Formula book 2009 - Gcecompilation

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Mathematics

Important points and formulas

Third Edition (May 2009)

Content

No. Topic / sub topic 1 Natural numbers 2 Whole Numbers 3 Integers 4 Rational Numbers 5 Irrational Numbers 6 Terminating Decimals 7 Recurring Decimals 8 Significant figures 9 Decimal Places 10 Standard Form 11 Conversion Factors 12 Time 13 Percentages 14 Simple Interest 15 Compound Interest 16 Speed, Distance and Time 17 Quadratic Equations 18 Expansion of algebraic expressions 19 Factorization of algebraic expressions 20 Ordering 21 Variation 22 PYTHAGORAS' THEOREM 23 Area and Perimeter 24 Surface Area and Volume 25 Angles on a straight line 26 Vertically opposite angles 27 Different types of triangles 28 Parallel Lines 29 Types of angles 30 Angle properties of triangle 31 Congruent Triangles 32 Similar Triangles 33 Areas of Similar Triangles 34 Polygons 35 Similar Solids 36 CIRCLE 37 Chord of a circle 38 Tangents to a Circle 39 Laws of Indices 40 Solving Inequalities 41 TRIGONOMETRY 42 Bearing 43 Cartesian co-ordinates 44 Distance ? Time Graphs 45 Speed ? Time Graphs 46 Velocity 47 Acceleration 48 SETS

Page 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 5 6 6 6 6 6 7 7 7 8 8 8 9 9 10 10 11 11 11 12 12 12 13 13 13

49 Loci and construction 50 Vectors 51 Column Vectors 52 Parallel Vectors 53 Modulus of a Vector 54 MATRICES 55 The Inverse of a Matrix 56 Transformations 57 Transformation by Matrices 58 STATISTICS 59 Probability 60 Symmetry

14 14 15 15 15 15 15 16 -17 18 19 20 21

NUMBER Natural Numbers: Numbers which are used for counting purpose are called natural numbers. Ex: 1, 2, 3, 4, ................100, ................... Whole Numbers: Natural numbers including 0 are called Whole Numbers. Ex: 0, 1, 2, 3, 4, .......................... Integers: Positive natural numbers, negative natural numbers along with 0 are called integers. Ex.: ....................., -4, -3, -2, -1, 0, 1, 2, 3, 4, ...............

Rational Numbers: Numbers which are in the form

of

(q

0)

where

p

and

q

are

positive

or

negative

whole numbers are called rational numbers.

Ex:

1,

2

3,

4

-5 , 49

7 -56

.......................

Irrational Numbers: Numbers like 2 , cannot be expressed as rational numbers. Such types of numbers are called as irrational numbers.

Ex: 5 , 17 , .............

Terminating Decimals These are decimal numbers which stop after a certain number of decimal places. For example,7/8 = 0.875, is a terminating decimal because it stops (terminates) after 3 decimal places.

Recurring Decimals These are decimal numbers which keep repeating a digit or group of digits; for example 137/259,=0.528 957 528 957 528 957 ...., is a recurring decimal. The six digits 528957 repeat in this order. Recurring decimals are written with dots over the first and last digit of the repeating digits, e.g. 0.528 957

The order of operations follows the BODMAS rule: Brackets Powers Of Divide Multiply Add Subtract

Even numbers: numbers which are divisible

by 2, eg, 2, 4, 6, 8, ...

Odd numbers: numbers which are not

divisible by 2, eg; 1, 3, 5, 7 ...

Real numbers are made up of all possible

rational and irrational numbers. An integer is a whole number. A prime number is divisible only by itself and

by one (1). 1 is not a prime number. It has only two factors. 1 and the number itself. The exact value of rational number can be written down as the ratio of two whole numbers. The exact value of an irrational number cannot be written down. A square number is the result of multiplying a number by itself. Ex: 12, 22, 32, ................ i.e. 1, 4, 9, ................. A cube number is the result of multiplying a number by itself three times. Ex: 13, 23, 33, ...................... i.e. 1, 8, 27,......... The factors of a number are the numbers which divide exactly into two. eg. Factors of 36 1, 2, 3, 4, 6, 9, 12, 18 Multiples of a number are the numbers in its times table. eg. Multiples of 6 are 6, 12, 18, 24, 30, ...

