GCSE Maths help

http://www.mathsgenie.co.uk/papers/2hjune2015ans.pdf
I don't understand Q21, Q27B, and Q27
pls help! thanks!

For question 21, it tells you that the flower beds are the same depth, in other words, there is no need to worry about the depth. It says the dimensions of the larger bed would be three times the dimensions of the smaller bed, therefore the scale factor is three(every dimension in the larger bed would be the same one of the smaller bed x3). He needs 180 kg of soil for the smaller bed( this would be the area). Now the scale factor for the dimensions i.e lengths is 3, so for area it would be 3^2=9, because the scale factor for area is always equal to the scale factor of length squared. An easy way to remember this is by looking at the units area is measured in i.e cm^2. Anyways, if the area for the smaller bed is 180, then the area for the larger bed would be 180*3^2= 180*9=1620 kg.

Q27. This is a little harder to explain but, it tells you to work out the vector OC, basically asks you how to get from O to C, for that you need to first know OA ( which is given) and then AC. To work out AC you first work out AB, which is a+b as shown in the link you provided. The question tells you that the line ABC is divided in the ratio AB:BC=2:5, which means that AB = 2/7th of AC, now you can make this into an equation so a+b(AB)=2/7AC, now if you rearrange, you would get AC=7/2(a+b) which = 7/2a+7/2b now you just add this to 2a+b(OA) to get your answer.

Hope that helps.

Alternatively, you could watch this YouTube video that goes through this paper: https://www.youtube.com/watch?v=GaOuMDM4qkA

what have you tried so far?

EDIT: Loool - that's the paper I sat last year xD

Thank you so much!!