Hard GCSE Maths Questions

This worksheet is a series of hard GCSE maths questions, and is aimed at around grade 6 higher level. There isn’t a specific board, although these types of problems might appear on Edexcel, OCR, AQA or Educas.

Download a copy of the questions here: Hard GCSE Maths Questions – Part 2

Here’s a copy of the written answers: Hard GCSE Maths Questions – Part 2 ANSWERS

Here’s the videos for each of the hard maths GCSE questions …. although please do
– stop the video
– work through the question
– compare your solutions

I hope the videos help and please do leave a comment – thanks!

Here’s the questions:

#GCSE #practice #revision #maths #math

1. ABCDEF is a regular hexagon with sides of length x.
This hexagon is enlarged, centre F, by scale factor ‘p’ to give hexagon FGHIJK.
Show that the area of the shaded region in the diagram is given by the formula shown. (4 marks)

2. 6x^2 = 7xy + 20y^2 where x ˃ 0 and y ˃ 0
Find the ratio x : y (4 marks)

3. The diagram shows a sector OACB of a circle with centre O.
The point C is the midpoint of the arc AB.
The diagram also shows a hollow cone with vertex O.
The cone is formed by joining OA and OB.
The cone has volume 56.8cm^3 and height 3.6cm
Calculate the size of angle AOB of sector OACB.
Give your answer correct to 3 significant figures. (5 marks)

4. There are only green pens and blue pens in a box.
There are three more blue pens than green pens in the box.
There are more than 12 pens in the box.
Simon is going to take at random two pens from the box.
The probability that Simon will take two pens of the same colour is 27/55
Work out the number of green pens in the box. (5 mark)

5. The equation of the curve is y = x^2 + ax + b where a and b are integers. The points (0, -5) and (5, 0) lie on the curve. Find the coordinates of the turning point of the curve. (4 marks)

Top Tips!

Always work methodically and show your working
Why is that information in the first few lines?
Check your calculations
Is it a reasonable answer?

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