Edexcel GCSE Maths Specification A (Linear) Foundation Revision Guide & Workbook Sample

Edexcel GCSE Maths Specification A (Linear) Foundation Revision Guide Sample

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17

NUMBER

GF

DC

E

Percentage changeThere are two methods that can be used to increase or decrease an amount by a percentage.

Method 1 Method 2

£28025% OFF

400 gPLUS

30%EXTR

A

Work out 25% of £280:

25 ____ 100 £280 £70

Subtract the decrease:£280 − £70 £210

Use a MULTIPLIER.100% 30% 130%

130 ____ 100 1.3

The multiplier for a 30% increase is 1.3400 g 1.3 520 g

Kaz buys a car. The normal price of the car is £7200Kaz gets a 10% discount.(a) Work out 10% of £7200

10 ____ 100 £7200 £720

(b) Work out how much Kaz pays for the car.£7200 £720 £6480

Only half of students got full marks on this question. Make sure you know that words like discount and depreciation mean that you have to decrease the price.You can also use the multiplier method:100% 10% 90% 90 ____ 100 0.9 so the multiplier for a 10% decrease is 0.9£7200 0.9 £6480

This was a real exam question that caught students out – be prepared!

A football club increases the prices of its season tickets by 4.8% each year.In 2010 a top-price season ticket cost £550Calculate the price of this season ticket in 2011.

4.8 ____ 100 550 26.4

£550 £26.40 £576.40A question may also ask you to write one quantity as a percentage of another. For a reminder have a look at page 16.

When working with money, answers must be given to 2 decimal places.

Check it!10% of £550 is £55, so 5% is £27.50£550 £27.50 £577.50, which is close to £576.40

grade

D

grade

E

1. The normal cost of a coat is £94In a sale the cost of the coat is reduced by 36%.Work out the sale price of the coat. (3 marks)

2. Alistair sells books.He sells each book for £9.12 including VAT at 20%.Work out how much each book costs before VAT. (4 marks)

grade

Cgrade

D

(cost of book before VAT) 1.2 £9.12

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85

GEOMETRY

GF

DC

E

Pythagoras’ theoremPythagoras’ theorem is a really useful rule. You can use it to fi nd the length of a missing side in a right-angled triangle.

a

b

c

short2 short2 long2

Pythagoras checklistIf you see the following then the question is probably about Pythagoras’ theorem:Right-angled triangle. Lengths of two sides known. Length of third side missing.

a 2 b 2 c 2 Learn this formula ✓

PQR is a right-angled triangle.PQ 6 cm. PR 14 cm.Calculate the length of QR.Give your answer correct to 2 decimal places.a2 b 2 c 262 b2 142

b2 142 62

196 36 160 b √

____ 160 12.6491…

QR 12.65 cm (2 d.p.)

6 cm14 cm

a

b

c

Q

P

R

More than three-quarters of students got no marks for this question. Be really careful when the missing length is one of the shorter sides.1. Label the longest side of the triangle c.2. Label the other two sides.3. Substitute the values into the formula.4. Rearrange and solve. Do not forget to square

root at the end.5. Write units with your answer.

This was a real exam question that caught students out – be prepared!

Calculate the area of this right-angled triangle. You need to fi nd the length of the missing side before you can fi nd the area of the triangle. You know the lengths of the other two sides and the triangle is right-angled, so you can use Pythagoras’ theorem.

7 cm25 cm

Diagram NOTaccurately drawn

Ramps

Flagpoles Ladders

Pythagoras questions come in lots of different forms. Just look for the right-angled triangle.

Calculator skillsUse these buttons to fi nd squares and square roots with your calculator.

x2

You might need to use the S D key to get your answer as a decimal number.

grade

C

grade

C





103

STATISTICS

Problem-solving practiceAbout half of the questions on your exam will need problem-solving skills.These skills are sometimes called AO2 and AO3.You can use a calculator on question 5, but practise the other questions without one. You might have to answer similar questions on your non-calculator paper.For these questions you might need to:• choose what method to use• use the maths you’ve learnt in a new context• plan your answer when solving harder problems• show your working clearly and give reasons for your answers.

AO2AO3

Abi has fi ve cards.Each card has a number written on it.

