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UKMT Junior Maths Challenge Past Papers Difficulties

Hey guys, so as any UK school kid in 1st or 2nd year in high school (year 7 and 8?) who enjoys maths may know, the UKMT challenge is happening this week and so I was doing some passp paper and hit a few questions, so with a family who's pretty poor at maths, I turned to THE INTERNET!

So I am struggling with question 16, 21 and 25. The rest I have done. For question 16 - well I don't even know where too start as I don't fully understand the question so if any one could explain it to me or show working as how a they got it, would be incredibly helpful. 21 has also stumped me - I think it has something to do with simultaneous equations, but when I tried that method suggested here: http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/simultaneoushirev1.shtml

I got varying answer when tried in different equations, straight up making no sense.

And on question 25 I again believe it to have something to do with simultaneous equations and not only have we not yet been taught it in school (which I find personally not an excuse) but I was struggling to carry out the method suggested by the BBC when it resulted to 3 equations at once. However I did managed to gather the equations needed to solve question 25 (or at least I think I did) which I will attach a photo of.

All questions are located below!

If anyone could help by showing me some working or how they did them, or in the case of 16, simply explaining what it wants me to do!

Thanks again,

Xvantok

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It Won't Fail Cause of Me.

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I think 16 means forward as in up and then you can go from there. It's like that computer program which involved that turtle which you could give instructions (e.g. fwd 19 etc.) idk if you're familiar with that. I think the answer is A, follow the instructions starting on a point with shortest edge and start by using the 2 units instruction to go along that edge.

 

With 21, it's best to start with the 2nd row (as two "algebraic" terms, I know 0 they are pictures) and also the 2nd and third column and make simultaneous equations.

 

Sorry, I know it isn't much help I've gotta head off to bed!

Good luck! In the junior maths challenge I somehow got a GOLD!! No revision or anything, my maths was good then compared to the rest of my year... Now in senior maths challenge I have gotten a bronze and this year no award! My maths skills have deteriorated haha, I am dependent on my calculator (bad habit btw!)

 

Good luck again!

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have I done something wrong here? 

059cc33efb.jpg

I get two answers x=32 

x=36

CPU: Intel 3570 GPUs: Nvidia GTX 660Ti Case: Fractal design Define R4  Storage: 1TB WD Caviar Black & 240GB Hyper X 3k SSD Sound: Custom One Pros Keyboard: Ducky Shine 4 Mouse: Logitech G500

 

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