Mathematics GCSE Revision Session

Mrs Claire Dixon

BSc (Hons), PGCE, MEd

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Teacher

Pentrehafod School, Swansea

Percentages

(Calculator)

Mathematics GCSE Revision Session

Session 1: Solving linear equations

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Session 2: Solving simultaneous equations

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Session 3: Percentages (Non-Calculator)

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Session 4: Percentages (Calculator)

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Session 5 (Live Session): Recap of sessions 1 – 4

Starter

1. Write the following percentages as decimals:
1. 35%
2. 14%
3. 2%

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2. Round each of the following to 2dp:
1. 3.575
2. 12.7777
3. 312.0903
4. 0.09898

Finding a percentage of a quantity

Success Criteria:

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• Multiply the quantity by the percentage

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• Divide by 100

Example

Find 27% of 65

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Finding a percentage of a quantity

Task

Find:

1. 82% of 51

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• 56% of 2834

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• 98% of 654

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• 4% of 620

Finding a percentage of a quantity

Expressing one number as a percentage of another

Success Criteria:

• One number divided by the other
• Multiply by 100

Expressing one number as a percentage of another

Example:

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Express 86 as a percentage of 160

Expressing one number as a percentage of another

Task

Express the following as a percentage of the other:

1. 92 out of 250
2. 24 out of 80
3. 6 out of 33

Expressing one number as a percentage of another

Example (Different Units):

Express 11 months as a percentage of 5 years

Expressing one number as a percentage of another

Task

Express each of the following as a percentage of the other:

1. 25 minutes of 3 hours
2. 12 days of a year
3. 8 months of 3 years
4. 555ml of 6L
5. 1200cm of 4km

Calculating percentage changes (increase and decrease)

Example

Joshua earns £12.50 per hour. He receives a pay increase of £1.50 per hour.

Calculate his pay increase as a percentage of the original price.

Calculating percentage changes (increase and decrease)

Example

A jumper originally costing £70 is reduced to £65.80.

Calculate the reduction as a percentage of the original price.

Calculating percentage changes (increase and decrease)

Task

1. A bike was bought for £5495. A year later it was sold for £1050 less. Calculate the loss in value as a percentage of the original price.

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• Charlie bought an antique painting for £10,500 and sold it for £20,000 a few years later. Find his profit as a percentage of

what he paid for the painting.

Calculating percentage changes (increase and decrease)

Multipliers

Success Criteria for an increase (or profit):

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• 100% + percentage increase

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• Divide by 100

Success Criteria for a decrease (or loss):

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• 100% - percentage increase

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• Divide by 100

Example

Write the multiplier for a 20% increase.

Multipliers

100%

20%

Example

Write the multiplier for a 30% decrease.

Multipliers

100%

30%

70%

Task

Write the multiplier for each of the following:

1. 32% increase
2. 12% profit
3. 6% decrease
4. 73% loss
5. 61% gain

Multipliers

Key words:

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Appreciation – when the value of an item increases.

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Depreciation – when the value of an item decreases.

Proportional changes: appreciation and depreciation

Success Criteria:

• Calculate the multiplier
• Multiply the quantity by the multiplier

Example

Jack buys a camera for £995. This camera increases in value over time. When Jack goes to sell the camera, it is worth an extra 3% to when he purchased it. Using multipliers, how much is the camera worth when Jack wants to sell it?

Proportional changes: appreciation and depreciation

Example

Catrin buys a phone for £415. The phone depreciates in value over time. When Catrin wants to sell her phone, it has decreased in value by 16%. Using multipliers, how much is the phone worth when Catrin wants to sell her phone?

Proportional changes: appreciation and depreciation

Task

1. A shop reduces all its prices by 24% during a sale. Using multipliers, what would be the new price of an item originally costing £180?

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• Emily’s salary increases by 2%. Originally, Emily was paid £34,200 per year. Using multipliers, how much is Emily’s salary now?

Proportional changes: appreciation and depreciation

Key words:

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Compound Interest – this is calculated on the original amount and the interest already accumulated.

Repeated proportional changes: appreciation and depreciation

Success Criteria:

• Calculate the multiplier
• Raise the multiplier to the number of years/months/days etc
• Multiply the quantity by the above

Example

Tom puts £500 in the bank at 3% compound interest per year.

After this £500, Tom does not take money out or put money in to the account. How much money will he have in the bank after 6 years?

Proportional changes: appreciation and depreciation

Example

Ella buys a car for £9995. The car depreciates by 7% per year.

How much is the car worth after 4 years?

Proportional changes: appreciation and depreciation

Task

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1. David invests £5000 into a bank account at 2.5% interest for 4 years. How much money does he have at the end of the 4 years?

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• A shop reduces all its prices by 15% earlier in the week and then a further reduction of 8% for the following 2 weeks. What would be the new price of an item originally costing £120?

Proportional changes: appreciation and depreciation

Percentages Plenary

Show clearly whether the following statement is true or false.

‘If you increase a positive number by 10% and then decrease that new value by 10%, you get back to your original number.’ [4]

Mathematics GCSE Revision Session

Session 1: Solving linear equations

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Session 2: Solving simultaneous equations

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Session 3: Percentages (Non-Calculator)

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Session 4: Percentages (Calculator)

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Session 5 (Live Session): Recap of sessions 1 – 4