Given I take respite from tutoring in Maths as and when the schools do, I have decided to set some questions for my students. Any teachers may be interested in these, and I am curious as to whether these adapted old-exam questions are still suitable for GCSE students. Any comments welcome!!

1) OK, so first, a question that uses some circle and triangle geometry:

In this circle, angle a = 30 degrees, and r = 3cm

a) what is angle b?

b) calculate the area of minor sector OBC (marked in pen). Give answer in terms of pi.

c) calculate the length of arc l in terms of pi. give answer in lowest terms.

d) find the area of the major sector ABC. Use a calculator to give an answer to 4 s.f.

2) Next a question about percentages.

I have a 100Kg sack of potatoes that is 99% water. I leave it to stand until it is 98% water. What does the sack weigh now?

3) A vector question.

ABCD is a parallelogram,, and PQRS are the mid-points of the sides. SP = y and SD = x (Normally, these would be written with arrows atop them, but the order is what we shall use here to define a vector, so DS = -x )

Find the following in terms of x and y:

a) DC e) CR

b) CA f) QD

c) QB g) DB

d) DA

NB – for g), it’s *not* -2y, but you would likely get a mark for it out of two possible marks… does anyone know if this is the case in GCSE marking schemes?

4) finally, and exponent question that makes use of powers of two. Might be worth saying, this is not a question about approximations, so advice on wording is needed…

Sophia has a test-tube with around 2^8 bacteria in it.

a) She decides to split the culture between two test tubes. How many are in each tube?

b) the bacteria double every 20 minutes. After two hours, how many bacteria are in each tube?

c) state 2^8 as a fraction of the final amount in each test-tube from question b).

Please let me know what you think about these questions – they are adapted and expanded from various past papers and revision books, so they *should* be GCSE level. Please let me know if not! The circle question, final part, requires many steps, but all are available to a student in a calculator and non-calculator paper…

Penny for your thoughts! 😀

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I would give one mark for 4x-2y but not -2y. -2y displays a lack of knowledge of how vectors work. I’ve only really seen that type of vector question get 1 mark each, but that’s just based on a quick survey of the papers I have on my iPad.

For 1d, the only method I could thnk of used a fact that isn’t in my textbook at all (though it could just be an omission in mine, as I remember learning it in school…). In that question you have also marked the angle at A as b, while also having a separate point B, at which it is later useful to work out the angle (at least the way I did it). As people often name angles after the point they’re next to, you might want to change this.

You can just take out the approx in 4 if you think it would be confusing. Just say she counted them if kids ask. I tried to think of a way to adapt it into a question about computing time to be more exact, bt couldn’t think of an analogue for b.

I’m vey jealous of your tutees. Mine would just stare at me and look confused, then ask if you needed to add or not :S