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Some Common Math Errors


Errors #1:

This image shows a student’s working. What went wrong?

Well, obviously x should = 17, not the square root of 17. Perhaps a better way to explain the error is like this:

When solving equations (expressions with an equal sign) like this, remember the algebraic rule:

“Whatever you do to one side, do to the other!”

So, here the student undid the sq. root on the LHS but did not undo it on the RHS. So, there should be no root sign on the RHS. “If you sq. root one side, sq. root the other too!  (from mathmistakes.org)

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10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

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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