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Continue
to improve in mathematics
Clement
Radcliffe, Contributor
AFTER
THE improved performance recorded
last year in mathematics, it is imperative
that we build on these gains. No less
than further improvement is acceptable
this year.
While
two hours is not a long time for a
presentation, it proves a reasonable
framework to enable us to establish
a meaningful revision framework. To
achieve this, the following conditions
are required:
a.
Students must be serious in their
desire to be successful.
b.
Students must be willing to pay attention
to the guidelines given and collect
all available materials.
c.
They should involve themselves in
extensive study, practice and revision
up to the examinations.
d.
They also need to possess the basic
capability required for students sitting
the CSEC general proficiency examinations.
BEST
PRACTICES
The
following are some best practices
in studying mathematics.
1.
You cannot afford to wait until it
is too late to begin preparation.
This exercise should be intense and
ongoing.
2.
You should familiarise yourselves
with the structure of the question
papers, the weight of the questions
included and the instructions presented
with each paper.
3.
Preparation should be in the form
of studying and reviewing concepts
and practising appropriate examples
(past paper questions, preferably).
Please note that practice helps to
develop both your confidence and your
competence in the various topics.
Ensure that your choice of topics
incorporates an appropriate mix to
include fundamental concepts which
were taught early, and new work, especially
those topics in Section Two of Paper
2.
4.
You need to procure the following:
The current CXC mathematics syllabus.
From this you should have worked out,
by now, your own revision syllabus.
Revision should continue up to the afternoon
before the exam and should reflect topics
to be done on particular days and at
what time.
A suitable textbook.
*
Past papers and model answers booklets,
for example, CXC Solutions, Mathematics,
General Proficiency, 1990-1999, by
Raymond Toolsie.
Mathematical tools such as calculator,
geometry set, etc., and you must improve
your competence in the use of these.
A hardcover notebook, or a folder, is
recommended. Students, you must ensure
that work done throughout is kept for
easy reference,
You
are also advised to pay attention
to the following:
- Involvement
in extra classes where required.
-
Constant review of materials presented
in the print media and on the Internet.
While
you should endeavour to cover the
syllabus, it is wise to select at
least FOUR topics in the Optional
section of Paper Two. Prepare these
as effectively as possible so that
you can do well on these topics should
they appear on the exam paper.
The
following should be observed in the
organisation of your answers:
Begin each question on a different page.
All rough working should be done in
the answer booklet.
It is most useful if you are able to
ensure that your answers are reasonable
and more importantly, to check your
answers. Such questions where checking
is possible are the solution of simultaneous
equations and factorisation.
COMMON
ERRORS TO AVOID WHEN SITTING THE EXAM
Being
adequately prepared and armed with
the knowledge of the structure of
the mathematics question paper, then
you need to carefully read and obey
the instructions on the cover of the
exam paper.
All working must be clearly shown; failure
to do so could result in loss of marks.
Note
the following:
(a)
Present all formulae - these usually
earn you marks.
(b)
Avoid omitting important steps in
the solution of a problem - you will
be credited even if the answer is
incorrect.
(c)
Never approximate values in the middle
of a solution.
(d)
Be very careful in the use of units
during computation. Care should be
taken to ensure that the units are
consistent. Units could be used as
a guide in solving a problem, for
example, if the answer is required
in km h-1, then this should inform
you that you are required to convert
the values appropriately.
All instructions included in the questions
must be carefully followed, for example,
(a)
Estimate implies that the accurate
answer is not required, especially
in finding 'area'.
(b)
If a particular method is requested,
then you will lose the marks if an
alternative method is used. Here is
an example:
Solve
the equation 2x - 3x - 1 = 0 using
the formula method. It would be unacceptable
to use Completion of Squares or Graph,
even though these methods may be used
to solve the equation.
(c)
When instructed, 'Hence or otherwise',
then you should use the previous solution
to evaluate this section.
Do not cancel work relevant to your
answer. Far too often correct work is
cancelled. Of course, this results in
loss of marks.
Be sure to use the correct formula.
As most of these are given in the
question paper, there is no reason
to have difficulties here if you ensure
that in preparation for the examination
you are familiar with the use of all.
You must attempt ALL questions in Section
A even if you are unable to complete
them. Marks are earned for specific
responses and methods presented. Students
are known to earn most of the marks
for appropriate method and follow through,
even if the answer is incorrect.
AREAS
OF GENERAL WEAKNESS
The
very weak performance of students
generally suggests that most concepts
provide challenges for a significant
number of students. It is frightening
how all concepts are difficult for
so many students who sit the examinations.
The following are some of the more
critical examples of weaknesses:
While students tend to be prepared in
topics at the grades 10 and 11 levels,
work done in the lower forms is not
always adequately prepared. You are
therefore being asked to pay particular
attention to the following topics: area
and volume of shapes, directed numbers,
profit and loss, etc.
