Stage 8 - Q1 - 2 marks
Input 3. Apply the first rule, then the second.
Hint
Record the intermediate output after each rule.
Stage 8 - Q2 - 2 marks
Input 5. Apply the first rule, then the second.
Hint
Record the intermediate output after each rule.
Stage 8 - Q3 - 3 marks
The final output is 131. Find the original input.
Hint
Record the intermediate output after each rule.
Stage 8 - Q4 - 3 marks
The final output is 102. Find the original input.
Hint
Record the intermediate output after each rule.
Stage 8 - Q5 - 4 marks
For input 1, compare the two possible orders of these rules.
Hint
Record the intermediate output after each rule.
Stage 8 - Q6 - 4 marks
For input 3, compare the two possible orders of these rules.
Hint
Record the intermediate output after each rule.
Stage 8 - Q7 - 5 marks
A chain triples the input, subtracts 4, then doubles. Find the input that gives output 34.
Hint
Reverse the order of operations as well as each operation.
Stage 8 - Q8 - 5 marks
Compare chains A: \(2x+3\) then \(4x-1\), and B: \(4x-1\) then \(2x+3\). Find the difference in outputs for any input x.
Hint
Expand the two composed expressions before subtracting.
Stage 8 - Q9 - 5 marks
The first rule is \(3x+2\). Find a second rule of the form \(ax+b\) that makes the two-rule chain equal to \(6x-5\) for every input.
Hint
The second rule acts on the entire first output.
Stage 8 - Q10 - 5 marks
Use each rule A, B, C exactly once, starting with input 1. Find the order that gives output 31 and show that it is the only order.
Hint
There are six orders of three different rules. Keep a systematic record.