Unit 1 Pupil Book 5-7 Math Worksheet Page 6
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1
2
3
4
5
6
7
8
9
10Level 6
Simplify these, leaving your answers in index form.
I can use the
5
6
9
3
5
3
5
2
a
4
4
b
8
8
c
6
6
d
(4
4
)
4
index laws
4
5
2
3
6
4
5
2
for multiplying and
e
3
3
f
7
7
g
5
5
h
2
2
dividing numbers in
index form
Use prime factor decomposition to fi nd the HCF of these numbers.
Complete prime factor decomposition: 42 = 2
3
7
42 and 154
×
×
I can fi nd the
HCF of two
154 = 2
7
11
×
×
numbers using
Identify common factors, and multiply them:
HCF = 2
7 = 14
×
their prime factor
decompositions
a
30 and 48
b
30 and 100
c
180 and 210
d
176 and 350
I can fi nd the
Use prime factor decomposition to fi nd the LCM of these numbers.
LCM of two
84 and 308
Complete prime factor decomposition: 84 = 2
2
3
7
numbers using
×
×
×
their prime factor
308 = 2
2
7
11
×
×
×
decompositions
Multiply together all the factors but only include overlaps once:
2
2
3
7
11 = 924
×
×
×
×
a
35 and 42
b
30 and 100
c
180 and 810
d
176 and 350
I can prove that
3
3
3
a
Write down the value of 2
. What is the value of 2
2
?
any number to
the power zero is 1
3
3
b
Use an index law to simplify 2
2
.
0
c
What is the value of 2
?
Level 7
Work these out, writing your answers as decimals.
I can understand
3
4
7
10
2
1
2
a
10
10
b
10
10
c
10
10
d
10
10
and use negative
indices
2
3
a
Use an index law to simplify 2
2
.
1
b
What is the value of 2
?
c
A whole number raised to a negative power is smaller than 1. True or false?
I can use the
Use prime factor decomposition to simplify these.
index laws to
Give your answers in index form.
simplify multiplication
and division
2
4
45
48
45 = 3
5 and 48 = 2
3
×
×
calculations
2
4
4
3
so 45
48 = 3
5
2
3 = 2
3
5
×
×
×
×
×
×
a
24
32
b
60
21
c
1500
75
d
126
30
A
B
Factor line
Highest common formula
• Calculate the HCF of 12 and 20.
Using your answers from Q6 and Q7, or
• Draw a pair of axes and join the points (0, 0) and
otherwise, copy and complete this table.
(12, 20) with a straight line. How many points
HCF
b LCM
Number a Number b
a
with whole-number coordinates (not including
30
42
(0, 0)) does the line pass through? What do you
notice?
30
100
• Make a prediction: how many points with whole-
180
210
number coordinates (not including (0, 0)) will the
Write down a formula for the LCM.
line connecting (0, 0) to (12, 15) pass through?
Can you explain why it works?
Test your prediction to see if you are correct.
lowest common multiple (LCM)
prime factor
prime factor decomposition
9
1.3 Prime factor decomposition
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