MODULE 3 WORKBOOKPercentages

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7 May 2019

Contents

Lesson 1 p 3

Lesson 2 p 8

Lesson 3 p 13

Apply (Non-calculator) p 18

Apply (Calculator) p 21

2

Module 3

Percentages PODS Before continuing, make sure you have watched and have access to the following Pods. To find these, simply log in to GCSEPod and enter the codes given into the search bar (or click on the titles below).

1. Converting to percentages | MATHS-29-001

2. Finding percentages | MATHS-11-001

3. Comparing using percentages | MATHS-11-002

4. Percentage change | MATHS-11-003

5. Simple interest | MATHS-11-005

6. Growth and decay | MATHS-10-008

Lesson 1

Conversions between fractions, decimals and percentages PODS

1. Converting to percentages | MATHS-29-001

Quiz

Watch the Pods and answer the questions below.

Do not use a calculator.

1. Which of the following is not equivalent to 0.25?a) 2.5%

b) 25%

c) ¼

d) 20/80

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2. Which is the odd one out?a) 5%

b) 1/20

c) 0.5

d) 5/100

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3. Write 0.3 as a percentage.

a) 30%

b) 33%

c) 3%

d) 0.3%

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4. Which of the following is not equivalent to 10%?

a) 1/10

b) 0.010

c) 25/250

d) 0.10

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5. Write 43% as a fraction in its simplest terms.

a) 43/100

b) 4/3

c) 4.3/10

d) 11/25

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6. Which fraction is in its simplest form and is equivalent to 80%?

a) 80/100

b) 40/50

c) 8/10

d) 4/5

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7. Write 55% as a fraction and cancel it down as much as possible.

a) 55/100

b) 11/20

c) 5.5/10

d) 5/100

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8. Write 3/6 as a percentage.

a) 50%

b) 36%

c) 30%

d) 25%

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9. Convert two fifths into a percentage.

a) 20%

b) 25%

c) 40%

d) 50%

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10. Write 85% as a decimal.

a) 0.085

b) 0.85

c) 8.5

d) 85.00

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5

Practise

Practise converting to percentages.

Do not use a calculator.

1. Show that 18% is less than 1/5.

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2. There are 30 people on a bus. 18 are getting off the bus. What percentage is this?

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3. Zane wants to find the decimal that is equivalent to 86%. Lucy says

“It is 0.43 because 86% is 86/100 which cancels to 43/50”

Is Lucy correct? You must give a reason for your answer.

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4. 0.65 can be written as x/20. Find the value of x.

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5. In a class of 20 students, 9 take German and the rest take Spanish. What percentagetake Spanish?

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6

Practise

Practise converting percentages.

You may use a calculator.

1. Susie says that 1/3 is the same as 33% because 33/100 = 1/3. Is she correct? You mustgive a reason for your answer.

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2. Show that 40% is greater than 3/8.

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3. There are 48 people on a bus. 17 people are getting off the bus. What percentage ofpeople are staying on the bus? Give your answer correct to 1dp.

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4. If 14 out of every 15 people in a school enjoy maths, is this greater than 95%? Showworking to support your answer.

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5. Write these in ascending order:

3/5, 62%, 0.58, 11/20

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Lesson 2

Percentages of Amounts

PODS

2. Finding percentages | MATHS-11-001

3. Comparing using percentages | MATHS-11-002

Quiz

Watch the pod and answer the questions below.

You may use a calculator for questions 5, 7 and 10.

1. 10% of £26 is equal to x% of £52. Calculate the value of x.

a) 20%

b) 5%

c) 10%

d) 2.6%

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2. Which of the following has a different value from the others:

a) 20% of 300

b) 50% of 120

c) 10% of 600

d) 25% of 250

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3. Find 45% of 500.

a) 200

b) 125

c) 225

d) 22.5

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4. Find 6% of 40.

a) 24

b) 0.024

c) 0.24

d) 2.4

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5) Use a calculator to find 16.4% of 345

a) 56.58

b) 5.658

c) 565.8

d) 0.5658

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6. What is 40 as a percentage of 50?

a) 0.8%

b) 80%

c) 8%

d) 20%

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7. Use a calculator to find 5 as a percentage of 135 correct to 1 decimal place.

a) 37.0%

b) 27%

c) 3.7%

d) 0.27%

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8. A test score is 12/25. What percentage is this?

a) 3%

b) 0.48%

c) 50%

d) 48%

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9. A limited-edition toy is bought for $100. It is sold for $130. What is the percentageprofit?

a) 13%

b) 30%

c) 130%

d) 76.9%

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10. A test score is 24/35. Use a calculator to calculate this as a percentage. Give youranswer correct to 1 d.p.

a) 68.6%

b) 0.69%

c) 1.46%

d) 6.89%

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10

Practise

Practise finding and comparing using percentages.

