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

[caption id="attachment_4440" align="alignleft" width="286"] 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 = 1^st 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 =  < 90^{o     /}      Obtuse Angle = >90^o < 180^{o  /}     Reflex Angle =  >180^o < 360^{o     /}   2 right angles =  180^o

Complementary angles added together = 90^{o       /}   Supplementary angles added together = 180^o

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 90^o 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 = 180^o

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

IF YOU THINK WAEC MATHS IS HELL,HERE ARE 84 STEPS TO MATHS HEAVEN (7)

BASIC QUICK REVISION MATHS FORMULAS & HINTS FOR WAEC EXAM

PREAMBLE

Most of the material in this write-up are basic indeed.However,those still struggling with foundation maths or maths clinics will find them very useful.Going through the write-up it will be very obvious that the formulas and hints were identified and listed using the 7 branches of maths as earlier listed by us…


We have listed 7 class activities or private study uses for the content of this write up and we shall be willing to implement them in any school in Nigeria. Please note, however, that another list made up of  slightly different formulas/ hints  of a slightly improved standard will come on line soonest to complement our efforts in these areas.

ARITHMETIC (STRUCTURE EXCLUDED)

 THE BINARY SYSTEM

 A number in Base 2 is called a BINARY NUMBER

A binary number is a sum of multiples of powers of 2

In base 2 we have only two numbers 0 & 1 to work with

To express a binary number as a decimal number write the binary number as a sum of multiples of 1, 2, 4, 8, 16 etc

WORD PROBLEMS AND FRACTIONS

You should be able to express word problems in numerical terms

You should be able to  simplify expressions having brackets and fractions

NON – RATIONAL NUMBERS AND APPROXIMATIONS

Rational numbers consist of all counting numbers, integers and fractions (positive and negative)

A class of non – rational numbers include square roots of natural numbers which are not perfect squares

An important example of non – rational number is π (PI)

Approximations of square roots which are non – rational can be obtained by using trial and error method.

 ALGEBRA

FACTORIZATION

You should be able to factorize expressions of the form a² – b². Same for

 a² + 2ab + b²

You should be able to factorize quadratic expressions by completing the square.

SIMPLE EQUATIONS INVOLVING FRACTIONS

Find the L.C.M of all denominators.

Then multiply each term in the equation by this L.C.M.

 Simplify and solve the resulting equation.

 SIMULTANEOUS LINEAR EQUATIONS

You should be able to solve a given system of linear equations by graph, by elimination or by substitution methods

To solve using the graph, we will first draw two lines or graphs for the equations given. The point of intersection of the two lines  is the solution. If the two graphs coincide, then there is an infinite number of solutions.

The graphical method is the slowest method.

VARIATION

Direct Variation: A varies directly as B can be expressed as A α B means A α B means A=K/B  where K is known as the constant of the variation.

 Inverse Variation: A varies inversely as B can be expressed as A α 1/B i.e. A=K/B where K is also the constant

 Joint Variation: A jointly varies directly as B and inversely as the square of C= A α B/ C²
or A = K/ C²   

Partial Variation: Suppose A varies directly as B and partly as the square of C then A can be broken into parts A₁ α A₂ such that A =  A₁+A₂ where A₁ = k₁ B and A₂ = k₂ C^2. Then A = K₁ B + K₂ C²

    CHANGE OF SUBJECT IN FORMULA

 A formula is an equation containing two or more variables and it describes how the variables are related.

We solve many problems in maths by the use of formulae But we often need to simplify by rearranging it to make one of the variables the subject of the formula. Making a specified variable the subject of the formula simply means expressing the specified variable in terms of the other variables. When values are given for other variables in a formula then we can find the value of any of the other variables.

 GEOMETRY/ MENSURATION

 VIEWS AND PLANS

 You should be able to draw common solids with your hands (free hand drawing).

 One way of drawing a solid shape is known as the method of Parallel Projection.

 You should also be able to draw views and plans of common solids. We have the Top View, Side View, Front View and Back View.

