Programme de physique-chimie et mathématiques de première STI2D
CPGE de la filière TSI, etc Ce programme d’enseignement de physique-chimie poursuit cet objectif, dans la continuité des apprentissages du collège et de la classe de seconde Il s’agit de renforcer la culture scientifique des futurs bacheliers de la série STI2D, de les faire
Teaching Mathematics using Augmented Reality
We have to run the programme Autodesk Maya on a computer to create a model A type od model can be chosen by clicking a button on the model menu on the top left of the screen The size and position can be adjusted by dragging a mouse to create the chosen model The Fig 1 shows the cube model created by Autodesk Maya
ADVANCED PROGRAMME MATHEMATICS CORE MODULE: CALCULUS AND
pc = °22 (2) (b) 55 70 1,2 22=×+ − t grade 12 examination: advanced programme mathematics – page 9 of 10 core module: calculus and algebra – marking
Mathématiques Cours, exercices et problèmes Terminale S
programme complet (B O spécial n°8 du 13/10/2011) indique clairement qu’on ne saurait se restreindre aux capacités minimales attendues Notations Une expression en italique indique une définition ou un point important Logiciels Une liste de logiciels libres ou de liens librement accessibles est donnée sur le blog www ac-grenoble
Mathematiques - Niveau L1 Tout le cours en fiches
du programme, plus «classique», sur les suites et le calcul intégral Pour l’algèbre, la présentation reprend celle de l’ouvrage Calcul Vectoriel (Collection Sciences Sup), en allant un peu plus loin :Rn, réduction, espacesvectoriels Malgré tout le soin apporté à la rédaction, nous demandons l’indulgence du lecteur
REPARTITION DES PROGRAMMES DU BACCALAUREAT SEMESTRE 1
Sciences expérimentales - option PC et Sciences Mathématiques - options A et B 6 1 Programme et volume horaire Répartition horaire (Cours + Exercices) Domaine secondaire Parties du programme Domaine principal AUTO-APPRENTISSAGE PRESENTIEL PC SC MATHS PC SC MATHS Introduction Questions qui se posent au physicien 1 1 1 1 e
PROGRAMME GUIDE FOR BACHELOR OF COMPUTER APPLICATIONS (BCA)
ii) Students while pursuing BCA programme cannot enroll for any course(s) offered under the same programme under ‘Associate Studentship Scheme’ 1 9 Student Support Services In order to provide individualized support to its learners, the University has created a number of Study Centres throughout the country for this Programme
Programme de physique-chimie de seconde générale et - SNES
Organisation du programme Une attention particulière est portée à la continuité avec les enseignements des quatre thèmes du collège Ainsi, le programme de seconde est-il structuré autour de trois de ces thèmes : « Constitution et transformations de la matière », « Mouvement et interactions » et « Ondes et signaux »
[PDF] relation de conjugaison exercices corrigés 1ere s
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[PDF] taille d'une cellule
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[PDF] relation de conjugaison miroir sphérique
[PDF] phrase hypothétique anglais
[PDF] phrase hypothétique italien
[PDF] système hypothétique définition
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GRADE 12 EXAMINATION
NOVEMBER 2015
ADVANCED PROGRAMME MATHEMATICS
CORE MODULE: CALCULUS AND ALGEBRA
MARKING GUIDELINES
Time: 2 hours 200 marks These marking guidelines are prepared for use by examiners and sub-examiners, all of whom are required to attend a standardisation meeting to ensure that the guidelines are consistently interpreted and applied in the marking of candidates' scripts. The IEB will not enter into any discussions or correspondence about any marking guidelines. It is acknowledged that there may be different views about some matters of emphasis or detail in the guidelines. It is also recognised that, without the benefit of attendance at a standardisation meeting, there may be different interpretations of the application of the marking guidelines. GRADE 12 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS - Page 2 of 10 CORE MODULE: CALCULUS AND ALGEBRA - MARKING GUIDELINESIEB Copyright © 2015 PLEASE TURN OVER
2 12 2 2 11 2 221 22 1 22 12 3 n n log log log n log n n
QUESTION 1
1.1 (a) 3 x e ln3x ln30,35 x
(4) (b) tan 2x1,107 xk
tan 2 x1,107 xk
1,11 2,04 4,25 5,18x or or or (6)
(c) 12 2 log log 2 n xx 22log log 2xn x 22
11 log log 2 22
n OR 12n
3n (4)
1.2 (a) (1)70 1 22 P
92 C (2)
(2) Limit as t22PC (2)
(b)55 70 1,2 22
t40 70 1,2 22
t4,1245mints 7,449mints
4,12 7,45t (7)
[25] GRADE 12 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS - Page 3 of 10 CORE MODULE: CALCULUS AND ALGEBRA - MARKING GUIDELINESIEB Copyright © 2015 PLEASE TURN OVER
QUESTION 2
Prove true for n = 1:
LHS = 25 1 24
Which is a multiple of
8Assume true for n = k:
2 5 18 k p pNProve true for n = k + 1:
2122
2 51
5 .5 1
5 8125 8 1 1
200 24
8 25 3 whichisamultipleof 8.
