1.
Draw lines on the diagram to show which values are equal.
One line has been drawn for you.
2
–8x–2
4
64
8
4
3
16
3
8
32
25
64
(Total 3 marks)
2.
(a)
Work out the cube of 4.
.....................…………………………………………………………………………
Answer ............................................
(1)
(b)
Work out 0.2
2
.....................…………………………………………………………………………
Answer ............................................
(1)
(c)
A list of numbers is given below.
15
16
From this list, write down
(i)
a cube number,
19
27
34
42
45
..........………………………………………………………………………….
Answer ............................................
(1)
(ii)
a prime number.
..........………………………………………………………………………….
Answer ............................................
(1)
(Total 4 marks)
The Robert Smyth School
1
3.
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)
(Total 2 marks)
4.
Write down the values of
(a)
42
......................................................................................................................................
Answer .........................................................................
(1)
(b)
81
......................................................................................................................................
Answer .........................................................................
(1)
(Total 2 marks)
5.
Work out
(a)
53
......................................................................................................................................
Answer ………………………………….........
(1)
(b)
82
23
.....................................................................................................................................
.....................................................................................................................................
Answer ………………………………….........
(2)
(Total 3 marks)
The Robert Smyth School
2
6.
Which is greater, 32 or 70 ?
You must show your working.
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
Answer ....................................................
(Total 3 marks)
7.
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 ............................................
(Total 2 marks)
8.
(a)
Work out 33
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
Answer ..........................................................................
(1)
(b)
Give an example of a cube number that does not divide exactly by three.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
Answer ..........................................................................
(1)
(Total 2 marks)
9.
(a)
Write down the square root of 49.
.....................................................................................................................................
Answer .........................................................................
(1)
(b)
4
Work out the value of 10
.....................................................................................................................................
Answer .........................................................................
(1)
(Total 2 marks)
The Robert Smyth School
3
10.
Work out the value of
(a)
53
.....................................................................................................................................
Answer ..........................................................
(1)
(b)
10
4
.....................................................................................................................................
Answer ..........................................................
(1)
(Total 2 marks)
11.
Work out the value of 53  43.
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
You may use a calculator for
the remaining questions
12.
(a)
Answer ...............................................
(Total 2 marks)
Which is larger, 43 or 34?
You must show your working.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
Answer .....................................................
(2)
(b)
Place the following numbers in order of size, starting with the smallest.
2
3
2.08
1.52
2.237
2.64
5
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
Answer .....................................................
(3)
(Total 5 marks)
The Robert Smyth School
4
13.
Here is a list of numbers.
(a)
40
50
60
70
80
Which number in the list is a square number?
90
100
Answer ..............................................................
(1)
(b)
Work out the total of all the numbers in the list.
......................................................................................................................................
Answer ..............................................................
(1)
(Total 2 marks)
14.
(a)
Find the square root of 1225.
......................................................................................................................................
Answer ..................................................................
(1)
(b)
1
Find the value of
1225
Give your answer to 3 decimal places.
......................................................................................................................................
Answer ..................................................................
(2)
(Total 3 marks)
15.
(a)
22  5
Calculate
Give you answer to two significant figures
......................................................................................................................................
Answer .........................................................................
(2)
(b)
225  2.3
3
Calculate
......................................................................................................................................
Answer .........................................................................
(2)
(Total 4 marks)
16.
From the list of numbers
4
9
20
27
32
51
65
81
125
write down the cube numbers.
..................................................................................................................................................
..................................................................................................................................................
Answer ..........................................................................
(Total 2 marks)
The Robert Smyth School
5
17.
Ed thinks that when you square a number you always get an even number.
Give an example to show that Ed is wrong.
................................................................................................................................................
................................................................................................................................................
................................................................................................................................................
................................................................................................................................................
(Total 2 marks)
18.
Use your calculator to work out
1
0 .2 2
.................................................................................................................................................
.................................................................................................................................................
Answer ………………………………….........
(Total 2 marks)
19.
Calculate
(a)
45
Answer .........................................................................
(1)
(b)
5
98
Answer .........................................................................
