chapter 1 number - pearson education · ... square number square root chapter 1 number 4 ... the...
TRANSCRIPT
common factor common multiple factor tree highest common factor (HCF)
Chapter 1 Number
2
GCSE 2010N c Use the concepts and vocabulary of factor (divisor), multiple, common factor, Highest Common Factor (HCF), Least Common Multiple (LCM), prime number and prime factor decomposition
FS Process skillsSelect the mathematical information to use
FS PerformanceLevel 1 Select mathematics in an organised way to fi nd solutions
Specifi cation 1.1 Understanding prime factors, LCM and HCF
Concepts and skills
• Identify factros, multiples and prime numbers from a list of numbers.
• Find the prime factor decomposition of positive integers.
• Find common factors and common mulitples of two or three numbers.
• Find the HCF and LCM of two or three numbers.
Functional skills
• L1 … multiply and divide whole numbers using a range of strategies.
Prior key knowledge, skills and conceptsStudents should already know their
• multiplication tables up to 10 × 10.
• be able to fi nd factors, multiples and prime numbers (NC).
Starter
• Check that students understand the terms prime number, factor and multiple. List the factors of 12. (1, 2, 3, 4, 6, 12) List the multiples of 6 between 10 and 40. (12, 18, 24, 30, 36) List the fi rst ten prime numbers. (2, 3, 5, 7, 11, 13, 17, 19, 23, 29)
• Introduce the word ‘common’ into some questions.Find two common factors of 12 and 18. (1, 2, 3, 6) Find two common multiples of 3 and 4. (12, 24, 36 etc)
Main teaching and learning
• Tell students that they are going to fi nd out how to write any positive whole number as a product of its prime factors. Check that students understand the meaning of the word product.
• Explain that this can be done by using a factor tree (or repeated division). Draw a factor tree to show how 120 can be broken down into its prime factors (see Example 2).
• Discuss the fact that you can start with any two numbers that multiply to give 120. Draw a second factor tree for 120 starting with a different factor pair to show that the same result is reached.
• Tell students that they are going to fi nd the HCF and LCM of two numbers.
• Explain that there are different methods that can be used to do this depending on the size of the numbers involved.
• Discuss the best method for fi nding the HCF and LCM for two small numbers (e.g. 4 and 6). Show students how these can be found by making a list of the factors and fi rst few multiples of 4 and 6.
• Discuss why this method would not be appropriate for large numbers (e.g. 240 and 280).
• Explain how writing large numbers as the product of prime factors can be used to fi nd the LCM and HCF.
Common misconceptions
• Remind students to include the multiplication signs when writing a number as a product of its prime factors. (These are often incorrectly replaced by addition signs or commas.)
Enrichment
• Suggest that students use the Venn diagram method to fi nd the HCF and LCM of three large numbers (e.g. 240, 300 and 420).
• Students might like to know that the HCF of two numbers must be a factor of the difference between them. So the HCF of 210 and 250 must be a factor of 40. They may like to explore this and consider why this is the case.
Plenary
• Ask for the HCF of pairs of small numbers e.g. 2 and 6 (2), 4 and 10 (2), 6 and 12 (6).
• Ask for the LCM of pairs of small numbers e.g. 2 and 6 (6), 4 and 10 (20), 6 and 12 (12).
Linkshttp://www.bbc.co.uk/education/mathsfi le/shockwave/games/gridgame.html
ActiveTeach resourcesMultiples and factors quizLadder method interactiveHCF and LCM interactive
Resources
M01_MSAH_TG_GCSE_0822_C01.indd 2 12/05/2010 11:40
lowest common multiple prime factor
Section 1.1 Understanding prime factors, LCM and HCF
3
Sec
tio
n 1
.1 U
nd
erst
and
ing
pri
me
fact
ors
, LC
M a
nd
HC
F
3A
1
Writ
e do
wn
all t
he fa
ctor
s of
eac
h of
the
follo
win
g nu
mbe
rs.
a 12
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b
30 ..
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c 36
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d 40
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2
Use
this
fact
or tr
ee to
writ
e 54
as
a pr
oduc
t of i
ts p
rime
fact
ors.
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3
Com
plet
e th
e fo
llow
ing
fact
or tr
ees.
a
b
c
4
Writ
e ea
ch o
f the
follo
win
g nu
mbe
rs a
s th
e pr
oduc
t of i
ts p
rime
fact
ors.
How
can
fact
or tr
ees
be d
raw
n be
fore
wor
king
thro
ugh
to fi
nd o
ut h
ow m
any
fact
ors
ther
e ar
e?
a 24
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b
40 ..
