Mathematics [Summary]

Size: px

Start display at page:

Download "Mathematics [Summary]"

Madeline Long
6 years ago
Views:

1 Mthemtics [Summry] Uits d Coversios. m = 00 cm. km = 000 m 3. cm = 0 mm 4. mi = 60 s 5. h = 60 mi = 3600 s 6. kg = 000 g 7. to = 000 kg 8. litre = 000 ml = 000 cm 3 9. $ = km/h = m/s. m = cm. km = m Simple Iterest I = PRT 00 P = pricipl R = rte (%) T = time (yers) Algebric Frctios. + c = +c b b b. c = c b b b 3. c = c b d bd 4. + c = d b d 5. d+bc bd b c d = d d bc bd Prime Fctoristio = 3 3 Compoud Iterest Totl mout = P ( + r 00 ) P = pricipl R = rte (%) = umber of period Totl mout = pricipl + iterest + bc = bd bd bc = bd bd 6. c = d = d b d b c bc Mp scle : Distce : Are : Iequlities If > b,. + c > b + c. c > b c 3. c > bc, if c > 0 4. c < bc, if c < > b c c c < b c Number ptter Lier Qudrtic, if c > 0 T, if c < 0 + b + b + c Lowest Commo Multiple LCM = = 68 Highest Commo Fctor HCF = 3 = 6 Qudrtic Equtios x + bx + c = 0 x = b ± b 4c Fctoristio. ( + b) = + b + b. ( b) = b + b 3. b = ( + b)( b) 4. x + bx + y + by = x( + b) + y( + b) = (x + y)( + b) Lier Iequlity b c Solve b d b c seprtely 04 Horizo Eductio. All Rights Reserved. Versio

2 Mthemtics [Summry] Idices. m = m+. m = m 3. ( m ) = m 4. 0 = 5. ( b) = b 6. ( b ) = b 7. = 8. ( b ) = ( b ) 9. m 0. = m = Lie segmet Legth of lie segmet = (x x ) + (y y ) Stdrd Form A 0 < A < 0 = iteger Equtio of stright lie y = mx + c Commo prefixes Tetr 0 (trillio) Gig 0 9 (billio) Meg 0 6 (millio) Kilo 0 3 (thousd) Milli 0 3 (thousdth) Micro 0 6 (millioth) No 0 9 (billioth) Pico 0 (trillioth) Grdiet of stright lie m = y y x x m = grdiet c = y itercept m = +ve m = ve Direct proportio y x y = kx Iverse proportio y x y = k x m = 0 m = Pythgors Theorem (for rightgle trigles oly) + b = c c = hypoteuse d b re shorter sides 04 Horizo Eductio. All Rights Reserved. Versio

3 Mthemtics [Summry] Mesurtio Figure Are Volume Circle πr Trigle bh Trpezium Pyrmid Cylider Coe Sphere ( + b)h Add re of ll sides bse re h πh + πr πr h πrl + πr 3 πr h 4πr 4 3 πr3 Trigoometry (rightgle trigles). si A = opp = BC hyp AC. cos A = dj hyp = AC AB 3. t A = opp = BC dj AC Circulr mesures Cogruecy Similrity. Circumferece = πr. Are = πr 3. π rd = Are of sector = θ 360 πr = r θ 5. Arc legth = π 360 πr = rθ 6. Are of segmet = r (θ si θ) Trigoometry Sie rule: si A = b si B = c si C Cosie rule = b + c bc cos A Are of trigle : b si C Tests for cogruecy: SSS SAS ASA RHS S = side A = gle R = right gle H = hypoteuse Trigomometry (obtuse gles) si A = si(80 A) cos A = cos(80 A) A = D, B = E, C = F = b = c d e f A = ( l ) ; V = ( l ) 3 = m A l V l m To prove similr trigles, fid pirs of equl gles (AA Similrity). Agles i regulr polygo If is the umber of sides, Iterior gle = ( ) 80 Exterior gle = Horizo Eductio. All Rights Reserved. Versio

