Actual Formula Test #1 Test #2 Formula. (x h) 2 + (y k) 2 = r 2 General equation of a circle

Transcription

1 Actul Formul Test # Test # Formul ( + b)( b + b ) 3 + b 3 = ( b)( + b + b ) 3 b 3 = x = b ± b 4c f(x) = f( x) f( x) = f(x) Qurtic Formul Test for even functions Test for o functions (x h) + (y k) = r Generl eqution of circle y = r x Eqution of semi-circle 0 lim x fi x = sin π 4 = cos π 4 = tn π 4 = 3 3 sin π 3 = sin π 6 = cos π 3 = cos π 6 =

2 3 tn π 3 = 3 sinθ cosθ cosθ sinθ tn π 6 = tnθ = cotθ = sin θ + cos θ = + cot θ = cosec θ tn θ + = sec θ sina = sinb b = b + c bccosa cosa = b + c bc A = b sinc Other trig ientity Other trig ientity Sine rule Cosine rule for sie Cosine rule for n ngle Are of tringle using trig cosx cosy + sinx siny cos(x y) = cosx cosy sinx siny cos(x + y) = sinx cosy + cosx siny sin(x + y) = sinx cosy cosx siny sin(x y) = tnx + tny tnx tny tn(x + y) =

3 tnx tny + tnx tny tn(x y) = sinx cosx sin x = cos x sin x sin x cos x tnx tn x cos x = tn x = t tn q Rtios: t tnθ = t + t cosθ = t + t sinθ = rsin(θ + α) sinθ + bcosθ = rsin(θ α) sinθ bcosθ = rcos(θ α) cosθ + bsinθ = rcos(θ + α) cosθ bsinθ = r = + b tn α = b Where r = n α =

4 θ = π n + (-) n α θ = π n ± α θ = π n + α Generl solution for sine Generl solution for cosine Generl solution for tn Grphs = (x x ) + (y y ) Distnce formul x P = + x y, + y Mipoint Formul m = y y x x Grient Formul m = tnθ y y = m(x x ) y y x x = m = m y y x x Grient using trig Point-grient formul Two-point formul Prllel lines proof m m = - x + by + c Perpeniculr lines proof = Perpeniculr + b istnce formul m tnθ = m Angle between two + mm lines x = y = mx + nx m + n my + ny m + n Diviing intervl in rtio m:n

5 y x = lim f(x + h) f(x) h fi 0 h First principle ifferentition n x n x xn f'(x)n [f(x)] n x [f(x)]n = vu' + uv' vu' uv' v x = b x uv x u v Axis of symmetry in qurtic = b 4c b c e x = 4y (0, ) (0, 0) (x h ) = 4(y k) (h, k) (h, k + ) x = t y = t The iscriminnt Sum of roots Sum of roots two t time Sum of roots three t time Sum of roots four t time Eqution of bsic prbol. Focus Vertex Generl eqution of prbol. Focus Vertex Prmetric form of: x = 4y

6 T n = + (n ) S n = n ( + l) Sum S n = n [ + (n )] S = (n ) 80 A = lb A = x Term of n rithmetic series of n rithmetic series Sum of interior ngles of n n- sie polygon Are of rectngle Are of squre A = bh Are of tringle A = bh Are of prllelogrm xy Are of rhombus A = h( + b) Are of trpezium A = π r S = (lb + bh + lh) V = lbh S = 6x V = x 3 S = π r + π r h Are of circle Surfce re of rectngulr prism Volume of rectngulr prism Surfce re of cube Volume of cube Surfce re of cyliner

7 V = π r h S = 4π r V = 4 π 3 r3 S = π r + π rl Volume of cyliner Surfce re of sphere Volume of sphere Surfce re of cone V = 3 π r h Volume of cone x n + n + + c h [(y 0 + y n ) + (y + y y n )] where h = b n h 3 [ (y 0 + y n ) + 4(y + y 3 ) + (y + y 4 )] where h = b n (x + b) n + + c (n + ) V = π y x V = π x y n x x Trpezoil rule Simpson s Rule n (x + b) x Volume bout the x-xis Volume bout the y-xis e x x ex f'(x) e f(x) e x + c x e f(x) e x x

8 ex + b + c log x + log y log x log y x + b e x log (xy) log x y n log x log x = log e x log e x f'(x) f(x) log e x + c log e f(x) + c log x n Chnge of bse rule x log e x x log e f(x) x x f'(x) f(x) x 80 π rins = C = πr l = rθ Circumference of circle Length of n rc A = r θ Are of sector A = r (θ sinθ) sinx» x tnx» x cosx» Are of minor segment Smll Angles

9 f'(x) cos [f(x)] f'(x) sin [f(x)] f'(x) sec f(x) sin(x + b) + c cos(x + b) + c tn(x + b) + c x + sin x + c 4 x sin x + c 4 N t kq Q = Ae kt = k(n P) N = P + Ae kt = x v x = cos(nt + ). ẋ = n x sin [f(x)] x cos [f(x)] x tn f(x) x cos(x + b) x sin(x + b) x sec (x + b) x cos x x sin x x Exponentil Growth & Decy Q t = Quntity Complex growth n ecy Specil result for ccelertion Displcement for SHM Accelertion for SHM

10 π n v = n ( x ). x = Vcosθ. y = Vsinθ. x = 0. y = g x = Vt cosθ y = Vt sinθ gt y = gx V ( + tn θ) + xtnθ t = V sinθ g x = V sin θ g x = V g h = V sin θ g f - [f(x)] = f[f - (x)] = x Amplitue of SHM Perio of SHM Velocity of SHM Initil Velocity of projectile Accelertion of projectile Horizontl isplcement Verticl isplcement Crtesin eqution of motion Time of flight Rnge Mx Rnge Gretest height Proof for mutully inverse functions sin - x sin - ( x) = π cos - x cos - ( x) =

11 tn - x tn - ( x) = π r = T T T n = r n S n = (rn ) r for r > S n = ( rn ) for r < r S = r sin - x + cos - x = Common rtio in geometric series Term of geometric series Sum of geometric series Sum to infinity of geometric series A = P + r Compoun interest 00 n formul If f + b Hlving the intervl = 0 metho = f() Newton s metho f'() of pproximtion n k + k n! (n r)! n! s!t!... (n )! b T K + T K = n Pr = Arrngements where some re like Arrngements in circle