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date in the last presidential election the average length of all books about statistics the variation in the weight of 100 boxes of cereal selected from a factory’s production line INTERPRETATIONYou are most likely to be familiar with this branch of sta-tistics because many examples arise in everyday life Descriptive statistics

-1)

MATHEMATICS A

David Turner, Ian Potts

eBook included

Uncorrected proof, all content subject to change at publisher discretion. Not for resale, circulation or distribution in whole or in part. ©Pearson 2017

-1)

MATHEMATICS A

David Turner

Ian PottsUncorrected proof, all content subject to change at publisher discretion. Not for resale, circulation or distribution in whole or in part. ©Pearson 2017

COURSE STRUCTURE

ABOUT THIS BOOK

ASSESSMENT OVERVIEW

UNIT 1

UNIT 2

UNIT 3

UNIT 4

UNIT 5

FACT FINDERS

CHALLENGES

GLOSSARY

ANSWERS

INDEX

ACKNOWLEDGEMENTSIVVI

VII 2 96
174
236
298
372
382
384
388
446

454Uncorrected proof, all content subject to change at publisher discretion. Not for resale, circulation or distribution in whole or in part. ©Pearson 2017

2 is the rst and only even prime number. cannot be written

as an exact fraction; this denes it as an irrational number. If is a whole number (integer) bigger than 0, the value of 2 is always divisible by 2. Fermat"s Last Theorem states that there are no integers which have a solution to when is bigger than 2.

M02_IGMA_SB_1444_U02.indd 9604/07/2016 16:13Uncorrected proof, all content subject to change at publisher discretion. Not for resale, circulation or distribution in whole or in part. ©Pearson 2017

UNIT 297

LEARNING OBJECTIVES

BASIC PRINCIPLES

KEY POINT

EXAMPLE 1

NUMBER 2

The smallest measurable thing in the Universe is the which if written in full is 0.000 000 000 000 000 000 000 000 000 000 000 016

2 metres.

The size of the observable universe is approximately a giant sphere of diameter 880 000 000 000 000 000 000 000

000 metres.

These numbers can both be written more

conveniently in a simpler format called standard form. The rst length is 1.62 × 10 -35 m and the second measurement is 8.8 × 10 26
m. fifiMax Planck (1858-1947)

Write a number in standard form

Calculate with numbers in standard form Work out a percentage increase and decrease Solve real-life problems involving percentages

10 2

× 10

3 = 10 5 10 m

× 10

n = 10 m n 10 2

÷ 10

3 = = 10 -1 10 m

÷ 10

n = 10 m n (10 3 2 = 10 6 (10 m n = 10 mn Standard form is always written as π b a, where a is between 1 and 10, but is never equal to

10 and

b is an integer which can be positive or negative.

Write 8

250

000 in standar

d form. 8 250

000 = 8.25 × 1

000

000 = 8.25 × 10

6 Standard form is used to express large and small numbers more efficiently.

M02_IGMA_SB_1444_U02.indd 9704/07/2016 16:13Uncorrected proof, all content subject to change at publisher discretion. Not for resale, circulation or distribution in whole or in part. ©Pearson 2017

UNIT 298

EXAMPLE 2

ACTIVITY 1

EXERCISE 1

EXERCISE 1*

000 = 375 000

Write each of these in standard form.

1 456
3

123.45

5 568
7

706.05

2 67.8
4

67 million

6 38.4
8

123 million

W rite each of these as an ordinary number. 9

4 × 10

3 11

4.09 × 10

6 13

5.6 × 10

2 15

7.97 × 10

6 10

5.6 × 10

4 12

6.789 × 10

5 14

6.5 × 10

4 16

9.876 × 10

5 17 The approximate area of all the land on Earth is 10 8 square miles. The area of the British

Isles is 10

5 square miles. How many times larger is the Earth"s area? 18

The ar

ea of the surface of the largest known star is about 10 15 square miles. The area of the surface of the Earth is about 10 11 square miles. How many times larger is the star"s area? Calculate these, and write each answer in standard form. 19 (2 × 10 4 ) × (4.2 × 10 5 ) 21(4.5 × 10 12 ) ÷ (9 × 10 10 20 (6.02 × 10 5 ) ÷ (4.3 × 10 3 ) 22(2.5 × 10 4 ) + (2.5 × 10 5

Write each of these in standard form.

1 089
3 2 050
4

54 billion

000 000

000 neurons,

and over the human lifespan 1 000 000 000 000

000 neural

connections are made.

Write these numbers in standard form.

Calculate the approximate number of neural

connections made per second in an average human lifespan of 75 years.

Q4 HINT

1 billion = 10

9

M02_IGMA_SB_1444_U02.indd 9804/07/2016 16:13Uncorrected proof, all content subject to change at publisher discretion. Not for resale, circulation or distribution in whole or in part. ©Pearson 2017

UNIT 299

Earth Sun

Calculate these, and write each answer in standard form. 5 10 10 2

× 8 10 million ÷

10 6 11 10 7

÷10

7 6 (10 3 2 9 10 12 10 9

× 12

10 12

1 million

7 10 9 10 4 10 (10 2 4 Calculate these, and write each answer in standard form. 13 (5.6 × 10 5 ) + (5.6 × 10 6 ) 15 (3.6 × 10 4 ) ÷ (9 × 10 2 14 (4.5 × 10 4 ) × (6 × 10 3quotesdbs_dbs14.pdfusesText_20
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