advanced mathematics topics

Advanced Mathematics Topics Grade 12 Study Guide

The Grade 12 Advanced Mathematics Topics (Study Guide) is a summary of the mathematics topics in Grades 11 and 12. The topics neatly picked from the Advanced Mathematics School Syllabus is for the Grade 12 students to use as a checklist when preparing for the mathematics national exam.
This list is made available for free through PNG Insight new initiative to #CloseLearningGapInMath. Students can download the editable MS Doc and create a study outline from the list of topics. We believe this can help the Grade students to revise for the Advanced Mathematics Exam at the end of the year.

Advanced Mathematics Topics – Grade 11 and 12

PNG Insight understands that the students, parents, and guardians will have difficulty reading and understanding the Advanced Mathematics Syllabus and Teachers Guide. That is why we list the core contents in the Grade 12 Mathematics Revision Guide to put in perspective the Advanced Mathematics topics that students learn at Grades 11 and 12.

Grade 12 Mathematics Topics – Core Content Areas

There are four (4) Core Content Areas Grade 11 and three (3) in Grade 12. The *editable* version of the list of topics is available for download. Click on the link to download the editable MS Word file containing the list of Advanced Mathematics topics.

Download the file the use it to arrange your revision questions or questions from the past papers under the topics and revise accordingly. Take a look at what we did for the Grade 10s if you need inspirations – Grade 10 Maths Exam Questions and Answers.

GRADE 11 Advanced Mathematics Core Units/Topics

1) 11.1. Number and Application
1.1) Basic numeracy
1.2) Units of measurement
1.3) Ratio and proportion
1.4) Basic algebra

2) 11.2. Graphs and Functions
2.1) Algebraic Expressions
2.2) Graphs and Functions

3) 11.3. Managing Data
3.1) Statistics
3.2) Permutation and combination
3.3) Probability

4) 11.4. Geometry
4.1) Congruency, similarity and construction
4.2) Circles

GRADE 12 Advanced Mathematics Core Units/Topics

5) 12.1. Patterns and Algebra
5.1) Sets
5.2) Sequences and series
5.3) Binomial theorem
5.4) Determinants

6) 12.2. Trigonometry and Vectors
6.1) Trigonometry
6.2) Vectors

7) 12.3. Calculus
7.1) Differentiation
7.2) Integration

Key Points: Advanced Mathematics Revision Guide

Covering the content units is fundamental to students achieving good marks in Grade 12 Mathematics assessments and end-of-the-year examinations. Here are three pointers about the use of the mathematics study guide for grade 12. The topics are from the Advanced Mathematics Upper Secondary School Syllabus (Grades 11 and 12).

Advanced Mathematics topics form the basis of classroom teachings and assessments. It is important for students to use the topics as guides when revising for major mathematics examinations.

The new and experienced Advanced Mathematics teachers at Grade 11 and 12 levels should (and must) cover the topics in-depth and at greater length. Where there are GAPS in learning, students can use their initiatives to learn. Therefore, this guide will help students to identify topics of interests and revise accordingly.

Download Grade 12 Mathematics Study Guide

Note that the outline of this study guide correlates to the Advanced Mathematics Examination questions, both past and present. Refer to the link at the end of this article to download the PDF version of the Grade 12 Advanced Mathematics Study Guide, Upper Secondary School GM Syllabus and the Teachers Guide.

The Grade 12 Mathematics Study Guide, is a collection of the compulsory Units/Topics in Grades 11 to 12 coursework. The intent is to help students know about what they are studying at these levels and guide to planning their mathematics revisions.

You can download the editable version of the study guide now. (Download Grade 12 Advanced Mathematics Study Guide WORD DOC)

Grades 8 and 10 Math Topics and Exam Revision Guides

We produce similar Exam Revision Guides for Grades 8, 10 and 12 (General Mathematics). Check out the ‘Exam Study Guide’ menu above if you want to download the editable versions of the respective files.


  • Students can use the outline to COMPILE revision questions for the GRADE 12 ADVANCED MATHEMATICS EXAM
  • Teachers can use this outline with the Grade 12 AM Upper Secondary School SYLLABUS AND TEACHERS’ GUIDES
  • Download the Editable Version – see link in the article.
  • The Upper Secondary School (Advanced Mathematics Syllabus) and Teachers Guide is available in PDF for download.

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