Significant figures; Example; 8064 = 8000 (correct to 1 significant figures) 8064 = 8100 (correct to 2 significant figures) 8064 = 8060 (correct to 3 significant figures) 0.00508 =0.005 (correct to 1 significant figures) 0.00508 = 0.0051 (correct to 2 significant figures) 2.00508 = 2.01 (correct to 3 significant figures)

Decimal Places Example 0.0647 = 0.1 (correct to 1 decimal places) 0.0647 = 0.06 (correct to 2 decimal places) 0.0647 = 0.065 (correct to 3 decimal places) 2.0647 = 2.065 (correct to 3 decimal places)

Standard Form: The number a x 10n is in standard form when 1 a < 10 and n is a positive or negative integer.

Eg: 2400 = 2.4 x 103 0.0035 = 3.5 x 10-3

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Mathematics - important points and formulas 2009

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Conversion Factors:

Length: 1 km = 1000 m 1 m = 100 cm 1 cm = 10 mm

means kilometer means meter means centimeter means millimeter

Mass: 1 kg = 1000 gm 1 gm = 1000 mgm 1 tonne = 1000 kg

where kg means kilogram gm means gram mgm means milligram

Volume: 1 litre = 1000 cm3 1 m3 = 1000 litres

1 kilo litre = 1000 litre

1 dozen = 12

Time:

1 hour = 60 minutes = 3600 seconds 1 minute = 60 seconds. 1 day = 24 hours 1 year = 12 months

= 52 weeks = 365.25 days.

1 week = 7 days

1 leap year = 366 days 1 light year = 9.46 ? 1012 km.

Percentages: Percent means per hundred. To express one quantity as a percentage of another, first write the first quantity as a fraction of the second and then multiply by 100. Profit = S.P. ? C.P. Loss = C.P. ? S.P. Profit percentage = - ? 100

Loss percentage = - ? 100

where CP = Cost price and SP = Selling price

Simple Interest:

To find the interest:

=

100

where

P = money invested or borrowed

R = rate of interest per annum

T = Period of time (in years)

To find the amount: = +

where A = amount

Compound Interest: A = 1 + r n

100

Where, stands for the amount of money accruing after year. stands for the principal stands for the rate per cent per annum stands for the number of years for which the money is invested.

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Speed, Distance and Time: Distance = speed x time

Speed

=

Time

=

Average speed = ALGEBRA

Units of speed: km/hr, m/sec Units of distance: km, m Units of time: hr, sec

5 km / hr ? 18 = m / sec

18 m / sec ? 5 = km / hr

D S T

Quadratic Equations:

An equation in which the highest power of the variable is 2 is called quadratic equation. Thus ax2 + bx + c = 0 where a, b, c are constants and a 0 is a general equation.

Solving quadratic equations:

We can solve quadratic equation by method of,

a) Factorization b) Using the quadratic formula c) Completing the square

(a) Solution by factors: Consider the equation c ? d = 0, where c and d are numbers. The product c ? d can only be zero if either c or d (or both) is equal to zero. i.e. c = 0 or d = 0 or c = d = 0.

(b)Solution by formula:

The solutions of the quadratic equation ax2 + bx + c = 0 are given by the formula:

-? 2-4 =

2 (c) Completing the square

Make the coefficient of x2 , i.e. a = 1 Bring the constant term, i.e. c to the right side of equation. Divide coefficient of x, i.e. by 2 and add the square i.e. ( )2 to both sides of the equation.

2

Factorize and simplify answer

Expansion of algebraic expressions

+ = +

(a + b)2 = a2 + 2ab + b2

(a ? b)2 = a2 ? 2ab + b2

a2 + b2 = (a + b)2 ? 2ab

a2 ? b2 = (a + b)(a ? b)

Factorization of algebraic expressions

2 + 2 + 2 = ( + )2

2 - 2 + 2 = ( - )2

2 - 2 = + ( - )

Ordering: = is equal to is not equal to > is greater than

is greater than or equal to < is less than is less than or equal to

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