These are algorithms that students should know from memory (or with very little help from a reference).
1. Insertion sort.
2. Merge sort.
4. Root finding (binary search, Newton's method).
5. Matrix multiplication (basic algorithm).
6. Gaussian elimination.
7. Radix conversion (e.g. binary to decimal and vice-versa).
8. Tree and graph traversals (preorder, postorder, depth-first, breadth-first)