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c 50
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d 72
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e 10
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5
a W
rite
out a
ll th
e fa
ctor
s of
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6 ...
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iii
10
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6 ...
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v
20 ..
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b U
se p
art a
to h
elp
you
writ
e do
wn
the
high
est c
omm
on fa
ctor
(HCF
) of
i
4 an
d 10
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ii 6
and
16 ..
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iii
4 a
nd 2
0 ...
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. iv
16
and
20 ..
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v
10 a
nd 1
6 ...
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6
a W
rite
out t
he fi
rst t
en m
ultip
les
of
i
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6 ...
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b W
rite
out t
he fi
rst s
ix m
ultip
les
of
i
10 ..
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ii 16
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20
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Writ
e do
wn
the
fact
ors
in p
airs
.
23
33
69
54
21
42
10
70
21
84
Rem
embe
r to
draw
fact
or t
rees
fi rs
t.
Fact
ors
are
num
bers
tha
t go
ex
actl
y in
to t
he g
iven
num
ber.
Gu
ided
pra
ctic
e w
ork
shee
t
D C C
M01
A_M
SAH
_TG
_GC
SE_0
822_
CD
C01
.indd
2
12/0
5/20
10
11:3
9
Sec
tio
n 1
.1 U
nd
erst
and
ing
pri
me
fact
ors
, LC
M a
nd
HC
F
3B
Gu
ided
pra
ctic
e w
ork
shee
t
c U
se y
our a
nsw
ers
to p
arts
a a
nd b
to h
elp
you
writ
e do
wn
the
low
est c
omm
on m
ultip
le (L
CM) o
f
i
4 an
d 6
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ii 6
and
10
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iii
4 a
nd 1
6 ...
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16
and
20 ...
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v
6 a
nd 2
0 ...
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.
7
a U
se y
our a
nsw
ers
to q
uest
ion
3 to
writ
e 42
, 70
and
84 a
s pr
oduc
ts o
f the
ir pr
ime
fact
ors.
i
42 ...
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ii
70
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b Fi
nd th
e H
CF a
nd L
CM o
f 42
and
70.
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c Fi
nd th
e H
CF a
nd L
CM o
f 70
and
84.
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8
Find
the
HCF
and
LCM
of t
he fo
llow
ing
pairs
of n
umbe
rs.
a 60
and
84
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...
b 70
and
105
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...
c 72
and
96
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d 84
and
96
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Mul
tipl
es a
re t
he n
umbe
rs in
the
tim
es t
able
of t
he g
iven
num
ber.
C
M01
A_M
SAH
_TG
_GC
SE_0
822_
CD
C01
.indd
3
12/0
5/20
10
11:3
9
M01_MSAH_TG_GCSE_0822_C01.indd 3 12/05/2010 11:41
cube cube number cube root square square number square root
Chapter 1 Number
4
GCSE 2010N d (part) Use the terms square, positive… square root, cube and cube rootN e (part) Use index notation for squares, cubes …
FS Process skillsUse appropriate mathematical procedures
FS PerformanceLevel 1 Use appropriate checking procedures at each stage
Specifi cation 1.2 Understanding squares and cubes
Concepts and skills
• Recall integer squares from 2 × 2 up to 15 × 15 and the corresponding square roots.
• Recall the cubes of 2, 3, 4, 5 and 10.
• Use index notation for squares and cubes.
Functional skills
• L1 … multiply … whole numbers using a range of strategies.
Prior key knowledge, skills and concepts
• Students should already know how to multiply and divide positive and negative integers.
Starter
• Ask students to work out the value of 1 × 1, 2 × 2, 3 × 3 up to 10 × 10 (1, 4, 9, 16, 25, 36, 49, 64, 81, 100) and then 1 × 1 × 1, 2 × 2 × 2 up to 5 × 5 × 5 (1, 8, 27, 64, 125). Identify these as the square numbers and cube numbers respectively.
Main teaching and learning
• Explain that 102 is a shorter way of writing 10 × 10 and that (–53) is a shorter way of writing –5 × –5 × –5.
• Discuss how square root is the inverse (opposite) of square, therefore 100 = 10
because 102 = 100. Likewise –1253
= –5 because (–53) = –125.
• Ask students if it is possible for them to tell you the square root of any number. Which numbers can you write down the square root for without a calculator? (The square numbers.)
• Discuss the fact that each positive number has both a positive and negative square root.
