2/(9(/ 3 ,1',&(6
48(67,21 6
1
1
35 2312 9216
(a) Simplify (3x3)2 .
-1
(b) Given that (16) 2 × k = 1, evaluate k.
XK l
j
161
516 4
I
XK
4
Answer (a) ................................................. [1]
1
(b) k = ........................................... [1]
K 4
2
(a) The number 222.222 is written in the answer space.
Circle the digit which represents the value 2 × 10 0.
2 1 2
(b) Write 5 × 10–2 as a fraction in its simplest form.
2
(c) Evaluate 8 3 .
5 10
5
2
8
23
42
Egg L
2 5 22 4
Answer (a)
O
222.222
[1]
(b) ....................................................[1]
4
(c) ................................................... [1]
3
25 1
(a) Evaluate 52 + 50.
26
(b) Simplify
–2
(i)
!1x " ,
(ii)
! "
1
x6 2 .
F
It
x2
23
26
Answer (a) ....................................................[1]
x2
(b)(i) ............................................... [1]
23
(ii) ............................................... [1]
2
___________________________________________________________________________
4
(a) Simplify
25x2 ÷ 5 x– 4 .
(b) Solve
(2x – 3)(x + 2) = 0.
22 3
53 4
22 3
2 14
5
a
6
5
0
I N
2
0
2
M
3
Answer (a) ..............................................[1]
(b) x = ................ or ...................[1]
___________________________________________________________________________
5
(a) Find the fraction which is exactly halfway between 5–9 and 8–9 .
(b) Estimate the value of
5000 , giving your answer correct to one significant figure.
3–
(c) Evaluate 30 × 4 2 .
19 Add
2
2
4
Jj
x
go
Is Too
Etf
12
bl
4 10
13
14 30
1
4
x
2
27
I x 8
8
70
Answer (a) ..............................................[1]
(b) ..............................................[1]
(c) ...............................................[1]
___________________________________________________________________________
3
6
Evaluate
(a) 17 0,
5
2
2
(b) 4 ,
(c) (0.2)–2.
72 24E 25 32
E
É
25
5
Answer (a) ....................................................[1]
(b) ....................................................[1]
(c) ....................................................[1]
7
0
(a) Add 620 grams to 3.7 kilograms.
Give your answer in kilograms.
1000 3700g
t 620g
432 g
1000
Answer (a) ...........................................
kg [1]
4 32
(b) Write the following numbers in order of size, starting with the smallest.
31
3–1
(–1)3
30
I b
30
3 [1]
Answer (b) ........... , ...........
3 , ........... , ...........
smallest
413
8
Evaluate
(a) 90,
(b) 9–2,
3
2
I
(c) 9 .
E
34
33 27
Answer (a) ............................................[1]
(b) ............................................[1]
27
(c) ............................................[1]
4
9
Evaluate
(a) 3 1 – 2 2 ,
5
3
3
2
(b) 4 .
I 5
243 22
48,540
23
E
8
Answer (a) ............................................[1]
(b) ............................................[1]
10
Evaluate
(a) 91 + 90,
9 1
10
10
Answer (a) ...................................... [1]
(b)
!"
1
1 2.
9
I
t
Answer (b) ..................................... [1]
5
11
(a) Evaluate 40 + 41 .
Y tu
5
5
Answer (a) ....................................... [1]
(b) Evaluate
1 –2
.
4
!"
11
16
16
Answer (b) ....................................... [1]
12 (a) Evaluate 50 – 5–1.
4 t
55
I
Answer (a) ...................................... [1]
2
(b) Simplify (5 x3) .
se
5
2574
Answer (b) ...................................... [1]
1
16 2
(c) Simplify ! –––
" .
n16
1 I
Answer (c) ...................................... [1]
6
13
Evaluate
2–
(a) 8 3 ,
(b)
1 –2
6 .
14 (a) Evaluate
23 7 22 4
237
Ez
4
–2
!" .
1
4
43 5 4
41
!
Answer
........................................ [1]
Answer
........................................ [1]
Answer
........................................ [1]
16
14
16
43
(b) Evaluate 64 .
(c) Simplify
........................................ [1]
31
4
2
3
4
Answer
"
16
16
1
4x2 y9 2
.
x4 y
124 ys
R
22
y
x z
É
29
x
Answer
........................................ [2]
7
15 (a) Simplify (3a4)2.
alt
3
gas
(b) Evaluate
gas
Answer
....................................... [1]
Answer
....................................... [1]
1 –2
.
4
!"
16
4
16
(c) Given that x3 = 27 0, find x.
I
1
JI
x
I
x
1
Answer x = ................................. [1]
1
(d) Evaluate
12 2
3
32
.
135
Is É
4
Answer
4
....................................... [1]
8
16
(a) Evaluate 40 – 4–2 .
I
I
it
it
Answer
....................................... [1]
Answer
....................................... [1]
(b) Simplify (2x2)3 .
23 a
3
826
17 (a) Write 83 in the form 2k.
23
(b) Evaluate
b
EtE
Answer
..................................... [1]
Answer
..................................... [2]
9 × 212 – 3 × 210 .
3 × 28
3
31
3 24
22
48
44
4
9
18 (a) Find the value of
(ii)
Il
121,
(i)
3
Answer
..................................... [1]
Answer
..................................... [1]
3
–27.
3
(b) Write the following numbers in order of size, starting with the smallest.
23
32
40
5–1
8
9
1
I
................
5
smallest
................
Answer
23
32
40
................