 In Parallel Projection, Vertical Lines are always drawn vertical, parallel edges are always drawn parallel, perpendicular lines are not always drawn perpendicular and lines which have equal lengths in the solids may not have equal lengths in the drawing.

 When edges and faces of the solid that are equal in size are drawn to have equal sizes we call this Proportional Drawing. If we combine Parallel Projection with Proportional Drawing then we call this method Orthogonal Projection. Orthogonal projection therefore means drawing to scale.

 SIMPLE CONSTRUCTIONS

 Use sharp pencil and ruler with straight edges and compasses that are not loose.

 Make, clear, thin points of intersection as opposed to an “area of intersection”

 You can copy angles, bisect angles, construct perpendicular bisector of a line segment, construct a perpendicular line to a given line segment from a point either on it or outside it. You can also construct medians and altitudes of triangles, construct circumscribed and inscribed circles of triangles or construct special angles of 60, 120, 30, 15, 90, 45 or any other combination.

 SIMILAR FIGURES AND ENLARGEMENT

 Shapes of the same sizes are similar

 All squares are similar

 All equilateral triangles are similar

 All cubes are similar

 All n-sided regular polygons are similar

 Triangles having equal corresponding angles (i.e. equiangular triangles) are similar.

 Triangles whose corresponding sides are in a constant proportion are similar. What is important about similar figures is the shape and not the size

 In scale drawing the drawing may be smaller (reduction) or bigger (enlargement)

 If the ratio of corresponding sizes of two shapes is a constant and the corresponding angles are equal then the two shapes are similar.

 Any two circles or spheres are “similar”.

 The corresponding arcs subtending equal angles at the centre of a sphere are similar and they are in constant ratio of their radii. (This is the idea behind π)

 CONCLUSION

 If two figures are similar with scale factors 1: a then the length in the second figures is “a” times the corresponding figure and the volumes in the second figure is “a” times the corresponding volume in the first figure.

 FURTHER MENSURATION

 TRIANGLE, PARALLELOGRAM, RHOMBUS(KITE) AND TRAPEZIUM

 Any side of a triangle can serve as it base with a chosen corresponding height when calculating its area.

 We can calculate the area of a triangle if we know its base and its height or two of its sides and the included angle

 We can calculate the area of a parallelogram if we know its base and its height orits sides and angles or

the diagonals in the case of a rhombus. (Note that the diagonals of a rhombus divides it into equal triangles. Note also that a kite is a rhombus)

 The area of a rhombus = ½ of the product of its diagonals.

 The area of a trapezium is equal to half of all the product of the sum of the parallel sides and the perpendicular distances between them. Or A = ½ (sum of parallel sides) × perpendicular distance between them

CIRCLES

 Area of circle= πr²

 Circles having the same centre are called concentric circles and the area between two concentric circles is called an annulus

 A semi-circle is half of a circle and a quadrant is one quarter of a circle.

 The area of an annulus is equal to the difference between the areas of the two circles.

 TRIGONOMETRICAL RATIOS







c= HYPOTENUSE(H),    a= OPPOSITE(O),    b= ADJACENT(A)

The sine of an angle included in a right- angled triangle is the ratio of the length of the opposite side to the   hypotenuse i.e. Sin X^O = O/H (SOH)


 The sine of an angle is also equal to the cosine of its complement.

 The cosine of an acute angle in a given right-angled triangle is the ratio of the length of the adjacent side to the hypotenuse i.e Cos X^O = A/H (CAH)

The tangent of an acute angle in a given right-angled triangle is the ratio of the length of the opposite side to the adjacent side of the triangle i.e. Tan X^O = O/A (TOA)

Note also that Tan X^O = sine x^o / cos x^o   = O/H x A/H = O/H × H/A = O/A

The first 3 formulas  under Trigonometry are also labeled as SOHCAHTOA

 PYTHAGORAS THEOREM

 Hypothenuse² = (opposite)² + (Adjacent)²

 PROBABILITY

 Usually expressed as a fraction.  If required, this fraction can be converted to a % or decimal.

