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.

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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

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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%

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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

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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

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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



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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