X STD - Padasalai -10th Study Materials

2y ago
65 Views
8 Downloads
469.42 KB
10 Pages
Last View : 20d ago
Last Download : 2m ago
Upload by : Lilly Kaiser
Transcription

www.kalvisolai.comwww.Padasalai.NetMATHSX STDTry , try and try again you will succeed atlastP.THIRU KUMARESA KANIM.A., M.Sc.,B.Ed., (Maths)Govt.Girls High School ,Konganapuram Salem (Dt.)Cell No. 9003450850Email : kanisivasankari@gmail.com and kanisiva2012@gmail.com1

www.kalvisolai.comwww.Padasalai.Net1 . SETS AND FUNCTIONSCommutative property1.AUB BUAA B B A2.Associative propertyAU( BUC) (AUB)UCA ( B C) (A B) C3.Distributive propertyAU( B C) (AUB) (AUC)A ( BUC) (A B)U(A C)4.De Morgan’s lawsi) (AUB)’ A’ B’ii) (A B)’ A’ U B’iii) A ‐ (BUC) (A ‐ B) (A ‐ C)iv) A ‐ (B C) (A ‐ B)U (A ‐ C)5.Cardinality of setsi) n(AUB) n(A) n(B) ‐ n(A Β)ii) n(AUBUC) n(A) n(B) n(C) ‐n(A B) ‐n(B C) ‐n(A C) n(A B C)6.Representation of functionsa set of ordered pairs, a table , an arrow diagram, a graph7.Types of functions1. One-One functionEvery element in A has an image in B.2 Onto functionEvery element in B has a pre-image in A.3. One-One and onto functionBoth a one-one and an onto function.4. Constant functionEvery element of A has the same image in B.5. Identity functionAn identity function maps each element of A into itself.2. SEQUENCES AND SERIES OF REAL NUMBERSArithmetic sequence or Arithmetic Progression (A.P.)1.2.General forma , a d , a 2d , a 3d , . . . . .Three consecutive termsa ‐d , a , a d3.The number of terms n 4.5.6.General term tn a (n ‐ 1 )dThe sum of the first n terms (if the common difference d is given.) Sn [ 2a (n ‐ 1)d ]The sum of the first n terms (if the last term l is given.)Sn [ a l] 12

www.kalvisolai.comwww.Padasalai.NetGeometric Sequence or Geometric Progression (G.P.)7. General form8. General terma , ar , ar2 ,ar3 , . . . ,arn ‐ 1 , arn , . . . .tn arn ‐ 19. Three consecutive terms a / r , a , ar110. The sum of the first n terms1Special series11.The sum of the first n natural numbers,1 2 3 . . . .12. n The sum of the first n odd natural numbers,1 3 5 . . . . ( 2k ‐ 1 ) n213.The sum of first n odd natural numbers (when the last term l is given)1 3 5 . . . . 14.l The sum of squares of first n natural numbers,12 22 32 . . . . k2 15.The sum of cubes of the first n natural numbers,13 23 33 . . . . k3 3. ALGEBRA1(a b)2 a 2 2ab b22(a - b) 2 a 2 - 2ab b23a2 - b2 (a b) (a-b)22 (a b) 2 - 2ab4a b5a2 b2 (a - b) 2 2ab8a3 b3 (a b) (a2 – ab b2)9a3 - b3 (a - b) (a2 ab b2)10a3 b3 (a b)3 – 3ab (a b)11a3 - b3 (a - b)3 3ab (a - b)12a4 b4 (a2 b2)2 - 2 a2 b213a4 - b4 (a b)(a - b)(a2 b2)14(a b c)215(x a) (x b)16(x a)(x b)(x c) x3 (a b c) x2 (ab bc ca) x abc a2 b2 c2 2(ab bc ca) x2 (a b) x ab3

