IF YOU THINK WAEC MATHS IS HELL,HERE ARE 84 STEPS TO MATHS HEAVEN (4)

[caption id="attachment_2628" align="alignleft" width="500"] WAEC EXAM HALL[/caption]

100 EXAMPLES OF QUESTION-PHRASES USED BY WAEC IN MATHS EXAMS

QUESTION  TYPES, VISUALIZATION & CRYSTALLIZATION

46. Learning maths through concepts and rules will be difficult without visualization of concepts in the mind. Learning maths vocabulary makes little practical sense to a student when learnt by itself. For example “numerators” or “denominators” are famously important yet they serve no practical purpose for most learners except when they provoke thoughtfulness and program understanding. Most vocabulary and rules lead to what is called inert knowledge .But students can make sense with a slight shift of emphasis to VISUALIZATION as a central concept.

47. The difference between a ”good” and “bad” maths  student is the amount of visualization each brings to bear on the subject. Non-performing students need careful help to visualize. Apart from the activities listed under 44 above, lots of instructional objects/educational aids need to be used in the classroom. Visualization crystallizes what can be called “PICTURES IN THE MIND”. Class activities directing students on how to visualize questions and concepts IN THE MIND should be emphasized with many instructional materials.

48. The problem that students face when they are confronted with maths questions are mostly in 3 areas:

              a. Inability  understanding the questions asked.

              b. Lack of knowledge of how to start or how to proceed in finding a solution to questions.

              c. Ignorance of what is really expected by the examiner.

49. To overcome these problems there is also a need for students to get familiar with mathematical question phrases Since maths is a science  of precision and exactness, the words used in forming the  questions or the concepts combined within each questions show or require specific meanings  or visualizations which must be  understood by students. The terms usually as follows:

 50. CALCULATE: Ascertain the solution by maths methods you know

51. CONSTRUCT: Form by putting together the part, build up, fit together, frame according to certain conditions.

52. DETERMINE: Settle, decide what is to be done, ascertain or calculate.

53. DRAW: Make a neat pencil figure, clearly or neatly.

54. EVALUATE:  Determine the value or the amount.

55. EXPRESS: State definitely (or show clearly)

56. FACTORIZE: turn into factors or break the multiples into smaller units.

57. FIND: Discover, seek out or obtain by search.

58. LOCATE: Find the place or discover the exact place or determine the where about.

59. MAKE A SUBJECT: Separate out, make to stand  alone or express in terms of others.

60. MEASURE: State the size or weight or ascertain the amount by quantifying.

61. PROVE: Ascertain as a truth by argument or otherwise i.e. show that something is true or not.

62. SHOW: Present a better view, allow or cause to be seen.

63. SIMPLIFY: Make less difficult or easier to understand.

64.  SKETCH: Give only a rough line of a figure of it. Make out a rough finished drawing. 

65. SOLVE: find the answer to the problem.

66. In the exam hall the problem of students and candidate principally is how to understand the meaning of the questions asked, determine applicable concepts and  visualize what principles are been tested. There is also a general lack of ability to answer questions orderly or meaningfully.

67. Please find below a list of 100 exam question-phrases usually used by examiners for class or private study exercises on imagination and visualization (numerically, graphically and pictorially).

 CAN YOU VISUALIZE THESE  WAEC MATHS QUESTION-PHRASES/CONCEPTS IN YOUR MIND?

MATHEMATICS IS ALL ABOUT PSYCHOLOGY.BUT YOUR UNDERSTANDING IS ALSO USUALLY AFFECTED BY HOW VAST YOUR ENGLISH VOCABULARY IS.IT IS NOT JUST WHETHER YOU ARE BRILLIANT OR NOT. IT IS IMPORTANT THAT YOU CAN INTERPRETE FACTS, FIGURES & CONCEPTS CONTAINED IN THE PHRASES BELOW.

