Showing posts with label Arithmetic Progression. Show all posts
Showing posts with label Arithmetic Progression. 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.

 
Enhanced by Zemanta

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

 
Enhanced by Zemanta

10 February 2013

YOU THINK WAEC MATHS IS HELL,HERE ARE 84 STEPS TO MATHS HEAVEN (8)


[caption id="attachment_4440" align="alignleft" width="286"] YOU THINK WAEC MATHS IS HELL,HERE ARE 84 STEPS TO MATHS HEAVEN (8) living maths[/caption]

MORE MATHS FORMULAS AND HINTS FOR WAEC QUICK REVISION(1)


PREAMBLE

Under BASIC QUICK REVISION MATHS FORMULAS & HINTS FOR WAEC EXAM we introduced you to simpler formulas and hints for the maths exams.The additional ones being added through this post are slightly different cause they require more thought for their application.It is not that they are more “difficult” but were separated so that those listed under the “basic” posts can contribute to understanding them more.As a matter of fact they cannot be new to most students in their final years (ss3). But what is most important to note is that they are listed  for quick revision purposes under private or group study sessions.Please remember to call the attention of your school tutors to areas that might need further assistance for your complete understanding. Good luck!

A.   NUMBER BASES

1. When a number is not specified to be in base 2 or any other base it is assumed to be in base 10

Note the following, however:

a. How to convert a number in any base to a number in base 10

b. How to convert a number in an unknown base to a number in base 10

c. How to convert an unknown number in a known base to unknown number in base 10

2. a. How to convert a number in base 10 to a number in any other base

Divide the given no with the base you are converting to till the given number vanishes. Write out the remainder as you divide, where there is no remainder, zero is written out. Remainder are written in ascending order as the answer from the last division to the first.

b. How to convert fractional numbers from one base to another should also be known.

............................................................................................................................................................................................................................................................

B.  FRACTIONS

BODMAS is a rule usually used for solving fractional problems.Remember the order of applications as shown below and never depart from it!

B = BRACKET, O = OFF, D = DIVISION, M = MULTIPLICATION, A = ADDITION, S = SUBTRACTION

…………………………………………………………………………………………………………………………………………………………………………………………………………………………

C.   GAIN (PROFIT) AND LOSS %

Where SP= Selling Price and CP = Cost Price

GAIN % = SP– CP /CP  x 100%   and

LOSS % = CP – SP/CP x 100%

…………………………………………………………………………………………………………………………………………………………………………………………………………………………..

D.    SIMPLE/COMPOUND INTEREST
Where A = Amount, P = Principal, R = Rate, T =Time, I = Interest,   n= Number,

 SIMPLE

Principal (P) = I × 100/ RT (in Naira)

Rate (R) = = I × 100/PT  (in %)

Time (T) = I × 100/PR   (in years or months)

Amount = P  +  I  i.e  A = I ×100/RT + PRT/100

COMPOUND

A = P(I + R/100)n

…………………………………………………………………………………………………………………………………………………………………………………………………………………………

E. SEQUENCE

ARITHMETIC PROGRESSION (AP)

Where Tn  = nth term, Sn = sum of n terms, a = 1st term, d= common difference, n = number of terms.

 Tn  = a + d(n +1)

Sn = n/2( 2a + d(n-1))

6

∑ 5n – 3  means the sum of the first 6  terms of the series 1,3,5

n=1

GEOMETRIC PROGRESSION (GP)

Tn = ar n – 1 where a is the1st term, r is the common ratio and n is the number of terms.

Sn = a(rn– 1)/ r – 1   where r is greater than 1     or     a(1 – rn)/ 1 – r  where r is smaller than 1

……………………………………………………………………………………………………………………………………………………………………………………………………………………………..

F. ALGEBRA

LAW OF INDICES

an × bn              = ( a × b)n

an / bn               = ( a /b)n

√a x √b              = √ab

√a / √b              = √a/b

n√a × n√b      = n√ab

n√a /n√b       = n√a/b

LAWS OF LOGARITHM

Log b m + Log b n= Log b (m × n)

Log b m – Log b n = Log b (m/n)

Log b mp =p Log b m

Log1010 = 1

Log b N = Log N/Log b

SURDS

√a × √b = √ab (see indices above)

Note: Please extract more examples from your textbook.

FACTORIZATION

a2 – b2 = (a + b) (a – b)

a4 – b4 = (a2 – b2) (a2+ b2) = (a + b) (a – b) (a2+ b2)

QUADRATIC EQUATION FORMULA



………………………………………………………………………………………………………………………………………………………………………………………….

G.  GEOMETRY

Acute Angle =  < 90o     /      Obtuse Angle = >90o < 180o  /     Reflex Angle =  >180o < 360o     /   2 right angles =  180o

Complementary angles added together = 90o       /   Supplementary angles added together = 180o

PYTHAGORAS THEOREM

 BASIC QUICK REVISION MATHS FORMULAS & HINTS FOR WAEC EXAM

CIRCLE THEOREMS

Angles in the same segment of a circle are equal. Conversely angle subtended at the circumference of a circle by a chord or an arc is equal.

Angle in a semicircle is a right angle conversely a diameter of a circle subtends angle of 90o at any point on the circumference of the circle.

Angle subtended at the center of a circle by an arc is double the angle subtended at the circumference.

Opposite angles of a cyclic quadrilateral are supplementary i.e. their sum = 180o

When one side of a cyclic quadrilateral is produced the exterior angle formed is equal to the interior opposite angle.

THE SECOND AND LAST SET OF FORMULAS AND HINTS  INCLUDE REVISION FORMULAS FOR THE FOLLOWING

- latitude and longitude

-mensuration

-cuboid/rectangular blocks

-walls of a room

-prism/pyramid/ellipse/sphere

-right circular cylinder

-ring/annulus

-circle/sectors

-cone

-polygons

-probability

-trigonometry

-usual mathematical assumptions/other question formats
Enhanced by Zemanta