Showing posts with label Measurement. Show all posts
Showing posts with label Measurement. Show all posts

13 February 2013

WAEC MATHS:WHY CHEAT AFTER WAEC PROVIDED YOU WITH THESE GUIDES?(3)

WAEC MATHEMATICS:WHY CHEAT WHEN WAEC HAS PROVIDED YOU WITH THESE GUIDES?(3)

WAEC exams

 

WAEC – May/June. 2009


 

General Comments


 

The standard of the paper like in previous years was reported to have been maintained. The questions were within the syllabus and covered a wide area of the syllabus. The rubrics as well as the marking scheme were reported to be clear, generous and quite liberal.

 

However, the performance of the candidates generally fell below those of previous years. Notwithstanding, there were isolated reported cases of brilliant ones who did excellently well in the paper.

 

Candidates’ Weaknesses

 

Apart from not giving answers to the required degree of accuracy, majority of the candidates could not apply the basic concepts and theorems correctly in some aspects of the syllabus. Such areas of the syllabus as reported included:
(1)     Mensuration of three dimensional shapes;
(2)     Circle theorems;
(3)     Trigonometry;
(4)     Geometrical Construction.

 

Many candidates were said to be able to solve the inequality in question 2 but they were unable to get the three greatest integral values of x.

 

Suggested Remedies

 

(1)Teachers should put in more effort in the teaching of plane and solid geometry.

 

(2)Teachers and students should be encouraged to use teaching aids
during mathematics lessons in order to make some mathematical concepts clearer to the pupils.

 

(3)Candidates should be groomed on the rudiments of answering questions.

 

(4)Candidates are encouraged to adequately prepare for the examinations by practicing on a wide range of problems.

 

(5)Mathematics syllabus should be adequately covered.

 

(6)Teachers should spend more time in teaching those areas of the syllabus where candidates’ performance had been consistently poor such as Geometry.

 

Candidates’ Strengths

 

From the responses of candidates, it was stated that their performance in the following areas had improved which was commendable:
(1)Surds;
(2)Indices;
(3)Statistics;
(4)Set theory.

 

GCE – Nov/Dec. 2009


 

General Comments


 

It was reported that the standard of the paper compared very favourably with those of the previous years.  The rubrics were clear and unambiguous and the instructions were precise.  The questions were also clear, straight-forward and had a good coverage of the syllabus.  Accuracies required were well stated and the diagrams were clear.  The marking scheme was reported to be quite liberal, clear and generous.  The marks distributions were adequate and student-centred.

 

Generally, the performance of candidates was reported not to be different from those of previous years although they appear to have improved over that of last year.  It was also observed that candidates whose performance on the question on Geometrical construction and graphs were above average, performed well in the paper.

 
Candidates’ Weaknesses

 

Many candidates were adjudged not to have adhered to the given instructions.  It was observed that candidates relied so much on tables and calculators even in questions which stated otherwise while others presented their responses poorly.

 

The chief examiner was also of the opinion that candidates exhibited weaknesses in their:

 

 interpretation and application of geometric statement and theorems as in

 

questions 5 and 9.

 

    interpretation of graphs.  Some candidates even drew histograms with

 

class limits instead of class boundaries.

 

solution to problems on probability especially where it involved addition

 

and multiplication of probabilities.

 

 simplification of simple surds.  

 

response to word problems.

 

Though the question on number bases was well attempted, many candidates resorted to first converting to base ten rather than working in the base given in the question.

 

Suggested Remedies
Candidates should study the syllabus in order to know the scope of coverage.

 

Candidates should adequately prepare for examinations by engaging private teachers or attending coaching classes.
    
Candidates should possess adequate materials such as four-figure tables, Mathematical sets etc.
    
Candidates should be well exposed to past WASSCE questions.

 

 
Candidates’ Strengths

 

Generally, no outstanding performance was observed.  However, there were observed improvement in candidates’ response in the following areas:

 

Simplification of fractions and simple algebraic equations.

 

Computation of tables and drawing of graphs.
    
Mensuration – areas of plane shapes.
    
Operations on number bases.

 

Candidates’ performance in Arithmetic Progression (A.P) and longitude and latitude were also commendable.

 
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WAEC MATHS:WHY CHEAT AFTER WAEC PROVIDED YOU WITH THESE GUIDES?(2)

WAEC MATHEMATICS:WHY CHEAT WHEN WAEC HAS PROVIDED YOU WITH THESE GUIDES?(2)


General Mathematics Paper 2,May/June. 2008


General Comments


The paper was quite fair and within the reach of any candidate who had prepared well for the examination.  All the questions were within the content of the syllabus and there was no ambiguity of any sort.  The standard of the paper as well as the clarity of the rubrics were maintained.

The marking scheme was as usual, flexible to accommodate various approaches presented by the candidates in solving the problems. Apparently, the performance of the candidates was not significantly different from those of the previous years.

