# Measurement and Trigonometry - October 2004, All Stages

## Problems

### Robot Monsters

##### Stage: 1 Challenge Level:

Use these head, body and leg pieces to make Robot Monsters which are different heights.

### Sizewise

##### Stage: 1 Challenge Level:

Can you match the mass and length or height of these things to their pictures?

### Triangle Edges

##### Stage: 1 Challenge Level:

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

### Chocoholics

##### Stage: 2 Challenge Level:

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

### Uncanny Triangles

##### Stage: 2 Challenge Level:

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

### Money Measure

##### Stage: 2 Challenge Level:

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

### Square It

##### Stage: 1, 2, 3 and 4 Challenge Level:

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

### Buses

##### Stage: 3 Challenge Level:

A bus route has a total duration of 40 minutes. Every 10 minutes, two buses set out, one from each end. How many buses will one bus meet on its way from one end to the other end?

### An Unhappy End

##### Stage: 3 Challenge Level:

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

### Cuboids

##### Stage: 3 Challenge Level:

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

### Salinon

##### Stage: 4 Challenge Level:

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

### Sliced

##### Stage: 4 Challenge Level:

An irregular tetrahedron has two opposite sides the same length a and the line joining their midpoints is perpendicular to these two edges and is of length b. What is the volume of the tetrahedron?

### Tubular Stand

##### Stage: 4 Challenge Level:

If the radius of the tubing used to make this stand is r cm, what is the volume of tubing used?

### Bend

##### Stage: 5 Challenge Level:

What is the longest stick that can be carried horizontally along a narrow corridor and around a right-angled bend?

### Gosh Cosh

##### Stage: 5 Challenge Level:

Explore the hyperbolic functions sinh and cosh using what you know about the exponential function.

### Complex Sine

##### Stage: 5 Challenge Level:

Solve the equation sin z = 2 for complex z. You only need the formula you are given for sin z in terms of the exponential function, and to solve a quadratic equation and use the logarithmic function.