Assessed student work
Mathematics SL and HL teacher support material

Criterion |
A |
B |
C |
D |
E (SL) |
E (HL) |
Total (SL) |
Total (HL) |
---|---|---|---|---|---|---|---|---|

Achievement level awarded |
3 |
3 |
2 |
2 |
6 |
6 |
16 |
16 |

Maximum possible achievement level |
4 |
3 |
4 |
3 |
6 |
6 |
20 |
20 |

A3—The work is concise, as it proves the conjecture in fewer than seven pages. It fulfills the aims, is well organized and complete. The exploration would benefit from more complete explanations (refer to page 7 annotation).

B3—Condone use of “N” rather than “n” in the table on page 4. The class was familiar with the modular arithmetic, so definitions were not needed.

C2—There was evidence of sufficient personal interest to award a level 2.

D2—It links areas of maths. There is reflection on the elegance of the mathematics (page 7).

E6—It is highly unlikely that a mathematics SL student will produce work of this calibre, but it obviously achieves level 6.

E6—It is commensurate with the level of the course, precise and demonstrates thorough knowledge, insight, sophistication and the rigour expected for mathematics HL.

Background information from the teacher:

“The student is a further mathematician and as such has been taught the ‘Discrete’ and ‘Sets, relations and groups’ options. He is therefore familiar with the language of modular arithmetic and had encountered Fermat’s little theorem in class. The proof of this theorem, although not required in the syllabus, was set as a homework. In his research of this, he also encountered Euler’s totient theorem. He then asked to do a pure mathematics exploration. He absolutely did understand everything he wrote. If only all students were like him!”

The teacher’s comment provides evidence that the student was personally engaged in the exploration and explains why some of the terms were not fully defined, as they were fully understood by the student and his class, which was his intended audience.