Class 10 Formula Icse

8/12/2019 Class 10 Formula Icse

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Class XSubject Mathematics Formulae

1.Compound Interest ( Imp chapter) S.I = PTR

100. Amt = Pri ( 1 + Rat ) Time

100 Note : If you are asked to compute the interest semi-annually ( Half yearly) the above formula is to

be modified, by taking time x 2, and rate 2 If the rates are given differently for the consecutive years, then

For example if the rates are 8 % , 12 % and 15 % respectively, then Amt = Pri ( 1 + 8 ) ( 1 + 12 ) ( 1 +15 )

100 100 100. Here, you need not menti on time as exponent. Depreciation Certain items value will be diminished as the time passes, then it is known as

depreciation. For example the value of a car, refrigerator, machinery etc. in that case.Final Value of machine = Actual value ( 1 Rat ) Time

100 In population growth problems, If present population is given and asking for

i) The population n yrs ago , then take Amount as Present population , and find Principal ii) The population after n yrs, then take Principal as Present population , and find Amount

2.Sales Tax & VAT.

Selling price = Marked price + x % of sales tax. Selling price = Marked price x % Discount . Tax % = Tax x 100

MP Discount % = Discount x 100

MP.While computing VATIn step1 : Take manufacturing cost and Calculate VAT on Manufacturing Cost In step2 : Take Profit 1, and Calculate VAT on Profit 1 only In step3 : Take Profit 2, and Calculate VAT on Profit 2 only In step4 : Take Profit 3, and Calculate VAT on Profit 3 only

Add all to get Total VATSelling price = Manufacturing cost +Profit 1 +Profit 2 + Profit 3 etc., + Total VAT

3.BankingSavings Bank account While taking the entries you have to bear in mind that

While computing the interest always take time as 1 /12 , irrespective of the total number of monthsgiven. i.e in PTR / 100, take time as 1 /12, instead of total no of months.


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If entry of a particular month is not given, then you have to take the last entry of the previous month(Here at times there is chance of making mistake, choose the value from the question.)

I f you are asked to find the amount that will be obtained on closing the accountThen take last entry from the Question + Interest obtained

( But DO NOT take the Total principal )

Recurring Deposits :

4.Shares & Dividends Dividend = [x % of Face Value] x No of shares No of shares = Investment .

Market Val of one share Income of a person may be taken as the Divide nd given by the company,

therefore income % = Income x 100Investment

5.HCF & LCM of polynomials

In step1 : Factorize the given polynomials,a) Either by splitting the terms, (OR) b) Using formulae ( a + b) 2 = a 2 + 2ab + b 2

( a b) 2 = a2 2ab + b 2.a2 b2 = (a + b)(a b).a4 b4 = (a 2 ) 2 (b2 ) 2.

(a2 + b 2 ) (a 2 b2 )

(a2 + b 2 ) (a b ) (a + b )( a + b) 3 = a3 + b 3 + 3ab (a +b)a3 + b 3 = (a + b)( a2 + ab + b 2)

( a b)3 = a 3 b3 3ab (a b )a3 b3 = (a b)( a2 + ab + b 2) (or)

Trial & Error method .In step2 : Take the product of Common terms as their HCF. In step3 : Take the product of All the terms , Omit, the HCF value which gives you the value of LCM.Product of LCM x HCF = Product of the two polynomials.

Note: If cubical expression is given, it may be factorized by using Trial & Error method. 6.Quadratic Equations.

Note : To find the value of x you may adopt either splitting the middle term or formula method ,unless specified the method.


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Note: when x = y, is given, then use ruler to measure the vertical distance of the point from the line, andthen take the same distance on the other side to obtain it s reflection.

8.Ratio & Proportion.

Duplicate ratio of a : b is a 2 : b2 ( Incase of Sub-d uplicate ratio you have to take Square root ) Triplicate ratio of a : b is a 3 : b3 ( Incase of Sub- triplicate ratio you have to take Cube root ) Proportion a : b = c : d, Continued Proportion a : b = b : c,(Middle value to be repeated)

1st 2nd 3rd 4 th proportionals 1 st 2nd 2nd 3rd proportionals Product of Means (Middle values) = Product of Extremes (Either end values) If a = c is given, then Componendo & Dividendo is a + b = c + d

b d a b c dDo you have a question Where to take K method ? You may adopt it in the following situations

Length on the map / model = k times the original length.Area on the map / model = k 2 times the original Area. Volume of the model = k 3 times the original Volume.