www.kalvisolai.comwww.Padasalai.Net17Quadratic polynomials18sum of zeros ( α β ) - coefficient of x / coefficient of x2 (19product of zeros ( α β ) constant term / coefficient of x2 ( )20Quadratic polynomials with zeros α and β. :20Relation between LCM and GCD :21Solution of quadratic equation by formula method x 22Nature of roots23Formation of quadratic equation when roots are givenax 2 bx c 0)x2 - ( α β ) x ( α β )L CM x GCD f(x) x g(x) Δ b2 - 4acΔ 0 Real and unequalΔ 0 Real and equal.Δ 0 No real roots. (It has imaginary roots)X2 – ( sum of roots) x ( product of roots ) 04. MATRICES12.3456.78910Row matrix :A matrices has only one row.Column matrix :A matrices has only one column.Square matrix :A matrix in which the number of rows and the number of columns are equalDiagonal matrix :A square matrix in which all the elements above and below the leadingdiagonal are equal to zeroScalar matrix :A diagonal matrix in which all the elements along the leading diagonal areequal to a non-zero constantUnit matrix :A diagonal matrix in which all the leading diagonal entries are 1Null matrix or Zero-matrix :A matrices has each of its elements is zero.Transpose of a matrix :A matrices has interchanging rows and columns of the matrixNegative of a matrix :The negative of a matrix A is - AEquality of matrices :Two matrices are same order and each element of A is equal to thecorresponding element of B4

www.kalvisolai.comwww.Padasalai.Net1112Two matrices of the same order, then the addition of A and B is a matrix CIf A is a matrix of order m x n and B is a matrix of order n x p,then the product matrix AB is m x p.13Properties of matrix additionCommutativeA B B AAssociativeA (B C) (A B) CExistence of additive identityA O O A AExistence of additive inverseA (‐A) (‐A) A O14Properties of matrix multiplicationNot commutative in general A B BAAssociativeA(BC) (AB)Cdistributive over addition A(B C) AB AC(A B)C AC BC15Existence of multiplicative identityAI IA AExistence of multiplicative inverseAB BA I(AT)T A; (A B)T AT BT ; (AB)T BT AT5. COORDINATE GEOMETRY1Distance between Two pointsAB 2The line segment joining the two points A(x1,y1), and B(x2,y2) internally in the ratio l : mis P (3,)The line segment joining the two points A(x1,y1), and B(x2,y2) externally in the ratio l : mis P (,4The midpoint of the line segment5The centroid of the triangle G (6Area of a triangleM )(,),) A sq. unitor A sq. unitA 7Area of the Quadrilateral7Collinear of three points –(or) Slope of AB Slope of BC or slope of AC.8sq. unitIf a line makes an angle θ with the positive direction of x- axis, then the slope m tan θ9Slope of the non-vertical line passing through the points10Slope of the line11The straight line ax by c 0 , y-intercept c12Two lines are parallel if and only if their slopes are equal. : m1 m2ax by c 0 ism m 5y -

www.kalvisolai.comwww.Padasalai.NetTwo lines are perpendicular if and only if the product of their slopes is -1 : m1 m2 - 113Equation of straight lines141516171819202122x-axisy-axisParallel to x-axisParallel to y-axisParallel to ax by c 0Perpendicular to ax by c 0Passing through the originSlope m, y-intercept cSlope m, a point (x1 , y1)23Passing through two points24y 0x 0y kx kax by k 0bx ‐ ay k 0y mxy mx cy ‐ y1 m(x ‐ x1)1x-intercept a , y-intercept b6GEOMETRY1Basic Proportionality theorem or Thales TheoremIf a straight line is drawn parallel to one side of a triangle intersecting theother two sides, then it divides the two sides in the same ratio.2Converse of Basic Proportionality Theorem ( Converse of Thales Theorem)If a straight line divides any two sides of a triangle in the same ratio,then the line must be parallel to the third side.3Angle Bisector TheoremThe internal (external) bisector of an angle of a triangle divides theopposite side internally (externally) in the ratio of the corresponding sidescontaining the angle.4Converse of Angle Bisector TheoremIf a straight line through one vertex of a triangle divides the oppositeside internally (externally) in the ratio of the other two sides, then the line bisectsthe angle internally (externally) at the vertex.51.2.3.Similar trianglescorresponding angles are equal (or) corresponding sides have lengths in thesame ratioAA( Angle-Angle ) similarity criterionIf two angles of one triangle are respectively equal to two angles ofanother triangle, then the two triangles are similar.SSS (Side-Side-Side) similarity criterion for Two TrianglesIn two triangles, if the sides of one triangle are proportional (in the same ratio)to the sides of the other triangle, then their corresponding angles are equalSAS (Side-Angle-Side) similarity criterion for Two Triangles6

