M21/5/MATHY/SP2/ENG/TZ1/XX/M
Markscheme
May 2021
Mathematics:
applications and interpretation
Standard level
Paper 2
16 pages
, –2– M21/5/MATHY/SP2/ENG/TZ1/XX/M
© International Baccalaureate Organization 2021
All rights reserved. No part of this product may be reproduced in any form or by any
electronic or mechanical means, including information storage and retrieval systems,
without the prior written permission from the IB. Additionally, the license tied with this
product prohibits use of any selected files or extracts from this product. Use by third
parties, including but not limited to publishers, private teachers, tutoring or study services,
preparatory schools, vendors operating curriculum mapping services or teacher resource
digital platforms and app developers, whether fee-covered or not, is prohibited and is a
criminal offense.
More information on how to request written permission in the form of a license can be
obtained from https://ibo.org/become-an-ib-school/ib-publishing/licensing/applying-for-a-
license/.
© Organisation du Baccalauréat International 2021
Tous droits réservés. Aucune partie de ce produit ne peut être reproduite sous quelque
forme ni par quelque moyen que ce soit, électronique ou mécanique, y compris des
systèmes de stockage et de récupération d’informations, sans l’autorisation écrite
préalable de l’IB. De plus, la licence associée à ce produit interdit toute utilisation de tout
fichier ou extrait sélectionné dans ce produit. L’utilisation par des tiers, y compris, sans
toutefois s’y limiter, des éditeurs, des professeurs particuliers, des services de tutorat ou
d’aide aux études, des établissements de préparation à l’enseignement supérieur, des
fournisseurs de services de planification des programmes d’études, des gestionnaires de
plateformes pédagogiques en ligne, et des développeurs d’applications, moyennant
paiement ou non, est interdite et constitue une infraction pénale.
Pour plus d’informations sur la procédure à suivre pour obtenir une autorisation écrite
sous la forme d’une licence, rendez-vous à l’adresse https://ibo.org/become-an-ib-school/
ib-publishing/licensing/applying-for-a-license/.
© Organización del Bachillerato Internacional, 2021
Todos los derechos reservados. No se podrá reproducir ninguna parte de este producto
de ninguna forma ni por ningún medio electrónico o mecánico, incluidos los sistemas de
almacenamiento y recuperación de información, sin la previa autorización por escrito del
IB. Además, la licencia vinculada a este producto prohíbe el uso de todo archivo o
fragmento seleccionado de este producto. El uso por parte de terceros —lo que incluye,
a título enunciativo, editoriales, profesores particulares, servicios de apoyo académico o
ayuda para el estudio, colegios preparatorios, desarrolladores de aplicaciones y
entidades que presten servicios de planificación curricular u ofrezcan recursos para
docentes mediante plataformas digitales—, ya sea incluido en tasas o no, está prohibido
y constituye un delito.
En este enlace encontrará más información sobre cómo solicitar una autorización por
escrito en forma de licencia: https://ibo.org/become-an-ib-school/ib-publishing/licensing/
applying-for-a-license/.
, –3– M21/5/MATHY/SP2/ENG/TZ1/XX/M
Instructions to Examiners
Abbreviations
M Marks awarded for attempting to use a correct Method.
A Marks awarded for an Answer or for Accuracy; often dependent on preceding M marks.
R Marks awarded for clear Reasoning.
AG Answer given in the question and so no marks are awarded.
FT Follow through. The practice of awarding marks, despite candidate errors in previous parts, for their
correct methods/answers using incorrect results.
Using the markscheme
1 General
Award marks using the annotations as noted in the markscheme eg M1, A2.
2 Method and Answer/Accuracy marks
• Do not automatically award full marks for a correct answer; all working must be checked, and
marks awarded according to the markscheme.
• It is generally not possible to award M0 followed by A1, as A mark(s) depend on the preceding
M mark(s), if any.
• Where M and A marks are noted on the same line, e.g. M1A1, this usually means M1 for an
attempt to use an appropriate method (e.g. substitution into a formula) and A1 for using the
correct values.
• Where there are two or more A marks on the same line, they may be awarded independently;
so if the first value is incorrect, but the next two are correct, award A0A1A1.
• Where the markscheme specifies A3, M2 etc., do not split the marks, unless there is a note.
• The response to a “show that” question does not need to restate the AG line, unless a Note
makes this explicit in the markscheme.
• Once a correct answer to a question or part question is seen, ignore further working even if this
working is incorrect and/or suggests a misunderstanding of the question. This will encourage a
uniform approach to marking, with less examiner discretion. Although some candidates may be
advantaged for that specific question item, it is likely that these candidates will lose marks
elsewhere too.
• An exception to the previous rule is when an incorrect answer from further working is used in a
subsequent part. For example, when a correct exact value is followed by an incorrect decimal
approximation in the first part and this approximation is then used in the second part. In this
situation, award FT marks as appropriate but do not award the final A1 in the first part. Examples:
Correct Further Any FT issues?