k k kBut p by assumption
p p p Hence, we have shown that if the expression is divisible by 8 by any one natural value of n then it is also true for the next consecutive value. But it is true for n =1, therefore also true for n =2, 3 , 4 and so on for all natural values of n. OR by the P.M.I. the statement is true for n [14]QUESTION 3
3 .1 22a bi a bi ab 22
22
2 a b abi ab 22
22
ab real part ab (7) 3.2
One other solution is
37xi .
2 2 376 9 49
6 58 0xi
xx xxBy inspection:
232(2 1)( 6 58) 258 x x x x px qx p = -13 q = 122 (10) [17] GRADE 12 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS - Page 4 of 10 CORE MODULE: CALCULUS AND ALGEBRA - MARKING GUIDELINES
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QUESTION 4
4.1 tan 3 21 3( ) r Pythag
3 radians2r (6)
4.2Area of sector =
2 2 2 1 2 1 2. 232,09 r units tan2
3,46AB
AB units
Area of
OAB 2 12 3,46
23,46units
Shaded area = 3,46 - 2,09 = 1,37 units
2 (9) [15] GRADE 12 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS - Page 5 of 10 CORE MODULE: CALCULUS AND ALGEBRA - MARKING GUIDELINESIEB Copyright © 2015 PLEASE TURN OVER
QUESTION 5
5.1 (a) 1 () 2 3px x 2 2 '( ) 2 3 (3) 3 23px x x (4) (b) 1 23
x y 1 32y
x 1 12 3 x px x (4) 5.2 (a) ()pqx (3) (b) ()r px (3) 5.3 2 6 25
x gx x 2 2
2 52 62'( )25 x xxgxx
220 4 10 2 12 x xx
20 56 xx
6; 1 xx
6; 1 yy (8)
[22] GRADE 12 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS - Page 6 of 10 CORE MODULE: CALCULUS AND ALGEBRA - MARKING GUIDELINESIEB Copyright © 2015 PLEASE TURN OVER
QUESTION 6
(a) (i) There will be two x-intercepts unless a factor cancels, i.e. (x + 1) gives p = 5. (2x - 1) gives p = -8,5 (ii) p = 5 and p = -8,5 ( see above) Denominator is a perfect square, i.e. x = -4 or x = 4. (b) (i) 2 2 21 121
54 4 1
xx xx fx xx x x1 0,5 1 4x or x or x
(ii) x-intercepts: x = -1; x = 0.5 y-intercept: y = -0.25 vertical asymptotes: x = 1 and x = 4 horizontal asymptote: y = 2 shape4 1 0.5
-1 GRADE 12 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS - Page 7 of 10 CORE MODULE: CALCULUS AND ALGEBRA - MARKING GUIDELINESIEB Copyright © 2015 PLEASE TURN OVER
6.2 (a) Prove continuity: Prove differentiability: 0 0 lim ( ) 3 lim ( ) 33(3) 3 3 0 x x gx gx g continuous at x 0 0 0 0 lim '( ) lim ( 2 1) 1 lim '( ) lim 1 1 0 x xquotesdbs_dbs16.pdfusesText_22