9.Remainder theorem.If (x 2 ) is a factor of the given expression, then


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10.Matrices

Some times, you may be asked to find A 2 + AB + 7 is given, you have to assume itas A 2 + AB + 7 I, Here, I is the Identity matrix.

in which all the principal diagonal values are 1, and the res t are Zero .

11.Distance & Section Formulae

Distance = \/ (x 2 x1) 2 + (y 2 y1) 2 . ( The same formula is to be used to find the length of linesegment, sides of a triangle, square, rectangle, parallelogram etc.,)

To prove co-linearity of the given three points A,B, and C, You have to findThe distance of AB + The distance of BC = The distance of AC.

Section formula: point (x, y) = m 1 x2 + m 2 x1 , m1 y2 + m 2 y1

m1 + m 2 m1 + m 2

Mid point = x 1 + x 2 , y1 + y2 2 2

Centroid of a triangle = x 1 + x 2 + x 3 , y1 + y2 + y 3 3 3

12.Equation of a line.

If two points are given, then Slope (m) = y 2 y1 x2 x1

If a point, and slope are given, then Slope (m) = y y1 x x1

If two lines are Parallel to each other then their slopes are equal i.e m 1 = m 2 If two lines are Perpendicular to each other then product of their slopes is 1. i.e m 1 x m 2 = 1 Depending upon the question You may have to use a) y = mx + c, where c is the y -intercept.

13.Similarity. If two triangles are similar then, ratio of their sides are equal.

i.e if ABC ~ PQR then AB = BC = ACPQ QR PR.


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If ABC ~ PQR then Area of ABC = Side 2 = AB 2 = BC 2 = AC 2 Area of PQR Side 2 PQ 2 QR 2 PR 2

Size transformation:Length of the model = k times the actual length. [Here k is to be taken as 1 / 10000 ]

Area of the model = k 2

times the actual area. [Here k 2

is to be taken as (1 / 10000) 2

]Volume of the model = k 3 times the actual volume. [Here k 3 is to be taken as (1 / 10000) 3 ]

14.Symmetry.A line which divides the given figure into two identical parts is known as line of Symmetry

1. An angle has One line of symmetry.2. A Square has 4 lines of symmetry.3. A Rectangle has 2 lines of symmetry.4. A Parallelogram has No lines of symmetry.5. A Rhombus has 2 lines of symmetry.6. An Isosceles Triangle has One line of symmetry.7. An Equilateral Triangle has 3 lines of symmetry.8. A Circle has Infinite lines of symmetry.9. A Regular Polygon with n sides has n lines of symmetry.

For ex: A Regular pentagon (5 sides) has 5 lines of symmetry


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A Regular hexagon (6 sides) has 6 lines of symmetry. Note: Angle of a regular polygon = ( 2n 4 )90

n. OR

Here n refers number of sides of a polygon.

( This formula may be used to construct a regular Polygon.)

15.Loci. The Locus of a line segment is it s Perpendicular bisector. The Locus of an angle is it s Angle bisector.

For solving most of the Locus problems, the above two points are good enoug h. In addition tothese points, You should have the basic knowledge of geometrical constructions. Also look at the

given figure in terms of either line segments or angles16.Circles, & Tangents.

Equal chords of a circle are equi distant from the center.

The sum of opposite angles of a cyclic quadrilateral is always 180 0.

17.Circumference & Area of a Circle. Area of a Circle = r 2. Perimeter of a Circle = 2 r Area of sector = . x r 2.

360 Length of an arc = . x 2 r.

360


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Area of ring = ( R 2 r 2 ) Distance moved by a wheel in one revolution = Circumference of the wheel.

Number of revolutions = . Total distance moved . Circumference of the wheel.Area of an equilateral triangle = \/3 Side

2.4

Note: While solving Mensuration problems, take care of the following.1. If diameter of a circle is given, then find the radius first

(Have you made mistake earlier by taking d as radius and solved the problem ?) 2. Check the units of the entire data. If the units are different, then convert them to the same units.

For Example: Diameter = 14 cm, and Height = 3 mTherefore Diameter = 14 cm, and Height = 300 cm (Have you ever committed such mistake ?)