Candidates’ Weaknesses From candidates’ responses, it was evident that questions from some areas of the syllabus were poorly handled.  This may be attributed to inadequate preparation or poor interpretation of the demands of the questions. The identified areas are:
(1) Commercial arithmetic
(2) Geometry – majority of the candidates avoided the question on construction. Some of those who
     attempted it did not go beyond constructing angles 90˚ and <120˚;
(3) Word problems leading to simple linear equations;
(4) Mensuration
(5) Statistics as in question 5.
Suggested Remedies

 Candidates should be encouraged to study effectively and be exposed to mathematical facts, concepts and principles as well as how to apply them accurately in answering questions.   \

Candidates should be taught to adhere to the rubrics, study and comprehend the demands of the questions before attempting them. 

Candidates should be well exposed to past WASSCE questions
Candidates’ Strengths

Many candidates showed a good understanding of the following areas of the syllabus:
(1)  Set theory       -  drawing of Venn diagrams
(2)  Algebra           -  computing the table of values as well as drawing of algebraic graphs
(3)  Arithmetic progression.
(4)  Trigonometry   -          angles of elevation and depression.

The performance of candidates in Geometric Progression (G. P.) was only fair. Furthermore, a good number of the candidates were able to apply the sine rule correctly.  There was also a noticeable improvement in the performance of candidates in problems involving longitude and latitude.

GCE – Nov/Dec. 2008


General Comments


The paper was quite fair and within the reach of any candidate who had prepared well for the examination.  All the questions were within the content of the syllabus and there was no ambiguity of any sort.  The standard of the paper as well as the clarity of the rubrics were maintained.

The marking scheme was as usual, flexible to accommodate various approaches presented by the candidates in solving the problems. Apparently, the performance of the candidates was not significantly different from those of the previous years.

Candidates’ Weaknesses

From candidates’ responses, it was evident that questions from some areas of the syllabus were poorly handled.  This may be attributed to inadequate preparation or poor interpretation of the demands of the questions. The identified areas are:
(1) Commercial arithmetic
(2) Geometry – majority of the candidates avoided the question on construction. Some of those who attempted it did not go beyond constructing angles 90˚ and <120˚;
(3) Word problems leading to simple linear equations;
(4) Mensuration.
(5) Statistics as in question 5.

Suggested Remedies

Candidates should be encouraged to study effectively and be exposed to mathematical facts, concepts and principles as well as how to apply them accurately in answering questions.Candidates should be taught to adhere to the rubrics, study and comprehend the demands of the questions before attempting them. Candidates should be well exposed to past WASSCE questions.

Candidates’ Strengths

Many candidates showed a good understanding of the following areas of the syllabus:
(1) Set theory  -  drawing of Venn diagrams
(2) Algebra -   computing the table of values as well as drawing of algebraic graphs.
(3) Arithmetic progression.
(4) Trigonometry   -  angles of elevation and depression.

The performance of candidates in Geometric Progression (G. P.) was only fair. Furthermore, a good number of the candidates were able to apply the sine rule correctly.  There was also a noticeable improvement in the performance of candidates in problems involving longitude and latitude

 
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10 February 2013

IF YOU THINK WAEC MATHS IS HELL,HERE ARE 84 STEPS TO MATHS HEAVEN (5)

[caption id="attachment_2609" align="alignleft" width="125"]IF YOU THINK WAEC MATHS IS HELL,HERE ARE 84 STEPS TO MATHS HEAVEN (5) waec logo[/caption]

THOSE WHO FAILED WAEC MATHS ALSO MISSED THESE KEY AREAS IN


THEIR PREPARATIONS!


1.WAEC MATHS FORMULAS, SIGNS,NOTATIONS,SYMBOLS AND HINTS.

2.THE SIX PROCEDURAL STEPS FOR  SOLVING ALL WAEC MATHS  QUESTIONS (VERY IMPORTANT)!

Now lets explain these two a bit more as follows:

 RECOGNITION / IMPORTANCE OF MATHS  FORMULAS, SIGNS, SYMBOLS,NOTATIONS & HINTS

68. A maths formula is a set of rules expressed in symbols or as an acronym for simplification purposes. A formula is a shorthand expression of a mathematical relationship which often is the master key for finding solutions. Since a maths formulas are often tools for solutions the best attitude for students is not to dread or avoid them but to develop familiarity with them.

69. Similarly students need to be familiar with maths signs, symbols, notations and hints as would be indicated later in this write-up. The table below points to the most important areas for fishing for relevant formulas during private studies e.t.c.

































S/N AREA OF MATHSAREA OF KEY FORMULAS(FOR SSS)
1/2ARITHMETIC/STRUCTUREThe laws of indices, Logarithm, Series and formulas relating to  business arithmetic.
3ALGEBRAThe  “almighty formula” and identity relations.
4TRIGONOMETRYTrigonometrical ratios, Pythagoras and related theorems.
5GEOMETRYMensuration formulas for plane and spherical geometrical including circles.
6/7PROBABILITY& STATISTICSFormulas for sum of probability, and likelihood estimates, mean, mode, median, quartile, variances and standard deviations.

