Meaningful revision structure for maths
Clement Radcliffe, Contributor

I wish to welcome you, students, to this very worthwhile annual exercise. I do hope that you will benefit more from the exercise, as it is being held earlier 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 structure.

The following are some best practices in studying mathematics.

1. You cannot afford to wait until it is too late to begin preparations. This exercise should be intense and ongoing.

2. 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 Two.

3. You should familiarise yourselves with the structure of the question papers, the weight of the questions included and the instructions presented with each paper.

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.
  
  
• 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.
  
  
• 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 the period of preparation is kept for easy reference.

5. 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.

6. 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, you must check your answers. Such questions where checking is possible are the solutions 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, you then need to be aware of the usual errors which are commonly made.

1. Failure to obey instructions which are printed on the cover of the question paper.

2. All working must be clearly shown; failure to do so could result in loss of marks. This is avoided by respecting the following:

• Present all formulae - these usually earn you marks.
  
  
• Avoid omitting important steps in the solution of a problem - you will be credited even if the answer is incorrect.
  
  
• Never approximate values in the middle of a solution. This may lead to a wrong answer, especially when an accurate one is required at the end.
  
  
• Be very careful in the use of units during computation. Care should be taken to enssure 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 requird to convert the values appropriately.

All instructions included in the questions must be carefully followed, for example, Estimate implies that the accurate answer is not required, especially in finding 'area'.

3. If a particular method is requsted, then you will lose the marks if an alternative method is used. Here is an example:

Solve the equation 2x² + 3x - 1=0 using the formula method.

It would be unacceptable to use 'completing the squares' or 'graph' methods, even though these may be used to solve the equation.

4. When instructed, 'hence or otherwise', then you should use the previous solution to evaluate this sction.

5. Do not cancel work relevant to your answer. Far too often correct work is cancelled. Of course, this results in loss of marks.

6. 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. Please note that some formulae are presented on the question paper.

7. 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.

Area 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:

1. While students tend to be prepared in topics at the grades 10 and 11 levels, work done in the lower forms are not always adequately revised. You are, therefore, being asked to pay particular attention to the following topics - area and volume of shapes, directed numbers, profit and loss, etc.

2. Students generally have difficulty in determining the order in which various arithmetic operations should be done. Please be reminded that you should use BOMDAS.

3. The handling of directed numbers (manipulation of negative and positive whole numbers) provides significant challenges for some students. These, therefore, create problems as students attempt the following problems: (a) substitution; (b) solution of equations; and (c) factorisation.

The key is to be comfortable with directed numbers.

4. 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.

5. Problems based on three-dimensional situations, for example, bearing and earth problems.

6. Use of the formula method to solve simultaneous equations.

Points to note

• The entire numerator is over 2a. A common error is to use b2 - 4ac over 2a, separating -b.

In other words, the incorrect formula
is sometimes used.

• Care should be taken in manipulating the negative signs.
  
  
• The ± enables you to obtain two roots.
  
  
• 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.

7. 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 by 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.

8. Construction: You must clarify if you are allowed to use a protractor. Construction lines must be clearly shown and should NEVER BE ERASED.

9. Finding inverse functions for f(x)

• In this case, you need to show clearly the interchange of variables x for y.
• In all cases, the final function, being the inverse, must be clearly stated.

For example:

y = f(x) = 3x-7. In order to find the inverse of f(x)

y = 3x-7
ie. 3x = y + 7

10. You need to know the difference between significant figures and decimal places.

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 arithmtic operations (+ - x ÷) to vulgar fractions, whole numbers and directed numbers.
• LCM, variation, estimation decimal places, significant figures and standard form
• Venn diagrams
• Decimals and percentages
• Algbra
• Simplifying algebraic expressions
• Solution of linear, simultaneous and quadratic equations
• Factorisation common factor, grouping, quadratic and difference of two squares
• Substitution
• Indices
• Trigonometry
• 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, midpoint, length of line, and equation of lines
• Construction
• Vectors

Please be reminded that an understanding of the above is critical if you re 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. The calculator must be used in Paper Two only. It is important, therefore, for you to practise using one before the day of the examination.

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 Papers One and Two. You will recall that Paper One, the multiple-choice paper, consists of 60 items and deserves as much attention as Paper Two. Do not treat this paper lightly, for your final grade depends on your performance in BOTH papers. There is no room for guessing. Work out the answers! Please ensure, also, 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.

Clement Radcliffe is the principal of Glenmuir High School in May Pen.