Answer
..................................... [1]
Answer
..................................... [1]
Answer
..................................... [1]
Answer
..................................... [1]
................ [1]
3
(c) Evaluate 16 2.
45
43 64
64
19 (a) Evaluate
(i) 51 + 50,
5 1
(ii)
4 –2
!3" .
(b) Simplify
6
L
E
6
#2x2$3 .
2 3 243
86
10
20
(a) Find the value of a when 3a ÷ 34 = 32 .
4
Ra
35
4
a
a
2
6
6
Answer a = .............................. [1]
(b) Find the value of b when 8b = 2 .
23
2
23h
I
3b
1
b
3
I
Answer b = .............................. [1]
21 (a) Evaluate
(i) 50 + 52,
1 25 26
1
(ii)
536
36 2 ,
^2 h .
2
3
(iii)
............................................ [1]
Answer
............................................ [1]
Answer
............................................ [1]
6
231 24 16
6
26
Answer
6
16
1 k
(b) c m = 9
3
Find the value of k.
3
32
y
R
2
K
K
2
Answer k = ...................................... [1]
2
11
2 2 2
2
22 (a) Evaluate 4–2 �
Answer
�������������������������������������������� [1]
1
9xy
e 3 2o �
x y
6 2
(b) Simplify
9,1
5
344
ly
x
yet
at
s
3,1
Answer
23
�������������������������������������������� [2]
Giving each answer as a fraction in its lowest terms, evaluate
(a)
3 # ^2h3
,
6#9
2 -2
3
(b) c m
2
.
Iss a
4
Answer
................................................ [1]
Answer
................................................ [1]
s
12
3
5 -2
c m .
3
24 (a) Evaluate
2
925
Answer
1
9 2
(b) Simplify c 6 m .
t
(c) Simplify
1
3
If
Es
............................................... [1]
5
Answer
............................................... [1]
Answer
............................................... [1]
si
2x 3 y
.
6xy 2
p
25 (a) Solve 2^5 h = 250 .
5
125
XP 57
P 3
3
Answer
p = .................................................... [1]
Answer
.......................................................... [1]
Answer
.......................................................... [1]
(b) Simplify
(i) 1 ' x -5 ,
I
(ii)
s
Xs
Xs
3a 9a 2
.
'
4
8
3gIga
Fa
13
26 (a) Evaluate
(i)
3
6
216 ,
6
Answer .............................................................. [1]
1
(ii) 16 2 - 16 0 .
56 I
4 1
3
Answer .............................................................. [1]
J 3a 2 b N- 2
O .
(b) Simplify K
4
12
ab
L
P
Is
II
4 3
42 by
as
16b
a
Answer .............................................................. [2]
27
(a) Find n when
3
5
n
3# 3 # 3 = 3 .
303
31 35 3
33
3
1 5
3
31 31
(b) Find the value of 32 5 .
2 32
n 9
Answer
n = ................................... [1]
Answer
......................................... [1]
Answer
......................................... [1]
25 s
23 8
J N-2
(c) Find the value of K1O .
L5P
5 27
25
14
28 (a) Simplify p2 ^p3 - 3p-2h.
PTFE
ps
ps
Eff
Answer
............................................. [2]
Answer
............................................. [2]
1
(b) Simplify ^27x 6h3 .
273
xb
5
xD's
322
29 Given that 6x = 9, write down the value of
x
(a) 6 -x ,
In I
6
64
Answer .............................................. [1]
x
(b) 6 2 ,
64
9t
59
3
Answer .............................................. [1]
(c) 6 0 + 6 x .
1 9
10
Answer .............................................. [1]
15
30 (a) Evaluate
(i) 2 0 + 2 3 ,
9
1 8
9
Answer�������������������������������������������� [1]
1
J1N 2
(ii) K O .
L9P
s
Answer�������������������������������������������� [1]
-2
(b) Simplify ^4x 2h .
4 42
161 4
Answer�������������������������������������������� [1]
31 (a) Evaluate 9
- 12
.
s
Answer
........................................ [1]
Answer
........................................ [1]
Answer
x = .................................. [1]
103 – 100.
(b) Evaluate
1000
1
999
3
2
(c) Solve x = 8.
2 8
x 1252 22 4
16
32
3 0
(a) Evaluate c m .
2
I
3 -1
(b) Evaluate c m .
2
Answer ................................................. [1]
B
Answer ................................................. [1]
(c) Simplify (9x3)2 .
92123
6
81
33
Answer ................................................. [1]
Simplify
(a)
5x 7 y
,
15x 3 y 4
It Yi
(b) c
- 12
4t 2
m .
v4
v4
II
24 E
Answer ........................................... [1]
EE
2
tx
I
Answer ........................................... [1]
34
(a) Evaluate 23 - 20 .
8
1
7
Answer .......................................... [1]
(b) Simplify
É
12xy
.
9x 2
It
Answer .......................................... [1]
17
35 (a) Evaluate 32 + 31 + 30 .
9 3
1
13
Answer .......................................... [1]
J4 N-2
(b) Evaluate K O .
3
L P
E
Answer .......................................... [1]
1
6 2
(c) Simplify ^16y h .
Kitty't
4th y't
4y
Answer .......................................... [1]
36 (a) Evaluate
(i) 3–2,
2
Answer ........................................... [1]
(ii)
2
125 3 .
53
5333
52 25
Answer ........................................... [1]
1
2a 2 b 5 2
m .
(b) Simplify c
18a 4 b
q
I
b4
34
t
a I
ÉIE
3
Answer
a
.......................................... [2]