No.127
Herring Trawling Off Afghanistan
was at least printable. In Question 3,
anti-Funkies would say: ‘Caught A
Herring .’
x
= cos48°; x= 10cos48° = 6.69
10
That 20Hz rumble is John Durran,
revolving in his grave. John Smith’s
line was that cos48° is what you
multiply the 10 by to get the length of
the adjacent, so that without invoking
a ratio x= 10cos48°. In Mechanics
you are constantly wondering what
the sides of such triangles are; my
own fluency was sabotaged by the
ratio glitch, and had I not come to
Winchester I would have spent my
career putting sand in the sumps of
countless pupils. The trouble was
that Silly Old Harry is effective in the
short term and its JP acolytes were
doing better in tests. But John Smith
wrote the Christmas exams and
knew how to fix them: ‘Ahm going
to set them a question their stupid
mnemonics won’t work on’. Some of
my 16 readers will remember it.
The Trusty Servant
I was getting my work table up the
curling staircase (still the most elegant
period feature of any house I have
lived in) when a frail-seeming man
appeared in the doorway of 4a and
invited me in. His flat had the same
plan as mine, but the ceilings were
high and corniced, and glamorous
full-height sash windows basked
in brick-red radiation – sunset on
Kingsgate Street. He gave me my first
taste of madeira, and when I told
him I was filling the boots of Vernon
Wilkins (78-86) he poured another.
Manisty was allowed, by then, to tell
me he’d been at Bletchley Park with
Alan Turing, fighting his own Algebra
War against the Wehrmacht, but this
time he wanted to talk about my train
advice: he advised me to learn the
rules of Winchester football. I side-
stepped by saying that I’d been
employed to run the fives, all my
courts had a kink in their left wall,
and one local perversion of a much-
loved game was enough to be going
on with. I literally didn’t cross worms
for the next seven years, but then it
was to coach OTH, which I am still
doing 27 seasons later, so Tombling
won in the end — I was as wrong
about Winchester’s versions of fives
and football as I was about algebra.
To change the subject, I asked what I
should teach my Jun Men. ‘Brackets,’
he said, ‘nothing but brackets until
Illuminā, though you might leaven
it with a little trigonometry.’ I had
been taught that brackets were an
impediment to algebraic progress that
must be removed on sight, so that’s
what I taught my pupils. As usual, the
opposite was true and John Smith’s
Christmas exam had my lot on toast,
but not, perhaps, the magnificent
eight who are with me still.
QUESTION 5.
Factorise fully
(3x 2 + 2x − 5) 2 − (x 2 + 3x − 4) 2
QUESTION 4.
In the diagram below, which is not
Dutifully
my and
pupils
to Question
scale, all the
narrow
angles are
4. In
the diagram
below, which is not to scale, all the narrow angles
are " 30°
the removed the
brackets, a feat in itself, and stared
and the lengths of the hypotenuses
of the
hypotenuses
order of size are h 1 , h 2 , h 3 , … with glumly
h 1 = at
243.
the
the If
debris:
in lengths
increasing
order
of size are h 1 in
, h 2 increasing
,
h diagram
If the diagram
3 , … with h
is 1 =243.
continued,
find h 11 is .
8x 4 + 6x 3 − 27x 2 + 4x + 9.
continued, find h 11 .
Back to Tombling, who was still in the
Wykeham Arms. ‘How do we do this
thing of Funky’s?’ ‘Ah, MacKinnon.
Question 4. In the diagram below, which is not to scale, all the narrow angles are " 30° and the
Simon Bolivar
So you didn’t spend the whole of
lengths of the hypotenuses in increasing order of size are h 1 , h 2 , h 3 , … with h 1 = 243. If the
Short Half on brackets, then?’ He
diagram is continued, find h 11 .
showed me the trick, with which my
journey from Balloch Central; did I
Provided
your
class
followed
Funky realise
on multipliers
they saved
could
do this
four readers have achieved
Provided
your
class
followed
Funky
I would have
£5.70
with in seconds:
10 from Balloch Pier because the
(4x + 9)(2x + 1)(x − 1) 2 , but it was a year
on multipliers they could do this in
a ticket
3
10
before I worked out how Funky made
seconds:
Lomond-side
station was being
h 11 = your 243
÷ (cos30°)
= 3 5 they ÷ could do Loch
= 2 10 = 1024.
Provided
class followed
Funky on multipliers
this in seconds:
the question go so nicely.
th September?
10
decommissioned
on
28
2
(
)
3
10
5
10
h 11 = 243 ÷ (cos30°) = 3 ÷
= 2 = 1024.
He warmed to his theme, claret was
QUESTION 6.
( 2 )
decanted,
and we talked
of timetables
The
anti-Funkies
were
still
trawling
off
Afghanistan
when the
exam ended. An investment increases by 20% and
The anti-Funkies were still trawling off Afghanistan when the exam ended.
as mathematicians do. He told me
The anti-Funkies were still trawling
then decreases by 20%. What is the
Peter
Tombling
46-52; Co Ro,
John Afghanistan
Manisty (38-87) was
the first the
mathmā
don I met. I’d been given
4b (very
convenient (Coll,
for
off
when
exam
overall percentage change?
John
(38-87)
first staircase
mathmā
don
I met.
I’d to
been
4b (very convenient for
KPO)
and Manisty
while I was getting
my work was
table up the
the curling
(still the
most
elegant
57-98)
was
the
best don
ask given
if I
ended.
was mortifying, and then
period feature of any house I have lived in) when a frail-seeming needed
man appeared
in the
practical
I would (still It the
KPO)
while
getting
work
table
up were
the advice,
curling and
staircase
most elegant
doorway
of and
4a and invited
me I in. was
His flat
had first
the same my
plan as
mine, but
the ceilings
John
Manisty
(38-87)
was
the
exhilarating,
to be told by John Smith
find
him in
the Wykeham
Arms.
high
and
corniced,
and
glamorous
full-height
sash
windows
basked
in
brick-red
radiation
–
mathmā
don I met.
I’d
been
given
4b lived in) when a frail-seeming man appeared
that every
method I had learned was
period
feature
of
any
house
I
have
in
the
sunset on Kingsgate Street. He gave me my first taste of madeira, and when I told him I was
Tombling did indeed have practical
wrong. ‘Don’t add 20% and then
(very
convenient for KPO) and while
filling the boots of Vernon Wilkins (78-86) he poured another. Manisty was allowed, by then,
doorway of 4a and invited me in. His flat had the same plan as mine, but the ceilings were
high and corniced, and glamorous full-height sash windows basked in brick-red radiation –
sunset on Kingsgate Street. He gave me my first taste 3 of madeira, and when I told him I was
filling the boots of Vernon Wilkins (78-86) he poured another. Manisty was allowed, by then,
to tell me he’d been at Bletchley Park with Alan Turing, fighting his own Algebra War
against the Wehrmacht, but this time he wanted to talk about my train journey from Balloch
Central; did I realise I would have saved £5.70 with a ticket from Balloch Pier because the
Loch Lomond-side station was being decommissioned on 28 th September? He warmed to his
theme, claret was decanted, and we talked of timetables as mathematicians do. He told me
Peter Tombling (Coll, 46-52; Co Ro, 57-98) was the best don to ask if I needed practical