18.Solids.1. Cylinder : Volume of a cylinder = r 2h

Curved surface area = 2 r hTotal surface area = 2 r h + 2 r 2 2 r ( h + r )

Volume of hollow cylinder = R 2h r 2h ( R 2 r 2) hTSA of hollow cylinder = Outer CSA + Inner CSA + 2 x Area of ring.

2 R h + 2 r h + 2 x [ R 2 r 2]( Of course, If you want, you may take common )

2. Cone : Volume of a Cone = r 2

h.CSA of a Cone = r ( Here refers to Slant height which may be obtained by

using Pythagoras theorem ) TSA of a Cone = r + r 2. r ( + r )

3. Sphere : Surface area of a Sphere = 4 r 2. ( In case of Sphere, there is no CSA, TSA separately)

Volume of hemi sphere = r 3

[Take half the volume of a sphere]CSA of hemisphere = 2 r 2 [Take half the SA of a sphere] TSA of hemisphere = 2 r 2 + r 2 3 r 2

While solving the combination of solids it would be better if you take common

If a solid is melted and, recast into number of other small solids, then Volume of the larger solid = No x Volume of the smaller solid

For Ex: A cylinder is melted and cast into smaller spheres. Find the number of spheresVolume of Cylinder = No x Volume of sphere.


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If an Ice cream cone with hemispeherical top is given then you have to take a) Total Volume = Volume of Cone + Volume of Hemisphere

b) Surface area = CSA of Cone + CSA of hemisphere (usually Surface area will not be asked)

19.Trigonometric Identities. Wherever Square appears think of using the identities i) Sin 2 + Cos 2 = 1

ii) Sec 2 Tan 2 = 1iii) Coseec 2 Cot 2 = 1

Try to convert all the values of the given problem in terms of Sin and Cos Cosec may be written as 1/Sin Sec may be written as 1 /Cos Cot may be written as 1 /Tan Tan may be written as Sin / Cos Wherever fractional parts appears then think taking their LCM Think of using ( a + b ) 2, ( a b ) 2, ( a + b ) 3, ( a b ) 3formulae e tc., Rationalize the denominator [ If a + b, (or) a b format is given in the denominator] You may separate the denominator For Ex : Sin + Cos as Sin + Cos

Sin Sin Sin 1 + Cot

If you are not able to solve the LHS part completely, Do the problem to such an extent you can solve,then start working with RHS, and finally you will end up the problem at a step where LHS = RHS

Sin ( 90 ) = Cos : Cos ( 90 ) = Sin . Sec( 90 ) = Cosec : Cosec ( 90 ) = Sec Tan ( 90 ) = Cot : Cot ( 90 ) = Tan

20.Heights & Distances.

21.Graphical Representation. Don t forget to write the scale on x -axis, and on y-axis. To find the Lower quartile take N /4 [Here N is f] then take the corresponding point on X-axis To find the Upper quartile take 3N /4, then take the corresponding point on X-axis

To find the Median take N /2, then take the corresponding point on X-axis22.Measures of Central Tendency.

For un-grouped data Arithmetic Mean = Sum of observations


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No of observations Mode = The most frequently occurred value of the raw data.

To find the Median first of all arrange the data in Ascending or Descending order, thenMedian = (N+1) /2 term value of the given data, in case of the data is having odd no of observations.

Median = [(N /2) + (N+1) /2)] / 2 term value of the given data, in case of the data is havingeven number of observations.

For grouped dataArithmetic Mean = fx (Direct method)

fArithmetic Mean = a + f d (short cut method)

f Arithmetic Mean = a + f u x

c(step-deviation method)

f

23.Probability.Probability of an event : P(event) = Number of favora ble outcomes

Total number of outcomesIn a deck of playing cards, there are four symbols

(Spades in Black colour) having A, 2,3,4,5,6,7,8,9,10,J,K, and Q total 13 cards

(Clubs in Black colour) having A, 2,3,4,5,6,7,8,9,10,J,K, and Q total 13 cards (Hearts in Red colour) having A, 2,3,4,5,6,7,8,9,10,J,K, and Q total 13 cards (Diamond in Red colour) having A, 2,3,4,5,6,7,8,9,10,J,K, and Q total 13 cards

52 cardsJack, King and Queen are known as Face Cards , As these cards are having some pictures on.

Note: Drawing rough sketches is always advisable, though, you may not get marks for them, but, theywill

give a clear cut idea to solve the problem.

Class 10 Formula Icse

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