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Problem-Solving Problems

July18

Check out the sets of problem-solving questions on the NZMaths website. Copymasters are included and there are excellent problems for all levels, covering Algebra, Measurement, Geometry, Statistics, etc. Here is one example, from Level 2:

“There are 2 pirates and 4 treasure chests on an island.

The pirates have 1 small boat to take the treasure to their ship.

The boat can take 2 pirates or 1 pirate and 1 chest of treasure.

How many trips do the pirates have to take to get all the treasure and both pirates onto the ship?”

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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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