The Robert Smyth School
Mathematics Faculty
Topic 7
Powers & Roots HW2
Innovation & excellence
Topic 7 (foundation) – Homework on Powers & Roots
1.
Here is a list of numbers.
7
(a)
9
14
17
23
27
36
Write down the even numbers.
......................................................................................................................................
Answer .........................................................................
(1)
(b)
Write down the cube number.
......................................................................................................................................
Answer .........................................................................
(1)
2.
From the list of numbers
2
(a)
13
25
30
34
40
49
write down a multiple of 6,
Answer .................................................................
(1)
(b)
write down the square numbers.
Answer .................................................................
(2)
4.
Write down the values of
(a)
42
......................................................................................................................................
Answer .........................................................................
(1)
(b)
81
......................................................................................................................................
Answer .........................................................................
(1)
5.
(a)
(i) Find all the factors of 18.
...........................................................................................................................
...........................................................................................................................
Answer ...............................................
(2)
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The Robert Smyth School
Mathematics Faculty
(ii)
Topic 7
Powers & Roots HW2
Innovation & excellence
Find all the factors of 30, and hence list the numbers which are both factors of 18
and factors of 30.
...........................................................................................................................
...........................................................................................................................
Answer ...............................................
(3)
3.
(a)
Find all the factors of 12.
......................................................................................................................................
......................................................................................................................................
Answer .........................................................................................................
(2)
(b)
Write down the factors of 12 which are also factors of 30.
......................................................................................................................................
......................................................................................................................................
Answer ..................................................................
(3)
6.
(a)
Write down the square root of 49.
.....................................................................................................................................
Answer .........................................................................
(1)
(b)
Work out the value of 104
.....................................................................................................................................
Answer .........................................................................
(1)
7.
State which of the numbers
3
(a)
4
9
10
13
21
25
35
39
are factors of 24?
.....................................................................................................................................
Answer.........................................................................................................................
(1)
(b)
are multiples of 7?
.....................................................................................................................................
Answer.........................................................................................................................
(1)
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The Robert Smyth School
Mathematics Faculty
8.
Topic 7
Powers & Roots HW2
Innovation & excellence
James thinks that when you square a number you always get an odd number answer.
Give an example to show that James is wrong.
................................…………………………………………………………………………
................................…………………………………………………………………………
Answer ............................................
(2)
9.
Kim states that the product of two consecutive whole numbers is an odd number.
By means of an example, show that Kim is not correct.
................................…………………………………………………………………………
................................…………………………………………………………………………
Answer ................................................
(2)
10.
(a)
Paul thinks that when an even number is halved the answer is always even.
Give an example to show that Paul is wrong.
.....................................................................................................................................
.....................................................................................................................................
(1)
(b)
p is an odd number.
Is 2p + 1 an odd number, an even number or could it be either?
Tick the correct box.
odd
even
either
(1)
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The Robert Smyth School
Mathematics Faculty
1.
Innovation & excellence
Topic 7
Powers & Roots HW2
(a)
14, 36
B1
(b)
27
B1
[2]
2.
(a)
30
B1
B0 if extras offered
(b)
25
B1
49
B1
– 1 for each extra offered
[3]
3.
(a)
16
(b)
9
B1
B1
Accept –9, 9 × 9, 92
[2]
4.
(a)
5 25
,
35 100
(b)
(i)
1, 2, 3, 6, 9, 18
B1 for 4 of these listed, – 1 for wrong factors
B2
(ii)
1, 2, 3, 5, 6, 10, 15, 30
B2
1,2,3,6
as above
B1
B1, B1
[7]
5.
(a)
1, 2, 3, 4, 6, 12
B1 for any 4 or 5 of these, could be in working
B2
(b)
1, 2, 3, 5, 6, 10, 15, 30
Any 4 factors of 30 seen
B1
1, 2, 3, 6
B2
B1 for 2 or 3 of these
In each section, deduct one mark only for extra, wrong factors
on the answer lines
[5]
6.
(a)
7
B1
Or – 7
Allow 7 × 7, – 7 × –7, 72
(b)
10 000
B1
[2]
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The Robert Smyth School
Mathematics Faculty
7.
Innovation & excellence
Topic 7
Powers & Roots HW2
(a)
3 and 4
B1
(b)
21 and 35
B1
[2]
8.
(any example, could be odd)
a=8
a2 = 64 which is even
As shown and is even
B1
B1
[2]
9.
eg 5 × 6 = 30 which is even
B1 for use of 2 consecutive
whole numbers and × sign
For B2, need example, with correct result which is even.
B2
[2]
10.
(a)
Example eg 10 ÷ 2 = 5
Accept eg 5 × 2 = 10, 1 + 1 = 2
Ignore any incorrect trials
B1
(b)
Odd
B1
Any clear indication
[2]
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