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Summary Math IEB syllabus outline (SAGS document)
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An outline of the entire IEB mathematics syllabus, including all the sections tested in both paper 1 and paper 2.
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27/1MATHEMATICS (Updated June 2020)
A. MEANS OF ASSESSMENT (GRADE 12)
Paper 1 3 hours [150]
Paper 2 3 hours [150]
School Based Assessment (SBA) [100]
400 marks
B. REQUIREMENTS
Included with the papers is a formula sheet.
MATHEMATICS EXAMINATION PAPER 1 (GRADE 12)
Weighting of Content Areas
Description Marks
Algebra and Equations (and inequalities) 25 ± 3
Patterns and Sequences 25 ± 3
Finance, growth and decay 15 ± 3
Functions and Graphs 35 ± 3
Differential Calculus 35 ± 3
Probability 15 ± 3
TOTAL 150
Trigonometric graphs will only be examined in Paper 2.
MATHEMATICS EXAMINATION PAPER 2 (GRADE 12)
Weighting of Content Areas
Description Marks
Bookwork 6
maximum
Statistics 20 ± 3
Analytical Geometry 40 ± 3
Trigonometry 40 ± 3
Euclidean Geometry and Measurement 50 ± 3
TOTAL 150
Questions will be arranged roughly according to level of difficulty from easier to
more difficult through the full length of the paper rather than grouped into content
focus questions that go from easy to more difficult within a specific content
question, i.e. a simple stand-alone trigonometry question could be question 1, but
there could be another stand-alone trigonometry question towards the end of the
paper that assesses problem solving. This does not exclude a question with some
sub-questions that address similar content at a similar level of difficulty.
IEB Copyright © 2014–2020 NATIONAL SENIOR CERTIFICATE HANDBOOK:
IMPLEMENTATION: GRADE 12, 2021
, 27/2
WEIGHTING ACCORDING TO TAXONOMY OF COGNITIVE LEVEL FOR BOTH
PAPER 1 AND PAPER 2
Assessment tasks are designed to the following weighting
Level %
1 Knowledge 20 (± 3)
2 Routine procedures 30 (± 3)
3 Complex procedures 35 (± 3)
Problem solving and investigations – reasoning
4 15 (± 3)
and reflecting
Total 100
SCHOOL BASED ASSESSMENT (SBA)
SBA comprises 25% of the total assessment for the National Senior Certificate. The
requirements for the school-based component of the senior certificate assessment are
outlined in the table below.
LEARNER FILE REQUIREMENTS FOR GRADE 12
Descriptions Weighting Mark
2 short items chosen from the selection 2 10 20
1 long item chosen from the selection 30 30
Two tests: Standardised and at least 45 minutes to an
hour in duration in controlled environment, consisting of 2 10 20
Paper 1 and Paper 2.
Grade 12 Preliminary Examination consisting of Paper 1
2 15 30
and Paper 2
Total Marks: 100
Work in the learner file must be done in the current academic year. Tasks tackled in grade
10 and grade 11 may not be submitted in the grade 12 learner file. All schools must make
available the Grade 12 SBA evidence should it be required by the IEB or Umalusi.
These subject assessment guidelines must be read in conjunction with the IEB manual for
the moderation of School Based Assessment (2011) available at www.ieb.co.za.
Grade 10 and 11
Although SBA in grade 10 and 11 will not be monitored by the IEB, it is proposed that SBA
in grade 10 and 11 follow the same format as that for grade 12.
Short Items
Learner must select two from this list
• Translation Task • Journal
• Question setting • Performance of a Song, dance or speech*
• Formula Sheet • Meta Cog
• Teaching a lesson • Lesson to a friend
• Written explanations • Error spotting
• Guided Discovery • Computer products*
• Skills analysis • Problem solving of an untraditional nature
• Olympiads • Cheat Sheet
• Investigation • Modelling*
IEB Copyright © 2014–2020 NATIONAL SENIOR CERTIFICATE HANDBOOK:
IMPLEMENTATION: GRADE 12, 2021
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These items require at least 45 minutes to complete. Two different tasks in this category
must be selected and weighted 10 marks each. These tasks should in most cases be
done under controlled circumstances. The exceptions to this rule would be those marked
with an asterix*. See above. Those marked with an asterix would need to be monitored so
that the teacher can establish that this is indeed the work of the learner. Evidence of
monitoring should be provided (e.g. evidence of teacher/learner meetings and formative
assessment or orals where the teacher talks to the learner to establish that the learner has
ownership of the work.)
