Analysing - June 2009, Stage 4&5

Analysing a problem in order to decide on appropriate mathematical procedures plays a key role in successful problem-solving. Do we estimate or approximate or do we use more accurate methods of calculation? Do we use diagrams or graphs? Do we manipulate numbers or use algebraic techniques? Do we check our working regularly? Do we record our work, our solutions and our conclusions in the most effective way? These are some of the important questions that we may need to ask ourselves.

Problems

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Power Countdown

Stage: 4 Challenge Level: Challenge Level:1

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

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Take a Square II

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What fractions can you divide the diagonal of a square into by simple folding?

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Folding Squares

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?

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Six Discs

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?

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Curved Square

Stage: 5 Challenge Level: Challenge Level:1

Can you find the area of the central part of this shape? Can you do it in more than one way?

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Integration Matcher

Stage: 5 Challenge Level: Challenge Level:1

Match the charts of these functions to the charts of their integrals.

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PCDF

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

When can a pdf and a cdf coincide?