Consultation with position holders in competitive examination reveals that you must know rules, type of questions being asked in examinations, and practice them to get good marks. There are 152 rules,187 types of variations in questions, and 708 types of questions being asked in examinations to get mastery over arithmetic, Similar work be done in the case of geometry, coordinate geometry, mensuration, trigonometry. Learn only 5 questions and 5 rules per day. Revise them another day. It will take 50 days to complete the course and 10 days to do mock tests. Please remember to do one mock test per month till examinations are over and make the examination handbook ready for revision.

Alternatively, there are 17 topics in Arithmetic. Decide to learn one topic per two days and keep one day per topic for revision. Part three will take six months to be clearly understood the mathematics

**Number System.**

Number is used for evaluation, measurement, calculation, and analysis, algebra, and data interpretation. If 20 questions per day are learned the course can be finished in 50 Numbers-Group of digits is called number or numbers like 23,234, 2345, 23456 etc are numbers

Value of a digit-Digit can be expressed by two types of values depending upon its face or place/value-Face value of 4 is four, when it is placed with a number 450 it is four hundred or 140 it is forty

There is another system of calling i.e, Natural number-1,2,3,……… infinity,

Whole number, counting numbers with zero(0) is called the whole number, Numbers which can be divided by two are called even number, Numbers which can not be divided by 2 are called odd number like 1,3,5,7,9, Numbers which cannot be divided by any number except 1 or itself are called prime number eg 2,3,5,7,11.1 are not a prime number. Number divided by 1 or4, 6,8,9,10,12 are composit number/imprime number.

**Number Series**

The numbers are in different forms of number series eg misfit numbers(does follow rule of sequence)1.8.27.84.125,questions based on absent number 1,2,6,7,20,30 questions based on last number 1,7,20,46,98,202.?,questions based on place of terms2,6,11,17 ,6th term

**HCF **and **LCM**– a number divides two or more numbers exactly than it is called a common factor. The highest or greatest number among factors is called HCF or GCD eg 8 is HCF in 24,32,40; a divisible number by a given number is known as multiple and number of divisible by given by two or more numbers is called common multiple and least number divisible by given all numbers is called LCM EG 60 Iis divided exactly by 10,15,20and 30. It will be good if we know different types of questions being asked in examinations.

**Fraction**

If a quantity be divided into some equal parts, then one or more of these parts is known as a fraction 1 is divided income is 4 parts3 parts is ¾. The upper part is called the numerator and the lower number is known as the denominator.Denominators are of three types Simple fraction(1/2),Decimal fraction(4/100=.04),continued fraction(1/2+3/4+5/6).A recurring decimal fraction is another form of a decimal fraction(o.33444,.0303)They are further divided into perfect recurring(, decimal fraction, Mixed recurring, and Decimal fraction

**Simplification**

Simplification are done by using formulas(a2+b2),(a3+b3),(a+b)2,,(a+b)3.

**Ratio and Proportion**.

If a:b;;c;d,a and b are end terms (extreams) but b and c are middle terms(meams),product of end terms=product of middle terms or ad=bc,if x;y=a;b and y;z=m;n

Therefore x;y;z=ma;mb;nc

**Percentage**-per cent means per hundred, percent increase/decrease means increase /decreseper hundred,%increase/decrease= total increase*100/original % 10.Profit and loss.Cost price>sale price=loss,%profit=total profit*1OO/COST PRICE,

**Discount**–

Means reducing the printed price eg a book containing marked price Rs 2 sold at a discount of paisa 25 is sold at Rs 1.75.Discount=marked price-selling price

**Simple interest**–

Pricipal*Rate of interest*time/100 13.Compound interest=Amount-Principal=P(1+R/100)N-P

- Time and works-capacity or efficiency=work done in unit time or1/time taken for whole work, Time is taken to finish the whole work=i/capacity of efficiency
- Boats and streams-rete of river/stream/upstream/down stream=speed of up/down streamwater

- Pipes and cisterns-capacity or efficiency of outlet pipe=part emptied by it in unit time(part emptied in one area or in one minute), capacity or efficiency of inlet pipe=part filled by it in unit time
- Speed,time,and distance-Distance=speed*time,1km/hour=5/18 m/sec Trains-Distance=speed*time
- Average-a+b+c/3 19.Roots

