The hard grade 9 maths questions thread 2023

OP

Example 3 is particularly difficult... https://www.youtube.com/watch?v=2eU0mKXF_CU&list=PLCG7Y8fJFRr8_7LapkRI5p5zBA3aH-f-k&index=6

Reply 2

Original post by Aloysius O'Hare

Example 3 is particularly difficult... https://www.youtube.com/watch?v=2eU0mKXF_CU&list=PLCG7Y8fJFRr8_7LapkRI5p5zBA3aH-f-k&index=6

Certainly a bit of a slog. Id probably have shown that its
pi r^2 (1 + sqrt(1 + a/k^2))
which cuts out about 1/2 the algebra from the surface area part (with a final line to justify its in the form they want).

Reply 3

OP

Original post by mqb2766

Certainly a bit of a slog. Id probably have shown that its
pi r^2 (1 + sqrt(1 + a/k^2))
which cuts out about 1/2 the algebra from the surface area part (with a final line to justify its in the form they want).

Interesting way of looking at it - certainly more efficient.

Reply 4

Original post by Aloysius O'Hare

Interesting way of looking at it - certainly more efficient.

tbh its (much) closer to the way you express the surface area at the start and with the defn of the k<->h relationship from the volume, you can almost write down that a=4^2=16. Sometimes working back a step or two from the expression they want to show can give a fair bit of insight.

Reply 5

OP

https://www.youtube.com/watch?v=OZ-C-VhhgQY - another algebra question. Not too hard, but quite sneaky!

Reply 6

Original post by Aloysius O'Hare

https://www.youtube.com/watch?v=OZ-C-VhhgQY - another algebra question. Not too hard, but quite sneaky!

The extraneous solution x=2 has been hidden. A reasonable thing to do at the start would be to factorise the exponent numerator so
x(x-2)
then cancel with the exponent denominator if possible. Obviously the "x" doesnt, but the factor (x-2) does cancel. That way, youve eliminated one source of extraneous solutions. If not, youve got to be careful with the working/verify the potential solutions at the end.

Reply 7

OP

https://www.youtube.com/watch?v=D4MAwBnjxZY - I think most people know how to do this simply from seeing it so much, but still, it's an interesting question to apply only GCSE knowledge to.

Reply 8

Original post by Aloysius O'Hare

https://www.youtube.com/watch?v=D4MAwBnjxZY - I think most people know how to do this simply from seeing it so much, but still, it's an interesting question to apply only GCSE knowledge to.

Once youd drawn the equilateral triangle(s) of side 4, then the rest should be reasonably straightforward, so areas of sector, triangle, segment. The equilateral triangle construction on a given straight line is straight out of Euclid, book 1, proposition 1
http://aleph0.clarku.edu/~djoyce/elements/bookI/propI1.html
so its simply going back to basics where you define a circle as being the locus of points which are equidistant from the center. Alternatively, just think about how a regular hexagon lies inside a circle and is made from 6 equilateral triangles. When you have a problem like this, its usually (very) useful to connect relevant points on the circumference with the center, so "always" draw in relevant radii.

Reply 9

Original post by mqb2766

Once youd drawn the equilateral triangle(s) of side 4, then the rest should be reasonably straightforward, so areas of sector, triangle, segment. The equilateral triangle construction on a given straight line is straight out of Euclid, book 1, proposition 1
http://aleph0.clarku.edu/~djoyce/elements/bookI/propI1.html
so its simply going back to basics where you define a circle as being the locus of points which are equidistant from the center. Alternatively, just think about how a regular hexagon lies inside a circle and is made from 6 equilateral triangles. When you have a problem like this, its usually (very) useful to connect relevant points on the circumference with the center, so "always" draw in relevant radii.

Why are u bringing up all of this fancy terminology on a gcse post, its not that deep bro.

Reply 10

OP

Original post by BigJ123

Why are u bringing up all of this fancy terminology on a gcse post, its not that deep bro.

I'd assume most people on a grade 9 maths questions thread would be looking to pursue maths at a further level, suggesting that this terminology would be useful for them in the future.

Reply 11

Notnek

Original post by BigJ123

Why are u bringing up all of this fancy terminology on a gcse post, its not that deep bro.

Triangle?

Reply 12

Original post by Aloysius O'Hare

I'd assume most people on a grade 9 maths questions thread would be looking to pursue maths at a further level, suggesting that this terminology would be useful for them in the future.

It really wouldnt lol. To me it just seems so cringe speaking like that about a gcse question, no offence to the guy.

Reply 13

Original post by BigJ123

Why are u bringing up all of this fancy terminology on a gcse post, its not that deep bro.

Id agree that the question wasnt that deep though it made the papers at the time. The description was for background (for those aiming at top grades/further maths) and the hint at the end about always drawing radii was arguably the "hard" part about the question. Nothing cringy about it.

(edited 7 months ago)

Reply 14

OP

https://docs.google.com/document/d/1uVgHK8WDO_6DVwfy2FUJKnmrb2imxnYnfX7SU-OIEIA/edit?usp=sharing - this paper has some particularly tough questions (my personal favourite being question 7) and covers the majority of grade 9 topics.

https://imgur.com/a/SddRmYX ( solutions).

https://www.thestudentroom.co.uk/showthread.php?t=5214688 (the original thread).

Reply 15

Original post by Aloysius O'Hare

https://docs.google.com/document/d/1uVgHK8WDO_6DVwfy2FUJKnmrb2imxnYnfX7SU-OIEIA/edit?usp=sharing - this paper has some particularly tough questions (my personal favourite being question 7) and covers the majority of grade 9 topics.

https://imgur.com/a/SddRmYX ( solutions).

https://www.thestudentroom.co.uk/showthread.php?t=5214688 (the original thread).

Q14 is a little dodgy. The question wants an equation for y=f(x) yet the guys made an equation for the roots of the function. Just needs to be set equal to y instead of 0.

This paper is way too hard for gcse lol, i feel like its a bit pointless almost apart from one or two questions.

Reply 16

OP

Original post by BigJ123

Q14 is a little dodgy. The question wants an equation for y=f(x) yet the guys made an equation for the roots of the function. Just needs to be set equal to y instead of 0.

This paper is way too hard for gcse lol, i feel like its a bit pointless almost apart from one or two questions.

For the majority of GCSE students, I agree, this paper is too hard. However, if you can answer a decent proportion of the questions on the paper, you should find any GCSE question trivial, and thus, achieve a strong grade 9.

Some of the questions are a bit strange, BUT THE PAPER WAS WRITTEN BY A YEAR 11! - a fantastic achievement.

Reply 17

Original post by Aloysius O'Hare

For the majority of GCSE students, I agree, this paper is too hard. However, if you can answer a decent proportion of the questions on the paper, you should find any GCSE question trivial, and thus, achieve a strong grade 9.

Some of the questions are a bit strange, BUT THE PAPER WAS WRITTEN BY A YEAR 11! - a fantastic achievement.

Sure but the paper doesn't help someone who wants a grade 9 in anyway in my opinion. Its just kind of pointless, i see a lot of these papers but they're just way too hard lol.

Reply 18

OP

Original post by BigJ123

Sure but the paper doesn't help someone who wants a grade 9 in anyway in my opinion. Its just kind of pointless, i see a lot of these papers but they're just way too hard lol.

Perhaps, but for me (a new year 11), being able to answer these questions would assure me that I can achieve a grade 9, alongside instilling within me a deeper interest in maths. They are really hard though! :smile:

Reply 19