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GCSE Maths · Higher · Chapter 2: Fractions, ratio and proportion · Lesson 2

Percentage change and comparison

Grades 4–7About 45 minutesCalculator allowed38 marks
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NameClassDate
A

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

  1. A1
    Needed today

    Write out of as a percentage.

    [1 mark]
    Answer
  2. A2
    Last lesson

    Work out .

    [1 mark]
    Answer
  3. A3
    Key Stage 3

    Work out when .

    [1 mark]
    Answer
  4. A4
    Key Stage 3

    Solve .

    [1 mark]
    Answer
B

Example, then your turn

Grades 4–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

Increase £84 by 17.5%.

Hint An increase of 17.5% means you end with 117.5% of the amount. Write that as a decimal multiplier.
  1. B1

    Increase £136 by 8.5%.

    [2 marks]
    Answer
Example 2

A price falls from £85 to £68. Work out the percentage decrease.

Hint Work out the change, then divide it by the ORIGINAL amount.
  1. B2

    A season ticket rises from £360 to £387. Work out the percentage increase.

    [2 marks]
    Answer
Example 3

Decrease 2350 kg by 12%.

Hint A decrease of 12% leaves 88% of the amount. The multiplier is .
  1. B3

    Decrease £680 by 6.5%.

    [2 marks]
    Answer
C

Practice

Grades 5–6
  1. C1

    Write 45 cm as a percentage of 1.2 m.

    [2 marks]
    Answer
  2. C2

    Sam scored 34 out of 40 in French and 52 out of 60 in Spanish. In which test did he score the higher percentage? Show how you decide.

    [2 marks]
    Answer
  1. C3

    A coat sells for £68, which is £17 more than the shop paid. Find the percentage profit, to 1 d.p.

    [2 marks]
    Answer
  2. C4

    Find the single multiplier for a 15% increase followed by a 15% decrease.

    [2 marks]
    Answer
  3. C5

    Shop A sells a jacket for £45 with off. Shop B sells the same jacket for £42 with 25% off. Which shop is cheaper, and by how much?

    [3 marks]
    Answer
  4. C6

    A car is bought for £8400 and sold a year later for £6930. Work out the percentage loss.

    [2 marks]
    Answer
D

Exam-style questions

Grades 6–7
  1. D1

    Kai says, "Members fell from 120 to 90, a 25% decrease. So a rise from 90 to 120 is a 25% increase."

    Explain why Kai is wrong. Work out the correct increase, to 1 decimal place.

    [2 marks]
  1. D2

    A museum had 18 500 visitors in May. In June the number of visitors rose by 14%. In July there were 19 240 visitors.

    (a)

    Work out the number of visitors in June.

    [2 marks]
    Answer
    (b)

    Work out the percentage decrease from June to July. Give your answer to 1 decimal place.

    [3 marks]
    Answer
    (c)

    Work out the percentage change from May to July. Say whether it is an increase or a decrease.

    [2 marks]
    Answer
    Total for D2: 7 marks
  2. D3

    In a school, 55% of the students are girls. 40% of the girls and 30% of the boys have a pet. What percentage of all the students have a pet?

    [3 marks]
    Answer
E

Extension

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

  1. E1

    The length of a rectangle is increased by 25%. Its area stays the same. By what percentage must its width be decreased?

    [3 marks]
    length lwidth w
    Not drawn accurately
    Hint 1 · What to try

    Call the length and the width . Write the new length.

    Hint 2 · The first line

    New width , so the new width is .

    Hint 3 · The full method

    , which is a multiplier for a decrease of .

    Answer
F

How did it go?

Colour one circle on each line.
Not yetNearlyYes
I can increase or decrease an amount by a percentage using a multiplier.
I can write one amount as a percentage of another.
I can work out a percentage change from the original amount.

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