Stage 8 - Q1 - 2 marks
Make x the subject.
Hint
Undo the last operation first and keep both sides balanced.
Stage 8 - Q2 - 2 marks
Make x the subject.
Hint
Undo the last operation first and keep both sides balanced.
Stage 8 - Q3 - 3 marks
Make x the subject.
Hint
Undo the last operation first and keep both sides balanced.
Stage 8 - Q4 - 3 marks
Make x the subject.
Hint
Undo the last operation first and keep both sides balanced.
Stage 8 - Q5 - 4 marks
A hire cost is \(C=14h+9\) dollars for h hours. Rearrange for h, then find h when \(C=261\).
Hint
Undo the last operation first and keep both sides balanced.
Stage 8 - Q6 - 4 marks
A hire cost is \(C=8h+11\) dollars for h hours. Rearrange for h, then find h when \(C=35\).
Hint
Undo the last operation first and keep both sides balanced.
Stage 8 - Q7 - 5 marks
Rearrange \(v=d/t\) to make t the subject. State the restrictions needed in both the original and rearranged formula.
Hint
Remove the denominator first.
Stage 8 - Q8 - 5 marks
Use \(P=3n+b\) to find n when \(P=47\) and \(b=8\) in two ways: rearrange first, and substitute first. Explain why they agree.
Hint
Track the subtract 8 and divide 3 operations in each route.
Stage 8 - Q9 - 5 marks
A pupil rearranges \(y=ax+b\) as \(x=(y-b)/a\). What happens when \(a=0\)? Describe separately \(y=b\) and \(y\ne b\).
Hint
Substitute \(a=0\) into the original formula, not the divided version.
Stage 8 - Q10 - 5 marks
Two hire companies use \(A=4h+18\) and \(B=7h+3\) dollars. Rearrange both for h. Find the duration at which their costs agree and explain which is cheaper for longer durations.
Hint
Compare the formulas by subtracting one cost from the other.