Action
answer seen working seen
1. 5.65685... No. Award A1 for the final mark
8 2 (incorrect Last part in question. (condone the incorrect further
decimal value) working)
2. 35 0.468111… Yes. Award A0 for the final mark
(incorrect Value is used in (and full FT is available in
72 decimal value) subsequent parts. subsequent parts)
Markscheme
May 2021
Mathematics:
applications and interpretation
Standard level
Paper 2
16 pages
, –2– M21/5/MATHY/SP2/ENG/TZ1/XX/M
© International Baccalaureate Organization 2021
All rights reserved. No part of this product may be reproduced in any form or by any
electronic or mechanical means, including information storage and retrieval systems,
without the prior written permission from the IB. Additionally, the license tied with this
product prohibits use of any selected files or extracts from this product. Use by third
parties, including but not limited to publishers, private teachers, tutoring or study services,
preparatory schools, vendors operating curriculum mapping services or teacher resource
digital platforms and app developers, whether fee-covered or not, is prohibited and is a
criminal offense.
More information on how to request written permission in the form of a license can be
obtained from https://ibo.org/become-an-ib-school/ib-publishing/licensing/applying-for-a-
license/.
© Organisation du Baccalauréat International 2021
Tous droits réservés. Aucune partie de ce produit ne peut être reproduite sous quelque
forme ni par quelque moyen que ce soit, électronique ou mécanique, y compris des
systèmes de stockage et de récupération d’informations, sans l’autorisation écrite
préalable de l’IB. De plus, la licence associée à ce produit interdit toute utilisation de tout
fichier ou extrait sélectionné dans ce produit. L’utilisation par des tiers, y compris, sans
toutefois s’y limiter, des éditeurs, des professeurs particuliers, des services de tutorat ou
d’aide aux études, des établissements de préparation à l’enseignement supérieur, des
fournisseurs de services de planification des programmes d’études, des gestionnaires de
plateformes pédagogiques en ligne, et des développeurs d’applications, moyennant
paiement ou non, est interdite et constitue une infraction pénale.
Pour plus d’informations sur la procédure à suivre pour obtenir une autorisation écrite
sous la forme d’une licence, rendez-vous à l’adresse https://ibo.org/become-an-ib-school/
ib-publishing/licensing/applying-for-a-license/.
© Organización del Bachillerato Internacional, 2021
Todos los derechos reservados. No se podrá reproducir ninguna parte de este producto
de ninguna forma ni por ningún medio electrónico o mecánico, incluidos los sistemas de
almacenamiento y recuperación de información, sin la previa autorización por escrito del
IB. Además, la licencia vinculada a este producto prohíbe el uso de todo archivo o
fragmento seleccionado de este producto. El uso por parte de terceros —lo que incluye,
a título enunciativo, editoriales, profesores particulares, servicios de apoyo académico o
ayuda para el estudio, colegios preparatorios, desarrolladores de aplicaciones y
entidades que presten servicios de planificación curricular u ofrezcan recursos para
docentes mediante plataformas digitales—, ya sea incluido en tasas o no, está prohibido
y constituye un delito.
En este enlace encontrará más información sobre cómo solicitar una autorización por
escrito en forma de licencia: https://ibo.org/become-an-ib-school/ib-publishing/licensing/
applying-for-a-license/.
, –3– M21/5/MATHY/SP2/ENG/TZ1/XX/M
Instructions to Examiners
Abbreviations
M Marks awarded for attempting to use a correct Method.
A Marks awarded for an Answer or for Accuracy; often dependent on preceding M marks.
R Marks awarded for clear Reasoning.
AG Answer given in the question and so no marks are awarded.
FT Follow through. The practice of awarding marks, despite candidate errors in previous parts, for their
correct methods/answers using incorrect results.
Using the markscheme
1 General
Award marks using the annotations as noted in the markscheme eg M1, A2.
2 Method and Answer/Accuracy marks
• Do not automatically award full marks for a correct answer; all working must be checked, and
marks awarded according to the markscheme.
• It is generally not possible to award M0 followed by A1, as A mark(s) depend on the preceding
M mark(s), if any.
• Where M and A marks are noted on the same line, e.g. M1A1, this usually means M1 for an
attempt to use an appropriate method (e.g. substitution into a formula) and A1 for using the
correct values.
• Where there are two or more A marks on the same line, they may be awarded independently;
so if the first value is incorrect, but the next two are correct, award A0A1A1.
• Where the markscheme specifies A3, M2 etc., do not split the marks, unless there is a note.
• The response to a “show that” question does not need to restate the AG line, unless a Note
makes this explicit in the markscheme.
• Once a correct answer to a question or part question is seen, ignore further working even if this
working is incorrect and/or suggests a misunderstanding of the question. This will encourage a
uniform approach to marking, with less examiner discretion. Although some candidates may be
advantaged for that specific question item, it is likely that these candidates will lose marks
elsewhere too.
• An exception to the previous rule is when an incorrect answer from further working is used in a
subsequent part. For example, when a correct exact value is followed by an incorrect decimal
approximation in the first part and this approximation is then used in the second part. In this
situation, award FT marks as appropriate but do not award the final A1 in the first part. Examples:
Correct Further Any FT issues?
Action
answer seen working seen
1. 5.65685... No. Award A1 for the final mark
8 2 (incorrect Last part in question. (condone the incorrect further
decimal value) working)
2. 35 0.468111… Yes. Award A0 for the final mark
(incorrect Value is used in (and full FT is available in
72 decimal value) subsequent parts. subsequent parts)
