Education and Leadership › Women’s Academy › School to University Pathway › Mathematics – Level 4 › Course Materials
This course is part of the Women’s Academy’s “School to University” programme and is equivalent to grade 12 and pre-university preparation. Its main topics are functions, advanced trigonometry, an introduction to calculus, vectors and matrices, and exam preparation. The content is based on topics covered in international curricula (such as Cambridge Lower Secondary and IGCSE) and global assessment frameworks such as PISA, with everyday examples and step-by-step practice.
Course page in the learning system
Course details
| Level | Level 4 of 4, equivalent to grade 12 and pre-university preparation |
| Estimated duration | 55 hours of study and practice |
| Prerequisite | Mathematics – Level 3 or a pass in the placement test |
| Language of instruction | Farsi-e-Dari (with key terms in English) |
| Cost | Free |
| Assessment | A test after each section and a final exam; pass mark 70%; certificate after approval by the Academy |
After this course you will be able to
- Functions: understand functions and domain, exponential functions and logarithms, and use them to solve problems
- Advanced trigonometry: understand the unit circle, identities and trigonometric equations, and use them to solve problems
- Introduction to calculus: understand limits, derivatives and applications of derivatives, and use them to solve problems
- Vectors and matrices: understand vectors, matrices and systems of equations using matrices, and use them to solve problems
- Exam preparation: understand mixed problems, exam strategy and practice tests (such as SAT Math), and use them to solve problems
Course outline
- Functions and domain
- Exponential functions
- Logarithms
- The unit circle
- Identities
- Trigonometric equations
- Limits
- Derivatives
- Applications of derivatives
- Vectors
- Matrices
- Systems of equations using matrices
- Mixed problems
- Exam strategy
- Practice tests (such as SAT Math)
Week-by-week learning path
With about 30 to 45 minutes of study and practice a day, you will complete this course in 6 weeks:
| Week | Topic | Weekly outcome |
|---|---|---|
| Week 1 | Functions | Lessons, practical exercises and a short section quiz |
| Week 2 | Advanced trigonometry | Lessons, practical exercises and a short section quiz |
| Week 3 | Introduction to calculus | Lessons, practical exercises and a short section quiz |
| Week 4 | Vectors and matrices | Lessons, practical exercises and a short section quiz |
| Week 5 | Exam preparation | Lessons, practical exercises and a short section quiz |
| Week 6 | Final project and final exam | Completed project and a score of 70% or higher |
Final project
“Problem portfolio”: ten applied problems from everyday life (shopping, construction, budgeting, maps) based on the topics of this level, with full solutions, an explanation of each step and a check of each answer.
Project assessment criteria:
- Correct solutions
- Clear explanation of steps
- Link to real life
- Care in checking answers
Key course terms
Equation
Variable
Function
Slope
Fraction
Percentage
Probability
Proof
Assessment and certificate
- After each section: a short quiz (70% recommended before moving on)
- Practical exercises in each lesson are for learning; send your questions via the Questions .
- End of course: final exam (pass mark 70%) and submission of the final project
- Digital certificate after review and approval by the Academy: Request a certificate
Teaching method
Each lesson includes learning objectives, explanations with real examples and images, key terms in Dari and English, common mistakes, practical exercises, a self-test and a summary. In every lesson you can ask the teacher questions using the Questions button. Courses are impartial, free and open to all young people.
Get ready now
- Review the summaries and quizzes from “Mathematics – Level 3”
- Set aside a notebook just for this course
- Set aside 45 to 60 minutes a day for study and practice
Free and reliable resources
These resources were selected by the Academy team. Most are in English; Chrome’s Translate feature can help if needed. Large files (books, exercise files, videos) will be placed in the Academy’s official Google Drive folder when the course opens and linked from this page.
- Khan Academy, free lessons in mathematics, science and economics
- CK-12 Foundation, free mathematics and science books and exercises
- PhET – University of Colorado, free interactive simulations for physics, chemistry, biology and mathematics (in several languages, including Farsi)
- MIT OpenCourseWare, free course materials from MIT
Note: This is an educational and preparatory programme and does not count as an official school certificate or official equivalence; its aim is to prepare young people for exams, scholarships and university study.
Help and questions
Questions about this course: [email protected] · All courses: Online Learning Centre · Active course: Computer and Internet Basics
Women’s Academy, Afghanistan Youth Parliament · Free and open to all young people