JKSSB EXAMS GENERAL MATHEMATICS (ARITHMETIC) EBOOK BY KASHMIR STUDENT
CONTENTS:-
Chapter 1: NUMBER SYSTEM, HCF & LCM
Chapter 2: SIMPLIFICATION
Chapter 3: RATIO, PROPORTION & PARTNERSHIP
Chapter 4: AVERAGE, PROBLEM ON AGES
Chapter 5: PERCENTAGE, PROFIT & LOSS
Chapter 6: TIME, SPEED & DISTANCE
Chapter 7: MIXTURE & ALLIGATION
Chapter 8: TIME & WORK
Chapter 9: INTEREST
Chapter 10: MENSURATION
Chapter 11: DATA INTERPRETATION
Chapter 1: NUMBER SYSTEM, HCF & LCM
NUMBER SYSTEM
The ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are called digits, which can represent any number.Natural Numbers : These are the numbers (1, 2, 3, etc.) that are used for counting.
Even numbers : Natural numbers which are divisible by 2 are even numbers.
Odd numbers : Natural numbers which are not divisible by 2 are odd numbers.
Prime Numbers : Natural numbers which have exactly two factors, i.e., 1 and the number itself are called prime numbers. The lowest prime number is 2. 2 is also the only even prime number.
Whole Numbers : The natural numbers along with zero (0), form the system of whole numbers.
Integers : The number system consisting of natural numbers, their negative and zero is called integers.
Real Numbers : All numbers that can be represented on the number line are called real numbers.
Real numbers = Rational numbers + Irrational numbers.
Rational numbers : Any number that can be put in the form of p/q, where p and q are integers and q not = 0 , is called a rational number. It is denoted by Q.
Zero (0) is also a rational number.
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FACTORS
A number may be made by multiplying two or more other numbers together. The numbers that are multiplied together are called factors of the final number.
Factors of 12 = 1, 2, 3, 4, 6, and 12.
All the numbers have a factor of one.
Common factor : A common factor of two or more given numbers is a number which divides each given number completely. Common factor of 12 and 18 are 1, 2, 3, 6.
Co-prime numbers : Two or more numbers that donot have a common factor are known as co-prime or relatively prime.
For example : 4 and 15 are Co-prime numbers.
The product of two numbers :
H.C.F. of numbers × L.C.M. of numbers = Product of numbers
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Chapter 2: SIMPLIFICATION
BRACKETS
Types of brackets are :
(i) Vinculum or bar –
(ii) Parenthesis or small or common brackets : ( )
(iii) Curly or middle brackets : { }
(iv) Square or big brackets : [ ]
The order for removal of brackets is (), {}, []
‘BODMAS’ Rule
Now a days it becomes ‘VBODMAS’ where,
‘V’ stands for “Vinculum”
‘B’ stands for “Bracket”
‘O’ stands for “Of”
‘D’ stands for “Division”
‘M’ stands for “Multiplication”
‘A’ stands for “Addition”
‘S’ stands for “Subtraction”
Same order of operations must be applied during simplification.
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Chapter 3: RATIO, PROPORTION & PARTNERSHIP
RATIO
The ratio of two terms ‘x’ and ‘y’ is denoted by x : y.
Compound ratio : The compound of a : b and c : d is ac : bd
The duplicate ratio of x : y is x2 : y2.(raised power 2)
The triplicate ratio of x : y is x3 : y3.(raised power 3)
Inverse ratio Inverse ratio of x : y is y : x.
PROPORTION
When two ratios are equal, the four quantities composing them are said to be in proportion.
If a/b = c/d then a, b, c, d are in proportions.
If four quantities are in proportion, the product of the extremes is equal to the product of the means. Let a, b, c, d be in proportion, then a/b = c/d
>ad = bc.
PARTNERSHIP
If the period of investment is the same for each partner, then the profit or loss is divided in the ratio of their investments.
