Stage 8 - Q1 - 2 marks
Find the output for the given input.
Hint
Double the input, then add four.
Stage 8 - Q2 - 2 marks
Find the output for the given input.
Hint
Multiply first; subtraction is the second step.
Stage 8 - Q3 - 2 marks
Find the output for the given input.
Hint
Keep the negative sign during multiplication.
Stage 8 - Q4 - 2 marks
Find the output for the given input.
Hint
Halving a mixed-number input can produce a quarter.
Stage 8 - Q5 - 2 marks
Write an equation for “add 6, then multiply by 3”.
Hint
Use brackets to preserve the order.
Stage 8 - Q6 - 2 marks
Find the linear rule that maps 0, 2, 5 to 4, 10, 19.
Hint
The zero input reveals the fixed addition.
Stage 8 - Q7 - 3 marks
A pupil says inputs 2 and \(-2\) giving the same output makes a function invalid. Explain with \(y=x^2\).
Hint
Distinguish one input with two outputs from two inputs with one shared output.
Stage 8 - Q8 - 3 marks
Two linear machines are A: \(y=2x+7\) and B: \(y=5x-2\). Find an input that gives the same output.
Hint
The machines receive the same input.
Stage 8 - Q9 - 4 marks
A linear machine maps 2 to 9 and 6 to 25. A pupil proposes \(y=5x-1\). Test and correct it.
Hint
Test both pairs, not only the first.
Stage 8 - Q10 - 5 marks
Challenge: an unknown linear machine multiplies by a and adds b. It maps 3 to 17 and 7 to 37. Find a and b, then find the input that gives output \(-13\).
Hint
Use the change between the two known pairs to determine the multiplier.