# 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

### Power Countdown

##### Age 14 to 16 Challenge Level:

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

### Folding Fractions

##### Age 14 to 16 Challenge Level:

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

### Folding Squares

##### Age 14 to 16 Challenge Level:

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?

### Six Discs

##### Age 14 to 16 Challenge Level:

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?

### Curved Square

##### Age 16 to 18 Challenge Level:

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

### Integration Matcher

##### Age 16 to 18 Challenge Level:

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

### PCDF

##### Age 16 to 18 Challenge Level:

When can a pdf and a cdf coincide?