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Prepare for the hard stuff!

June29

teachingcalcMy teacher was very clear at the introduction to Calculus, “This is going to be a very difficult topic and you will need to concentrate your hardest in order to get through!” Little did I know that his words were correct. They were words that helped me mentally prepare for a course that, although different and difficult, I really enjoyed. I enjoyed it simply because I was mentally prepared for it. I like that – honesty from a teacher who knows that mental preparation helps his or her students prepare themselves for the mental battles ahead! How about you? Have you ever been mentally prepared like this for a difficult test or a new topic? If you are a Mathematics teacher, prepare your students honestly and let them know the kind of mental preparation that is required for a course. If you are a student and you are not sure what amount of preparation is needed to succeed in a course, ASK! (PS: my teacher and his family became lifelong friends of ours and we highly value their friendship to this day).

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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