Do not use a calculator.

1. 15% of a number is 30. What is 50% of the number?

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2. James has a pizza. He eats 2 slices of it which is 40% of the pizza. How many slices ofpizza does he have left?

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3. Kylie sits two maths tests. She scores 17/25 in the first one, and 14/20 in the secondone. Which test has she done better in?

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4. A car is bought for £2000. It is sold for £2500. What is the percentage profit?

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5. 25% of animals in a kennel are cats. If there are 100 cats, how many animals are there?

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Practise

Practise finding and comparing using percentages.

You may use a calculator.

1. Jamie wants to find 125% of an amount. Paul says that this is the same as multiplying bythe decimal 12.5 as 125% = 12.5. Is Paul correct? You must explain your answer.

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2. A car is bought for £4595 and is sold for £3250. What is the percentage pricedecrease? Give your answer correct to 1 decimal place.

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3. Which of these is the largest?

63% of £120

42% of £180

115% of £65

95% of £80

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4. Paula sits two science tests. She gets 34 out of 63 in her biology test, and 30 out of 55in her chemistry test. Which test has she done better in?

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5. Jane spends 30% of her money on a lamp. She spends 50% of the remaining moneyon a rug. She has £35 left. How much money did she start with?

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Lesson 3

Percentage Changes

PODS

4. Percentage change | MATHS-11-003

5. Simple interest | MATHS-11-005

6. Growth and decay | MATHS-10-008

Quiz

Watch the pods and answer the questions.

You may use a calculator for questions 5 and 6.

1. Increase 30 by 45%.

a) 43.5

b) 13.5

c) 58.5

d) 31.35

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2. Decrease 550 by 70%.

a) 935

b) 165

c) 385

d) 7.86

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3. To increase an amount by 12% you can multiply by:

a) 0.12

b) 1.12

c) 12.0

d) 0.88

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4. To decrease an amount by 18% you can multiply by:

a) 0.82

b) 0.18

c) 1.82

d) 1.18

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5. Use a calculator to increase 355 by 12%.

a) 42.6

b) 294.8

c) 397.6

d) 375.2

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6. Use a calculator to decrease 3467 by 4%

a) 3328.32

b) 3605.68

c) 138.68

d) 1387.2

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7. If you save £400 for 3 years with a simple interest rate of 5% per annum, the totalamount of interest you will earn is:

a) £20

b) £460

c) £15

d) £60

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8. Calculate 60% of 50% of 100.

a) 60

b) 50

c) 30

d) 10

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9. A rabbit population increases by 20% each year. If the colony has 100 rabbits initially,how many will there be after 2 years?

a) 132

b) 120

c) 140

d) 144

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10. A car value increases by 5% per year. If you buy a car for £1000, which calculationcould you use to find out how much it will be worth after 3 years?

a) 1000 × 1.5(

b) 1000 × 1.05(

c) 1000 × 1.05 × 3

d) 1000 ÷ 1.05

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15

Practise

Practise percentage change, simple interest and growth and decay.

Do not use a calculator.

1. Sophie buys a coat which originally cost £40 in a 35% off sale. How much does shepay for the coat?

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2. A shop buys cheese at £0.85 per 100g and sells it on with a 40% profit. How much dothey sell 100g for?

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3. The price of a new fridge is £400. There are 2 deals offered by the company: ‘30% off’or ‘£100 off if you spend over £300’. Which is the better deal to buy the fridge? Youmust explain your answer.

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4. You invest money in a bank that offers you simple interest of 2% p.a. If you originallyinvest £500, how much will you have after 6 years?

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5. Stu is a runner. He runs 5km in 25 minutes. During training he knocks 20% off his time.He then knocks a further 5% off this time in a race to achieve his personal best. Whattime did he achieve?

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Practise

Practise percentage change, simple interest and growth and decay.

You may use a calculator.

1. Sue’s council tax is rising by 4.3% next year. Currently she pays £1300 split into 12 equalinstalments. How much will she be paying extra each month with the rise?

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2. Ted’s car depreciates by 14.5% each year. If he bought it for £5995, how much will itbe worth after 7 years?

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3. Shivani saves money in a bank account offering simple interest of 4.7% per year. Sheinvests £500. How many years will it take for her savings to be worth more than £600if she does not add any more money to the account?

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4. The population of rhinos in a safari park is falling by 12% each year. If there are 72rhinos this year, how many would you expect in the park in 5 years?

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5. Gina buys 3 tickets for a concert. The tickets are £49 each, plus VAT, and then plus a£2.50 booking fee. How much will she pay? (VAT is charged at 20%)

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17

Apply

Apply what you have revised about percentages.

