Year 9 Interactive Maths - Second Edition

Problem Solving Unit

Problem 1.1  Paths

A unit cube is a cube whose edges are each one unit long.

Two vertices of a unit cube are labelled X and Y so that they are diametrically opposite each other.

How many paths of length 3 units are there from X to Y that follow the edges of the cube?

Problem 1.2  Number of Smaller Cubes

A white cube whose sides are n units long is painted yellow.  It is then sliced into n³ smaller cubes of equal size.  Find a general formula for the number of smaller cubes that have exactly one yellow side.

Problem 1.3  The Date

What is the date when the month of February 2002 is 21 660 minutes old?

Problem 1.4  How Much?

I want to buy 50 nails.  I can buy a package of 24 nails for 75 cents, or I can buy the nails individually for 5 cents each.  How much can I save if I buy three packages of nails instead of buying the nails individually?

Problem 1.5  How Long?

How long is the night when the sun sets at 6:24 PM and rises at 7:13 AM?

Problem 1.6  Storm Clouds

It takes 12 seconds for storm clouds to travel 3 km.  How long does it take the storm clouds to travel 0.20 km?

Problem 1.7  A Bus

A bus runs between two cities 1200 kilometres apart at an average speed of 60 km/h.  How much would the bus's speed have to increase in order to decrease the running time by 2 hours?

Problem 1.8  A Train

A train 0.4 km long travelling at a speed of 80 km/h enters a tunnel 0.6 km long.  How many seconds will it take the train to pass the tunnel completely?