# GCSE Maths - Get help and advice from an ex-tutor who specialised in GCSE Maths.

I taught the GCSE Maths syllabus for 3 years as an academic tutor and am offering my advice and guidance to those who feel they need it. I worked with a variety of students from low ability Year 7 with SEND needs to higher GCSE students - no topic about maths is off limits!

Please feel free to drop any questions here that you have and I will help you as best I can.

Some useful resources I will always recommend looking at are:
https://www.mathsgenie.co.uk/
and
https://corbettmaths.com/
(edited 1 month ago)
Hi, I hope you are well!

Question: "Prove that X^3 +4X = 1 has a solution between 0 and 1"

Can you please tell me which topic this question is from as I have tried to find but cannot find it. I have learn't this topic before but I want to watch video on this topic again. Please let me know which maths topic is this

I hope you will response me soon as possible. I would really appreciate it.
Thanks
Original post by Harman Kaur
Hi, I hope you are well!
Question: "Prove that X^3 +4X = 1 has a solution between 0 and 1"
Can you please tell me which topic this question is from as I have tried to find but cannot find it. I have learn't this topic before but I want to watch video on this topic again. Please let me know which maths topic is this
I hope you will response me soon as possible. I would really appreciate it.
Thanks

Hi Harman,

Thank you for your question. Please see my explanation for this question below!

This topic is 'Iteration' and can be found on mathsgenie.

Essentially, you just substitute in the value when x=0 and when x=1. First though, we must make the equation equal 0, as this is the first step when ascertaining solutions to quadratics and cubics.

so x^3+4x=1 becomes x^3+4x-1=0.

Then we can plug in x=0 -> (0)^3+4(0)-1 this is -1
Then we can plug in x=1 -> (1)^3+4(1)-1 this is 4

Because there is one positive and one negative answer and the value of 0 and 1 are between those answers, imagining this on a graph, this means there is a solution between 0 and 1 and that's your answer. With it being proofs you will need to write a sentence to get the mark. Something like: "One positive and one negative, therefore solution is between 0 and 1."

You can try exactly the same method with: Prove that x^3-3x^2=4 has a solution between 3 and 4 if you wanted a bit of practise too!
(edited 1 month ago)
Original post by Yipiyap_EthanP
Hi Harman,
Thank you for your question. Please see my explanation for this question below!
This topic is 'Iteration' and can be found on mathsgenie.
Essentially, you just substitute in the value when x=0 and when x=1. First though, we must make the equation equal 0, as this is the first step when ascertaining solutions to quadratics and cubics.
so x^3+4x=1 becomes x^3+4x-1=0.
Then we can plug in x=0 -> (0)^3+4(0)-1 this is -1
Then we can plug in x=1 -> (1)^3+4(1)-1 this is 4
Because there is one positive and one negative answer and the value of 0 and 1 are between those answers, imagining this on a graph, this means there is a solution between 0 and 1 and that's your answer. With it being proofs you will need to write a sentence to get the mark. Something like: "One positive and one negative, therefore solution is between 0 and 1."
You can try exactly the same method with: Prove that x^3-3x^2=4 has a solution between 3 and 4 if you wanted a bit of practise too!

thank you so much, I really appreciate you help.
Original post by Harman Kaur
thank you so much, I really appreciate you help.

Any time!
Original post by Yipiyap_EthanP
I taught the GCSE Maths syllabus for 3 years as an academic tutor and am offering my advice and guidance to those who feel they need it. I worked with a variety of students from low ability Year 7 with SEND needs to higher GCSE students - no topic about maths is off limits!
Please feel free to drop any questions here that you have and I will help you as best I can.
Some useful resources I will always recommend looking at are:
https://www.mathsgenie.co.uk/
and
https://corbettmaths.com/

is it possible for me to go from a 6 to a 8/9??
Original post by codyvarga
is it possible for me to go from a 6 to a 8/9??

Hi there,

Assuming you're doing the Higher GCSE, it absolutely is if you put the right amount of work in.

The great thing about GCSE maths is that a lot of the questions are quite process driven. I would encourage you to look at some problem solving questions in order to understand some of those questions better, as the same themes in questions often appear.

On Mathsgenie if you can nail all of the grade 7 work, then you'll be able to access some grade 8. I would brush up on a couple of those topics to build your confidence.