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Standard form
Model Answers 1
Level
Subject
Exam Board
Topic
Sub Topic
Booklet
Time Allowed:
IGCSE
Maths
Edexcel
Numbers and Algebra
Standard form
Model Answers 1
59 minutes
Score:
/ 49
Percentage:
/100
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1 x = a × 10n where n is an integer and 10 ! a < 10
Find, in standard form, an expression for x2.
Give your expression as simply as possible.
.................................. . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question is 3 marks)
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2 The table gives the diameters, in metres, of four planets.
Planet
Diameter (metres)
Mercury
4.88 × 106
Venus
1.21 × 107
Earth
1.28 × 107
Mars
6.79 × 106
(a) Which planet has the largest diameter?
.................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(b) Write 6.79 × 106 as an ordinary number.
.................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(c) Calculate the difference, in metres, between the diameter of Venus and the diameter (1)
of Mercury.
Give your answer in standard form.
............................................ . . . . . . . . . . .
(2)
(Total for Question is 4 marks)
metres
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3 The mass of the Space Shuttle is 7.8 × 104 kilograms.
(a) Write 7.8 × 104 as an ordinary number.
................................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
The Space Shuttle docks with the International Space Station.
The mass of the International Space Station is 4.62 × 105 kilograms.
(b) Calculate the total mass of the Space Shuttle and the International Space Station.
Give your answer in standard form.
......................................... . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question is 3 marks)
kg
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4 The table shows the diameters, in kilometres, of five planets.
Planet
Diameter (km)
Venus
1.2 × 104
Jupiter
1.4 × 105
Neptune
5.0 × 104
Mars
6.8 × 103
Saturn
1.2 × 105
(a) Which of these planets has the smallest diameter?
................................... . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(b) Calculate the difference, in kilometres, between the diameter of Saturn and the
diameter of Neptune.
Give your answer in standard form.
The diameter of the Moon is 3.5 × 103 km.
The diameter of the Sun is 1.4 × 106 km.
.............................................. . . . . . . . . . . . . . . . .
(2)
km
(c) Calculate the ratio of the diameter of the Moon to the diameter of the Sun.
Give your answer in the form 1 : n
.................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question is 5 marks)
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5 (a) Write as an ordinary number
(i) 4.2 × 106
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) 3.82 × 10–4
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(b) Here are three numbers written in standard form.
Arrange these numbers in order of size.
Start with the smallest number.
5.6 × 10–7
8.6 × 10–9
5.64 × 10–8
Has the lowest index so is the smallest, has the second lowest index, has the hugest index
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . .
(2)
(Total for Question is 4 marks)
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Pacific as it has the largest exponent, 8
Pacific
((((((((((((((((((((((((((((((( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (
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In order to add exponents must be the same.
Pacific = 15.6 x 10 Add coefficients:
(7.68 + 6.86 + 15.6 + 2.03 + 1.41 ) x 10
= 3.358 x 10
3.358 x 10
((((((((((((((((((((((((((((((((((((((((((( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (
NP
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Divide coefficients and subtract indexes
3.358 x 10
100 = 65.8
5.10 x 10
65.8
((((((( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (
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7 (a) x = 9 × 102m where m is an integer.
Find, in standard form, an expression for
x
Square root is equivalent to a power of a half
........................................................
(2)
(b) y = 9 × 102n where n is an integer.
3
Find, in standard form, an expression for y 2
Give your answer as simply as possible.
From part a we can see y =
Therefore y = (3 x 10 )
Coefficient must be less than 10 and greater than zero
........................................................
(3)
(Total for Question is 5 marks)
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8 The table shows the land areas, in km2, of four countries.
Country
Land area (km2)
Ethiopia
1.13 × 106
Algeria
2.38 × 106
Nigeria
9.24 × 105
Kenya
5.83 × 105
(a) Which country has the largest land area?
Algeria has the largest exponent and coefficient
Algeria
. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(b) Calculate the total land area, in km2, of all four countries.
Give your answer in standard form.
Ensure numbers have the same exponent then add coefficients.
(11.3 + 23.8 + 9.24 + 5.83) x10
5.017 x 10
5.017 x 10
........................................................
km2
(2)
Population density is calculated by the formula
Population density = Population ÷ Land area
(c) In one year, the population of Ethiopia was 7.91 × 107
Calculate the population density of Ethiopia for that year.
Population density =
Subtract exponents, and divide coefficients
...........................
people / km2
(2)
(Total for Question is 5 marks)
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9 The table shows the population of each of three countries in 2012.
Country
Population
India
1.21 × 109
Turkey
7.48 × 107
Singapore
5.2 × 106
(a) Find the total population of India, Turkey and Singapore in 2012.
Give your answer in standard form.
Ensure the exponents are the same then add coefficients
1210 + 748 + 5.2 x 10
1290 x 10
1.29 x 10
1.29 x 10
..............................................................
(2)
Population density is calculated by the formula
Population density = Population ÷ Land area
The land area of India is 3.29 × 106 km2
(b) Calculate the population density of India in 2012.
Give your answer correct to 3 significant figures.
Population density =
...............................
people/km2
(2)
(Total for Question is 4 marks)
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10 (a) Write 1.2 × 10–5 as an ordinary number.
1.2 x0.00001= 0.000012
0.000012
............................
(1)
(b) Work out 7.9 × 105 + 6 × 104
Give your answer in standard form.
............................
(2)
(Total for Question is 3 marks)
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11 (a) Write 0.000076 in standard form.
7.6 x 10
7.6 x10
........................................................
(1)
The area covered by the Pacific Ocean is 1.6 × 108 km2
The area covered by the Arctic Ocean is 1.4 × 107 km2
(b) Write 1.6 × 108 as an ordinary number.
160 000 000
........................................................
(1)
The area covered by the Pacific Ocean is k times the area covered by the Arctic Ocean.
(c) Find, correct to the nearest integer, the value of k.
PO x k = AO
K = AO/PO
Divide coefficients and subtract exponents
1.6/1.4 x 10
=K= 1.1 x10 = 11
k = . . . . . . . . . . . . . . . .11
. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question is 4 marks)
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12 a)
Exponent of the all of the surface areas is the same.
(2.57 + 6.01 + 5.80 + 1.91 + 8.21 ) x 10
24.5 x 10 = 2.45 x 10 10
10)
1.22 x 10 = k( 7.45 x 10 ) 1.22 x 10 /( 7.45 x 10 ) 1.22/7.45 x10
1640
=1.64 x 10