Self teaching Gcse and A-Level maths

In summary, a 16-year-old homeschooled student is pursuing a mathematics degree and has recently developed a passion for the subject. They plan to take A-levels in maths and further maths and are seeking guidance on resources and books to help them achieve an A* or A grade. They have found a collection of articles and resources on Physics Forums and are looking for more personalized advice and tips on studying mathematics.
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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.
 
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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
 
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Related to Self teaching Gcse and A-Level maths

1. What are the benefits of self-teaching Gcse and A-Level maths?

Self-teaching Gcse and A-Level maths allows you to work at your own pace and focus on areas that you find challenging. It also helps develop self-discipline and critical thinking skills.

2. Is it possible to self-teach Gcse and A-Level maths without any prior knowledge?

While some prior knowledge in maths can be helpful, it is not necessary. With dedication and perseverance, anyone can self-teach Gcse and A-Level maths.

3. How can I ensure that I am covering all the necessary material when self-teaching Gcse and A-Level maths?

It is important to have a structured plan and follow a curriculum or syllabus. You can also use textbooks, online resources, and practice questions to cover all the necessary material.

4. Can self-teaching Gcse and A-Level maths be as effective as traditional classroom learning?

Yes, self-teaching can be just as effective as traditional classroom learning. It depends on the individual's dedication, discipline, and learning style.

5. Are there any tips for staying motivated while self-teaching Gcse and A-Level maths?

Set achievable goals, take regular breaks, and find a study method and schedule that works for you. It can also be helpful to join online communities or study groups for support and motivation.

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