4 Mthemtics [Summry] Cumultive Frequecy Curve BoxdWhisker Plot Geometricl Figures Distce Time (d t) grph Grdiet = speed Averge speed Averge speed = totl distce trvelled totl time tke Q = lower qurtile Q = medi Q 3 = upper qurtile Iterqurtile rge = Q 3 Q Rge = mximum miimum Speed Time (s t) grph Grdiet = ccelertio Are uder grph = distce trvelled Probbility Probbility of evet A occurrig No. of fvourble P(A) = outcome Totl umber of possible outcomes 0 P(A) P = 0 impossible evet P = sure evet P(A) + P(ot A) = P(A) + P (A) = For mutully exclusive evets tht cot hppe together, P(A d B) = P(A) + P(B). Isosceles trigles. Equilterl trigle 3. Prllelogrm 4. Rectgle 5. Squre 6. Rhombus 7. Kite 8. Trpezium Sets ε uiversl set or { } empty set A B A itersects B A B A uio B A B A is proper subset of B A B A is subset of B A complemet of set A (A) Number of x A elemets i set A x is elemet of set A Probbility Probbility c be foud usig the probbility digrm or the tree digrm. P(H d T) = = 0.5 P(H d T) = 8 = 0.5 For idepedet evets, P(A d B) = P(A) P(B) 4 04 Horizo Eductio. All Rights Reserved. Versio

5 Mthemtics [Summry] Sttistics Me = verge Σfx Σf Mode = most frequet Medi = middle vlue (dt rrged i scedig order) Stdrd Devitio: Σfx Σf (Σfx Σf ) Additio d Subtrctio of Mtrices b q ( ) ± (p c d r s ) = ± p b ± q ( c ± r d ± s ) Sclr Multiplictio of Mtrices k ( b kb ) = (k c d kc kd ) Completig the squres x + bx + c = 0 x + bx = c x + bx + ( b ) = c + ( b ) [x + ( b )] = c + ( b ) x = ± c + ( b ) ( b ) (Two swers; typicl cse) Rtio of re of similr trigles Use similr trigle method: A = ( l ) A l A ABC = ( BC A ADE DE ) Multiplictio of Mtrices b x ( ) (w c d y z ) w + by x + bz = ( cw + dy cx + dz ) Squre of Mtrices If A = ( b c d ), the A = b b ( ) ( c d c d ) = ( + bc b + bd c + cd bc + d ) Qudrtic grphs y = x + bx + c > 0, grph is shped < 0, grph is shped c is the yitercept Lie of symmetry: x = b (Mximum / miimum poit will lie o lie of symmetry) Rtio of re of osimilr trigles Use commo height method (QR)h (RS)h A PQR A PQR A PQS = A PQS = QR RS Specil Mtrices Idetity Mtrix I = ( 0 0 ) Null Mtrix (0); ( 0 0 ); (0 0 0) 0 0 Vector A qutity with both mgitude d directio. Equl vectors: Prllel vectors: = kb Additio of Vectors: by Trigulr Lw d Prllelogrm Lw Null vectors + b = 0 Negtive vectors 5 Mgitude of vector Mgitude of colum vector ( x y ) is give by x y = x + y. 04 Horizo Eductio. All Rights Reserved. Versio

6 Mthemtics [Summry] Grphs of y = x > 0 < 0 3 Circles 0 d Agle bisector 3 Agle t cetre (O) is twice the gle t circumferece Tget from exterl poit re equl i legth Lie joiig exterl poit to cetre of circle bisect gle betwee the tgets (i.e. CBO = ABO) Perpediculr bisector 6 04 Horizo Eductio. All Rights Reserved. Versio

7 Mthemtics [Summry] Agle Properties Digrm Property Remrk Sum of complemetry gles = 90 Agles i sme segmet ( XAY d XBY) re equl Sum of supplemetry gles = 80 Adjcet gles o lie = 80 Verticlly opposite gles re equl Correspodig gles re equl vert. opp. s p = r ; q = s Exmple: = e Agles i opposite segmets ( DAB d BCD) re supplemetry Alterte gles re equl Perpediculr bisector of chord psses through cetre Iterior gles re supplemetry Exmple d + e = 80 Agle i semicircle ( ACB) is right gle Agle betwee tget d rdius is right gle Equl chords re equidistt from cetre END 7 04 Horizo Eductio. All Rights Reserved. Versio

Add Maths Formulae List: Form 4 (Update 18/9/08)

Add Maths Formulae List: Form 4 (Update 18/9/08) Add Mths Formule List: Form 4 (Updte 8/9/08) 0 Fuctios Asolute Vlue Fuctio f ( ) f( ), if f( ) 0 f( ), if f( ) < 0 Iverse Fuctio If y f( ), the Rememer: Oject the vlue of Imge the vlue of y or f() f()