Download Standard Form practice

Q1.
x, y and z are standard form numbers.
5
x = 2.5 × 10
(a)
Calculate
4
y = 3.8 × 10
6
z = 1.9 × 10
x–y
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Answer ..................................................
(1)
(b)
Calculate
x
2
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Answer ..................................................
(1)
(c)
Calculate
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Answer ..................................................
(1)
(Total 3 marks)
Q2.
A company produces 35 million packets of crisps and snacks each week.
Production is 7 days a week, 24 hours a day.
(a)
On average, how many packets are produced in one day?
Give your answer in standard form.
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Answer ................................................
(2)
Page 1 of 14
(b)
Each packet makes an average profit of 12p.
Calculate the average hourly profit for this company.
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Answer £.............................................
(2)
(Total 4 marks)
Q3.
For each calculation circle the answer that is correct and is in standard form.
(a)
5
7
(3 × 10 ) × (4 × 10 )
Answer
12 × 10
12
1.2 × 10
36
35
12 × 10
13
1.2 × 10
(1)
(b)
–8
–2
(4 × 10 ) ÷ (8 × 10 )
Answer
–6
0.5 × 10
5 × 10
4
–7
5 × 10
5 × 10
–5
(1)
(Total 2 marks)
Q4.
A builder has 7200 kg of sand.
(a)
Write 7200 kg in grams.
Give your answer in standard form.
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Answer ................................................. g
(2)
(b)
One grain of this sand weighs 0.0006 g.
Write the weight of one grain of sand in standard form.
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Answer ................................................. g
(1)
Page 2 of 14
(c)
How many grains of sand are there in 7200 kg of sand?
Give your answer in standard form.
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Answer .................................................
(2)
(Total 5 marks)
Q5.
In 2002 the number of visitors to four tourist attractions is shown in the table.
(a)
Blackpool Pleasure Beach
6.2 million
Edinburgh Castle
1 153 000
Giant’s Causeway
4.07 × 105
Tate Modern
4.6 million
Write the number of visitors to Edinburgh Castle in standard form.
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Answer .................................................
(1)
(b)
Blackpool Pleasure Beach claimed that it had more visitors than the other three
added together.
Is this claim true?
You must show your working.
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(2)
(Total 3 marks)
Page 3 of 14
Q6.
(a) The star Alpha Centauri is approximately 40 653 230 000 000 kilometres from Earth.
Write this number in standard form to 3 significant figures.
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Answer .................................................
(2)
(b)
Light travels at approximately 298 000 kilometres per second.
There are 86 400 seconds in a day.
How many days will light take to reach the Earth from Alpha Centauri?
Give your answer to an appropriate degree of accuracy.
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Answer ................................................. days
(4)
(Total 6 marks)
Q7.
The population of France is 5.83 × 107 people.
The area of France is 5.47 × 105 square kilometres.
Mean number of people =
Calculate the mean number of people per square kilometre in France.
Give your answer to a suitable degree of accuracy.
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Answer .................................................
(Total 3 marks)
Page 4 of 14
Q8.
The table gives the diameter, in metres, of planets in the solar system.
The diameters are given to an accuracy of 3 significant figures.
(a)
Planet
Diameter (metres)
Mercury
4.88 × 106
Venus
1.21 × 107
Earth
1.28 × 107
Mars
6.79 × 106
Jupiter
1.43 × 108
Saturn
1.21 × 108
Uranus
5.11 × 107
Neptune
4.95 × 107
Pluto
2.39 × 106
Which planet has the largest diameter?
Answer .................................................
(1)
(b)
Which planet has the smallest diameter?
Answer .................................................
(1)
(c)
Which planet has a diameter approximately 10 times that of Venus?
Answer .................................................
(1)
(d)
Write
as an ordinary number.
Answer .................................................
(1)
Page 5 of 14
(e)
What is the diameter of Pluto in kilometres?
Give your answer in standard form.
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Answer ................................................. km
(2)
(Total 6 marks)
Q9.
Some large numbers are written below.
1 million = 106
1 billion = 109
1 trillion = 1012
(a)
How many millions are there in one trillion?
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Answer ....................................................
(1)
(b)
Write 8 billion in standard form.
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Answer ....................................................
(1)
(c)
Work out 8 billion multiplied by 3 trillion.
Give your answer in standard form.
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Answer ....................................................
(2)
(Total 4 marks)
Page 6 of 14
Q10.
(a)
A calculator displays a number in standard form as
Which of the following numbers does the display show?
Circle the correct answer.