70. Let’s refer a bit to signs and symbols in maths. One is bound to ask what their uses are because  lots of  misconception and phobia are attached to them by students. Tutors must therefore  spend some time explaining  their utility during exams,tests or homework to students. The purpose shall be to chip off  part of the phobia and fear fear and let them understand that there is nothing really special or difficult about mathematical signs and symbols. Students need to understand that they are just representations adopted as shorthand to quicken and simplify the process of computation in maths. However, after a long period, regularity, frequency and consistency of use, these signs and symbols became standard signs for specific purposes in the history of mathematics e.g. “∑” (sigma) which has become a standardized sign for summation or “θ”(theta) which has come to represent the sign for a regular angle. As stated earlier, they vary importantly because they have helped to determine or get many formulas defined or expressed through them. Some of the commonest mathematical, signs, symbols notations and hints have been listed for further reference by students.

a. Key mathematical signs, symbols. and notations

b. Basic quick revision formulas & hints  for WAEC maths clinic or Js3 exams

c.  Senior School Revision formulas and hints

Due to the length of b and c above they have been separated and shall be published as whole units for reference purposes.

KEY MATHEMATICAL SIGNS, SYMBOLS AND NOTATIONS

71. Apart from popular signs such as  +,  -,  ×,  =,  >,  <,  ≥,   ≤,  √, % we also have =, ∑, α, =>, ↔,è, Π, {}, Ł, ι, Δ, /. Please spend some time  to searching for their meanings. You should not wait to be spoon-fed all the time. We are already familiar with most of them or are we not?

72. Students should also know the signs and symbols used to represent the following words even though many relate more to the sciences. These include meter, kilogram, seconds, radian, Newton joule, watt, volt, ohm, Faraday, hertz, degree, Celsius, square meter, per cubic meter, etc.

73. Note that a full stop is written after symbols for units except when they occur normally at the end of the sentence. Note that symbols for units do not have plural forms e.g. 40 kilogram. Also pay close attention to the most popular Greek alphabets such as:

α= alfa or alpha =a, β= beta =b, γ= gama or gamma = g, Δ= delta = d, π=pi  = p, ∑= sigma =s, Θ= theta or teta = th, Φ=phi = f, Ω= omega = oi

Please  also note that  alphabets  have their capital and small letter forms which are mixed above. But curiously the capital and small forms don’t usually look alike.

74. The seven different branches of maths have their different symbols e.g . statistics have the following:

X-sample or arithmetic mean, Π – mean of population, S – standard deviation or sample, S²-variance of sample, Б -standard deviation, б²-variance of population.

PLEASE NOTE THAT MANY OF THESE SIGNS,HINTS,SYMBOLS ARE TO BE FOUND IN THE LISTS OF FORMULAS AND HINTS TO BE PUBLISHED  LATER ON THIS WEBSITE.


PROCEDURAL STEPS FOR  SOLVING WAEC MATHS PROBLEMS (VERY IMPORTANT!)

  75. STEP 1: IDENTIFY The branch of mathematics, key concepts and question phrase from the problem given. This is a mental effort  which should take a few seconds only.

  76. STEP 2: RE-STATE the relevant facts given starting with the phrase “GIVEN THAT …”in most cases.

Here you are only restating facts from the question without solving it but you will get marks in a theory examination paper for doing the obvious!

77. STEP 3: INTERPRETE The facts given into a numerical equation on a drawing or a pictorial expression if not already given and in most cases SIMPLIFY the mathematical expression further for  the next step you are likely to take..

78. STEP 4: APPLY the relevant formula after determining whether there is a formula applicable to the simplified form to get a solution. You may state the formula as follows “using the formula which states that…..”

79. STEP 5: COMBINE Your knowledge of arithmetical and algebraically rules with the simplified facts, formula or theory from step 4 to get an answer.

80. STEP 6: STATE your answer clearly on a different line .Don’t forget the unit of measurement such as m2 or km or cm3

CONCLUSION:

81. TO PASS WAEC MATHS

Know the branches of maths

Understand the concepts .


Know the question types.

Develop capability for recognizing  signs, symbols and notations.

Memorize as many of the formulas  and hints as you can and know how and when they can be applied.

Practice the 6 procedural steps outlined above.

Having mastered these six steps you can crown it all with continuous practice. But note that  engaging in continuous practice of math as many tutors would say without  grounding yourself in what maths is all about is an act of deceit capable of limiting  your success.


 Steps 82 to 84 have been separated and transferred to


BASIC ETIQUETTE FOR WAEC MATHS


They are however summarized as follows:


82.Certain student  practices usually  found pleasing to WAEC  maths examiners

83. Additional points to note for WAEC maths studies.

84. Topics identified by WAEC experts which might be useful for private studies

OUR "84 STEPS" TERMINATES HERE. BUT WE  HAVE ADDITIONAL HELPFUL NOTES ON WAEC MATHS FOR YOU.SO PLEASE READ ON.

THANK YOU AND GOOD LUCK.
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