• Explain why this is the case, e.g. 5 × 5 = 25 and –5 × –5 = 25.
Common misconceptions
• Remind students that squaring a negative number always gives a positive number.
• Warn students of the very common error: 32 = 6.
Enrichment
• Students could investigate the patterns formed from 112, 1112 etc.
• Some numbers can be expressed as the difference of two squares, for example 42 – 32 = 7, 32 – 12 = 8. Which numbers cannot be expressed as the difference of two squares? (2, 6, 10, 14, 18, …)
• How many squares are there on a standard chess board? (204 squares)
Plenary
• Ask students to give the values of, for example, 62 (36), 53 (125), 64 (8), 643
(4).
M01_MSAH_TG_GCSE_0822_C01.indd 4 12/05/2010 11:41
Section 1.2 Understanding squares and cubes
5
Section 1.2 Understanding squares and cubes
5A
1 Work out
a 32 ......................................................... b 42 ......................................................... c 52 .........................................................
d 72 ......................................................... e 102 .........................................................
2 Lizzy says that to work out 62 you do 6 × 2 so the answer is 12. Lizzy is wrong. Explain why.
.....................................................................................................................................................................................................................................
.....................................................................................................................................................................................................................................
.....................................................................................................................................................................................................................................
3 Work out
a 23 ......................................................... b 33 ......................................................... c 43 .........................................................
d 53 ......................................................... e 103 .........................................................
4 Here is a list of 8 numbers
1 4 8 12 16 25 64 100
From the numbers in the list write down
a all the numbers that are square numbers
.................................................................................................................................................................................................................................
b all the numbers that are cube numbers.
.................................................................................................................................................................................................................................
5 Work out
a (–2)2 ................................................................................ b (–2)3 ................................................................................
................................................................................ ................................................................................
................................................................................ ................................................................................
c (–6)2 ................................................................................ d (–8)2 ................................................................................
................................................................................ ................................................................................
................................................................................ ................................................................................
e (–3)3 ................................................................................
................................................................................
................................................................................
6 Write down
a 25 ............................................................................... b 100
................................................................................
................................................................................ ................................................................................
................................................................................ ................................................................................
Guided practice worksheet
M01A_MSAH_TG_GCSE_0822_CDC01.indd 4 12/05/2010 11:39
Section 1.2 Understanding squares and cubes
5B
Guided practice worksheet
c 4 ................................................................................ d 49 ................................................................................
................................................................................ ................................................................................
................................................................................ ................................................................................
e 9 ................................................................................
................................................................................
................................................................................
7 Write down
a 13
................................................................................ b −643
................................................................................
................................................................................ ................................................................................
................................................................................ ................................................................................
c 273
................................................................................ d −10003
................................................................................
................................................................................ ................................................................................
................................................................................ ................................................................................
e −83
................................................................................
................................................................................
................................................................................
8 Work out
a 52 + 22 ................................................................................ b 82 – 32 ................................................................................
................................................................................ ................................................................................
................................................................................ ................................................................................
c 4 × 10 ................................................................................ d 9
× 16
................................................................................
................................................................................ ................................................................................
................................................................................ ................................................................................
e 100 × 32 ................................................................................ f 92 + 16
................................................................................
................................................................................ ................................................................................
................................................................................ ................................................................................
g 25 × 36
................................................................................ h 81
+ (–1)2 ................................................................................
................................................................................ ................................................................................
................................................................................ ................................................................................
M01A_MSAH_TG_GCSE_0822_CDC01.indd 5 12/05/2010 11:39
Section 1.2 Understanding squares and cubes
5C
Guided practice worksheet
i 72 + 49 ................................................................................ j 42 – (–6)2 ...............................................................................
................................................................................ ................................................................................
................................................................................ ................................................................................
9 Work out
a 23 × 13
................................................................................ b 83 × 52 ................................................................................
................................................................................ ................................................................................
................................................................................ ................................................................................
c 42 + −83
................................................................................ d −1253
+ 5 ................................................................................
................................................................................ ................................................................................
................................................................................ ................................................................................
e 53 – 13 ................................................................................ f 43 ÷ 82 ................................................................................
................................................................................ ................................................................................
................................................................................ ................................................................................
g 10003
× 23 ................................................................................ h (–2)3 ÷ 4
................................................................................
................................................................................ ................................................................................
................................................................................ ................................................................................
i (–5)3 × 4 ................................................................................ j −643
× 273
................................................................................
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................................................................................ ................................................................................
