Stage 9 - Q1 - 2 marks
Write the multiplier for a 8% increase.
Hint
An increase uses a multiplier greater than 1.
Stage 9 - Q2 - 2 marks
Write the multiplier for a 13% decrease.
Hint
A decrease uses a positive multiplier below 1.
Stage 9 - Q3 - 3 marks
Increase 170 by 9%, then by 13%.
Hint
Multiply the two multipliers; do not add the percentages.
Stage 9 - Q4 - 3 marks
Decrease 190 by 11%, then by 13%.
Hint
Both multipliers are less than 1.
Stage 9 - Q5 - 4 marks
An item costs USD 210. Its price rises by 13%, then falls by 14%. Find the final price to the nearest cent.
Hint
The decrease is a percentage of the raised price.
Stage 9 - Q6 - 4 marks
An item costs USD 230. Its price rises by 15%, then falls by 14%. Find the final price to the nearest cent.
Hint
The decrease is a percentage of the raised price.
Stage 9 - Q7 - 5 marks
Find the single overall percentage change equivalent to a 17% increase followed by a 15% decrease.
Hint
Compare the combined multiplier with 1.
Stage 9 - Q8 - 5 marks
After a 19% rise and a 15% fall, a quantity is 273.105. Find its starting value exactly.
Hint
Undo a percentage multiplier by division.
Stage 9 - Q9 - 5 marks
Will a 21% increase followed by a 16% decrease give the same final amount if their order is reversed, with no intermediate rounding?
Hint
Represent each percentage change as multiplication.
Stage 9 - Q10 - 3 marks
A positive price rises by \(p\%\), then falls by the same \(p\%\), with no intermediate rounding. Its final value is 96% of the original. Find \(p\), where \(0<p<100\).
Hint
A rise and equal fall produce a difference of squares.