(1)
(Total 2 marks)
20.
Calculate
(a)
36
Answer .........................................................................
(1)
(b)
1
12.5
Answer .........................................................................
(1)
(c)
5.42 –
3.24
Answer .........................................................................
(1)
(Total 3 marks)
The Robert Smyth School
6
21.
Calculate
3.42 + 23
................................…………………………………………………………………………
................................…………………………………………………………………………
Answer ................................................
(Total 2 marks)
22.
(a)
Work out the cube of 17.
Answer ………………………………………
(1)
(b)
Work out
1
+ 2.62
3.2
Answer ………………………………………
(1)
(Total 2 marks)
23.
(a)
Find the square of 27.5
.....................................................................................................................................
Answer.........................................................................................................................
(1)
(b)
Find the square root of 196
.....................................................................................................................................
Answer.........................................................................................................................
(1)
(c)
Find the value of
1
1

0.4 1.6
.....................................................................................................................................
.....................................................................................................................................
Answer.........................................................................................................................
(3)
(Total 5 marks)
The Robert Smyth School
7
1.
4 correct lines
64 = 8
B3
43 = 64
3
8 =2
25 = 32
B2 for 3 correct
B1 for 1 or 2 correct
[3]
2.
(a)
64
B1
(b)
0.04
B1
(c)
(i)
27
B1
(ii)
19
B1
[4]
3.
(a)
14, 36
B1
(b)
27
B1
[2]
4.
(a)
16
(b)
9
B1
B1
Accept –9, 9 × 9, 92
[2]
5.
(a)
125
B1
(b)
64 or (23 =) 8
M1
8
A1
[3]
6.
9
B1
92 = 81
or 70 = 8. ...
70 < 9 or 9 >
M1
70
A1
[3]
7.
(any example, could be odd)
a=8
a2 = 64 which is even
As shown and is even
B1
B1
[2]
The Robert Smyth School
8
8.
(a)
27
B1
(b)
1 or 8 or 64 or 125 or 1000 or...
Allow I3 or 23 etc 1 × 1 × 1 etc
Do not accept 27 or 216 or ...
B1
[2]
9.
(a)
7
B1
Or – 7
Allow 7 × 7, – 7 × –7, 72
(b)
10 000
B1
[2]
10.
(a)
125
B1
(b)
10 000
B1
[2]
11.
125 or 64 seen
B1
61
B1
[2]
12.
(a)
43 = 64 or 34 = 81
34 is larger
oe
M1
A1
(b)
2.6 or 2.25 seen
M1
1
oe eg 2
4
2.08, 2.237, 2.25, 2.6, 2.64
–1 each error or omission
A2
[5]
13.
(a)
100
B1
Do not award if additional answers are given
(b)
490
B1
[2]
14.
(a)
35
B1
(b)
0.028(5714...)
or 0.028 on answer line
M1
0.029
A1
[3]
15.
(a)
(b)
4.7434164902(5)…..
B1
4.7 (2sf)
A1
25 + 12.167
M1
37.167
A1
[2]
The Robert Smyth School
9
16.
27
B1
125
B1
– 1 for each extra offered
[2]
17.
eg 7 × 7 or 72
B1
B1 for 6 × 6 = 36 (ie even result)
= 49 (which is odd)
Ignore incorrect comments
B1
[2]
18.
25
B2
2
5 or 0.04
B1
[2]
19.
(a)
1024
(b)
0.05102041
B1
B1
Condone .05102041
[2]
20.
(a)
729
(b)
0.08
B1
B1
Condone .08
(c)
27.36
B1
or 27.4
[3]
21.
(a)
100 000
1
Accept 100,000 or 100000
(b)
343
1
[2]
22.
11.56 + 8
M1
Either
= 19.56
A1
[2]
23.
(a)
4913
(b)
7.0725
B1
B1
or 7.1 or 7.07 or 7.073
[2]
24.
(a)
756.25
B1
(b)
14
B1
(c)
2.5
M1
0.625
M1
1.875
A1
[5]
The Robert Smyth School
10