M01A_MSAH_TG_GCSE_0822_CDC01.indd 6 12/05/2010 11:39
M01_MSAH_TG_GCSE_0822_C01.indd 5 12/05/2010 11:41
BIDMAS operation power, powers value
Chapter 1 Number
6
1.3 Understanding order of operations
Concepts and skills
• Multiply and divide numbers using he commutative, associative, and distributive laws and factorisation where possible, or place value adjustments.
• Use brackets and the hierarchy of operations.
Functional skills
• L1 Add, subtract, multiply and divide whole numbers using a range of strategies.
Prior key knowledge, skills and conceptsStudents should already know how to
• add, subtract, multiply and divide positive and negative integers (N a).
• Understand and use positive number and negative integers, both as positions and translations on a number line (N b).
Starter
• Give out a variety of different calculators. (The calculator function on less sophisticated mobile phones is useful here.)
• Ask students to work out 3 + 5 × 2 on the calculator they have been given. Ask for the answers from the calculators. You should get the answers 16 (incorrect) and 13 (correct).
• Discuss why the calculators (which are always correct!) are giving two different answers.
• Try some other calculations, e.g. 20 – 14 ÷ 2 (13), 2 × 3 + 4 × 2 (14)
Main teaching and learning
• Tell students that they are going to fi nd out about the order in which arithmetic operations should be carried out.
• Explain to students why it is important that there is a standard order of operations. (So that we all arrive at the same answer.)
• Discuss the meaning of the letters in BIDMAS.
Common misconceptions
• When working out calculations such as 2 × 32 remember to use BIDMAS; this must be worked out as 2 × 9 = 18.
• When left with just addition and subtraction then you must work from left to right, e.g. 6 – 10 + 2 = –4 + 2 = –2 (6 – 10 + 2 cannot be worked out as 6 – 12).
Enrichment
• Using just four 4s and any arithmetic operations, how many of the positive integers can you make? For example, 4 × 4 + 4 + 4 = 24; 4 ÷ 4 + 4 ÷ 4 = 2.
Plenary
• Have some pre-prepared questions on the board and ask students to work these out. For example, 7 + 4 × 2 (15), 24 – (8 × 2) (8).
GCSE 2010N q (part) Understand and use number operations and the relationships between them, including … hierarchy of operations
FS Process skillsUse appropriate mathematical procedures
FS PerformanceLevel 1 Apply mathematics in an organised way to fi nd solutions…
Specifi cation
ResourcesQuestions for plenaryVariety of calculators
ActiveTeach resourcesSquaring quizBIDMAS animationThe audience video
Resources
M01_MSAH_TG_GCSE_0822_C01.indd 6 12/05/2010 11:41
Section 1.3 Understanding order of operations
7
Sec
tio
n 1
.3 U
nd
erst
and
ing
ord
er o
f o
per
atio
ns
7A
1
Wor
k ou
t
a 5
+ 2
× 6
.....
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...
b 3
× 4
+ 2
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c 20
– 4
× 3
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d 6
+ 18
÷ 3
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..
2
Wor
k ou
t
a 5
× 6
+ 2
× 8
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.. b
30 ÷
3 –
2 ×
4
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c 9
× 4
+ 3
× 7
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.. d
8 ×
10 –
24
÷ 4
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3
Wor
k ou
t
a 5
× (6
+ 3
) ...
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M01
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.indd
8
12/0
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11:3
9
M01_MSAH_TG_GCSE_0822_C01.indd 7 12/05/2010 11:41
inverse operations reciprocal
Chapter 1 Number
8
1.4 Using a calculator
Concepts and skills
• Understand ‘reciprocal’ as multiplicative inverse, knowing that any non-zero number multiplied by its reciprocal is 1 (and that zero has no reciprocal because division by zero is not defi ned.)
• Find reciprocals.
• Understand that the inverse operation of raising a positive number to a power n is
raising the result of this operation tht power 1n .
• Understand and use unit fractions as multiplicative inverses.
• Use a calculator effectively and effi ciently.
• Know how to enter complex calculations.
• Understand, and interpret, the calculator display.
• Understand that premature rounding can cause problems when undertaking calculations with more than one step.
Functional skills
• L2 Carry out calculations with numbers of any size … to a given number of decimal places.
Prior key knowledge, skills and concepts
• Students should be able to use a calculator to enter numbers and carry out the four arithmetical operations.
Starter
• Ask students to use their calculators to work out the following2.452 (6.0025), 3.673 (49.430 863).
• Ask students how they used their calculators to work out these sums.