7000
0.700
0.007
700
0.0007
(1)
(b)
Use your calculator to work out
cos (tan–10.45)
(i)
Give all the figures in your calculator display.
Answer .................................................
(1)
(ii)
Write your answer to an appropriate degree of accuracy.
Answer .................................................
(1)
(c)
Use your calculator to work out
Answer .................................................
(1)
(Total 4 marks)
Page 7 of 14
Q11.
Astronomers measure distances in the solar system in astronomical units (AU).
One AU is 150 000 000 kilometres.
The distance from the Sun to Pluto is 39.5 AU.
How many kilometres is the Sun from Pluto?
Give your answer in standard form to a sensible degree of accuracy.
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Answer ................................................. km
(3)
(Total 3 marks)
Page 8 of 14
M1.
(a)
2.12 × 105 or 212 000
B1
(b)
6.25 × 1010
62 500 000 000
B1
(c)
5000
5 × 103
B1
[3]
M2.
(a)
35 000 000 ÷ 7
5 000 000
M1
5 × 106
A1
(b)
Their (a) × 0.12 ÷ 24
M1
25 000
ft their answer to (a)
A1ft
[4]
M3.
(a)
Circles 1.2 × 1013
B1
(b)
Circles 5 × 10–7
B1
[2]
Page 9 of 14
M4.
Incorrect standard form notation
Eg. 7.2 6 or 7.26
Penalise first time only
(a)
7200 × 1000
7.2 × 103 × 1000 or 7200 × 103
B1
7.2 × 106
eg. 7200 × 100 = 7.2 × 105... B0 B1
B1 ft
(b)
6 × 10-4
B1
(c)
(7.2 × 106) ÷ (6 × 10-4)oe
Or their (a) ÷ their (b) oe or 1.2 × 10?
M1
1.2 × 1010
Ft for 1.2 × 10? Only
A1 ft
[5]
M5.
(a)
1.153 × 106
Allow 1.153000 × 106
B1
(b)
Attempt to add 1 153 000, 4.07 × 105 and 4.6 million
Numbers all in same form with at least two correct
M1
6 160 000 (oe) and Yes
Must have both
A1
[3]
M6.
(a)
4.07 × 1013
B1 if incorrect rounding × 1013, 4.0713 is B1
4.07 × 10–13 is B0
B2
Page 10 of 14
(b)
their (a) ÷ (298000 or 86400)
Dividing by 86400 or 298000 at any point gets M1
M1
their (a) ÷ 298000 ÷ 86400
Dividing by other value gets DM1
DM1
= 1576 to 1584
Use of original value gives 1578.93…..
A1 ft
= 1580 or 1600
This mark is independent and can be given for any value greater
than 3 s.f. seen or implied rounded to 2 or 3 s.f.
B1 ft
[6]
M7.
5.83 × 107 ÷ (5.47 × 105)
Condone invisible brackets
Allow if not in standard form and at
least one correct or both 2 zeros out
(5.83 × 7) ÷ (5.47 × 5) M0
40.81 ÷ 27.35
M0
M1
106.58...
A1
110 or 107
ft to 2 sf or 3 sf
Allow 106.6 but no ft to 4 sf
B1 ft
[3]
Page 11 of 14
M8.
(a)
Jupiter
B1
(b)
Pluto
B1
(c)
Saturn
B1
(d)
4 880 000
B1
(e)
or 2 390 oe
B1
A1
[6]
M9.
(a)
106
oe
B1
(b)
8 × 109
B1
(c)
2.4 × 1022
B1 2.4 or 22 as power or
24000000000000000000000
oe
e.g. 24 × 1021
B2
[4]
M10.
(a)
0.007
B1
(b)
(i)
0.9119215(052)
B1
(ii)
0.9, 0.91, 0.912,
9 or 9.1 or 9.12 × 10-1
ft their answer for (b)(i) to 1, 2 or 3sf
eg Gradians
(b)(i) 0.02221673729
B0
(b)(ii) 0.02, 2 × 10–2, etc B1 ft
B1 ft
Page 12 of 14
(c)
0.00805 or 8.05 × 10-3
B1
[4]
M11.
Sight of digits 5925, 593, 59 or 6
M1
5 925 000 000 or 5.925 × 109
oe from award of M
A1
Rounded to 5.93, 5.9 or 6 × 109
ft. their value if ≥ 4 s.f if rounded to 3, 2 or 1 s.f.
NB If A0 awarded and final answer correctly
rounded but not in standard form still give B1.
B1 ft
[3]
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