 Probability = No of required outcomes/No of possible outcomes

 For two events A and B that are mutually exclusive, the probability that event A or B  will occur = P(A) + P(B). And the probability that event A and B occurs = P(A) × P(B).

 STATISTICS

 You should be able to present information as a frequency table, bar chart, line graph or pie chart or present it as a pictogram.

 Measures of average include the mode, median and mean.

 Where the number of data is even the median is calculated by dividing the sum of the two middle scores or calculated as ½ (nth)score/2  + (n+2)th score/2

Where n is odd then the median is the (n + 1)th score/2

 MODE

 Where the observation have been arranged in order of magnitude the mode can be determined from

the frequencies in a frequency table.

 the lengths of the line in a line graph.

 the lengths of the bars in a bar chart

 the sizes of the sectors in a pie chart

 the numbers of pictures in a pictogram

 MEDIAN

 The median can be determined from

 the data arranged in order of magnitude

 the frequency distribution

 the cumulative frequency distribution

MEAN

 If the mean is given and the number of scores in the data is known, then the total sum of all the data can be determined by multiplying the mean by number of scores.

 The sum of deviation from the mean is always zero.

 The range indicates the amount of Speed in the distribution of only given set of data. ( It is also the difference between the highest value and the lowest value)

 

IF YOU THINK WAEC MATHS IS HELL,HERE ARE 84 STEPS TO MATHS HEAVEN (5)

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THOSE WHO FAILED WAEC MATHS ALSO MISSED THESE KEY AREAS IN

THEIR PREPARATIONS!

1.WAEC MATHS FORMULAS, SIGNS,NOTATIONS,SYMBOLS AND HINTS.

2.THE SIX PROCEDURAL STEPS FOR  SOLVING ALL WAEC MATHS  QUESTIONS (VERY IMPORTANT)!

Now lets explain these two a bit more as follows:

 RECOGNITION / IMPORTANCE OF MATHS  FORMULAS, SIGNS, SYMBOLS,NOTATIONS & HINTS

68. A maths formula is a set of rules expressed in symbols or as an acronym for simplification purposes. A formula is a shorthand expression of a mathematical relationship which often is the master key for finding solutions. Since a maths formulas are often tools for solutions the best attitude for students is not to dread or avoid them but to develop familiarity with them.

69. Similarly students need to be familiar with maths signs, symbols, notations and hints as would be indicated later in this write-up. The table below points to the most important areas for fishing for relevant formulas during private studies e.t.c.

S/N	AREA OF MATHS	AREA OF KEY FORMULAS(FOR SSS)
1/2	ARITHMETIC/STRUCTURE	The laws of indices, Logarithm, Series and formulas relating to  business arithmetic.
3	ALGEBRA	The  “almighty formula” and identity relations.
4	TRIGONOMETRY	Trigonometrical ratios, Pythagoras and related theorems.
5	GEOMETRY	Mensuration formulas for plane and spherical geometrical including circles.
6/7	PROBABILITY& STATISTICS	Formulas for sum of probability, and likelihood estimates, mean, mode, median, quartile, variances and standard deviations.

70. Let’s refer a bit to signs and symbols in maths. One is bound to ask what their uses are because  lots of  misconception and phobia are attached to them by students. Tutors must therefore  spend some time explaining  their utility during exams,tests or homework to students. The purpose shall be to chip off  part of the phobia and fear fear and let them understand that there is nothing really special or difficult about mathematical signs and symbols. Students need to understand that they are just representations adopted as shorthand to quicken and simplify the process of computation in maths. However, after a long period, regularity, frequency and consistency of use, these signs and symbols became standard signs for specific purposes in the history of mathematics e.g. “∑” (sigma) which has become a standardized sign for summation or “θ”(theta) which has come to represent the sign for a regular angle. As stated earlier, they vary importantly because they have helped to determine or get many formulas defined or expressed through them. Some of the commonest mathematical, signs, symbols notations and hints have been listed for further reference by students.

a. Key mathematical signs, symbols. and notations

b. Basic quick revision formulas & hints  for WAEC maths clinic or Js3 exams

c.  Senior School Revision formulas and hints

Due to the length of b and c above they have been separated and shall be published as whole units for reference purposes.

