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.
- AREA OF THE CURVED SURFACE OF A CYLINDER
- LENGTH OF THE BASE RADIUS OF A CYLINDER
- MODAL CLASS
- VOLUME OF A RIGHT-SIDED CONE
- CYLINDRICAL CONTAINER
- CYCLIC QUADRILATERAL
- MINOR SECTOR OF A CIRCLE
- VERTEX OF A CONE
- HEMISPHERICAL BASE
- ARC WHICH SUBTENDS ANGLE AT CENTRE OF A CIRCLE
- HOLLOW CYLINDER/SPHERE
- ARC OF RADIUS
- RADIUS OF A TUBE
- PYTHAGORAS RULE
- PARALLEL OF LATITUDE
- ELEMENTS OF A SET/SUBSET
- COMPLEMENTS OF THE SET
- SECTOR OF A CIRCLE
- CENTER OF PARALLEL OF LATITUDE
- SHADED PORTION OF TWO CIRCLES OR OF A QUADRILATERAL
- LINEAR GRAPH
- PERCENTAGE ERROR
- VERTICAL CROSS SECTION
- HORIZONTAL CROSS SECTION
- FREQUENCY OF SEQUENCE
- SUM OF DEGREES
- ANGLE SUBTENDED AT THE CENTER OF THE EARTH
- ARC OF THE EQUATION
- SECANT VALUE
- OPPOSITE AND ADJACENT SIDES
- LOCUS OF POINTS
- CYCLIC QUADRILATERAL
- RIGHT CIRCULAR CYLINDER
- WALLS OF A ROOM
- CUBOID/RECTANGULAR BLOCK
- LINEAR SEQUENCE
- NAUTICAL MILE
- STANDARD ZERO
- BY SUBSTITUTION
- CORRECT TO 2 SIGNIFICANT FIGURES
- SHORTEST DISTANCE BETWEEN TWO POINTS
- THE NTH TERM
- CORRECT TO I DECIMAL PLACE
- DIFFERENCE IN LONGITUDE
- SATISFY INEQUALITIES
- AREA OF CURVED SURFACE
- ANGLE OF SECTOR OF AN ANGLE
- PERPENDICULAR TO/FROM
- AREA OF THE BASE OF THE CONE
- ILLUSTRATE ON GRAPH PAPER AND SHADE THE REGION
- DRAW THE GRAPH OF THE RELATION -2 × 2
- USING THE GRAPH TO SOLVE AN EQUATION
- ANSWER TO THE NEAREST 100KM
- DISTANCE BETWEEN TWO POINTS OF LATITUDE USING A RULER AND COMPASS
- CONSTRUCTING A TRIANGLE OR TRAPEZIUM OR A RECTANGLE
- THE LOCUS (LOCI) OF POINTS EQUIVALENT FROM 2 POINTS OR FROM 2 LINES WHICH PASS THROUGH A TRIANGLE
- LABELING POINTS OF INTERSECTION
- USING THE OGIVE 50TH PERCENTILE
- CALCULATING THE ANGULAR DISTANCE
- RANGE OF DISTRIBUTION
- LENGTH OF CORD
- SURFACE AREA OF A HOLLOW CYLINDER OR OF A CYLINDER CLOSED AT ONE END
- VOLUME OF A CONE
- CUTTING A SECTOR OF A CIRCLE TO FORM A CONE
- CALCULATING THE LENGTH OF ARC WHICH SUBTENDS AN ANGLE OF 700
- THE SCOPE OF A GRAPH
- DERIVATION OF EQUATIONS WHOSE COEFFICIENT ARE INTEGERS AND WHICH HAS ROOTS OF 1/2 & -7 (AS EXAMPLE)
- ARC OF A RADIUS
- SOLUTION SET OF INEQUALITIES
- AREA OF A SPHERE OF RADIUS CM
- AREA OF A CYLINDRICAL CONE CLOSED AT BOTH ENDS
- PRODUCT OF TWO % ERRORS
- VOLUME OF A RIGHT-ANGLED CONE
- VOLUME OF A HEMISPHERICAL TANK
- CONSTRUCTION OF A GROUPED DATA
- UNDEFINED EXPRESSION FOR VALUES OF Y
- A CYLINDER OF BASE RADIUS 4 GIVEN AT ONE END
- RATIO OF THE BASE OF A CYLINDER TO THAT OF ITS CURVED SURFACE
- EVALUATION WITH OR WITHOUT MATHEMATICAL TABLES
- CONVERSION OF 80KM/HR TO METERS/SECOND
- FINDING THE AREA OF THE ENCLOSED REGION OF 2 SEMI CIRCLES
- PERIMETER OF THE REGION
- FINDING THE COORDINATES OF A POINT
- COMMON RATIO OF A GP
- CUMULATIVE FREQUENCY CURVE OF DATA
- CLASS BOUNDARIES OF DISTRIBUTION
- SUBJECT OF THE FORMULA
- GRADIENT OF A LINE
- DIRECT/INVERSE VARIATION
- CALCULATING IPQI
- MEANING OF “TOSSING A FAIR DICE”
- MEANING OF “VERTICAL WALL OR HORIZONTAL GROUND”
- MEANING OF “CAPACITY OF” (VOLUME)
- MEANING OF “LINE OF SIGHT”
- MEANING OF “FLIGHT OF A BIRD OR OF AN EAGLE OR AN AEROPLANE”
- MEANING OF “TWO SHIPS LEFT PORT”
- MEANING OF FLIGHT DUE NORTH (ALONG THE MERIDIAN)
- 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?
HAVE YOU READ?
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BASIC ETIQUETTE FOR PASSING WAEC AND SCHOOL MATHEMATICS EXAMS