**Polygons** and their angles ends of center

Triangles and its various kinds of center Triangles and its various kinds of center Similarity and congruency of triangle Similarity and congruency of triangle Similarity and congruency of triangle circle, chord, Tangent circle, chord, Tangent circle, chord, Tangent circle, chord, Tangent

# Average Formula:

Let a1,a2,a3,……,an be a set of numbers, average = (a1 + a2 + a3,+……+ an)/n Average

# The formula for a proportion:

In a proportion, the product of the extremes (ad) equals the product of the means(bc),

Thus, ad = bc Ratio & Proportion

**Ratio & Proportion**

- Ratio & Proportion Percentage
- Profit & Loss
- Volume Surface Area
- Coordinates of the Point
- Heights & Distance
- various centers of a triangle in coordinates Logarithm
- Permutation, Combination SI&CI
- Arithmetic data&interpretation
- Pia chart
- Tabulations probability
- Verbal incl classification distance and area distance and area Equation of the line Areas and Perimeter Areas and Perimeter
- Verbal incl classification Analogy
- Decision-Making word-formation series
- Decoding &coding Symbols &Notations
- Statements and conclusions Sitting arrangements Volumes and Perimeter
- Prism and Pyramid

**Trignometry Ratio** of complementary angles TrignometryRatio of complementary angles Degrees and Radian measures

Degrees and Radian Mesures Degres Trigonometric identities

**Linear Equation** in two variable Quadratic Equations

Application of algebraic formulae

Indices and surds Indices and surds Histogram

Histogram Tabulation Tabulation Tabulation Line graph Bar chart Bar chart

# The formula for a proportion:

In a proportion, the product of the extremes (ad) equals the product of the means(bc),

Thus, ad=bc

# Percent:

Percent to fraction: x% = x/100

Percentage formula: Rate/100 = Percentage/base

Rate: The percent. Base: The amount you are taking the percent of.

Percentage: The answer obtained by multiplying the base by the rate

# Consumer math formulas:

**Discount**= list price × discount rate**Sale price**= list price −discount**Discount rate**= discount ÷ list price**Sales tax**= price of item × tax rate**Interest**=principal× rate of interest × time**Tip**s = cost of meals × tip rate**Commission**= cost of service × Commission rate

**Geometry formulas:** Perimeter

Perimeter of a square= s + s + s + s

s: length of one side

Perimeter of a rectangle: l+ w + l + w

** l** : length

**w**: width

The perimeter of a triangle:** a **+** b **+** c **

**a, ** **b**, and **c**: lengths of the 3 sides

# Area:

**Area of a square**: s × s

** s**: length of one side

Area of a rectangle: ** l** ×** w **

**l**: length

**w**: width

Area of a trapezoid: **(b1 + b2) × h/2**

** b1** and **b2**: parallel sides or the bases

** h**: length of height

# volume:

Volume of a cube: **s × s × s**

** s**: length of one side

Volume of a box:** l × w × h**

** l:** length

**w:** width

**h:** height

Volume of a sphere: **(4/3) × pi × r3**

**pi**: 3.14

**r:** radius of sphere

Volume of a triangular prism: area of triangle × Height = **(1/2 base × height) ×Height**

**base**: length of the base of the triangle height: height of the triangle

**Height:** height of the triangular prism

Volume of a cylinder:** pi ×r2 × Height**

**pi:** 3.14

** r: **radius of the circle of the base

**Height:** height of the cylinder

**Basic math formulas**

Find here a comprehensive list of basic math formulas commonly used when doing basic math computation

# Average formula:

Let a1,a2,a3,……,an be a set of numbers, average = (a1 + a2 + a3,+……+ an)/n

# Fractions formulas:

Converting an improper fraction to a mixed number:

# The Formula for a proportion:

In a proportion, the product of the extremes (ad) equal the product of the means(bc),

Thus, ad = bc

# Percent:

Percent to fraction: x% = x/100

Percentage formula: Rate/100 = Percentage/base

Rate: The percent. Base: The amount you are

taking the percent of. Percentage: The answer obtained by multiplying the base by the rate

**Consumer mat**h**formulas:****Discount**= list price× discount rate**Sale price**= list price − discount**Discount rate**= discount ÷ list price**Sales tax**= price of item × tax rate**Interest**= cost of service × commission rate