# Interpreting and evaluating - July 2009, Stage 4&5

This month our problems involve aspects of the process of interpreting the information in a question and examining in various ways the solution or methods used to get the solution. For example, are the assumptions and arguments made correct or appropriate? How does the solution relate to the initial problem? Can we make sense of someone else's finding? Can we compare strategies used?

## Problems

### Back Fitter

##### Stage: 4 Challenge Level:

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

### At Right Angles

##### Stage: 4 Challenge Level:

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

### Rationals Between...

##### Stage: 4 Challenge Level:

What fractions can you find between the square roots of 65 and 67?

### Four on the Road

##### Stage: 4 Challenge Level:

Four vehicles travel along a road one afternoon. Can you make sense of the graphs showing their motion?

### Calculus Countdown

##### Stage: 5 Challenge Level:

Can you hit the target functions using a set of input functions and a little calculus and algebra?

### Succession in Randomia

##### Stage: 5 Challenge Level:

By tossing a coin one of three princes is chosen to be the next King of Randomia. Does each prince have an equal chance of taking the throne?

### Tangled Trig Graphs

##### Stage: 5 Challenge Level:

Can you work out the equations of the trig graphs I used to make my pattern?

### Whose Line Graph Is it Anyway?

##### Stage: 5 Challenge Level:

Which line graph, equations and physical processes go together?

### Area L

##### Stage: 5 Challenge Level:

Draw the graph of a continuous increasing function in the first quadrant and horizontal and vertical lines through two points. The areas in your sketch lead to a useful formula for finding integrals.

### Operating Machines

##### Stage: 5 Challenge Level:

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?