100 KEY QUESTION-PHRASES REGULARLY USED BY WAEC MATHS EXAMINERS…YOUR PERFORMANCE MAY DEPEND ON HOW MANY OF THEM YOU REALLY UNDERSTAND!

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 are 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 candidates principally is how to understand the meaning of the questions asked, determine the 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 key question-phrases usually used by examiners for class or private study exercises on imagination and visualization (numerically, graphically and pictorially).

 CAN YOU VISUALIZE THESE USUAL 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 INTERPRET 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 CENTRE 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 OR FRIENDS?

GOOD LUCK!

HAVE YOU READ?

CONCEPTS AND PRINCIPLES OF WAEC MATHS FOR EXAM SUCCESS?

COMING UP NEXT:

BASIC ETIQUETTE FOR PASSING WAEC AND SCHOOL MATHEMATICS  EXAMS

 

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