Stage 8 - Q1 - 2 marks
Start with 300; increase by \(10\%\), then decrease by \(10\%\). Find the final value.
Hint
Use 1.1 and then 0.9.
Stage 8 - Q2 - 2 marks
Start with 160; decrease by \(25\%\), then increase by \(20\%\). Find the final value.
Hint
The second change starts from the reduced amount.
Stage 8 - Q3 - 2 marks
Start with 240; increase by \(20\%\), then increase by \(15\%\). Find the final value.
Hint
Successive increases multiply; their percentages do not simply add.
Stage 8 - Q4 - 2 marks
A price changes by multiplier 0.855. State the net percentage change.
Hint
Compare the overall multiplier with 1.
Stage 8 - Q5 - 3 marks
Shop A reduces USD 80 by \(15\%\). Shop B reduces USD 90 by \(25\%\). Which final price is lower?
Hint
The starting prices are different.
Stage 8 - Q6 - 3 marks
A quantity falls by \(30\%\). What percentage increase restores the original? Give the result to 1 d.p.
Hint
The original is now larger than the reduced value by a fraction of that reduced value.
Stage 8 - Q7 - 3 marks
Compare a \(12\%\) rise followed by a \(12\%\) fall with the reverse order. State both net changes.
Hint
Compare the products of the same two multipliers.
Stage 8 - Q8 - 4 marks
A quantity becomes 192 after a \(20\%\) increase followed by a \(20\%\) decrease. Find the original.
Hint
Combine the changes before reversing them.
Stage 8 - Q9 - 4 marks
Show that an increase of \(p\%\) followed by a decrease of \(p\%\) gives a net decrease of \(\frac{p^2}{100}\) percent for \(0<p<100\).
Hint
Use the difference-of-squares pattern, keeping p as a percentage number.
Stage 8 - Q10 - 5 marks
Challenge: a \(20\%\) discount followed by a \(10\%\) discount is to be matched by a single discount of \(p\%\), followed by a \(25\%\) increase. Find p and verify the result with an original price of USD 250.
Hint
Equate the overall multipliers before choosing a starting price.