Logically developed, easy to follow

Use appropriate mathematical language and representation

Define key terms, where required

Select appropriate mathematical tools (including information and communication technology)

Express results to an appropriate degree of accuracy

Express ideas clearly

Identify a clear aim and avoid irrelevance

Structure ideas in a logical manner

Include graphs, tables, and diagrams at appropriate places

Edit the exploration so that it is easy to follow

Cite references where appropriate

Work independently

Ask questions, make conjectures and investigate mathematical ideas

Read about mathematics and research areas of interest

Look for and create mathematical models for real-world situations

Consider historical and global perspectives

Explore unfamiliar mathematics

Discuss the implications of results

Consider the significance of the exploration

Look at possible limitations and/or extensions

Make links to different fields and/or areas of mathematics

Explain every tool/program you've learned or struggles you've went through throughout the whole process. For example, if you learned how to use GeoGebra, explain why, how you learned, and what difficulties you faced from learning and using the program

Reflection is very important; this is where most of the students get marked off. Reflection DOES NOT HAVE TO APPEAR AT THE END OF THE PAPER. Reflection could also be about when you come in and discuss with your teacher about the IA, and anything that your teacher advises and guides you on the direction of exploration and writing. 

Demonstrate knowledge and understanding

Apply mathematics in different contexts

Apply problem-solving techniques

Recognize and explain patterns, where appropriate

Generalize and justify conclusions

For HL, it is especially important to prove and justify the mathematics that you use. Demonstrate your full understanding of the derivations/proofs of important formulas/theorems that you use