IF YOU THINK WAEC MATHS IS HELL,HERE ARE 84 STEPS TO MATHS HEAVEN (2)

THE SEVEN BRANCHES OF WAEC MATHS

 OPENING VEILS TO REVEAL NATURE OF WAEC EXAM QUESTIONS  

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14.The branches of maths are Arithmetic, Algebra,Trigonometry, Geometry, Probability, Statistics and Structure. These categorizations are important because when you are asked a question in maths you should ask yourself two questions.

a.What branch of maths is this question from?

b.What topic in that branch of maths is the question?

  Now let us look at each branch briefly.

ARITHMETIC

15.The operations of arithmetic revolve around playing with numbers by changing them from one form to another. However some people define arithmetic as the laws of numbers on business arithmetic. This may be so because arithmetic is the basis of all commercial transactions be it computations, bargaining, negotiating or counting.

16.Arithmetic is also the basis of other branches of mathematics and other subjects such as Business Studies, Economics, Accounting, Law, Engineering etc. This means that Arithmetic holds the key of operation to these branches to understand them too.

17. 2 important laws under arithmetic, which should be explained by the tutor, are:

          The rule of BODMAS

          The law of PRECEDENCE

The two are interrelated in the sense that they specify the order for calculations in maths.

18. 6 key terms commonly used for questioning under arithmetic are: EVALUATE, SIMPLIFY, FACTORIZE, CALCULATE, FIND and EXPRESS. These should also be explained by the tutor or see relevant paragraphs later  for more explanation.

ALGEBRA

19. Unlike arithmetic which deals with known numbers, this is the branch of mathematics, which deals with what are grouped as “UNKNOWNS”. This is because not everything in life is known. The interest of algebra is to seek out the unknown number with what is known. To do this, the first step is that the unknown number which is sometimes called a variable is denoted in either English or Greek alphabets. These alphabets are then developed as algebraic expressions or equations. In summary, the point to note is that unlike arithmetic that relates to calculating with numbers known or definite in values, Algebra on the other hand relates to calculating with equations containing unknown numbers But the same arithmetic rules and steps of  BODMAS and PRECEDENCE are still used. Some people see algebra as a twin brother of arithmetic or as equations, which rely on rules of arithmetic for their solutions.

20. There are 4 key terms normally used for questioning under algebra. These are: SOLVE, SIMPLIFY, PLOT/CHART and FIND.Please note that key terms for the remaining branches of maths shall be specified under another write-up titled QUESTION TYPES,VISUALIZATION AND CRYSTALLIZATION…

TRIGONOMETRY

21. Trigonometry developed in the earlier days because of the need for measurements of days and distances between two points on the surface of the earth by human beings traveling from place to place. This was done by triangles. However, it was also extended to measurements of chords for music and arcs of a circle.

22.Trigonometry tests the ability of students on the use of triangles through TRIGONOMETRIC RATIOS and IDENTITIES using the acronym known as SOHCAHTOA.

23.Trigonometry covers the calculation of trigonometric functions of a certain angle from those of other angles using such typical relationship of formulae as: SIN 2A = 2 SIN A COS A.

24.Trigonometry tests the ability to understand the relationship between ratios of angles e.g. Tan Q = Sin Q/Cos Q.

25.Trigonometry also tests the knowledge of trigonometry tables and the ability to determine the form of angle ratios in various quadrants. It also shows how to plot, sketch or calculate values and measurements on Sine or Cosine curves.

GEOMETRY

26.This is the earliest developed branch of maths. It is the study of different shapes of figures and proportions of space and object. It developed to address the problems of shapes and beauty.

27.Geometry covers three major areas –plane, solid and analytical.

28.“Plane” refers to 2—dimensional flat surface e.g triangles and squares.

29.“Solid” refers to 3—dimensional objects i.e those with length, breadth and height e.g. Cuboids, Cylinder, Cone, Pyramid and Sphere.

30. The usual question on “Plane” geometry relates to length, breadth and areas of physical objects whereas, “solid” geometry include volume as an additional measure. 

31.“Analytical” usually refers to the addition of algebra to plain or solid geometry.

32.Under geometry there are many theories which student might be asked to “prove” they might also be asked to “trace” the shape of figures based on the principles of “Locus” of a point using mathematical instruments.

  PROBABILITY

33. We live in a world of uncertainties. A world in which no one knows what will happen the next minute. Our lives are governed by chances, which are unknown to us though they are clearly known to God. The study of probability developed in relations to things that are surround us. Probability is likened to a game of likelihood and revolves around the extent to which an event is likely to occur. It is measured by the ratio of the number of the favorable/likely cases to the number of the possible cases.

34. Probability is therefore a ratio of measurement and has a value that lies between 0(that is, the event not occurring at all) expected) and 1(tha is,the event occurring as expected). Re-stated in another way when the probability is zero it means that the event will not happen or take place, but when the probability is one it follows that the event will  certainly happen. For example, the probability that the sun will rise tomorrow is 1.

35. To measure probability, data must be collected, arranged and processed e.g the number of times rain falls in a month. Secondly, the data can be presented in various ways such as charts, figures; tables etc for explanatory purposes. Even graphs can be used. After presentation; those who want to use the data will then study and analyze them in terms of locations within the total set and according to dispersal from one another. Thereafter the data is interpreted for decision – making purposes. However when the data is used for prediction purposes if is said to be used for “Regression” and “Extrapolation”. The process then moves from collecting data to predicting future events. Sometimes people say probability is used for prophesy or for foretelling  future events so that human beings can take measures of safety before unfortunate events come upon them.

36.The different types of probability are: Experimental, Theoretical, Mutually exclusive probability and Independent events. (go over this again in your text books or seek  for assistance from your tutors). However take note of the following expressions and know their implications clearly.

               Mutually exclusive events (one event excludes the other e.g. positions in an exam)

               Mutually independent event (one event is not affected by another e.g. tossing a coin many times)

               Dependent event (when the outcome of an event depends on another. E.g.

              passing Jamb or not will affect your admission into a university.)

 STATISTICS

37. To prophesy under probability, we have to gather data which is then processed to predict an outcome. The data we gather is called statistics. It is therefore obvious that probability and statistics are related to one another.  

38. Data gathered as said earlier can be used to describe the habits shown by a set of information gathered. The principal measure is called a MEAN and others are the MODE, the MEDIAN, CENTRAL TENDENCY, VARIANCE and STANDARD DEVIATION. (your textbooks or tutors again please). These measurements are called descriptive statistics. Another type is called theoretical statistics, which depends on an  advanced form of mathematics called Probability and Games theory. In theoretical statistics the laws of probability are merged with statistical methods, to infer the nature or characteristic or ways of behavior of the composition of the population from the simple data. You may ask what statistics are used for, there are 3 major uses, and these are

             Scientific research, commercial and industrial activities.

             Social uses like elections and population census

             Inferences and predictions using estimation from arithmetic.

 STRUCTURE

39. This is the last and newest branch of mathematics relating to set theory and logic.

TO BE CONTINUED. WE STILL HAVE 45 STEPS TO GO.