1. Does hashing guarantee no collisions?
- Yes
- No
- Only with integer keys
Check the answer and reasoning
No
Distinct keys may map to the same finite hash location and require collision handling.
CS / A2 level
Floating point and data structures
Floating-point normalisation gives a conventional mantissa form and efficient use of precision. Finite representation creates rounding error, overflow and underflow; cancellation can amplify relative error.
Learning objectives
- Explain floating point and data structures using a concrete example.
- Apply the worked method and justify each step.
- Recognise the limitation described in the final check.
The big idea
Floating-point normalisation gives a conventional mantissa form and efficient use of precision. Finite representation creates rounding error, overflow and underflow; cancellation can amplify relative error.
Abstract data types describe operations independently of implementation. Linked lists, trees, graphs and hash tables support different access patterns and memory trade-offs.
Worked example
A binary search tree has root 8 and left child 3. Insert 5. Where does it go?
Follow the solution
5<8 takes the left branch; 5>3 takes the right branch of 3.
Investigate and explain
Predict the worked result before calculating. Change one input, record the new result, and explain which assumptions still hold.
Use the prediction activity below; a local model appears only where it supports this topic.
Check your understanding
2. A binary search tree has root 8 and left child 3. Insert 5. Where does it go?
- Right of 8
- Left of 3
- Right of 3
Check the answer and reasoning
Right of 3
5<8 takes the left branch; 5>3 takes the right branch of 3.
3. Can subtracting two nearly equal rounded numbers lose relative precision?
- Yes
- No
- Only in decimal arithmetic
Check the answer and reasoning
Yes
Cancellation removes leading shared digits, exposing the uncertainty in the remaining difference.