Main teaching and learning
• Tell students that they are going to learn how to use some of the buttons on their scientifi c calculators.
• Ask students to work out various calculations using their calculators and discuss the key sequences.
• Discuss the different ways that calculations such as 3 4 7 92 1 3. ..
+××
(1.79365…) can be evaluated correctly.
Common misconceptions
• The calculator does not always give the correct answer – it depends what was entered and how it was entered. Encourage students to work out approximations to calculations before using their calculators.
• Remind students to take care when using a calculator to work out a fraction that has a calculation in the numerator and/or denominator.
Plenary
• Give students various sums to be evaluated using their calculators.
GCSE 2010N q Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations.N v (part) Use calculators effectively and effi ciently….
FS Process skillsDecide on the methods, operations and tools, including ICT, to use in a situationUse appropriate mathematical procedures
FS PerformanceLevel 2 Use appropriate checking procedures and evaluate their effectiveness at each stage
Specifi cation
ResourcesCalculators
Resources
M01_MSAH_TG_GCSE_0822_C01.indd 8 12/05/2010 11:41
Section 1.4 Using a calculator
9
Sec
tio
n 1
.4 U
sin
g a
cal
cula
tor
9A
1
Wor
k ou
t
a 32
2 ...
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1.23
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c (–
5.1)
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2979
13
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3
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k ou
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a (2
.2 +
8.9
) × 3
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b
2.32 +
1.5
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c (1
9.4
– 7.
8)2
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3.13 +
92
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4
Wor
k ou
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ving
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r ans
wer
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rrec
t to
one
deci
mal
pla
ce
a 1.
73 × 7
.2
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. b
56 +
1.23 ..
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Gu
ided
pra
ctic
e w
ork
shee
t
Rem
embe
r, to
wor
k ou
t po
wers
on
your
cal
cula
tor,
use
the
yx o
r x o
r ^ k
ey.
M01
A_M
SAH
_TG
_GC
SE_0
822_
CD
C01
.indd
9
12/0
5/20
10
11:3
9
Sec
tio
n 1
.4 U
sin
g a
cal
cula
tor
9B
Gu
ided
pra
ctic
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ork
shee
t
c 8.
42 ÷
12 ...
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d 83 –
23
0 ......
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5
Wor
k ou
t, gi
ving
you
r ans
wer
s co
rrec
t to
thre
e si
gnifi
cant
fi gu
res
a 7
218
32
76.
..
− ...
......
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b 3
276
39
135
4.
..
.××
××
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c 65
419
58
23
46.
..
.+ −
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81
72
36
2
22
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.–
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6
Wor
k ou
t, gi
ving
you
r ans
wer
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rrec
t to
thre
e si
gnifi
cant
fi gu
res
a 46
568
27
6–
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b 8
74 17
45
06
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+
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c 78
35
64
87.
.−
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d 67 023
453
2
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7
Wor
k ou
t, gi
ving
you
r ans
wer
s co
rrec
t to
thre
e si
gnifi
cant
fi gu
res
a 43
62
384
1362
+ –.
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. b
62
17
75
34
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M01_MSAH_TG_GCSE_0822_C01.indd 9 12/05/2010 11:41
index number laws of indices
Chapter 1 Number
10
1.5 Understanding the index laws
Concepts and skills
• Use index laws to simplify and calculate the value of numerical expressions involving multiplication and division of integer… powers.
Functional skills
• L1 … multiply and divide whole numbers using a range of strategies.
Prior key knowledge, skills and conceptsStudents should
• be able to work out the square of a number and the cube of a number.
• understand index notation e.g. know that 34 = 3 × 3 × 3 × 3.
Starter
• Write 23 on the board and ask students what this means (2 × 2 × 2).
• Ask them for another way to write 6 × 6 × 6 × 6 (64).
• Have other similar examples written ready on the board to use for practice.
Main teaching and learning
• Tell students that they are going to learn the index laws, which will enable them to simplify expressions such as 32 × 34 and 65 ÷ 62.
• Ask students to write out 32 × 34 in full (3 × 3 × 3 × 3 × 3 × 3) and explain that this could be written as 36.
• Discuss other similar examples and encourage students to give a general rule for combining the powers to give a single power (add the powers).
• Ask students to investigate examples involving division and ask them to come up with a rule this time (subtract the powers).
• Ask students to explain the meaning of (72)3 (72 × 72 × 72). Discuss how this can be simplifi ed to 72+2+2 which can be written as 72×3 or 76. Encourage students to give a general rule for expressions of the form (am)n (multiply the powers).
