Year 1997 - Volume 33
2020 - Present

Welcome (belatedly) to a new year – I don’t know what life is like for you, but with the present cut-backs, it is getting harder and harder to have Parabola out on time.

Frank Reid
In a previous article (Parabola, Volume 32 Number 2), the swing and reverse swing of a cricket ball was discussed.

Peter G. Brown
In the 3-Unit Maths course you are asked to prove (by induction) various formulae such as
12+22+32+.....+n2= n ∑ x=1 x2=1/6 n(n+1)(2n+1),

Rodney James
When you began to sketch curves early in high school, you evaluated the “y -value” for several “x -values”, plotted the resulting points and then joined them up as smoothly as you could.

Q993 Consider
p(n)=a0+a1n+a2n2+⋯+aknk
q(n)=b0+b1(n 1)+b2(n 2)+...+bk(n k)

Rodney James
When you began to sketch curves early in high school, you evaluated the “y -value” for several “x -values”, plotted the resulting points and then joined them up as smoothly as you could.

Bruce Henry and Clio Cresswell You have probably all heard the expression “How long is a piece of string?”. It’s usually offered in rhetorical response to a question that has no sensible answer.

Peter G Brown.
Some years ago I saw the following problem in a mathematics competition. Solve the simultaneous equations
x+y+z=1
x2+y2+z2=29
x3+y3+z3=-29

JUNIOR DIVISION
Find the smallest positive integer n such that 13n is a perfect cube, 15n a perfect fifth power and 17n a perfect seventh power.

Q.1001 On the island described in question 2 of the Junior Division for this year’s mathematics competition, each town entered one Australian Rules football team in the national championship.

Q.985 For what values of the positive integer n
1. 5n+2
2. 7n+2
a perfect square? is

Once again we bring you two articles which illustrate how wide Mathematics is. The first (from our prolific writer Peter Brown) deals with the fascinating oddity of magic squares (and some of the history of Mathematics), while the second article (by Bill McKee) deals with the very practical area of waves.

Peter G. Brown
A Magic Square of order n is an arrangment of the numbers 1,2,…,n2 into a square array in which we get the same sum whenever we add the numbers in any row, column or diagonal.

Bill McKee
A great many aspects of our lives involve waves of one sort or another. We speak to each other via sound waves, light and radio signals travel via electromagnetic waves.

SENIOR DIVISION
First prize:
KUSILEK Jonathan, Hurlstone Agricultural High School

Q.1007 A student receives a mark out of 7 for each of the subjects English, Maths and Science. In how many ways can the student get a total mark of exactly 7; a total mark of at most 7; a total mark of exactly 16?

Q.1001 On the island described in question 2 of the Junior Division for this year’s mathematics competition, each town entered one Australian Rules football team in the national championship.