://www.physicsforums.com/insights/self-study-geometry-part-pure-geometry/

They may not all apply to what you will need at the moment, i.e. I don't know where exactly the lines between high school and college in the US are, but they can give you some impressions and hopefully hints on how to proceed. They're certainly worth to read them. In addition you can always make use of our homework section where you will get help to solve problems. Just make sure to use the (automatically inserted) template there, and show us where you got stuck (part 3 of the template), which is important to us for many reasons.

Here's a similar series for physics (22 parts)
https://www.physicsforums.com/insights/early-physics-education-in-high-schools/#toggle-id-1

If you're looking for books, you can find the content you'll probably need e.g. here:
https://openstax.org/subjects
Good sources are lecture notes. They can easily be found by googling e.g. "Calculus II + pdf"

I think they also can be ordered in a printed version, but I'm not sure. The internet is full of possible sources, but OpenStax has at least a recommendable reputation. As far as I remember, there are also a lot of exercises in the books, which you should try to solve. At least a significant amount of them. If nothing else, it can help you to narrow down your demands and help find appropriate sources, e.g. by asking us in a more specific way than above, but this assessment could easily be due to my lack of knowledge about the American system.

Finally some hints on how to deal with certain situations:
https://www.physicsforums.com/insights/things-can-go-wrong-complex-numbers/
https://www.physicsforums.com/insights/10-math-tips-save-time-avoid-mistakes/
https://www.physicsforums.com/insights/make-units-work/

and an interesting interview with Karen E. Smith
http://www.ams.org/publications/journals/notices/201707/rnoti-p718.pdf