www.kalvisolai.comwww.Padasalai.NetIf one angle of a triangle is equal to one angle of the other triangle andif the corresponding sides including these angles are proportional, then thetwo triangles are similar.6Pythagoras theorem (Bandhayan theorem)In a right angled triangle, the square of the hypotenuse is equal to thesum of the squares of the other two sides.7Converse of Pythagorous theoremIn a triangle, if the square of one side is equal to the sum of the squares of theother two sides, then the angle opposite to the first side is a right angle.8Tangent-Chord theoremIf from the point of contact of tangent (of a circle), a chord is drawn,then the angles which the chord makes with the tangent line are equal respectivelyto the angles formed by the chord in the corresponding alternate segments.9Converse of TheoremIf in a circle, through one end of a chord, a straight line is drawn makingan angle equal to the angle in the alternate segment, then the straight line is atangent to the circle.10If two chords of a circle intersect either inside or out side the circle, the areaof the rectangle contained by the segments of the chord is equal to the area of therectangle contained by the segments of the otherP A X PB PC X PDCircles and Tangents111213141516A tangent at any point on a circle is perpendicular to the radius throughthe point of contact .Only one tangent can be drawn at any point on a circle. However, froman exterior point of a circle two tangents can be drawn to the circle.The lengths of the two tangents drawn from an exterior point to a circle are ual.If two circles touch each other, then the point of contact of the circles lies onthe line joining the centres.If two circles touch externally, the distance between their centres is equal tothe sum of their radii.If two circles touch internally, the distance between their centres isequal to the difference of their radii.7 Trigonometry010203sin θ cosec θ 1cos θ sec θ 1tan θ cot θ 1; sin θ 1/ cosec θ; cos θ 1/ sec θ; tan θ 1/ cot θ04tan θ sin θ / cos θcot θ cos θ / sin θ7;;;cosec θ 1/ sin θsec θ 1/ cos θcot θ 1/ tan θ

www.kalvisolai.comwww.Padasalai.Netsin2θ cos2θ 1sec2θ – tan2 θ 1cosec2θ –cot2θ 1sin (90 – θ) cos θcos (90 – θ) sin θtan (90 – θ) cot θ05060708091011; sin2θ 1- cos2θ;; sec2θ 1 tan2 θ ;; cosec2θ 1 cot2θ ;cosec (90 – θ) sec θsec (90 – θ) cosec θcot (90 – θ) tan θComponendo and dividendo ruleangle0Sin0Cos1Tan030then4590 1 0 18Sl.No60 cos2θ 1 -sin2θtan2 θ sec2θ -1cot2θ cosec2θ – 1Name1Solid right circular cylinder2Right circularhollow cylinder3 MENSURATIONSurface Area(sq.units)Total Surface Area(sq.units)Volume(cu.units)πr2h2πrh2πr(h r)2π(R r) h2π(R r)(R-r h)Solid right circular coneπrlπr(l r)4Frustum--5Sphere4πr2-6Hollow sphere--π (R3 - r3)7Solid Hemisphere2πr23πr2πr38Hollow Hemisphere2π(R2 r2)π(3R2 r2)8π (R2 - r2) hπr2h(R2 r2 Rr) hπr3π (R3 - r3)

www.kalvisolai.comwww.Padasalai.Net910Conel ; h CSA of a cone Area of the sector; r r2πrl 11Length of the sector Base circumference of the cone12Volume of water flows out through a pipe13No. of new solids obtained by recasting141 m3L 2πr 1000 litres{Cross section area x Speed x Time } Volume of the solid which is melted-----------------------------volume of one solid which is made1 d.m3 1 litres1000 litres 1 k.l1000 cm3 1 litres11 STATISTICS–1RangeR 2coefficient of rangeQ 3Standard deviation (Ungrouped)1. Direct method2. Actual mean method3. Assumed mean method4. Step deviation method4 – Here d x ‐ – – Here d x – A xCHered Standard deviation (Grouped )1. Actual mean Method2. Assumed mean method3. Step deviation method Here d x ‐ – Here d x – Ax C Hered 5Standard deviation of the first n natural numbers,6Variance is the square of standard deviation.Standard deviation of a collection of data remains unchanged when each valueis added or subtracted by a constant.79

