GCSE Maths question

Swim Jim

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My son is retaking his maths exam in November. He didn’t fail it he just knows he could of achieved a much higher grade if he’d of put more revision in. I’m very handy at maths and I’m helping him we’re doing all the past papers. This one though has got me stumped o_O

Anyone fancy a go :unsure:

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spanky

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It took me a few moments... but the key is that a and b are vectors, not distances, so you can add and subtract them to find the missing net vector of a shape. i.e. once you have two sides of a triangle defined the third will fall out.

To prove a parallelogram you need to show two pair of parallel sides, which in vector terms means they are the same.

Step 1: EB is the opposite of BA and AE, so EB is -a-2b

Step 2: DC is the same as DE + EC, so DC is -a-2b (so we've proved EB and DC are parallel since they follow the same vector)

Step 3: we know DE is a - 3b, so we just need to find CB and check they are parallel

Step 4: CB is CE + EA + AB, -b + 2a -2b -a = a - 3b (Note the change in the signs because we're going backwards against the vector direction shown by the arrow).

Therefore EB is parallel to DC and CB is parallel to DE, so we have a parallelogram.

QED
 

Swim Jim

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Thanks Spanky
I suspected that vectors were involved after trolling through umpteen pages of online parallelogram related problems. I also use a site that has actual completed exam papers. What was throwing me was the negative signs. The specimen exam answer is underneath. I won’t lie I’m going to have to study this with the lad and go back over vectors. I’m sure once we get our heads around the positive a negative signs all will become apparent :eek:(y)
 

Dave Spence

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The Vector question that you posted is at the top end of the difficulty scale.

In simple terms, if two vectors are multiples of each other they are parallel. If two vectors are multiples of each other and share a common point they are a straight line; the term the awarding body look for is 'co-linear'.

If you don't already use it, search for 'Maths Genie' and follow the link to GCSE revision. Questions are graded level 5 to level 9, with solutions and also helpful video's if you get stuck.
 

spanky

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Thanks Spanky
I suspected that vectors were involved after trolling through umpteen pages of online parallelogram related problems. I also use a site that has actual completed exam papers. What was throwing me was the negative signs. The specimen exam answer is underneath. I won’t lie I’m going to have to study this with the lad and go back over vectors. I’m sure once we get our heads around the positive a negative signs all will become apparent :eek:(y)

If it helps, a vector is just a series of instructions on how to get from one point to another and they are directional. This direction is denoted by an arrow on the diagram.

So for sake of argument in the diagram, vector a contains the instructions to go from point B to point A. This could be something like go ten metres North then 1 metre East (the exact numbers don't matter, but might help you understand). Now vector a is not locked to any position it's just an instruction that can be applied to any point to move 10m North and 1m East.

Now if a is the instruction to get from B to A, then what if I want to get from A to B? Clearly I need to go in the opposite direction (ten metres South and 1 metre West), which is -a effectively if you go in the opposite direction to the vector direction on the diagram (against the arrow on the diagram) then you multiply the vector by -1

So when we move from one point to another (to solve the original problem) we need to look at whether we are following the arrows or not.

So if I go from B to E, I am following the vector from B to A and A to E, so I simply add the vector together ( a + 2b) since I am following the arrow.

But if I wish to go from E to B, I go from E to A ( -2b ) and the from A to B ( -a ), both against the arrow, giving -a - 2b.

Hope this helps!
 

muskrat

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..... So when we move from one point to another (to solve the original problem) we need to look at whether we are following the arrows or not.

So if I go from B to E, I am following the vector from B to A and A to E, so I simply add the vector together ( a + 2b) since I am following the arrow.
.....

I can't be faffed with all these vectors and stuff. I usually take the bus.
 

Swim Jim

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The Vector question that you posted is at the top end of the difficulty scale.

In simple terms, if two vectors are multiples of each other they are parallel. If two vectors are multiples of each other and share a common point they are a straight line; the term the awarding body look for is 'co-linear'.

If you don't already use it, search for 'Maths Genie' and follow the link to GCSE revision. Questions are graded level 5 to level 9, with solutions and also helpful video's if you get stuck.
Thanks Dave
Maths genie has been popping up on searches on YouTube. I didn’t realise it was so versatile I’ll certainly give it a look (y)
 

G0zzer2

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Never heard of vectors in maths - they hadn't been invented when I went to school....we had sines, cosines and tangents in my GCSE Maths paper.

Proving Pythagoras' Theorem is a doddle compared to that question.
 
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