Stage 8 - Q1 - 2 marks
Write the multiplier for a \(8\%\) increase.
Hint
Add the decimal percentage to 1.
Stage 8 - Q2 - 2 marks
Write the multiplier for a \(32\%\) decrease.
Hint
Find the fraction of the original that remains.
Stage 8 - Q3 - 2 marks
Write the multiplier for a \(175\%\) increase.
Hint
An increase above \(100\%\) gives a multiplier above 2.
Stage 8 - Q4 - 2 marks
What percentage change does multiplier 0.18 represent?
Hint
The multiplier gives the remaining proportion.
Stage 8 - Q5 - 2 marks
Decrease 640 by \(12.5\%\).
Hint
Use the remaining multiplier 0.875.
Stage 8 - Q6 - 2 marks
Increase 48 by \(225\%\).
Hint
Add the original \(100\%\) to \(225\%\).
Stage 8 - Q7 - 3 marks
A price rises from USD 96 to USD 132. Find the multiplier and the percentage increase.
Hint
The ratio new/original is the multiplier.
Stage 8 - Q8 - 3 marks
A quantity is multiplied by 0.72 and becomes 126. Find its original value.
Hint
Do not add \(28\%\) of the new value.
Stage 8 - Q9 - 4 marks
A quantity doubles. Find the multiplier and percentage decrease needed to return to the original.
Hint
The return percentage uses the doubled value as its starting point.
Stage 8 - Q10 - 5 marks
Challenge: a price is increased by \(25\%\). Find the percentage decrease that exactly restores its original value. Prove the result for any positive original price.
Hint
The two successive multipliers must have product 1.