Maths Item of the Month Archive 2006

December 2006

19 not out

Some positive numbers add up to 19. What is the maximum product?

Solution


November 2006

Coursework in mathematics

Following the recent decision to discontinue coursework in GCSE Mathematics, MEI have produced a discussion paper to promote general discussion that will inform national policy.

Summary:

  • Coursework was introduced for sound educational reasons; it is essential to understand these in order to be able to make sensible decisions about the most appropriate means of assessment.
  • Coursework in GCSE Mathematics will soon be discontinued; it became increasingly unpopular following the introduction of the data handling coursework.
  • Existing mathematics coursework at A-Level is fit for purpose; it should, therefore, be allowed to continue.
  • Statistics 1 coursework in the MEI A-level had similar aims to the GCSE data handling coursework but was much more successful in achieving them. The reasons for this are explored in the paper.
  • It is important that the skills we want our young people to acquire are measured and encouraged within the scheme of assessment.
  • All specifications should be required to assess these skills; there may be flexibility in how this is done, but all approaches should be properly evaluated.

You can read the paper in full.


October 2006

Power Darts

On a dartboard where the "doubles" count as squares and the "trebles" count as cubes how many 3 dart finishes are there starting from 501, finishing on a "double".
e.g. 20, "double" 9, "double" 20: 20 + 92 + 202 = 501

Self-describing numbers

E

F

H

I

N

O

R

S

T

U

V

W

X

1/6

4/3

7/6

11/6

1/2

1/3

5/6

2

2/3

3/2

5/3

1

13/6

Using these values, you will find O+N+E=1 and T+W+O=2. How much further can you go?

E

F

G

H

I

L

N

O

R

S

T

U

V

W

X

3

9

6

1

-4

0

5

-7

-6

-1

2

8

-3

7

11

Here we again have O+N+E=1 and T+W+O=2. Now how far can you go?

It turns out that (T+W+O)+(E+L+E+V+E+N) =13. Why does this guarantee that T+W+E+L+V+E =12?

Finally, if we insist that each letter takes a different value from all other letters, how can you prove that it will be impossible to find any system in which all the integers from one to thirteen describe themselves?


September 2006

Double angle formulae




Solution