Year 10 Interactive Maths - Second Edition

Projects

Project 10.1  Prime Numbers

A prime number has only two different factors, 1 and itself.

1.  Write all prime numbers between 1 and 200.

2.
a.  Is 319 a prime number?
b.  Which numbers do you have to use to determine the factors of 319?

Some of the prime numbers can be expressed as the sum of two squares (SOTS). For example,

Such numbers are referred to as SOTS; whereas, other prime numbers are called not SOTS.

3.  Find all prime numbers between 1 and 200 which are:
a.  SOTS
b.  Not SOTS

Is there a pattern? Explain.

Extension

4.
a.  Make a list of all prime numbers between 200 and 1000.
b.  Circle those prime numbers you think to be equal to the sum of two squares.

Justify your answer by giving reasons.

Your report should include all working.

Study Another Topic in Chapter 10: Factorisation Techniques

[ Highest Common Factor ] [ Factorisation using the Common Factor ] [ The Difference of Two Squares ] [ Quadratic Trinomials ] [ Cross-Multiplication Method ] [ Factors of Quadratic Trinomials of the Type ax² + bx + c ] [ Use of Perfect Squares ] [ Use of Substitution ] [ Use of a Common Factor ] [ Factorisation of Four Terms ] [ Grouping 'Three and One' ] [ Real Numbers ] [ Completing the Square ] [ Problem Solving Unit ] [ Projects ] [ Symbols ] [ Index ]