The conundrum, set by Edexcel, involves a girl called Hannah, her bag of sweets and a perplexing equation:
There are n sweets in a bag. Six of the sweets are orange. The rest of the sweets are yellow. Hannah takes a random sweet from the bag. She eats the sweet. Hannah then takes at random another sweet from the bag. She eats the sweet. The probability that Hannah eats two orange sweets is 1/3. Show that n²-n-90=0.Algebra! I never got it at school so I had a go at it when I was 26. It annoyed me to think I could not do it so I got out my father's Halls Algebra part one and worked my way through it. At the time I was very impressive with long division using algebra!
The problem I have with algebra is why a minus x minus become a plus? Who worked that one out?.
I can explain it now but is difficult concept to grasp at any age and on graph paper where + 2 on the x and + 2 on the y give you + 4 and the mirror minus co ordinates give -4. So how come this doesn't show up as +4?
I know there is a very rational answer but when you are 12 and can think visually this is a problem. Telling someone like me that it is when I can see it isn't doesn't give a child much confidence in the system.
Let me see if I can explain why multiplying two minuses make a plus. It goes something like this.
If you have a bill you don't owe and then receive another bill you don't owe even if you multiply them together you still don't it owe any of it and the money that you would have paid if you had owed them is still yours.
The only way to do algebra is to stick to the rules and the rules are difficult to remember if you are not using it every day or are under pressure. I was good at it and if necessary could get out my Hall's Algebra part 1 & 2 and be up and running in a couple of days but honestly I have never used it again in my life. Same for trigonometry as I do not fire guns.
I don't think it is fair to ask exam students to have to do this unless trained to do it or given lots of time to think.
If I were taking exams today and I didn't think a question was fair I think instead of trying to do it and making mess I should write out what was wrong with it. I recall my grandfather did this in 1904 in the Civil Service exam. He pointed out why the sum couldn't be done, It couldn't be done! He ended up eventually running Wembley Stadium. He came from the slums of Royston.
Sorry for rant but algebra bring out the worst in me.