7 9 3 2 ?The mean of the fi ve numbers is 6One of the numbers is hidden.Work out the hidden number. (2 marks)

Averages and range p. 95

You could try some different values for the hidden number and work out the mean each time. But you can save time by using the rule in the Top tip. There are fi ve numbers and the mean is 6, so the sum of the numbers must be 5 6 30.

This is a useful rule: mean number of data values

sum of data values

You could try some different values for

grade

D

The table shows information about the numbers of Year 7 pupils absent from Keith’s school last week.

Boys GirlsMonday 8 10Tuesday 11 9Wednesday 12 12Thursday 14 13Friday 13 11

Keith wants to compare the data.Draw a suitable diagram or chart. (4 marks)

Bar charts p. 92In this question you have to choose what type of diagram or chart to use. It is best to use a bar chart or a line graph.

• Label BOTH axes correctly. • Draw a key for boys and girls, or make sure it is clear which bars (or lines) are for boys and which are for girls.

have to choose what

grade

F




Edexcel GCSE Maths Specification A (Linear) Foundation Revision Workbook Sample


NUMBER

17

Percentage change1 Helen buys a jacket in a sale.

The normal price of the jacket is reduced by 35%.The normal price is £84Work out the sale price of the jacket.

Reduction 5 35 ____ 100 3 …………

5 …………

Sale price 5 84 2 …………

5 £………… (3 marks)

2 The price of rail tickets is increased by 4.5%.Before the price increase a rail ticket cost £74Work out the cost of the rail ticket after the price increase.

£………………… (3 marks)

3 A washing machine costs £420 plus 20% VAT.Calculate the total cost of the washing machine.

£………………… (3 marks)

4 Kevin works in a bookshop.He is paid £156 per week plus 8% of the total value of the books he sells that week.In one week he sold books with a total value of £1200Work out the total amount Kevin was paid that week.

Money from book sales 5 8 ____ 100 3 …………

5 £…………

Total amount 5 156 1 …………

5 £………… (3 marks)

5 Ali buys 120 cans of drink for a total of £30He wants to make a profit of 40%.Work out the price for which he should sell each can of drink.

………………… p (4 marks)

D Exam questions similar to this have proved especially tricky – be prepared!EXAM

ALERT

Guided

D

D

C

Guided

C

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GEOMETRY

85

Pythagoras’ theorem1 Work out the length of PQ.

Give your answer correct to 3 significant figures.

PQ2 5 6.52 1 …………

PQ2 5 …………

PQ 5 √__________

…………l PQ 5 …………………

PQ 5 ………… cm to 3 s.f. (3 marks)

2 Work out the length of AB.Give your answer correct to 3 significant figures.

………………… cm (3 marks)

3 Work out the length of DE.

DE2 1 ………… 5 262

DE2 5 262 2 …………

DE2 5 …………

DE 5 √__________

…………l DE 5 …………m (3 marks)

4 Work out the length of LM.Give your answer correct to 3 significant figures.

………………… km (3 marks)

C

6.5 cm

8.3 cmR

P

Q

Pythagoras’ theorem

ca

b

a2 1 b2 5 c2

Guided

C 19 cm

7 cm

A C

B

C

26 m10 m

D

F

EThe hypotenuse is 26 m so you subtract rather than add because you are finding one of the shorter sides.

Guided

EXAMALERT

Exam questions similar to this have proved especially tricky – be prepared!

C

7.5 km

23.4 km

M

L

N




STATISTICS

103

Problem-solving practice1 The table shows information about the numbers of boys and girls choosing each of four activities.

Canoeing Archery Climbing SailingBoys 5 8 6 4Girls 9 7 4 7

On the grid, draw a suitable chart or diagram to display this information.

(4 marks)

2 Grace rolls an ordinary dice. She then flips a fair coin. List all the possible outcomes she could get.

(1, H), (1, T) ……………………………………………………………………………………………. . .

…………………………………………………………………………………………………………. . .(2 marks)

3 James asked some people in a café to name their favourite drink.

Coffee

Tea45°

105°

Squash

Cola

The pie chart shows his results.

8 people named squash as their favourite drink. How many people named cola as their favourite drink?

………………… (3 marks)

F

One suitable chart would be a dual bar chart. Remember to label the axes and use a key.

E

It is sensible to use abbreviations; for example, use H for ‘head’ and T for ‘tail’.

Guided

E

Start by working out the size of the angle for squash.




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Edexcel GCSE Maths Specification A (Linear) Foundation Revision Guide & Workbook Sample