Do not use a calculator.

Remember

Percentage means “out of 100”.

Percentage ÷ 100 = decimal. Decimal x 100 = Percentage. Compare amounts by

converting them all into percentages first.

Increase and decrease amounts by multiplying by a decimal multiplier. E.g. 1.2 = increase by 20%, 0.88 = decrease by 12%.

Percentage profit / loss = (“change” ÷ original) x 100

1. Elliott scored 12/30 on a maths test. Jules scored 20/50 in a science test. Who scoredmore highly? You must explain your answer.

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2. A company wants to run a promotion on music downloads. It wants to give areduction of between 30% and 35%. Which of these fractions could they use? Youmust show working to explain your answer.

8/25 off original price

2/5 off original price

¼ off original price

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3. There are 70 sweets in a bag. Bill eats 2/5 of them. Jane eats 20% of them. Whatpercentage of sweets are left?

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4. On Sunday, Ethan completes 15 pages of his maths book, each with 12 calculations onit. On Monday, he completes 15% more calculations than on Sunday. How manycalculations does he complete on Monday?

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5. Richard buys a new TV in a 20% off sale. He also has a loyalty card which will get him afurther 10% off the new price. If the TV was £500 before the sale, how much doesRichard pay?

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6. In a school, the ratio of boys to girls is 3 : 7. 70% of the girls play sport after school.50% of boys play sport after school. What percentage of students play sport afterschool?

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7. A standard packet contains 12 biscuits. A special offer has 25% extra free. Joe eats 40%of a special offer packet. How many biscuits are left?

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8. Will spends 40% of his monthly wages on rent, ¼ on bills and 30% on food andentertainment. He saves the rest. If his rent is £600 per month, how much does hesave?

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9. There are 3 classes in year 2. Class 1 has 30 students, class 2 has 25 students and class 3has 20 students. On a day in May, 3 are absent from class 1, 80% of class 2 are presentand 5% of class 3 are absent. The school aims for 90% attendance. Has the schoolreached its target on this day?

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10. House prices in Hexville have risen by 5% each year for 2 years. If a house was boughtfor 120,000 2 years ago, how much is it worth now?

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Apply

Apply what you have revised about percentage.

You may use a calculator.

Remember

Percentage means “out of 100”.

Percentage ÷ 100 = decimal. Decimal x 100 = Percentage. Compare amounts by

converting them all into percentages first.

Increase and decrease amounts by multiplying by a decimal multiplier. E.g. 1.2 = increase by 20%, 0.88 = decrease by 12%.

Percentage profit / loss = (“change” ÷ original) x 100

1. A lightbulb company aim to have less than a 0.5% fault rate on their production line.Last week 25,460 bulbs were produced and 115 were found to be faulty. Is thecompany working within its aim? You must explain your answer.

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2. There are 1600 pupils in a school. 63% of these get the bus to school. Of thesestudents, 49% also get the bus home. How many students get the bus to and fromschool?

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3. Suzanne and Bill are losing weight. Suzanne started at 82kg and has lost 8% of herbody weight. Bill started at 91kg and has lost 11%. How many kilograms have they lostin total?

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4. A house is bought for £215,000. In the first 5 years it increases in value by 12%. In thenext 4 years it decreases in value by 12%. Ted says that the house is now worth thesame as it was bought for. Is Ted correct? You must explain your answer.

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5. Will wants to grow some carrots. He buys a packet of 80 seeds. The packet claims thatthe seeds have at least a 90% chance of germinating. Will sows 65% of these seeds. 47of the seeds grow. Does this meet the claims of the company?

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6. Haris wants to invest £1500 in a savings account for 1 year. He considers the following2 offers:

Offer A: Simple interest of 2% per month + £20 bonus for a full year of saving.

Offer B: Compound interest of 1.9% interest every month.

Which is the better deal? You must show your working.

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7. Sophie’s car depreciates by 12% per year. If she bought it for £5890, how many yearswill it take for the value to fall below £4000?

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8. Li wants to increase the number of days that she exercises each month by 10%.

In April, she ran on 20% of the days and cycled on 3/10 of them.

By June, she had run on 30% of the days and still cycled on 3/10 of them.

She never runs and cycles on the same day.

Has she increased the number of days she exercised by 10% each month? Showworking to support your answer.

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9. There are 2 colours of bead in a bag, red and blue in the ratio 7:2. When 34% of thered beads have been removed there are 462 red beads left. How many blue beadsare there?

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10. Pete wants to buy a new bike. He has found the bike he wants online in 3 differentshops.

Shop 1: £550 + VAT

Shop 2: £750 with 15% off

Shop 3: £150 + 12 monthly payments of £40

Which shop should Pete buy the bike from to get the best deal?

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