Year 9 Interactive Maths - Second Edition

Problem Solving Unit

Problem 6.1  Small Cubes

The surface of a 10 × 10 × 10 cube is painted red.  It is then cut into 1000 small cubes of equal size.

a.  How many of these small cubes will have:

1. one face painted red?
2. two faces painted red?
3. three faces painted red?
4. four faces painted red?

b.  How many of these cubes will have an even number of faces painted red?
c.  How many of these cubes will have an odd number of faces painted red?

Problem 6.2  Ones Digit

What is the ones digit of :

Problem 6.3  Square Root of the Cube

If the square root of the cube of a number is 27, then find the number.

Problem 6.4  Two Farms

A farmer drives from one farm to another farm averaging 70 kilometres per hour.  On the return trip he averages 60 kilometres per hour and it takes 50 minutes longer.  How far apart are the two farms?

Problem 6.5  The Smallest and the Largest

a.  What is the smallest number that can be written using the digits 0, 1 and 2?
b.  What is the largest number that can be written using the digits 0, 1 and 2?

Problem 6.6  A Race

In a 40 kilometre race, First beats Second by 4 kilometres and First beats Third by 10 kilometres.  If the runners maintain constant pace throughout the race, by how many kilometres does Second beat Third?