Notation List. For Cambridge International Mathematics Qualifications. For use from 2020

Size: px

Start display at page:

Download "Notation List. For Cambridge International Mathematics Qualifications. For use from 2020"

Rosaline James
5 years ago
Views:

1 Notatio List For Cambridge Iteratioal Mathematics Qualificatios For use from 2020

2 Notatio List for Cambridge Iteratioal Mathematics Qualificatios (For use from 2020) Mathematical otatio Eamiatios for CIE syllabuses may use relevat otatio from the followig list. 1 Set otatio is a elemet of is ot a elemet of { 1, 2, } the set with elemets 1, 2, { : } the set of all such that (A) the umber of elemets i set A the empty set the uiversal set, the uiversal set (for 0607 IGCSE Iteratioal Mathematics) A the complemet of the set A N the set of atural umbers, {1, 2, 3, } Z the set of itegers, {0, ±1, ±2, ±3, } p Q the set of ratioal umbers, : p, q Z, q 0 q R the set of real umbers C the set of comple umbers (, y) the ordered pair, y is a subset of is a proper subset of uio itersectio [a, b] the closed iterval { R : a b} [a, b) the iterval { R : a < b} (a, b] the iterval { R : a < b} (a, b) the ope iterval { R : a < < b} (S, ) the group cosistig of the set S with biary operatio 2 Miscellaeous symbols = is equal to is ot equal to is idetical to or is cogruet to is approimately equal to ~ is distributed as is isomorphic to is proportioal to < is less tha is less tha or equal to > is greater tha is greater tha or equal to ifiity implies is implied by implies ad is implied by (is equivalet to) 2

3 Notatio List for Cambridge Iteratioal Mathematics Qualificatios (For use from 2020) 3 Operatios a + b a b a b, ab a b, a b a plus b a mius b a multiplied by b a divided by b a a 1 + a a i i= 1 a the o-egative square root of a, for a R, a 0 a the (real) th root of a, for a R, where a 0 for a 0 a the modulus of a! factorial ( r ) the biomial coefficiet! for, r Z ad 0 r r!( 4 Fuctios f() f : A B f : y f 1 gf lim f( ) a the value of the fuctio f at f is a fuctio uder which each elemet of set A has a image i set B the fuctio f maps the elemet to the elemet y the iverse fuctio of the oe-oe fuctio f the composite fuctio of f ad g which is defied by gf() = g(f()) the limit of f() as teds to a, δ a icremet of dy d the derivative of y with respect to d y d the th derivative of y with respect to f (), f (),, f () () the first, secod,, th derivatives of f() with respect to yd the idefiite itegral of y with respect to b y d a the defiite itegral of y with respect to betwee the limits = a ad = b &, &&, K the first, secod, derivatives of with respect to t 5 Epoetial ad logarithmic fuctios e base of atural logarithms e, ep() epoetial fuctio of log a logarithm to the base a of l atural logarithm of lg, log 10 logarithm of to base 10 3

4 Notatio List for Cambridge Iteratioal Mathematics Qualificatios (For use from 2020) 6 Circular ad hyperbolic fuctios si, cos, ta cosec, sec, cot } si, cos, ta cosec, sec, cot sih, cosh, tah cosech, sech, coth } sih, cosh, tah cosech, sech, coth the circular fuctios the iverse circular fuctios the hyperbolic fuctios the iverse hyperbolic fuctios 7 Comple umbers i the imagiary uit, i 2 = 1 z a comple umber, z = + iy = r(cos θ + i si θ ) Re z the real part of z, Re z = Im z the imagiary part of z, Im z = y z the modulus of z, z = y arg z the argumet of z, arg z = θ where π < θ π z* the comple cojugate of z, iy 8 Matrices Μ Μ 1 det M, M I a matri Μ the iverse of the o-sigular square matri Μ the determiat of the square matri Μ a idetity (or uit) matri 9 Vectors a the vector a AB the vector represeted i magitude ad directio by the directed lie segmet AB â a uit vector i the directio of a i, j, k uit vectors i the directios of the Cartesia coordiate aes ( ), y the vectors i + yj (i 2 dimesios) ad i + yj + zk (i 3 dimesios) y z a, a the magitude of a AB, AB the magitude of AB a.b the scalar product of a ad b a b the vector product of a ad b 4

5 Notatio List for Cambridge Iteratioal Mathematics Qualificatios (For use from 2020) 10 Probability ad statistics A, B, C, evets A B uio of the evets A ad B A B itersectio of the evets A ad B P(A) probability of the evet A A complemet of the evet A P(A B) probability of the evet A coditioal o the evet B C r the umber of combiatios of r objects from, Cr ( r )! r!( P r! the umber of permutatios of r objects from, P r = ( X, Y, R, radom variables, y, r, values of the radom variables X, Y, R, 1, 2, observatios f 1, f 2, frequecies with which the observatios 1, 2, occur p() probability fuctio P(X = ) of the discrete radom variable X p 1, p 2, probabilities of the values 1, 2, of the discrete radom variable X f() value of the probability desity fuctio of a cotiuous radom variable X F() value of the cumulative distributio fuctio of a cotiuous radom variable X E(X) epectatio of the radom variable X E(g(X)) epectatio of g(x) Var(X) variace of the radom variable X G X (t) probability geeratig fuctio for the discrete radom variable X M X (t) momet geeratig fuctio for the radom variable X B(, p) biomial distributio with parameters ad p Geo(p) geometric distributio with parameter p Po(λ) Poisso distributio with parameter λ N(µ, σ 2 ) ormal distributio with mea µ ad variace σ 2 µ populatio mea σ 2 populatio variace σ populatio stadard deviatio sample mea, = s 2 1 i i = 1 ubiased estimate of populatio variace from a sample, = ( i ) 1 i= 1 s ρ product momet correlatio coefficiet for a populatio r product momet correlatio coefficiet for a sample φ probability desity fuctio of the stadardised ormal variable Z ~ N(0, 1) Φ cumulative distributio fuctio of the stadardised ormal variable Z ~ N(0, 1) H 0, H 1 ull ad alterative hypotheses for a hypothesis test 5

NANYANG TECHNOLOGICAL UNIVERSITY SYLLABUS FOR ENTRANCE EXAMINATION FOR INTERNATIONAL STUDENTS AO-LEVEL MATHEMATICS

NANYANG TECHNOLOGICAL UNIVERSITY SYLLABUS FOR ENTRANCE EXAMINATION FOR INTERNATIONAL STUDENTS AO-LEVEL MATHEMATICS STRUCTURE OF EXAMINATION PAPER. There will be oe 2-hour paper cosistig of 4 questios.