Long Items
These require about 5 hours to complete and in some cases some contact time in class.
• Projects: Multi-faceted
• Discovery: a sizeable piece of work
• Computer products, i.e. using Autograph to investigate elements of calculus
• Investigation: open ended and requiring significant effort
• Modelling a real life situation
• Revision Booklet on a significant piece of work (e.g. Functions)
• Formula Sheet
Standardised tests in a controlled environment.
These tests are to be written under controlled conditions within a specified period of
time. One test should cover content/skills Paper 1 and the second test should cover
content/skills Paper 2.
Examinations
Grade 10 Mid-year examination.
(one paper is acceptable)
Grade 11 Mid-year examination.
(two papers are suggested)
Grade 12 One examination (Paper 1 and Paper 2) according to the end of year
format.
More detailed descriptions of the School Based Assessment tasks listed under
short and long items above
1. Translation Task
A translation task tests the ability of a learner to change mathematical notation into
language and his/her ability to change language back to mathematical notation. It
could also include graphs to equations and equations to graphs. This is good
practice and should happen in all sections of work. If this is to be used as a short
piece it should include both aspects of the translation.
2. Journal
A journal requires that the learner writes and reflects on the learner's own practice.
It is a metacognitive activity.
IEB Copyright © 2014–2020 NATIONAL SENIOR CERTIFICATE HANDBOOK:
IMPLEMENTATION: GRADE 12, 2021
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Here are three possible categories.
• The learner identifies questions which caused his/her problems and then writes
notes discussing the problem and the solution.
• A teacher driven journal item instructs learners to reflect on a given situation or
problem and to use language to do this e.g. the teacher gives an alternate or
erroneous solution and asks learners to
‒ comment on the alternate solution (e.g. plusses and minuses of using) or
‒ identify and explain an erroneous solution and give a correct solution
• The learner is asked to reflect and comment on real world situations requiring a
mathematical interpretation; this could be an article in a magazine or
newspaper.
3. Question Setting
This could be used as a short item and can take the form of one question and even
be done in pairs. It could be a long item and have several facets to the task.
Learners could set a question or test and provide a memo. The learner then writes
another learner's test and marks the test of the person who wrote his/her test.
4. Performance (song, dance, speech and poster)
This is a very open ended topic which often encompasses innovative ideas. The
poster is perhaps most open to abuse. It could also allow for creative work requiring
other skills, namely, a cross number. Then we have the more off the wall type
presentation where songs, skits and dance are used, e.g. a rap song containing the
essence of a section of Mathematics. A poster can also be used to report an
investigation. Such a poster can, for example, describe the problem, the method
followed, the results found and give the conclusion.
5. Formula Sheets
This can be used as a short or long item. As a short item the learners could be
asked to redesign the formula sheet justifying the changes they make. They could
also be given a selection of formulae and asked to comment on how they are used.
For a longer item the whole sheet could be used and they could be asked to
provide examples on how these formulae are used, as well as redesigning the
sheet.
6. Teaching a lesson
A nice way of handling this is to make it a group exercise or to let learners work in
pairs. They could be given parts of a section of work not yet discussed in class to
prepare and present. The teacher and their peers could then assess them against
a set of freely available criteria designed to assess the achievement of the topics.
7. A lesson to a friend
Typically the learner writes to a friend explaining of a portion of work. This would be
based on work handled in class and would give the learner the opportunity to
reflect and clarify their own thinking. It would also require them to learn to express
mathematical ideas using written language.
IEB Copyright © 2014–2020 NATIONAL SENIOR CERTIFICATE HANDBOOK:
IMPLEMENTATION: GRADE 12, 2021
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