1. AREA OF THE CURVED SURFACE OF A CYLINDER


2. LENGTH OF THE BASE RADIUS OF A CYLINDER


3. MODAL CLASS


4. VOLUME OF A RIGHT-SIDED CONE


5. CYLINDRICAL CONTAINER


6. CYCLIC QUADRILATERAL


7. MINOR SECTOR OF A CIRCLE


8. VERTEX OF A CONE


9. HEMISPHERICAL BASE


10. ARC WHICH SUBTENDS ANGLE AT CENTER OF A CIRCLE


11. HOLLOW CYLINDER/SPHERE


12. ARC OF RADIUS


13. RADIUS OF A TUBE


14. PYTHAGORAS RULE


15. PARALLEL OF LATITUDE


16. ELEMENTS OF A SET/SUBSET


17. COMPLEMENTS OF THE SET


18. SECTOR OF A CIRCLE


19. CENTER OF PARALLEL OF LATITUDE


20. SHADED PORTION OF TWO CIRCLES OR OF A QUADRILATERAL


21. LINEAR GRAPH


22. PERCENTAGE ERROR


23. VERTICAL CROSS SECTION


24. HORIZONTAL CROSS SECTION


25. FREQUENCY OF SEQUENCE


26. SUM OF DEGREES


27. ANGLE SUBTENDED AT THE CENTER OF THE EARTH


28. ARC OF THE EQUATION


29. SECANT VALUE


30. RIGHT-ANGLED/ISOSCELES/SCALENE/TRIANGLE


31. RATIONALIZE/SIMPLIFY


32. OPPOSITE AND ADJACENT SIDES


33. LOCUS OF POINTS


34. CYCLIC QUADRILATERAL


35. RIGHT CIRCULAR CYLINDER


36. WALLS OF A ROOM


37. CUBOID/RECTANGULAR BLOCK


38. LINEAR SEQUENCE


39. NAUTICAL MILE


40. STANDARD ZERO


41. BY SUBSTITUTION


42. CORRECT TO 2 SIGNIFICANT FIGURES


43. SHORTEST DISTANCE BETWEEN TWO POINTS


44. THE NTH TERM


45. CORRECT TO I DECIMAL PLACE


46. DIFFERENCE IN LONGITUDE


47. SATISFY INEQUALITIES


48. AREA OF CURVED SURFACE


49. ANGLE OF SECTOR OF AN ANGLE


50. PERPENDICULAR TO/FROM


51. AREA OF THE BASE OF THE CONE


52. ILLUSTRATE ON GRAPH PAPER AND SHADE THE REGION


53. DRAW THE GRAPH OF THE RELATION -2 × 2


54. USING THE GRAPH TO SOLVE AN EQUATION


55. ANSWER TO THE NEAREST 100KM


56. DISTANCE BETWEEN TWO POINTS OF LATITUDE USING A RULER AND COMPASS


57. CONSTRUCTING A TRIANGLE OR TRAPEZIUM OR A RECTANGLE


58. THE LOCUS (LOCI) OF POINTS EQUIVALENT FROM 2 POINTS OR FROM 2 LINES WHICH PASS THROUGH A TRIANGLE


59. LABELING POINTS OF INTERSECTION


60. USING THE OGIVE  50TH PERCENTILE


61. CALCULATING THE ANGULAR DISTANCE


62. RANGE OF DISTRIBUTION


63. LENGTH OF CORD


64. SURFACE AREA OF A HOLLOW CYLINDER OR OF A CYLINDER CLOSED AT ONE END


65. VOLUME OF A CONE


66. CUTTING A SECTOR OF A CIRCLE TO FORM A CONE


67. CALCULATING THE LENGTH OF ARC WHICH SUBTENDS AN ANGLE OF 700


68. THE SCOPE OF A GRAPH


69. DERIVATION OF EQUATIONS WHOSE COEFFICIENT ARE INTEGERS AND WHICH HAS ROOTS OF 1/2 & -7 (AS EXAMPLE)


70. ARC OF A RADIUS


71. SOLUTION SET OF INEQUALITIES


72. AREA OF A SPHERE OF RADIUS CM


73. AREA OF A CYLINDRICAL CONE CLOSED AT BOTH ENDS


74. PRODUCT OF TWO % ERRORS


75. VOLUME OF A RIGHT-ANGLED CONE


76. VOLUME OF A HEMISPHERICAL TANK


77. CONSTRUCTION OF A GROUPED DATA


78. UNDEFINED EXPRESSION FOR VALUES OF Y


79. A CYLINDER OF BASE RADIUS 4 GIVEN AT ONE END


80. RATIO OF THE BASE OF A CYLINDER TO THAT OF ITS CURVED SURFACE


81. EVALUATION WITH OR WITHOUT MATHEMATICAL TABLES


82. CONVERSION OF 80KM/HR TO METERS/SECOND


83. FINDING THE AREA OF THE ENCLOSED REGION OF 2 SEMI CIRCLES


84. PERIMETER OF THE REGION


85. FINDING THE COORDINATES OF A POINT


86. COMMON RATIO OF A GP


87. CUMULATIVE FREQUENCY CURVE OF DATA


88. CLASS BOUNDARIES OF DISTRIBUTION


89. SUBJECT OF THE FORMULA


90. GRADIENT OF A LINE


91. DIRECT/INVERSE VARIATION


92. CALCULATING IPQI


93. MEANING OF “TOSSING A FAIR DICE”


94. MEANING OF “VERTICAL WALL OR HORIZONTAL GROUND”


95. MEANING OF “CAPACITY OF” (VOLUME)


96. MEANING OF “LINE OF SIGHT”


97. MEANING OF “FLIGHT OF A BIRD OR OF AN EAGLE OR AN AEROPLANE”


98. MEANING OF “TWO SHIPS LEFT PORT”


99. MEANING OF FLIGHT DUE NORTH (ALONG THE MERIDIAN)


100. STANDARD DEVIATION OF A GROUPED DATA          

CAN YOU IMAGINE, EXPLAIN OR DRAW YOUR INTERPRETATION OF THESE QUESTION-PHRASES TO A STUDY GROUP OF YOUR CLASSMATES?


GOOD LUCK!