If A and B are partners in a business, then
Investment of A / Investment of B =Profit of A / Profit of B or = Loss of A / Loss of B
If A, B and C are partners in a business, then
Investment of A : Investment of B : Investment of C = Profit of A : Profit of B : Profit of C, or = Loss of A : Loss of B : Loss of C
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Chapter 4: AVERAGE, PROBLEM ON AGES
Average or Mean =
Sum of given quantities / Number of quantities
The average of first n natural numbers =
(n + 1) / 2
The average of the first n consecutive even numbers = (n + 1)
The average of the first n consecutive odd numbers = n
The average of the squares of the first n natural numbers can be shown to be
1/6[ (n+1)(2n+1) ]
Average of cube of first n natural no. =
1/4 [n (n+1)^2 ]
Average of cube of first n even natural no. = 2n(n + 1)^2
Average of cube of first n odd natural no. = n (2n^2 – 1)
Average of first n multiple of m =
1/2 [m(n+1)]
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Chapter 5: PERCENTAGE, PROFIT & LOSS
Percentage
A percentage is a fraction with denominator hundred. It is denoted by the symbol %. Numerator of the fraction is called the rate per cent.
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Profit & Loss
Cost Price : The amount paid to purchase an article or the price at which an article is made, is known as its cost price.
The cost price is abbreviated as C.P.
Selling Price : The price at which an article is sold, is known as its selling price. The selling price is abbreviated as S.P. Profit : If the selling price (S.P.) of an article is greater than the cost price (C.P.), then the difference between the selling price and cost price is called profit. Thus,
If S.P. > C.P., then
Profit = S.P. – C.P.
• S.P. = C.P. + Profit
• C.P. = S.P. – Profit.
Loss : If the selling price (S.P.) of an article is less than the cost price (C.P.), then the difference between the cost price (C.P.) and the selling price (S.P.) is called loss. Thus,
if S.P. < C.P., then
Loss = C.P. – S.P.
• C.P. = S.P. + Loss
•S.P. = C.P. – Loss
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Chapter 6: TIME, SPEED & DISTANCE
The rate at which any moving body covers a particular distance is called its speed.
Speed = Distance / Time
Time = Distance / Speed
Distance = Speed × time
Unit : SI unit of speed is metre per second (mps). It is also measured in kilometers per hour (kmp) or miles per hour (mph).
Conversion of units :
(i) 1 hour = 60 minutes = 60 × 60 seconds.
1 km = 1000 m
1 km = 0.6214 mile
1 mile = 1.609 km, i.e. 8 km = 5 miles
1 yard = 3 feet, 1 foot = 12 inches
1 km/h = 5/18 m/sec, 1 m/sec = 18/5 km/h
1 miles/hr = 22/15 ft/sec.
Average speed =
Total Distance / Total time
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Chapter 7: MIXTURE & ALLIGATION
Chapter 8: TIME & WORK
TIME AND WORK
In most of the problems on time and work, either of the following basic parameters are to be calculated :
TIME :
If A can do a piece of work in X days, then A’s one day’s work= 1/X [ part of the whole work ]
If A can do a piece of work in X days and B can do it in Y days then A and B working together will do the same work in
XY/(X + Y) days.
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PIPES AND CISTERNS
The same principle of Time and Work is employed to solve the problems on Pipes and Cisterns. The only difference is that in this case, the work done is in terms of filling or emptying a cistern (tank) and the time taken is the time taken by a pipe or a leak (crack) to fill or empty a cistern respectively.
Inlet : A pipe connected with a tank (or a cistern or a reservoir) is called an inlet, if it fills it.
Outlet : A pipe connected with a tank is called an outlet, if it empties it.
If a pipe can fill a tank in x hours, then the part filled in 1 hour = 1/x
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Chapter 9: INTEREST
INTEREST
(i) Simple Interest :
Simple interest=
(Principal x Time x Rate) / 100
Amount = Principal + Interest
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(ii) Compound Interest :
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Chapter 10: MENSURATION
Area & perimeter of various figures like Circle, Triangle, Rectangle, Polygons, trapezium, etc etc.
Chapter 11: DATA INTERPRETATION
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