www.kalvisolai.comwww.Padasalai.Net8Standard deviation of a collection of data gets multiplied or divided by thequantity k, if each item is multiplied or divided by k.9Coefficient of variation,100C.V It is used for comparing the consistency of two or more collections of data.12 PROBABILITY12346789Tossing an unbiased coin onceS { H, T }Tossing an unbiased coin twiceS { HH, HT, TH, TT }Rolling an unbiased die onceS { 1, 2, 3, 4, 5, 6 }The probability of an event Alies between 0 and 1,both inclusive 01The probability of the sure event is 1.P(S) 1P( ) 0The probability of an impossible event is 0.The probability that the event A will not occur1P(A) 11011Addition theorem on probabilityP(AUB) P(A) P(B) ‐ P(A B)12If A and B are mutually exclusive events, Then P(A B) Thus P(AUB) P(A) P(B)Try , try and try again you will succeed atlastWish you all the BestP.THIRU KUMARESA KANIM.A., M.Sc.,B.Ed., (Maths)Govt.Girls High School , Konganapuram Edappady (Tk.) Salem (Dt.) Cell No. 9003450850Email : kanisivasankari@gmail.com and kanisiva2012@gmail.com10

X STD Try , try and try again you will succeed atlast . 10. terms The sum of the first n 5 . 6 GEOMETRY 1 Basic Proportionality theorem or Thales Theorem If a straight line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio. .

Related Documents:

std no. 202 std no. 203 std no. 301 std no. 302 std no. 401 std no. 402 std no. 403 std no. 404 std no. 405 std no. 406 std no. 407 std no. 408 std no. 409 std no. 410 std no. 411 std no. 412 city of montclair standards an

Plate Plan It is recommended that a plate plan be designed before starting the assay. A plate plan template is provided on page 28. The following is a suggested plate plan: 123456789101112 A BB B Std 7 C Std 6 D Std 5 E Std 4 F Std 3 G Std 2 H Std 1 Std 7 Std 6 Std 5 Std 4 Std 3 Std 2 Std 1 B blank (Assay Diluent), Standards 7 through 1 .

UKG 1500 1500 STD I STD II 1550 1550 STD III STD IV 1600 1600 STD V STD VI 1700 1700 STD VII STD VIII 1750 1750 STD IX STD X 1800 1800 STD XI STD XII 2500 2500 Installment Month Due Date With fine I II III IV V June - July Aug - Sept Oct - Nov Dec - Jan Feb - Mar Before Text Book Distribution

STANDARDS Military MIL-STD-481 MIL-STD-490 MIL-STD-681 MIL-STD-961 MIL-STD-1 174 MIL-STD-1267 MIL-STD-1 306 MIL-STD-1 464 DOD-STD-1 476 DOD-STD-1686 DOD-STD-2 167 MIL-STD-21 75 HANDBOOKS DOD-HDBK-263 Configuration Control - Engineering Changes, Deviations and Waivers (Short Form) Specificati

10. www.Padasalai.OrgThe radius of an atom is 200pm, if it crystallizes in a face centered cubic lattice, the length of the edge of the unit cell is a) 565.6pm b) 848.5pm c) 884.5pm d) 484.5pm 11. The ratio of close packed atoms to tetrahedral hole in cubic packing is a) 1:1 b) 1:2 c) 2:1 d) 1:4 12.

10th STD 10th STD TEST 34 9/19/2020 Geography Climate and natural vegetation - 10th STD 10th STD TEST 35 9/21/2020 UNIT 8 1. Ancient cities of Tamilagam 2. Society and Culture in Ancient Tamizhagam: The Sangam Age Notes 6th Social Science 6th STD Term 1 6th STD Term 3 TEST 36 9/23/2020 HISTORY 1

ö õ ÍhUP C À ö õ ÍhUP õhzuø» PÒ UP Gs. Ú õh SvPÒ i 1 E ›Ý K k öŒ#²Ò CÍ uª@Ç! 1 Eøμ øh uªÌö õÈ ß øh AÇQ À 7 öŒ#²Ò usi »[Põ

Jul 11, 2019 · CLASS: XI FIRST MID TERM-2019 MARKS: 90 QUESTION: 1 ENGLISH TIME: 2.30 HRS www.Padasalai.Org SECTION - A I. A) Choose the most appropriate synonym of the underlined lexical i