Common misconceptions
• A common error is to work out 34 as 3 × 4 rather than 3 × 3 × 3 × 3.
• Questions that ask students to ‘Simplify 46 × 43’ or ‘Write 46 × 43 as a power of 4’ want the answer to be given as 49; they are not asking the student to work out 49. Students should be encouraged to show their working i.e. writing 46+3 before the fi nal answer to show their method.
• Questions that use the word ‘evaluate’ or the phrase ‘work out’ do require an answer that is not in index form. For example, the answer to ‘Evaluate 22 × 23’ is 32.
• Students often multiply rather than add the powers in 26 × 25 and divide rather than subtract the powers in 28 ÷ 24.
• Students often multiply the numbers as well as adding the powers, i.e. to give the answer to 34 × 37 as 911 instead of 311.
• Students often think that 4 is the same as 40 rather than 41.
Plenary
• Ask students to simplify expressions such as 78 × 73 (711), 812 ÷ 82 (810), (64)2 (68)
GCSE 2010N f (part) Use index laws for multiplication and division of integer… powers
FS Process skillsUse appropriate mathematical procedures
FS PerformanceLevel 1 Use appropriate checking procedures at each stage
Specifi cation
ActiveTeach resourcesRP Number knowledge checkRP Multiples problem solving
Follow up25.1 Using zero and negative powers 25.3 Working with fractional indices
Resources
M01_MSAH_TG_GCSE_0822_C01.indd 10 12/05/2010 11:41
Section 1.5 Understanding the index laws
11
Section 1.5 Understanding the index laws
11A
1 Work out
a 43 ......................................................................... b 92 .........................................................................
c 26 ......................................................................... d 104 .........................................................................
e 35 .........................................................................
2 Write in index form
a 2 × 2 × 2 × 2 × 2 ......................................................................... b 6 × 6 × 6 .........................................................................
c 8 × 8 × 8 × 8 × 8 × 8 × 8 .......................................................... d 17 × 17 .........................................................................
3 Write as a power of 7
a 75 × 73 ......................................................................... b 72 × 78 .........................................................................
......................................................................... .........................................................................
c 73 × 7 ......................................................................... d 76 × 76 .........................................................................
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e 74 × 7 × 73 .........................................................................
.........................................................................
4 Write as a power of 5
a 56 ÷ 52 ......................................................................... b 59 ÷ 56 .........................................................................
......................................................................... .........................................................................
c 512 ÷ 54 ......................................................................... d 57 ÷ 5 .........................................................................
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e 55 ÷ 53 .........................................................................
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5 Write as a power of 3
a 39 × 32 ......................................................................... b 37 ÷ 33 ........................................................................
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c 310 ÷ 34 ......................................................................... d 3 × 34 .........................................................................
......................................................................... .........................................................................
e 37 × 32 ÷ 36 .........................................................................
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Guided practice worksheet
a m × a n = a m+n
a m ÷ a n = a m–n
C
M01A_MSAH_TG_GCSE_0822_CDC01.indd 11 12/05/2010 11:39
Section 1.5 Understanding the index laws
11B
Guided practice worksheet
6 Write as a power of 6
a (62)4 ......................................................................... b (64)3 .........................................................................
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c (68)5 ......................................................................... d (69)3 .........................................................................
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e (63)2 .........................................................................
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7 Write as a power of a single number
a 73 × 75 ......................................................................... b (94)2 .........................................................................
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c 84 × 82 ......................................................................... d 37 × 36 ÷ 35 .........................................................................
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e 5 × (54)2 ÷ 52 .........................................................................
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8 Write as a power of 5
a 5 5
5
2 5
3××
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b 5 5
5
8
4××
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c 5
5 5
16
2 6×× .........................................................................
d 5 55 5
3 5
6××
×× .........................................................................
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e 5 55 5
12
4 6××
×× .........................................................................
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(a m) n = a mn C
B
M01A_MSAH_TG_GCSE_0822_CDC01.indd 12 12/05/2010 11:39
Section 1.5 Understanding the index laws
11C
Guided practice worksheet
9 Work out
a 3 3
3
4 2
5××
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b 2 2
2
8
6××
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c 4
4 4
9
3 4×× .........................................................................
d 10 10
10
2 5
4××
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e 7 77 7
3 5
6××
××
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B
M01A_MSAH_TG_GCSE_0822_CDC01.indd 13 12/05/2010 11:39
M01_MSAH_TG_GCSE_0822_C01.indd 11 12/05/2010 11:41