KEY MATHEMATICAL SIGNS, SYMBOLS AND NOTATIONS

71. Apart from popular signs such as  +,  -,  ×,  =,  >,  <,  ≥,   ≤,  √, % we also have =, ∑, α, =>, ↔,è, Π, {}, Ł, ι, Δ, /. Please spend some time  to searching for their meanings. You should not wait to be spoon-fed all the time. We are already familiar with most of them or are we not?

72. Students should also know the signs and symbols used to represent the following words even though many relate more to the sciences. These include meter, kilogram, seconds, radian, Newton joule, watt, volt, ohm, Faraday, hertz, degree, Celsius, square meter, per cubic meter, etc.

73. Note that a full stop is written after symbols for units except when they occur normally at the end of the sentence. Note that symbols for units do not have plural forms e.g. 40 kilogram. Also pay close attention to the most popular Greek alphabets such as:

α= alfa or alpha =a, β= beta =b, γ= gama or gamma = g, Δ= delta = d, π=pi  = p, ∑= sigma =s, Θ= theta or teta = th, Φ=phi = f, Ω= omega = oi

Please  also note that  alphabets  have their capital and small letter forms which are mixed above. But curiously the capital and small forms don’t usually look alike.

74. The seven different branches of maths have their different symbols e.g . statistics have the following:

X-sample or arithmetic mean, Π – mean of population, S – standard deviation or sample, S²-variance of sample, Б -standard deviation, б²-variance of population.

PLEASE NOTE THAT MANY OF THESE SIGNS,HINTS,SYMBOLS ARE TO BE FOUND IN THE LISTS OF FORMULAS AND HINTS TO BE PUBLISHED  LATER ON THIS WEBSITE.


PROCEDURAL STEPS FOR  SOLVING WAEC MATHS PROBLEMS (VERY IMPORTANT!)

  75. STEP 1: IDENTIFY The branch of mathematics, key concepts and question phrase from the problem given. This is a mental effort  which should take a few seconds only.

  76. STEP 2: RE-STATE the relevant facts given starting with the phrase “GIVEN THAT …”in most cases.

Here you are only restating facts from the question without solving it but you will get marks in a theory examination paper for doing the obvious!

77. STEP 3: INTERPRETE The facts given into a numerical equation on a drawing or a pictorial expression if not already given and in most cases SIMPLIFY the mathematical expression further for  the next step you are likely to take..

78. STEP 4: APPLY the relevant formula after determining whether there is a formula applicable to the simplified form to get a solution. You may state the formula as follows “using the formula which states that…..”

79. STEP 5: COMBINE Your knowledge of arithmetical and algebraically rules with the simplified facts, formula or theory from step 4 to get an answer.

80. STEP 6: STATE your answer clearly on a different line .Don’t forget the unit of measurement such as m² or km or cm³

CONCLUSION:

81. TO PASS WAEC MATHS

Know the branches of maths

Understand the concepts .


Know the question types.

Develop capability for recognizing  signs, symbols and notations.

Memorize as many of the formulas  and hints as you can and know how and when they can be applied.

Practice the 6 procedural steps outlined above.

Having mastered these six steps you can crown it all with continuous practice. But note that  engaging in continuous practice of math as many tutors would say without  grounding yourself in what maths is all about is an act of deceit capable of limiting  your success.


 Steps 82 to 84 have been separated and transferred to


BASIC ETIQUETTE FOR WAEC MATHS


They are however summarized as follows:


82.Certain student  practices usually  found pleasing to WAEC  maths examiners

83. Additional points to note for WAEC maths studies.

84. Topics identified by WAEC experts which might be useful for private studies

OUR "84 STEPS" TERMINATES HERE. BUT WE  HAVE ADDITIONAL HELPFUL NOTES ON WAEC MATHS FOR YOU.SO PLEASE READ ON.

THANK YOU AND GOOD LUCK.

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!