In order to improve your ability to
calculate the value of expressions,
for example, 1? + (2* *), please be
reminded that you should use BOMDAS
to determine the order in which the
operations should be done.
Directed numbers, (manipulation of negative
and positive whole numbers) provide
significant challenges for some students.
These, therefore, create problems as
students attempt the following problems:
(a)
Substitution (b) Solution of equations
(c) Factorisation
The
key is to be comfortable with directed
numbers.
Problems with reasoning components are
not always well done. Three examples
of these are:
Selection of appropriate formula, for
a complex figure.
Determining the meaning of terms, for
example, in statistics (a) At most (b)
At least
Identifying and describing a complex
transformation, for example, a notation
followed by a translation.
In
all cases, you must be comfortable
with the topic. This may be achieved
through study and extensive practice.
You then extend these to examples
with reasoning components.
Problems based on three dimensional
situations, for example, bearing and
earth problems.
Some
specific examples which need to be
carefully revised are:
Use of the formula method to solve simultaneous
equations.
POINTS
TO NOTE
Care should be taken in manipulating
the negative signs.
The ± enables you to obtain two
roots.
The entire numerator is over 2a. A common
error is to use ?b2 - 4ac over 2a, separating
-b.
In
other words, the incorrect formula
- b ±?b2 - 4ac is sometimes
used.
2a
(Check
out above question)
The value within the square root should
always be positive. When this is not
so, it usually implies an error in calculation.
PLEASE CHECK YOUR WORKING.
If the value within the square root
is negative, then the equation has no
real roots.
Plotting of graphs. Please note the
following:
The
x and y axes must be CLEARLY LABELLED.
The
scale given must be used EXACTLY,
or if no scale is given, an appropriate
one should be used.
The
use of a suitable pencil (HB) is required.
Straight
line graphs should be drawn with a
RULER, while a curve must be drawn
FREE HAND.
No
matter the shape of the curve, under
no circumstance should a ruler be
used. Be very careful in completing
the table of values if they are not
all given, as unfortunately, you may
be penalised for any error you make.
The
existence of deviation by any point
from the straight line or the smooth
curve is an indication that an error
has been made. You must immediately
review your calculation.
Construction. You must clarify
if you are allowed to use a protractor.
Construction lines must be clearly shown
and should NEVER BE ERASED.
You need to know the difference between
significant figures and decimal places.
In finding the inverse of a function,
you need to show clearly the interchange
of variables x for y.
The
final function, being the inverse,
must be clearly stated.
HIGHLIGHTING
CONCEPTS/TOPICS THAT RECUR ANNUALLY
The
following topics are usually included
in the examination in one form or
another. It is in your best interest
therefore, to develop a clear understanding
of these.
Application of the arithmetic operations
( + - x ) to vulgar fractions, whole
numbers and directed numbers.
LCM, variation, estimation - decimal
places, significant figures and standard
form.
Decimals and percentages
ALGEBRA
Simplifying
Algebraic expressions
Solution
of linear, simultaneous and quadratic
equations
Factorisation
- common factor, grouping, quadratic
and difference of two squares:
Substitution
A knowledge of the standard two and
three dimensional shapes and how to
manipulate the formulae for areas and
volumes
-
Functions - including composite
and inverse
-
Graphs - linear and quadratic
-
Matrices - application of arithmetic
operations solution of simultaneous
equations transformation
- Statistics
- presentation of data: Histogram,
cumulative frequency
- Analysis
of Data - average, standard deviation,
probability
- Theorems
of Geometry - triangle - circle
- Coordinate
Geometry -gradient, mid point, length
of line, and equation of lines
-
Construction
-
Vectors
-
Venn Diagram
Please
be reminded that an understanding
of the above is critical if you are
to do well.
QUESTIONS
POSED BY STUDENTS
You
are invited to pose some which are
creating most difficulties.
FINAL
COMMENTS
In
closing, I wish to remind you of a
few points. I cannot overemphasise
the importance of PRACTICE. Not only
are you developing competence, but
you are also bolstering your confidence.
Practise different types of questions
from both Paper 1 and Paper 2. You
will recall that Paper 1, the Multiple
Choice paper consists of 60 items
and deserves as much attention as
Paper 2. Do not treat this paper lightly
for your final grade depends on your
performance in BOTH papers. There
is no room for guessing, therefore,
work out the answers! Please ensure
that you have the appropriate pencil
for this paper.
At
the end of the examination, check
for all the papers you have used,
write your candidate number on each
page and tie them together.
The
information given is geared towards
the students doing the general proficiency,
but it can be extended to those doing
the basic proficiency.
Please
revise, relax and do your best.
*
Clement Radcliffe is principal
of Glenmuir High School in Clarendon.
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